Seasonality in global government bond returns

Author Ana-Maria Morarescu

Student Number 385368

Master Program Financial Economics, Economics and Business MSc, Erasmus

School of Economics

Supervisor Martin Martens, PhD

Internship Supervisors1 Martin Martens, PhD and Johan Duyvesteyn, CFA

Date August 2014

1 This thesis was written as a part of the Super-Quant Internship Program at Robeco Asset Management, Rotterdam, The Netherlands

Abstract

This paper documents a new seasonal pattern in six developed government bond markets. Returns

are significantly higher in the second half of the year (July-December). The effect is robust to outliers and

persistent over time and across countries. Inflation is significantly higher in the first half of the year

(January-June). Residual bond returns from the time-series regression of bond returns on inflation rate no

longer exhibit the seasonal pattern. Hence, the seasonal pattern in bond returns is largely explained by the

seasonal pattern in inflation. This suggests nominal bond prices do not properly anticipate inflation. In

contrast, inflation-linked bonds whose coupons and face value depend on inflation do not exhibit a

seasonal pattern.

1

Contents

1. Introduction.........................................................................................................................................4

2. Literature Review................................................................................................................................6

2.1 Seasonality in government bond returns.....................................................................................6

2.1.1 January effect.............................................................................................................................7

2.1.2 Halloween effect.........................................................................................................................7

2.1.3 SAD factor...................................................................................................................................8

2.1.4 Other effects...............................................................................................................................9

2.2 Explanations for government bond patterns...............................................................................9

2.2.1 The January effect.....................................................................................................................10

2.2.2 The Halloween Effect................................................................................................................10

2.2.3 SAD effect.................................................................................................................................10

2.2.4 Explanations from equities.......................................................................................................10

2.3 Seasonality in inflation rate.......................................................................................................12

3. Data and methodology......................................................................................................................14

3.1 Data.................................................................................................................................................14

3.2 Methodology...................................................................................................................................19

3.2.1 A short review on methodologies employed in the literature..................................................19

3.2.2 Seasonal Pattern Discovery.......................................................................................................21

3.2.3 M-estimation – robust to outliers.............................................................................................22

3.2.4 Relationship between bond returns and explanatory factors...................................................24

3.2.5 Testing the economic significance............................................................................................24

4. Results...............................................................................................................................................26

4.1 Seasonal patterns in bond returns...................................................................................................27

4.1.1 Bond pattern dicovery..............................................................................................................27

4.1.2 Robustness to outliers..............................................................................................................30

4.2 Inflation explanation........................................................................................................................32

4.2.1 Seasonality of inflation rate..........................................................................................................32

4.2.2 The link between bond returns and inflation rate........................................................................34

4.2.2.1 Monthly analysis....................................................................................................................35

2

4.2.2.2 Quarterly analysis..................................................................................................................40

4.3 ILB – Comparator analysis................................................................................................................44

4.4 Interaction with SAD........................................................................................................................46

4.5 Other considered explanations........................................................................................................52

4.5.1 Annual cycle of economic activity.............................................................................................53

4.5.2 The Optimism cycle...................................................................................................................56

4.5.3 Macroeconomic data surprises.................................................................................................59

5. Robustness checks.............................................................................................................................61

5.1 Persistence over time......................................................................................................................61

5.2 Stock returns patterns.....................................................................................................................63

5.2.1 Seasonal patterns of stock excess returns................................................................................63

5.2.2 The relationship between stock returns and inflation..............................................................64

5.3 Economic Significance.....................................................................................................................65

5.3.1 Trading Strategies.....................................................................................................................66

5.3.2 Statistical Significance...............................................................................................................67

6. Conclusion.........................................................................................................................................68

References.................................................................................................................................................70

Appendix A................................................................................................................................................76

Appendix B................................................................................................................................................85

3

1. Introduction

The seasonality in asset returns represents the habit of returns to repeat similar dynamics within

the considered horizon (calendar year, month, week etc). Wachtel’s study from 1942 was among the

pioneer studies on seasonality patterns exhibited by asset returns. Since then, research studies have been

mostly confined to stock markets, while bond market seasonality and its determinants received scant

attention. Also the existing studies which cover the bond market focus on the discovered patterns in stock

markets: “The January effect2” of Wachtel (1942), “The Halloween indicator3 ” discovered by Bouman

and Jacobsen (2002) and the “Seasonal Affective Disorder (SAD)4 factor” of Kamstra, Kramer and Levi

(KKL) (2003). Clayton, Delozier and Ehrhardt (1989) document that long-term U.S. treasuries have lower

returns in January than in the rest of the year. Fridson (2000) finds that 10-year U.S. treasury returns

have higher returns from June to November and Athanassakos (2008) finds that Canadian bonds have a

higher performance from May to October. Kamstra, Kramer and Levi (2014) document a seasonal pattern

in U.S. treasury returns that coincides with the number of reported cases of Seasonal Affective Disorder

(SAD). SAD is related to the annual cycle of decreasing and increasing daylight on the Northern

Hemisphere. Kamstra, Kramer and Levi (2014) argue that the resulting increased risk aversion during the

fall leads to higher bond returns and once the daylight increases the returns of bonds are likely to be

below average.

Thus, there is no consensus in the literature on an overall pattern in government bond markets and

the investigated patterns are equity driven. Accordingly, the effects are adapted from the stock market.

Studying the bond price behavior is important for several reasons: the fixed-income markets have

grown significantly over the past decade (the outstanding of fixed-income instruments has increased from

$72 trillion in 2000 to $172 trillion5 in 2012) and the seasonality of fixed income instruments might be

driven by other factors that those driving stock returns. In practice, the seasonal pattern of bond/stock

returns plays a key role in portfolio management. A portfolio manager might achieve a better return by

conducting transactions at the right time in order to exploit observed fluctuations of returns. However, it

is important to note that an increase in the number of market players who are aware of the seasonality

could dampen the seasonal effects and the effectiveness of exploiting them. As Darrat, Li, Liu and Su

2 The first month of the year exhibits relatively higher stock returns compared to the others.3 Higher returns in stock markets during the November – April period compared with the rest of the year.4 This is consistent with lower stock returns in the fall as the risk appetite of the investors is affected by less daylight and relatively higher returns in the winter as the day becomes longer and the risk appetite of the investors recovers.5 According to McKinsey Global Institute, Haver and Bank for International Settlements statistics.

4

(2011) point out, understanding seasonality can also be beneficial from the perspective of

companies/government in need of capital, as they can select the right timing to issue new debt issues.

The aim of this research is to fulfill the gap observed in the literature on the seasonality in fixed

income instruments. As shown at the beginning of the introduction, the evidence on the existence of an

overriding pattern in bond markets is mixed in the literature. Moreover, most of the papers prove the

existence of a pattern without formally testing for an explanation. Therefore, the second goal of this study

is to explain the causes of bond returns seasonality. The analysis focuses on answering the following

research questions:

Q1: What is the seasonal pattern which caracterises the bond market6 ?

Q2: What is the most logical explanation for the seasonality in bond returns?

This empirical research yields the following interesting results. In line with the conclusions of

Schneeweis and Woolridge (1979), Smirlock (1985), Chang and Pinegar (1986) and Chan and Wu

(1993), the current research does not find a January effect. An Inverted Halloween effect which is the

opposite pattern found by Bouman and Jacobsen (2002) on stock markets, is weak and inconsistent across

countries. The research discovers a new pattern for government bonds – H1 H2 effect which implies a

better performance of bonds during July-December compared to the one recorded in the first half of the

year.

The study also points out that the seasonality in the inflation rate drives the discovered variation

in bond returns across the year. The explanatory power of inflation for bond seasonality is supported by

the following:

- the inflation rate exhibits an opposite pattern with higher values during January-June

- there is evidence of a significant time-series link between bond returns and inflation

- there is no seasonality left after taking into account inflation dynamics

- the returns of inflation-linked bonds (ILBs) do not display a seasonal pattern as inflation rate is

incorporated in their price.

The possible explanation of the inflation hypothesis is that investors do not pay attention to the

seasonal pattern in inflation as they focus on underlying inflationary trends which are reflected by

seasonally-adjusted numbers.

In what concerns the SAD factor introduced by KKL(2003), the analysis shows that SAD is

specific to the markets from where the data was gathered (North America). Accordingly, the SAD

6 The current study focuses on the seasonal pattern at monthly level across the calendar year. Therefore, daily and weekly dynamics are out of the scope of this research and the study will report lower frequency patterns from stock and fixed income markets.

5

variable has explanatory power for bond seasonality at a monthly frequency in the United States and

Canada, while at a quarterly frequency this factor is subsumed by the inflation rate.

This research adds to the literature in the following ways. It documents a new semi-annual

seasonal pattern on bond market. Shigeki, Takashi, Katsuhiko (2011) found evidence of the opposite

effect on the Japanese stock market (“Dekansho-bushi”). While most of the papers focus on United States

(U.S.) and Canada, this study conducts a broader analysis into six liquid government bond markets:

Australia, Canada, Germany, Japan, the United Kingdom (U.K.) and U.S. It provides a formal testing for

the considered hypotheses considering several proxies which have not been used in this context7. Many

studies on seasonality have put forward an explanation without bringing empirical evidence for it. This

study investigates the seasonality of ILBs which, to my knowledge, has not been investigated until now.

Finally, it brings evidence that the seasonality in inflation rate explains better than SAD the seasonal

variation in bond returns.

The remainder of the paper is organised as follows. Section 2 reviews the literature on calendar

anomalies from stock and bond markets and the related explanations. Section 3 presents the data and

gives an overview of the methodologies used in the literature and describes the econometric methodology

employed. Section 4 is dedicated to the presentation and discussion of the results, while Section 5

considers several robustness checks. This empirical study is concluded with a summary, the limitations of

the research and further research directions to be considered.

2. Literature Review

Chapter 2 reports the main findings on the seasonal patterns discovered on stock and bond

markets (Section 2.1), the explanations behind these (Section 2.2) and the drivers of inflation seasonality

(Section 2.3).

2.1 Seasonality in government bond returns

While the seasonality in equities has received extensive coverage in empirical papers, the

research on the patterns of fixed income instruments is sparse. Most of the fixed income studies focus on

corporate bonds, while government bonds have received even less attention in the literature. Moreover,

the number of analysed countries is limited in case of fixed income instruments (mainly U.S., only Smith 7 I consider investor sentiment proxies (consumer survey and implied volatility for stock options) and an index to gauge economic data surprises (Citi Economic Surprise Index – CESI).

6

(2002) considers six developed countries: United States, Japan, Germany, France, United Kingdom and

Canada), while evidence of stock seasonality is global. I will report the seasonal patterns discovered in

government bonds. Most of the studies test the existence of already discovered patterns from the stock

market on fixed income markets. Therefore, I will start with the evidence of the patterns for the stock

market and then report the findings for the bond market.

2.1.1 January effect

The January effect implies relatively higher stock returns in the first month of the year compared

to the average. The effect was first reported on the stock market by Wachtel (1942). This is one of the

most researched seasonal patterns in the literature and the evidence is mixed. The January effect was

confirmed for U.S. by Rozeff and Kinney (1976), by Gultekin and Gultekin (1983), by Keim (1983) and

Reinganum (1983), for the Canadian stock market by Berges, McConnell and Schlarbaum (1984), for The

Netherlands from 1966 to 1982 by Van den Bergh and Wessels (1985), for some emerging markets (Hong

Kong, Malaysia and Singapore) by Aggarwal and Rivoli (1989) and for the Japaneese market by Kato and

Schallheim (1985). More importantly, recent studies which consider larger samples of data and a wide

number of countries fail to find evidence for this effect in Australian stock market (Worthington (2010))

and on a long sample of 317-year of UK stock returns (Zhang and Jacobsen (2013)).

The existence of a January effect in U.S. Treasuries is rejected by the studies of Schneeweis and

Woolridge (1979), Smirlock (1985), Chang and Pinegar (1986), Chan and Wu (1993). The results of the

first three papers are questioned by Clayton, Delozier and Ehrhardt (1989) who find lower government

bond returns than average in January. They argue that problems related to the data sets and methodologies

used are not favourable for the discovery of a January effect. They conclude that U.S. Treasuries with a

maturity longer than four years record a lower level of returns in January compared to the rest of the year.

Smith (2002) extends the research of January effect at six developed countries: Canada, France,

Germany, Japan, the United Kingdom and the United States for both local currency and U.S. dollar

denominated debt instruments. He combines regressions with nonparametric tests to detect the January

and the effect survives only in case of the local currency government bonds of France.

The recent studies suggest that the January effect is not present on equities and bond markets, but

given its popularity I will formally test for its existence.

2.1.2 Halloween effect

7

Bouman and Jacobsen (2002) provide evidence that the popular saying from the financial press

“Sell in May and go away” is valid for stock returns from the U.S. and another 19 international markets.

This anomaly is known as the “Halloween Effect” as it implies that a good timing to buy stocks is around

Halloween as the stock returns between May and October are lower than those recorded during November

– April. The analyses of Abu Zarour (2007), Athanassakos (2008), Swinkels and Van Vliet (2010), Lean

(2011), Andrade, Chhaochharia and Fuerst (2012) bring worldwide support for the Halloween effect

(U.S., Canada, Middle-East and Asian stock markets).

Fridson (2000) documents a semi-annual seasonality effect of 10-year US Treasuries returns:

lower average returns during December-May than June-November. According to the Halloween effect

visible on stock returns, the poorer performance of Treasury returns during the period from December to

May seems to be associated with higher stock returns. The study of Athanassakos (2008) on Canada

reinforces the existence of a complementary pattern (stocks record a better performance during November

to April, whereas the May to October period is characterized by higher government bond returns)8.

These empirical analyses indicate that the Halloween effect constitutes a candidate pattern for

global bond returns. Therefore, I will investigate its validity on bond markets.

2.1.3 SAD factor

Based on equity indexes from nine countries, Kamstra, Kramer and Levi (2003) support the idea

that a seasonal depression (SAD) related to less daylight translates into a higher degree of risk aversion in

the fall and thus to below average stock returns. The inverse effect takes place once the daylight starts to

increase and this translates into relatively higher stock returns in the winter. In a subsequent paper, they

also find a more prominent SAD effect for riskier stocks (sorted by beta risk or standard deviation of

returns)9.

8 He also contends that the beginning of the year is characterized by the strength of equities, while government bond returns perform relatively better in the second part of the year.9 The SAD effect has received criticism in the literature. Jacobsen and Marquering (2008, 2009) and Kelly and Meschke (2010) argue that the correlation between the SAD factor and stock market dynamics cannot be considered a relation of causality. Jacobsen and Marquering (2008, 2009) point out that the influence of SAD on stock returns “could just be data-driven inference based on spurious correlations” and cast doubt on the noisiness of the data used, the robustness of the implemented tests and the weakness of the link between depression and risk aversion. Kelly and Meschke (2010) use as arguments the misinterpretation of the psychological literature and the misspecification of the model (the use of an overlapping dummy variable). They show that the magnitude of SAD impact is not linked to the distance from equator (contrary to the Kamstra, Kramer and Levi (2003) finding). The SAD effect does not manage to capture a different pattern in the stock markets of the Southern Hemisphere from those of the Northern Hemisphere (the latter is shown by Jacobsen and Marquering (2008)). Doeswijk (2008) argue that both hypotheses are subjected to data mining as they imply a cyclical pattern which is known in advance to mirror the seasonal pattern of equities.

8

Kamstra, Kramer and Levi (2003b) also provide evidence of a fall-winter complementary bond-

stock returns pattern (bond returns are higher than the average in September-November and lower in

February – April, while stock performance is relatively better in the beginning of the year and poorer in

the autumn)10. Interestingly, flows into equity and bond mutual funds mirror the pattern observed for

returns of each asset and thus, when flows are negative for equity funds, they are positive for bond funds

with a similar size.

KKL define a SAD variable in order to conduct the analysis. The SAD definition developed from

“the length of the night in the fall and winter relative to the mean annual length of 12 hours” (2003) to

“the change in the proportion of individuals actively experiencing depression symptoms”11 (2014). In this

paper I use the latter definition - the monthly Onset/Recovery variable (OR) build based on clinical

evidence of North Americans suffering from SAD12 (timing of the symptom onset and symptom

recovery). The reason for choosing this variable is that it constitutes an improved version which is

directly linked to the clinical evidence of SAD symptoms, while the previous version was indirectly

linked to SAD symptoms by the length of the night. The dynamics of the used SAD variable are displayed

in Figure A.1 in Appendix A.

Given evidence of the SAD effect in global equities and the U.S. bond market, it is interesting to

investigate if the SAD pattern holds for the international bond markets.

2.1.4 Other effects

Another type of semi-annual pattern is documented in the Japanese stock market between 1950

and 2008 by Shigeki, Takashi, Katsuhiko (2011). This effect called “Dekansho-bushi” implies a better

performance of returns in the first half of the year compared to the period July-December.

Hong and Yu (2009) find lower average stock returns during summer (July–September for

Northern Hemisphere countries and January–March for Southern Hemisphere countries) for 15 out of the

51 analyzed countries.

2.2 Explanations for government bond patterns

10 Ilmanen (2011) also mentions such a complementary pattern: bond returns during autumn outperform those recorded at the beginning of the year, while stocks record an opposite pattern.11 The measure used for the patients actively suffering from SAD is the difference between those patients who started experienced the SAD symptoms and those who have recovered from the symptoms.12 More details about the construction of this variable can be found in Section 2.1 of the KKL(2014) paper. Data can be downloaded from: http://www.markkamstra.com/data.html.

9

Even though the number of studies on fixed income seasonality is quite small, a consensus on the

drivers of the seasonal patterns is not reached.

2.2.1 The January effect

Clayton, Delozier and Ehrhardt (1989) advance the parking-the-proceeds hypothesis of Ritter

(1988) for lower returns of long-term government bonds in January as investors park their proceeds from

selling their stock holdings in the last month of the year into government debt paper and reinvest their

money into equities in January. This puts downward pressure on bond prices in January.

2.2.2 The Halloween Effect

Athanassakos (2008) links the seasonality pattern from equity and bond markets with institutional

factors (“window-dressing” or portfolio rebalancing in an attempt to influence remuneration).

2.2.3 SAD effect

Kamstra, Kramer and Levi (2003b, 2014) extend the SAD explanation to government bond

returns. Thus, they argue that the increased risk aversion during fall leads to higher bond returns and once

the daylight increases, the returns of bonds are likely to be below average.

2.2.4 Explanations from equities

The factors explaining the equity anomalies are related to the influence of institutional investors,

to psychological reasons, to the macroeconomic activity and incidence of macroeconomic data releases or

to data-mining problems. I will focus on the last three categories as they are potentially testable and

applicable for government bonds13.

An extensive part of the empirical studies have tried to link seasonality of stock returns with

psychological factors.

On the one hand, research studies focused on how weather conditions affect the mood of

investors which will be afterwards reflected in market dynamics. Therefore, several weather variables

caught the attention of the researchers: the amount of sunshine – Saunders (1993), Hirshleifer and

13 Appendix B provides a complete overview of the explanations put forward for equities and fixed income instruments.

10

Shumway (2003), the length of the daylight - Kamstra, Kramer and Levi (2003), the temperature – Cao

and Wei (2005) and lunar phases - Dichev and Janes (2003), Yuan, Zheng and Zhu (2006).

On the other hand, empirical analyses have considered that a change in investor optimism across

the year is responsible for the discovered seasonal patterns.

Ciccone (2011) argues that the January anomaly observed in the stock market is driven by

renewed optimism at the turn-of-the year (optimistic expectations hypothesis). This optimism and the

prolongation of the positive feeling around Christmas are related also to the Christmas hypothesis of

Wachtel (1942) for which Zhang and Jacobsen (2013) find support in U.S. and U.K. These hypotheses

imply that optimistic investors are likely to sell government bonds at the beginning of the year which

might translate into lower bond returns in January.

Doeswijk (2008) puts forward the time-varying optimism explanation for the Halloween effect

observed on stock returns. Accordingly, higher stock returns starting with November are supported by an

overly optimistic outlook for earnings at the beginning of the new calendar year. A similar explanation is

put forward by Shigeki, Takashi, Katsuhiko (2011) as they link the semi-annual pattern in Japanese stock

markets with the optimism of investors related to the feeling of a “fresh start” (a new calendar year, a new

fiscal year, the spring, national holidays). Doran, Jiang and Peterson (2012) support the idea of a

gambling preference of investors at the beginning of the year which is reflected in a strong performance

of risky stocks at the beginning of the New Year14. All of these explanations imply a boost in risk appetite

at the beginning of the year and suggest that bond returns are going to be lower at the start of the year.

Another category of studies tries to explain the seasonality in stock returns through the

seasonality in macroeconomic data. Ogden (2003) relates equity return patterns to the seasonality of

macroeconomic variables (real gross domestic product (GDP), industrial production, unemployment rate

and producer price index (PPI)). He finds complementary seasonalities in economic activity and stock

returns and he proposes as an explanation that “April through September losses reflect the development of

investors’ expectation of poor macroeconomic conditions for October through March, and this induces

them to adjust security prices to provide higher expected returns in October through March”.

Kamstra, Kramer and Levi (2014) also consider the hypothesis that the seasonality in bond prices

could be the result of macroeconomic seasonality and consider a wide range of variables: GDP, PPI,

industrial production, unemployment rate, consumer price index (CPI), but argue that they do not manage

to capture the seasonality fully.

Based on U.S. stock returns during 1980 – 2003, Gerlach (2007) finds that higher daily average

of returns during fall (October – December) is linked to the market response to macroeconomic news

14 January for U.S., the first month of the Chinese year for stocks from China.

11

scheduled in that period. Given the macroeconomic data have different implications for bonds and

stocks15, an opposite reaction is expected in case of bond returns.

Studies have also raised the problem of data-mining related to the discovery of seasonal patterns.

Sullivan, Timmermann and White (2001) point out that the seasonal patterns discovered on stock market

returns are the result of data-mining problems. Accordingly, the patterns might have been found by

chance, especially as data which contain outliers are prone to data-mining biases. This possibility is also

noted by Lakonishok and Smidt (1988). Zhang and Jacobsen (2013) also underline that the reported

monthly seasonal patterns might be the result of spurious regressions. Investigating the existence of the

January effect across 317-year period in UK stock market, they conclude that the anomalies are highly

dependent on the chosen sample period and length. Maberly and Pierce (2004) prove that the “Halloween

effect” does not hold when controlling for the impact of two strong negative returns (October 1987,

August 1998). However, Haggard and Witte (2010) show that the Halloween effect is robust to outliers in

U.S. during 1954-2008 and it remains significant at a global level (37 countries) when controlling for

outliers, but at a lower magnitude. These mixed findings about the stock returns patterns suggest that

bond return patterns can also be found by chance. Thus, tests are required to investigate if the effect

persists after controlling for outliers or conducting the analyses on out-of-sample data or using

uncorrelated/different data.

All the above three categories of explanations could be applied to the bond market: time-varying

optimism during the year, an annual cycle of economic conditions or the possibility that the seasonal

patterns are the result of data-mining problems. While the proposals from the literature can be used to test

for the last two hypotheses, it is difficult to find measures to quantify changes in investor sentiment.

However, the study proposes two proxies for investor sentiment: consumer confidence survey and the

implied volatility of stock options.

2.3 Seasonality in inflation rate

Among the variables which display seasonal patterns, the inflation rate is relevant for nominal

bond returns dynamics. According to Fabozzi, Martellini and Priaulet (2006, p. 455), the nominal yield

incorporates the expected inflation and an inflation risk premium related to uncertainty about consumer

price movements16. Balduzzi, Elton and Green (2001) show that the inflation rate impacts the prices of

15 Expectations of good economic conditions favour stocks, while expectations of an economic slowdown increase the attractiveness of bonds as they offer stable cash-flows.16 This is a variation of the Fisher Hypothesis.

12

U.S. Treasuries and that the relationship between bond returns and inflation rate is negative. Accordingly,

an increase in the inflation rate will mean lower bond prices as the expected inflation component from

nominal bond yield will increase. This is in line with the finding of Goldberg and Leonard (2003). Kim,

McKenzie, Faff (2004) also find a negative significant impact of an increase in inflation rates on U.S.

bond market returns.

Another direction through which the inflation rate influences the bond market is pointed out by

Brandt and Wang (2003). They find that news about inflation has an influence on the risk aversion of

investors. Accordingly, unexpected increases in inflation determine an increase in risk aversion which

bodes well for government bonds.

In the current low-inflation environment, the monthly changes in inflation rate could be explained

to a larger extent by the seasonal variation than by the underlying inflationary pressures. Thus, it is even

more important to understand the seasonal pattern of inflation. The percentage variation in the consumer

prices index is one of the measures used to track the inflation dynamics. The consumer price index

represents a weighted average of different components. Therefore, the seasonality in inflation rate is

driven by the dynamics of these components17.

One component is food prices. Unprocessed food prices are related to the agricultural output

supply dynamics and tend to decrease during summer-fall months when the harvest becomes available

and increase in winter (Bryan and Cecchetti (1995), Brondolo and Giani (2005), Ejsing, Garcia and

Werner (2007) support this pattern for U.S. and Euro Area respectively).

Brondolo and Giani (2005) also notice that seasonality plays a key role in case of discounted

sales prices (apparel, durable goods etc). In U.S., prices decrease during holiday sales seasons (November

– January) and June-July (Mirani, Pond and Skeoch (2012)). Sooben and James (2012) find a similar

timing of sale periods in Euro Area which triggers a fall in prices in January and July.

Evidence about energy prices is mixed. In Euro Area, Brondolo and Giani (2005) fail to find a

statistically significant pattern for energy components, whereas Mirani, Pond and Skeoch (2012) argue

that energy prices display a seasonal pattern in U.S. They increase during spring and decline in the last

quarter of the year.

Administrated prices (e.g. public transport, natural gas, electricity and fuel prices) and tax

changes tend to be altered at the same time in the year. Brondolo and Giani (2005) argue that from

statistical point of view they can be considered as displaying a seasonal pattern. Accordingly, they are

usually altered during the first month of the fiscal year (for most of the countries in January, while in case

of Japan and United Kingdom in April or in July for Australia).

17 The seasonality patterns of sub-components can differ from one country to another due to the characteristic of the economy which determines the imported goods, consumer preferences or the level of development which influences the weights of the products assigned in the consumer basket.

13

Inflation is seasonally adjusted in order to smooth the effects of price fluctuations of similar

magnitude and timing across the year (generated by weather conditions, production cycles, holidays and

sales)18. Non-seasonally adjusted inflation measures the actual change in prices of goods and services paid

by consumers and it is used in contract agreements, pension plans or the indexation of inflation-linked

bonds. Seasonally adjusted inflation reflects the long-term trend of consumer prices.

The inflation rate plays a key role also for inflation-linked bonds. The cash-flows of inflation

linked bonds are directly linked to the non-seasonally adjusted inflation rate. When investigating how

quickly U.S. Treasury Inflation-Protected Securities (TIPS) incorporate the information about future

inflation, Chu, Pittman and Yu (2011) find that TIPS prices fully reflect the US inflation data by the end

of the corresponding month, before the official announcement. Huberman and Schwert (1985) also found

that 85% of the reaction of inflation-linked bonds to inflation information occurs from two to five weeks

before the announcement, while the inflation is recorded. This finding suggests that the current inflation

rate should not have an influence on ILB prices as it is already incorporated.

While a seasonal variation in the components of inflation rate is mentioned in the literature, it is

difficult to assess the overall pattern in inflation rate as the dynamics of the components are mixed (e.g.

lower prices during holiday season (November-January) and higher food prices during the winter) and

different across countries.

3. Data and methodology

Chapter 3 covers the data used for the empirical analysis (Section 3.1) and a description of the

methodology (Section 3.2).

3.1 Data

This paper aims at discovering and explaining the seasonal patterns in government bond markets

returns. While prior research studies on bond markets are focused on one market (primarily U.S.), the

current study considers six developed liquid markets (Australia, Canada, Germany19, Japan, the United

Kingdom and the United States)20. At the end of June 2014, the six markets considered account for more

18 http://www.bls.gov/cpi/cpisaqanda.htm19 Germany is chosen as being representative for the European markets. Other European markets (e.g. France, Italy, Spain) are not considered to avoid the impact of specific events over time (e.g. European Union convergence (1993) or European Sovereign Debt Crisis (2009-2013)).20 To my knowledge, only the study of Smith (2002) uses international government data and considers the same number of bond markets. Five of them coincide with those of the current study, while Australia is replaced by France.

14

than three quarters of the J.P Morgan GBI Global Index. The index tracks the local-currency government

debt market of the most important developed countries and it is widely used by fixed income investors as

benchmark. These countries were chosen based on data availability and market capitalisation criteria.

Moreover, the countries also cover four continents and two hemispheres.

Table 3.1 shows descriptive statistics for total excess returns expressed in local currency on

nominal bonds, inflation-linked bonds, comparator indices and stocks for each of the considered

countries. For each asset class, excess returns are computed by subtracting the previous period three-

month interbank rate21 which is obtained from Bloomberg. For each country, the indices and three-month

rates are expressed in local currency and the excess returns are consistent with hedged returns

denominated in the local currency.

For bond markets, the Datastream total return indices for the period January 1980 – December

2013 are extracted from Thompson Financial Datastream22. To validate the persistence over time, a long

sample of US Treasuries from Center for Research in Security prices (CRSP) is considered. Based on

Campbell’s (1991) observation and consistent with Kamstra, Kramer and Levi (2014), the start of the

sample is 1952. The source of inflation-linked bond and so-called comparator bond indices is Barclays

Capital. The number of monthly observation is 390 for United Kingdom, but it is quite limited for some

countries (93 monthly observations in case of Germany for example).

The samples of inflation-linked bond and comparator indices are identical. The comparator

indices are made up of nominal bonds in order to match the characteristics of inflation-linked bonds (the

maturity of constituents and weights). This is useful for investors to compare the investment in a nominal

bond to the one in the real asset and also to run analyses on these two types of bonds. Table 3.1 shows

that there are some differences in the average modified duration between ILBs and comparator bonds

(nominal (comparator) bonds have higher yields and this is consistent with a lower duration than ILBs).

They also differ in what concerns the liquidity, credit risk and tax treatments23.

Given the different nature of government bonds and stocks24, I analyse the seasonal patterns in

equity returns. Moreover, most of academic papers are focused on the stock market and the explanation

found for bond seasonal patterns should also be consistent with the seasonal pattern in stock returns to the

21 LIBOR rates are considered. When LIBOR rates are not available, an alternative three-month Eurocurrency interest rate is used. Given that there is not a long history on LIBOR rates, for the US analysis I use T-bill rates for the period 1952-2013. The use of interbank money market rates for the main analysis is based on the fact that investors cannot borrow against T-bill rates. 22 This public short sample was chosen given concerns that the analysis cannot be replicated in the prospect of publishing the empirical study in an academic journal. The main analysis is based on Datastream Data, while results reported in Section 4.5 rely on a longer sample. This longer data set comprises broker data for 1975-1979, Datastream indices for 1980-1985 and JP Morgan indices for 1986-2013. 23 For more details see Swinkels (2012).24 A commonly employed diversification strategy in portfolio management is the combination of stocks and government bonds. This strategy has been advocated on the basis of the low – and sometimes negative – correlation often observed between these financial assets: Gulko (2002), Yang, Zhou and Wang (2009), Baur and Lucey (2010).

15

extent that the seasonality pattern is related. Thus, total return indices from Morgan Stanley Capital

International (MSCI) from Thompson Financial Datastream are used to measure the performance of local

equity markets for the period 1975 – 2013. These market cap indices are often used as a benchmark and

track the investment opportunities in the country.

For the analysis, I also consider inflation rate measures. The indices chosen to gauge inflation

dynamics are the official price indices used for the indexation of the cash-flows of inflation-linked bonds

(coupon payments and principal). Inflation data are extracted from Bloomberg and Datastream and span

from January 1980 to December 2013. More details about the indices can be found in Table A.1 in the

Appendix A.

Table 3.1: Descriptive Statistics

Country/Sample start Asset Class Nb. Obs. Average Standard

Deviation Minimum MaximumAverage Duration (Years)

Australia Inflation* 136 4.3% 1.8% -0.5% 4.1% -Mar-87 Nominal 322 2.1% 5.0% -5.9% 4.2% 4.4May-97 Infl-link 200 2.6% 5.0% -4.3% 5.2% 8.7May-97 Comparator 200 2.2% 6.1% -4.3% 6.7% 6.4Jan-75 Equities 468 5.9% 17.8% -42.2% 20.0% -

Canada Inflation 408 3.2% 1.4% -1.0% 2.6% -Jan-85 Nominal 348 3.0% 5.4% -5.6% 6.1% 6.0Jan-97 Infl-link 204 4.3% 7.5% -10.3% 8.7% 15.6Jan-97 Comparator 204 4.5% 6.9% -3.9% 7.3% 11.5Jan-75 Equities 468 5.1% 16.6% -22.4% 16.0% -

Germany Inflation 408 2.2% 1.1% -0.8% 1.7% -Jan-80 Nominal 408 1.8% 3.9% -5.0% 3.8% 5.0Apr-06 Infl-link 93 2.1% 4.5% -5.0% 5.4% 6.2Apr-06 Comparator 93 2.5% 4.0% -1.9% 3.1% 5.4Jan-75 Equities 468 6.6% 20.0% -25.2% 20.7% -Japan Inflation 408 0.9% 1.5% -1.1% 2.1% -Jan-82 Nominal 384 2.3% 3.7% -4.8% 3.9% 5.5Apr-04 Infl-link 117 2.1% 5.4% -9.8% 4.0% 6.9Apr-04 Comparator 117 1.7% 2.8% -2.9% 2.7% 6.7Jan-75 Equities 468 4.3% 18.4% -21.1% 19.6% -

United Kingdom Inflation 408 4.2% 1.7% -1.4% 3.4% -Jan-80 Nominal 408 1.9% 6.4% -7.5% 6.3% 6.8Jul-81 Infl-link 390 0.3% 7.2% -7.9% 9.3% 13.0Jul-81 Comparator 390 2.7% 8.0% -8.0% 8.9% 8.4Jan-75 Equities 468 7.8% 19.2% -26.8% 53.0% -

United States Inflation 408 3.3% 1.2% -1.9% 1.5% -Jan-80 Nominal 408 2.1% 5.5% -6.4% 8.1% 4.9Mar-97 Infl-link 202 3.1% 6.0% -8.6% 5.8% 8.4Mar-97 Comparator 202 3.2% 6.5% -6.5% 7.0% 7.2Jan-75 Equities 468 6.6% 15.2% -21.9% 12.8% -

16

Jan-52 CRSP Universe 744 1.6% 5.8% -6.2% 9.1% 10.7**Developed Inflation 408 2.8% 0.9% -0.9% 1.5% -

Jan-80 Nominal 408 2.1% 4.0% -4.1% 4.6% 5.4Jul-81 Infl-link 390 0.3% 6.3% -6.5% 7.8% 9.8Jul-81 Comparator 390 2.8% 7.6% -8.0% 8.9% 7.6Jan-75 Equities 468 6.0% 13.7% -24.9% 19.0% -

Notes: The table reports the descriptive statistics of the asset classes and the inflation rate considered in the analysis. The first column contains the start of the sample. For all series, the sample ends in December 2013. In case of the inflation rate, the start of the sample is January 1980 for all countries. The third column contains the number of observations in the sample. For each country, the table reports statistics on the local inflation rate (Inflation), the local nominal bond index (Nominal), the local inflation-linked bond index (Infl-link), the local nominal comparator bond index (Comparator) and the local stock market (Equities). In case of U.S., a longer sample on nominal bond indices from CRSP is added. CRSP Universe stands for an equally-weighted portfolio of U.S. Treasuries with maturities of 1Y, 2Y, 5Y, 7Y, 10Y, 20Y and 30Y. The table reports the annualised average return, annualised standard deviation, minimum, maximum monthly returns and the average modified duration of the bonds. Developed stands for an equally-weighted portfolio of the six markets. The number of countries included depends on the data availability. * For Australia, the frequency of inflation rate data is quarterly. The minimum and maximum values are thus reported at the quarterly frequency. ** For the CRSP Universe, the average maturity of the bonds in the portfolio is reported instead of average modified duration.

Table 3.1 shows that annual averages of nominal bond excess returns were of a similar magnitude

across countries ranging from 1.8% to 3.0%. As expected, equities recorded a better performance when

compared to nominal bonds in all cases, but also the risk borne by equity investors was higher.

Accordingly, the annualised volatility of nominal bonds stood between 3.7% and 6.4%, while equity

volatilities exceeded 15%. When combining the stock excess returns of the six countries, diversification

benefits lead to the lowest standard deviation recorded (13.7%).

The correlation matrix of nominal bond excess returns depicted in Table 3.2 shows that the bond

markets from United States and Canada are highly correlated. They display the highest correlation of

0.77. The lowest correlation coefficient is recorded for Japan and Australia (0.22). The fact that in 8 out

of 12 cases the correlation is below 0.5 indicates that there are diversification benefits by considering

other bond markets. More important, it also hints that the use of an international sample of countries adds

value to the analysis.

Table 3.2: Correlation matrix of bond returns

Nominal Bond Excess Returns Australia Canada Germany Japan United Kingdom United States

Australia 1.00 0.48 0.45 0.22 0.44 0.50Canada 1.00 0.53 0.33 0.56 0.77Germany 1.00 0.38 0.58 0.63Japan 1.00 0.32 0.33United Kingdom 1.00 0.53United States   1.00

17

Notes: This table shows correlation coefficients between bond returns time-series for the maximum overlapping period for each pair. The sample of nominal bond excess returns is shown in Table 3.1.

For most of the countries, the average realised returns of inflation-linked bonds is lower than the

one of comparator indices (Australia and Japan are the exceptions). This is related to the different

components of the nominal and ILB yield. Besides the real rate, the most important component of the

comparator (nominal) yield is the inflation rate risk premium25, while for the ILB yields the liquidity risk

premium26.

The Table 3.1 also reports the inflation characteristics. Australia and United Kingdom record the

highest average annualised inflation (4.3% and 4.2% respectively) and also the most volatile (1.8% and

1.7% respectively). On the opposite side, Japan recorded the smallest average inflation rate during the

period 1980 – 2013.

The normality and stationary properties of the series are formally tested using the Jarque-Bera

test, the Augmented Dickey-Fuller Test (ADF, 1979) and the Kwiatkowski-Phillips-Schmidt-Shin Test

(KPSS, 1992). The use of KPSS in addition to ADF is justified on the grounds that the ADF test has low

power in distinguishing between a unit root and a weakly-stationary series (Kwiatkowski, Phillips,

Schmidt, Shin (1992)). Based on the test results which can be found in the Table A.2 in the Appendix A,

the null hypothesis of normality is rejected which hints that the return series could be subjected to

outliers. The series are also stationary at the 5% significance level27.

The autocorrelation and heteroscedasticity of the returns and inflation series are also investigated.

The former is formally tested by applying Ljung-Box Q-test. To check if the series display conditional

heteroscedasticity, the ARCH test developed by Engle is implemented and the Ljung-Box Q-test on the

squared returns. The results centralised in Table A.3 from the Appendix A show that most of the

considered series display heteroscedasticity and autocorrelation. This suggests that the errors should be

corrected for autocorrelation and heteroscedasticity. The same tests are also applied on the residuals from

the Ordinary Least Squares (OLS) regressions, but they are not reported due to space constraints. For all

the regressions in the analysis, I report t-values based on autocorrelation and heteroscedasticity-consistent

standard errors (Newey-West Standard Errors). This approach is consistent with conservative t-statistics

because the chance of rejecting the null hypothesis is lower. Newey-West Standard Errors are usually

consistent with lower t-statistic values in absolute terms compared to OLS Standard Errors.

25 The compensation that investors in nominal bonds demand for bearing inflation risk.26 The compensation for the difficulty of finding a counterparty at a fair or an acceptable price. Campbell, Shiller, and Viceira (2009), Dudley, Roush and Ezer (2009), Gürkaynak, Sack and Wright (2010) have documented the existence of a time-varying liquidity premium embedded in TIPS yields.27 The exceptions are some inflation rate series and the returns of ILBs in United Kingdom and Developed portfolio based on KPSS test.

18

3.2 Methodology

Section 3.2 starts with an overview of the techniques used in the literature to determinate the

seasonality patterns and their drivers (Section 3.2.1). Section 3.2.2 describes the techniques used for the

discovery of the seasonal variation. Section 3.2.3 covers the robustness check techniques of the results to

outliers. Sections 3.2.4 is related to the second research question as it presents the method to test different

candidate hypotheses for the seasonality in bond returns. Besides the statistical significance, Section 3.2.5

considers the technique used to compare two investment strategies: one which exploits the H1 H2 pattern

and a simple buy and hold strategy.

3.2.1 A short review on methodologies employed in the literature

When testing for seasonality in equity or bond returns, two aspects are considered: the methods to

identify a seasonal pattern in the data and then the testing procedure for several hypotheses which might

explain the seasonality. Most of the papers focus on the first aspect, while those which put forward and

test explanatory hypotheses are often accompanied by robustness checks.

Parametric and non-parametric tests are employed in order to test for a seasonal pattern.

Introducing a dummy which captures a specific seasonal pattern in a regression and checking for the

significance of the coefficient using a t-test28 based on corrected errors is the most common approach. The

dummy can also be replaced by hypothesis specific variables29. Using the regression to test for the

difference in means has the advantage of adding other explanatory variables. Accordingly, control

variables are also introduced in the testing equation (for example Jacobsen and Marquering (2008) control

for correlation across countries, for the January anomaly and for the seasonality in changing

macroeconomic conditions) or as a robustness check (Bouman and Jacobsen (2002)). Table 3.3 provides

an overview of the estimation methods used by empirical studies. They differ from one paper to another,

but most of them employ several methods to show that the results are not related to econometric

problems.

Table 3.3: Estimation methods used in the literature in order to test for seasonality

28 A joint significance test such as a F-test or Wald test can also be considered, see for example Ogden (2003), KKL(2011), and Zhang and Jacobsen (2013).29 KKL(2003) use the length of the night in the fall and winter relative to the annual mean of twelve hours which was then transformed into the change in the proportion of individuals from North America displaying SAD symptoms (2014).

19

No. Empirical studiesSingle

equation OLS

Single equation GMM

Maximum likelihood-GARCH

Panel/pooled

regression

Robust estimations

Corrected errors30

1 Bouman and Jacobsen (2002)        2 Ogden (2003)        

3 Jacobsen and Marquering (2008)             31       

4 Dowling and Lucey (2008)    

5 Hong and Yu (2009)        

6 Kelly and Meschke (2010)        7 Haggard and Witte (2010)        32

8 Kamstra, Kramer and Levi (2012)          33     

9 Zhang and Jacobsen (2013)          34      

10 Andrade, Chhaochharia and Fuerst (2013)      35      

11 Kamstra, Kramer and Levi (2014)  36          

12 Frühwirth and Sögner (2014)              Notes: The table provides an overview of the estimation methods which are used in empirical studies to test for seasonality.

Some papers (Gerlach (2007), Doeswijk (2008), Shigeki, Takashi, Katsuhiko (2011)) use a t-test

for the difference between population means or use a Chi-square test for the difference in variances

(Shigeki, Takashi, Katsuhiko (2011)). As a step further these papers consider the comparison of a strategy

based on the discovered pattern and the reversed one37. As often the assumptions of parametric test are not

supported by the data or as a check for the reliability of the results, non-parametric tests for difference in

mean returns are also employed: the Wilcoxon rank test (Smith (2002)), the median test (Clayton,

Delozier and Ehrhardt (1989)) and the Kruskal and Wallis test (Rozeff and Kinney (1976), Zhang and

Jacobsen (2013)).

In order to confirm the seasonal pattern, studies often test for data mining problems: control for

outliers (Shigeki, Takashi, Katsuhiko (2011)), test for out-of-sample persistence (Andrade, Chhaochharia

and Fuerst (2013)), check consistency over subperiods (Doeswijk (2008), Haggard and Witte (2010),

Shigeki, Takashi, Katsuhiko (2011)) or across countries (Ogden (2003)), or perform bootstrapped tests

30 For heteroskedasticity and/or autocorrelation31 Seemingly Unrelated Regressions32 Techniques of Huber (1964) and Hampel (1974)33 Seemingly Unrelated Regressions34 M-estimator of Huber (1973)35 OLS and/or Prais-Winsten feasible generalized least squares (FGLS) with and without fixed effects36 For estimating systems-of-equations37 Based on a better performance of stocks in the first half of the year, Shigeki, Takashi, Katsuhiko (2011) consider a long position in the Nikkei 225 futures in the first half of the year which is compared with a long position in the second half. The outperformance of stocks during November-April is tested by Doeswijk (2008) using a sector-rotation strategy: long in cyclical stocks and short in defensive stocks during November-April and the strategies with the opposite signs during May-October. This is combined with Jensen’s (1968) alpha and beta to check the extent to which the strategy is explained by beta fluctuations.

20

(KKL (2014)). The empirical papers which advance an explanation for the found seasonal pattern also

provide robustness checks in order to reject other possible explanations for the observed phenomenon. In

an attempt to reject other explanations, several studies check if the higher returns are just a compensation

for bearing higher risk (Bouman and Jacobsen (2002), Gerlach (2007), Doeswijk (2008)) or analyse the

interaction between seasonal patterns (Bouman and Jacobsen (2002), Hong and Yu (2009), Zhang and

Jacobsen (2013)).

3.2.2 Seasonal Pattern Discovery

The first part of the research is to uncover the seasonal pattern in the excess bond returns. In order

to answer this question, two methods are used: a regression including dummy variables38 and the

economic significance of a strategy based on the statistically significant calendar anomaly.

The regression technique is a popular and simple method used in the literature, but it is also

dependent on the specification of the calendar anomaly. I use this method because it offers the possibility

to perform robustness checks by adding control variables and it constitutes a specific test. The

implementation of a standard F-test will give a general outcome – if the returns are different across

months, without detecting which months are causing the fluctuations. As KKL (2014) mentions “the test

for nonspecific monthly seasonality is a weak test for a specific form of seasonal variation”.

I use the relatively simple Ordinary Least Squares (OLS) technique as using more complex

techniques does not add value to the scope of this research which is discover a seasonal pattern and the

corresponding explanation. After using different techniques (e.g. OLS, GMM, Maximum Likelihood with

GARCH effects), Jacobsen and Marquering (2008) conclude “with the exception of some minor changes,

overall the results are very similar to the OLS results”.

Following a commonly used technique in the literature, dummies with ones and zeros are defined

and the following regression is estimated:

Ex rt=μ+α Dt+εt (1)

where Ex rt represents the excess returns, μ is the intercept term, α is the coefficient of the dummy

variable, Dtis the dummy variable and ε t is the error term. Specifying a dummy with ones for the months

in which higher returns are expected and zeros for the rest of the year makes the regression a simple mean

38 Tests for the difference between sample means reinforce the results of the regressions.

21

test. The goal is to analyse whether the returns in certain months (when the dummy takes ones) are

significantly different from the other months (when the dummies take zeros).

A t-test is applied on α . The null hypothesis is that α is equal to zero. In order to conclude that

there is a statistically significant seasonal pattern, the t-test applied on α should reject the null hypothesis.

Ordinary Least Squares (OLS) regression residuals are examined for autocorrelation and

heteroskedasticity using the Ljung-Box Q-test and Arch test. If these tests show the presence of

autocorrelation and heteroskedasticity, Newey-West standard errors are used. As Newey and West (1994)

suggest, the autocovariance lag used is equal to4 ( Nr Obs100 )

29 .

3.2.3 M-estimation – robust to outliers

Motivated by the fact the Halloween effect was put into question as it might be just the result of

outliers (Maberly and Pierce (2004)), I check the robustness of the results to outliers using the M-

estimation technique introduced by Huber (1973).

The difference between an OLS estimation technique used above and M-estimation is the fact that

when minimising the sum of squared errors, the weights attached to residuals are not equal to 1, but they

are decreasing to dampen the impact of large errors. Thus, for the general specification, Y¿ Xβ+σε, the

OLS estimator β̂OLS=( XT X )−1 XT Y will then become β̂=( XT WX )−1 XT WY where Y , ε are nx 1

vectors of the dependent variables and residuals respectively, X is an nxp matrix of regressors, σ>0 is a

scale parameter and W is a nxn diagonal weight matrix.

This technique has the advantage of eliminating the arbitrary choice of outliers and performing

well in terms of robustness to outliers39 and efficiency40. Hoaglin, Mosteller and Tukey (1983) consider

this as the method with the best results among robust estimations in case of small and moderate samples.

The M-estimation requires some choices for the weight function specification ψ (u ) and the scale

parameter σ . However, these choices are not as arbitrary as the subjective definition of outliers or the

numbers of outliers to consider. Moreover, not considering the extreme values or replacing the outliers

affects the properties of the data: sample size, the distribution function or the variance.

39 Resistant to deviations from the assumptions made.40 An estimator α̂ of a parameter α is efficient if no other estimator has a smaller variance.

22

The M-estimate of β is the solution of a system made up of p equations: ∑i=1

n

wi r i x ij=0 where

i=1,2…n, j=1,2…p, ri= y i−x i β is the residual and w i=ϕ ( r i

σ ) represents the weight function. The

specification of the weight function differs for each estimator.

The proposal of Huber for the M-estimator with the same name is: ϕ (u )=ψ (u )u

where

ψ Huber (u )={ k u≥ ku|u|<k−k u≤ k

, k is a tuning constant specified by the user. (2)

This constant stands for the gain in robustness for the loss of efficiency. As a common practice,

the scale estimator σ is approximated simply as the median absolute deviation of the residuals.

Huber’s estimates have the advantage of simplicity as the optimization will give a unique

solution, but they do not assign zero weights to large outliers. More cumbersome and robust to any types

of outliers are the weighting functions proposed by Tukey and Hampel. The disadvantage of these

complex specifications is that they might lead to multiple local minima and convergence might not be

achieved. To tackle this, a good starting point is required.

Tukey’s bisquare function proposal has the advantage of assigning zero weights to large outliers

ψ (u )→ 0 for u→ ∞. The weighting function has the following specification:

ψTukey (u )={ 0 u>ku(k−u2)2|u|≤ k

0 u<k where k is a tuning constant. (3)

Another specification which redescends to 0 is the one of Hampel. It involves a complex

specification including three tuning constants (a, b, c):

ψ Hampel (u )={u|u|≤ a

a∗sign (u )a≤|u|≤ ba∗[u−c∗sign (u ) ]

b−cb≤|u|≤ c

0 c ≤|u|

(4)

23

As the weights depend on β and scale estimator σ, the estimation method is iteratively re-

weighted least squares (IWLS). First, the OLS estimation is performed. The weights are then calculated

based on the OLS residuals and the approximated scale estimator σ. Then, weighted least squares

coefficient estimates are computed. Based on the residuals from the previous iteration, coefficient

estimates are computed until convergence is achieved. The method is iterative as the computation of the

weights and of the IWLS estimates are repeated until convergence.

To investigate the robustness of the results, I use the three specifications for the weight function

captured by equations (2), (3) and (4). The weight function ψ (u ) depends on tuning constants (k , a, b

and c) which capture the trade-off between efficiency loss and robustness gains. Studying the impact of

different specification of tuning constants on the robust estimators Hoaglin, Mosteller and Tukey (1983)

showed that a higher tuning constant is consistent with a higher efficiency at the expense of robustness.

As Haggard and Witte (2010), the chosen tuning constants belong to the middle of the range.

Accordingly, I perform Huber’s proposal based on k=1.500, Tukey’s proposal for k=4.685 and for

Hampel’s specification I use a=1.500, b=3.600 and c=8.000.

3.2.4 Relationship between bond returns and explanatory factors

The study also focuses on the identifying the drivers of seasonality. In order to explain the

seasonality in government bond returns, I regress these returns on other series which display seasonal

patterns (inflation rate, GDP growth, change in consumer confidence etc.) as shown below:

Ex rt=α+β Factort+εt (5)

where Ex rtis the bond excess return recorded in month t and Factort is the factor in the same month.

If the coefficient β is statistically significant, this means that the data series is important for bond

markets. Hence, I continue the analysis by running equation (1) for the estimated residuals to see if they

exhibit any seasonal pattern (repeating the analysis described in Section 3.2.2).

The same idea of verifying if there is a significant seasonal variation in the residuals of the

considered models is found in KKL (2014).

3.2.5 Testing the economic significance

24

The method described in 3.2.2 is focused on the statistical significance of the calendar anomaly.

This section covers the mean-variance analysis implemented in order to investigate the economic

significance of the seasonal pattern.

The purpose of this method is to analyse if a trading strategy which exploits the discovered

calendar anomaly is more profitable and less risky than a simple long strategy (buy and hold strategy

which constitutes the benchmark). For this I define a Long-Short strategy which considers that the

investor takes advantage of the observed seasonal pattern and thus buys the government bonds in July and

holds them until the start of January when he takes a short position in his portfolio.

For each strategy, I compute the excess returns as

Ex rt=( I t−I t−1

I t−1−r3 M t−1), (6)

where I t is the bond index level for month t and r3 M t−1 is the three-month interest rate for the month t-1,

for each leg and report the average for each period January-June or July-December.

The excess return thus represents the percentage increase in the price of the constituent bonds

over the three-month money market interest rate. This is consistent with a zero-investment strategy as the

investor could invest in the bond market with the money borrowed from the money market.

For an investment, it is also important to look at how much the bond index changes through time.

The standard deviation σ is the measure which captures the volatility and thus the risk profile of the asset.

The information ratio (IR) indicator of Grinold and Kahn (2000) is then computed as a ratio

between the excess returns and the standard deviation of excess returns (tracking error): IR=Ex r

σ∗√12.

Given that the benchmark rate is the risk-free rate in this case and that the volatility of risk-free rate is

quite low, this measure is similar to the Sharpe Ratio introduced by William Sharpe in 1966. The IR is

often used for evaluating investments.

The higher the Information ratio, the more compensation the investor receives per unit of risk. I

consider the following criterion that the best performing strategy is the one with the highest Information

ratio.

The calculations do not incorporate transaction costs. However, transaction costs should not be

high given that the strategies imply only two transactions per year. Moreover, the markets are liquid and

most countries have futures contracts to take positions.

25

In order to test if the returns of the strategies exploiting the seasonal pattern are statistically

significant higher than the benchmark (buying and holding the government bond during the whole year), I

run the following regression:

Strat¿t=α +β Ex rt+εt (7)

where Strat¿t is the excess return of the strategy which exploits the H1 H2 effect in month t and Ex rt is

the excess return of the buy and hold strategy (benchmark),

The defined strategy (Long-Short) outperforms the simple strategy of investing in the bond index

of each country if the null hypothesis that α coefficient (Jensen’s alpha) is zero is rejected and if α is

positive.

The statistical significance and magnitude of β is also important as β measures the risks

associated with the strategy compared to the risks when investing in the bond market. A β equal to one

hints that the strategy carries the same risks as when holding the government bonds of the country. In case

the β is smaller than 1, the correlation between the strategy and the bond market portfolio is low,

therefore diversification benefits exist.

4. Results

Chapter 4 tests for the seasonal patterns from the literature and documents a new pattern H1 H2

for bond returns41. Accordingly, bond returns are higher during July-December compared to the ones

recorded in January-June, as documented in Section 4.1.1. Section 4.1.2 indicates that the results are

robust to outliers. According to the analysis from Section 4.2.1, the inflation rate displays the opposite

pattern: higher inflation rates in the first half of the year compared to the second half. The seasonality in

inflation rate explains the discovered H1 H2 effect of bond returns, as shown in Section 4.2.2. The finding

from Section 4.3 that inflation-linked bond returns do not display seasonality support the inflation

hypothesis.

The SAD factor introduced by KKL (2014) is important for the bond markets of the countries

from which the data are gathered. Section 4.4 indicates that the SAD variable also compensates for the

noise in inflation and helps to remove the seasonality at monthly frequency, but fades away at quarterly

frequency.

41 In order to get the annualised value, I multiply it by √12 assuming that the returns are independent and identically distributed.

26

Three hypotheses from the literature (an annual cycle of economic activity, time-varying

optimism and macroeconomic data surprises) are also analysed in Section 4.5. The indicators used to

capture the optimism of investors (Consumer Survey data and VIX) partly explain the seasonal variation

in bond returns, while the other two are not valid for the considered bond markets.

4.1 Seasonal patterns in bond returns

4.1.1 Bond pattern dicovery

Figures 4.1 shows that the excess returns of government bonds from July-December generally

outperform those recorded during January-June. In spite of the monthly noise, bond returns are higher in

the second half of the year and lower in the first half of the year in all six countries. The difference is

more pronounced for the developed portfolio built as an equally weighted average of the existing

countries42.

Figure 4.1: Monthly Average of Nominal Bond Excess Returns

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.4%

0.0%

0.4%

0.8%

1.2%

Australia

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.4%

0.0%

0.4%

0.8%

1.2%

Canada

42 An opposite pattern was discovered on the Japanese stock market (“Dekansho-bushi effect”) by Shigeki, Takashi, Katsuhiko (2011).

27

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.4%

0.0%

0.4%

0.8%

1.2%

Germany

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.4%

0.0%

0.4%

0.8%

1.2%

Japan

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.8%

-0.4%

0.0%

0.4%

0.8%

1.2%

United Kingdom

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.8%

-0.4%

0.0%

0.4%

0.8%

1.2%

United States

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.4%

0.0%

0.4%

0.8%

1.2%

Developed (6)

Notes: The graphs depict the average of nominal bond excess returns constructed from Datastream indices for each calendar month for the considered countries and the Developed portfolio. The sample period covered for each country is shown in Table 3.1. The Developed portfolio is based on equally weighting the six countries provided data are available.

The calculations in Table 4.1 confirm the pattern observed on the graphs. Nominal government

bonds have higher returns in the second half of the year (H2) compared to the first one (H1) for all six

markets. With the exception of Japan, bond returns are close to zero or slightly negative in the first half of

the year (H1), while annualised returns during July-December range between 3.13% and 5.43% .

28

Table 4.1: Economic Importance

CountryNominal Bond Excess Returns

H1 H2Australia 0.26% 3.83%Canada 0.72% 5.24%Germany -0.06% 3.68%Japan 1.15% 3.44%United Kingdom -0.77% 4.63%United States 0.31% 5.43%Developed (6) 0.14% 4.00%US CRSP Universe 0.13% 3.13%

Notes: The table reports the annualised average bond excess returns January - June (H1) and July-December (H2) for the samples mentioned in Table 3.1. Average nominal bond excess returns are calculated based on Datastream Bond Indices with the exception of US CRSP Universe which represents the equally-weighted portfolio of US Treasuries with maturities of 1Y, 2Y, 5Y, 10Y, 20Y and 30Y downloaded from CRSP Database. The Developed portfolio is based on equally weighting the six countries provided data are available.

After the visual and computational evidence, I am going to investigate if the difference in bond

returns between July-December and January-June is statistically signficant. I regress the bond returns on

different dummy specifications inspired from the literature or observed from the graphs and the results are

depicted in Table 4.243.

Table 4.2: Seasonality tests for Nominal Bond Returns

Nominal Bond Excess Returns January H1 H2 SAD Inverted

HalloweenMonthly frequency        Australia -0.63 1.73 0.84 0.29Canada -0.42 2.28 2.58 2.40Germany -0.51 2.67 1.75 0.54Japan -1.25 1.69 0.42 -0.50United Kingdom -0.69 2.37 1.45 0.95United States -0.61 1.99 3.10 2.15Developed (6) -1.11 2.58 2.16 1.16

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression: Yt = α + βXt + εt

where Y are nominal bond excess returns (calculated based on Datastream bond indices) at the monthly frequency. X depends on the seasonal pattern tested. In case of January effect, X is a dummy that takes the value of 1 for January and 0 otherwise. In case of H1 H2, X is a dummy that takes on the value of 1 for July to December and 0 otherwise. For SAD, X is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. Inverted Halloween effect is the opposite of the one discovered by Bouman and Jacobsen (2002) for the stock market. To capture the Inverted Halloween effect, X is a dummy which takes on the value of 1 for May to October and 0 otherwise. The Developed portfolio is based on equally weighting the six countries provided data are available. The number in parenthesis next to Developed portfolio stands for the number of countries

43 Starting with three countries in January 1980 (Germany, United Kingdom and United States) and as data become available the others are incorporated until all six are part of the portfolio starting with March 1987.

29

from the portfolio. The numbers in Bold show statistical significance at least at 5% significance level, while those in Blue at 10% significance level.

Nominal bond excess returns do not display a January effect, in line with the conclusion from the

literature. The coefficient of the dummy which captures higher returns in the second part of the year is

statistically significant at the 10% significance level in all countries. The effect is statistically significant

at the 1% level for Germany and Developed portfolio and at the 5% significance level for Canada, the

United Kingdom and the United States. Moreover, the sign of the coefficient is positive and consistent

across countries.

The SAD factor which was first introduced by KKL for stock returns (2003) and then extended

for bond returns (2014) is statistically significant for Canada and United States at 1% level and for

Germany at 10% significance level. The relevance of SAD in Canada and United States is not surprising

as the variable was built based on a proportion of the North American population that suffers from

seasonal affective disorder. As KKL (2014) mentions that the depression is related to the reduced daylight

during the fall and the winter, the expectation is that countries from the Southern Hemisphere display the

same effect with a six month lag. This is due to the fact the seasons are opposite to those from Northern

countries and there is also a reversal in the change in the number of hours of daylight. This should result

in an inverted sign of the dummy coefficient. However, the SAD variable is not statistically significant

for Australian bond returns and does not exhibits the opposite sign as expected. This result is in line with

Jacobsen and Marquering (2008) as they also do not observe the inverse SAD effect on the stock market

of the Southern Hemisphere countries.

The limited coverage across countries (three out of six) and relatively lower t-values in absolute

terms make the SAD effect weaker than the new H1 H2 effect.

The Inverted Halloween effect is also weaker than H1 H2 as its incidence is two (Canada and the

United States) and the sign of the coefficient is not consistent across countries (negative for Japan and

positive for the rest of the countries).44

4.1.2 Robustness to outliers

As Maberly and Pierce (2004) point out that the “Halloween effect” does not hold when

controlling for the impact of outliers, I check the robustness of the seasonal patterns. I apply the

estimation techniques robust to outliers employed by Haggard and Witte (2010), given the subjective

choice of outliers in case of removing them.

44 The results of the test for the difference between population means when variances are unknown and unequal confirm the results of the dummy regressions.

30

Dampening the influence of extreme returns by applying reduced weights (Huber) or zero weight

(Tukey and Hampel) to the extremes does not alter the statistical significance of the effects as shown in

Table 4.3. Moreover, in some cases the statistical significance is improved: the t-statistic for H1 H2 effect

increased from 1.73 to 2.00 when applying Huber’s M-estimation for Australia. The same holds for H1

H2 effect in other bond markets like Japan, the United Kingdom, the United States or Developed

portfolio.

In what concerns the SAD effect, it not visible in Australian or Japanese nominal bond excess

returns, while it gained statistical significance at 5% level in case of United Kingdom (t-statistic increased

from 1.45 to 2.06).

Table 4.3 also comprises t-statistic values for simple OLS regressions. These values are higher in

absolute terms compared to the Newey-West t-stats. This proves that by using Newey-West techniques, it

is more difficult to reject the null hypothesis that the coefficient of the dummy is zero, making it

conservative, as argued at the end of Section 3.1.

The full table with the estimates and t-statistics can be found in the Table A.4 from Appendix A.

The magnitude of the effects (H1 H2 and SAD) also does not seem to be altered with the exception of

Canada and Germany. In other bond markets, the effect is even stronger.

Table 4.3: Robust Regressions of Monthly Nominal Bond Returns

Nominal Bond Excess Returns Dummy OLS Newey-West Huber Tukey Hampel

Monthly frequency          

Australia H1 H2 1.86 1.73 2.00 2.10 2.02SAD 0.94 0.84 1.25 1.44 1.28

Canada H1 H2 2.28 2.28 2.00 1.79 1.96SAD 2.68 2.58 2.22 1.95 2.20

Germany H1 H2 2.78 2.67 2.30 2.04 2.28SAD 1.78 1.75 1.24 0.97 1.22

Japan H1 H2 1.76 1.69 2.20 2.30 2.31SAD 0.46 0.42 0.92 1.17 1.05

United Kingdom H1 H2 2.47 2.37 2.72 2.82 2.75SAD 1.66 1.45 2.06 2.17 2.11

United States H1 H2 2.17 1.99 2.37 2.34 2.38SAD 2.86 3.10 3.14 3.12 3.16

Developed (6) H1 H2 2.83 2.58 2.98 2.89 2.99SAD 2.26 2.16 2.33 2.31 2.33

Notes: This table shows t-values based on different estimation techniques: OLS, Newey-West standard errors, M-estimation based on the proposal of Huber, Tukey and Hampel respectively for the β in the regression:

Yt = α + βXt + εt

where Y are bond excess returns (calculated based on Datastream bond indices) at the monthly frequency. X depends on the seasonal pattern tested. In case of H1 H2, X is a dummy that takes on the value of 1 for July to December and 0 otherwise. For SAD, X is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. The number in parenthesis next to Developed portfolio stands for the number of countries from the portfolio. Huber M-estimation is performed with k=1.500 and

31

Tukey’s estimation with k=4.685. Hampel estimation is performed with a=1.5, b=3.6 and c=8. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

4.2 Inflation explanation

4.2.1 Seasonality of inflation rate

As discussed in Section 2.3, the dynamics of inflation rate also seem to be repeated across the

calendar year by a similar magnitude. This is due to the seasonality of its components. In the section 4.2.1

I investigate this empirically by following the same steps as in case of nominal bond returns.

First, I look at the monthly average of inflation rate across the calendar year. Figure 4.2 shows

that non-seasonally adjusted inflation displays the opposite pattern compared to that observed on

government bond returns. With the exception of Japan, the inflation rate is higher in the first half of the

year. I proceed with formally testing for seasonality in inflation rate.

Figure 4.2: Monthly Average of Inflation Rate

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.4%

0.0%

0.4%

0.8%

1.2%

Canada

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.4%

0.0%

0.4%

0.8%

1.2%

Developed (5)

32

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.8%

-0.4%

0.0%

0.4%

0.8%

1.2%

Japan

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.4%

0.0%

0.4%

0.8%

1.2%

United Kingdom

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.4%

0.0%

0.4%

0.8%

1.2%

United States

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec-0.4%

0.0%

0.4%

0.8%

1.2%

Developed (5)

Notes: The graphs depict the average of non-seasonally adjusted inflation rate for each calendar month for five of the six considered countries and the Developed portfolio. Australia inflation rate is not displayed as the frequency of the inflation data is quarterly. Details about the indices considered to measure inflation can be found in Table A.1 from the Appendix A. The sample period covered for each country is the same as in case of nominal bond excess returns (shown in Table 3.1). The Developed portfolio is based on equally-weighting the five countries with monthly inflation rates (with the exception of Australia).

Based on Table 4.4, relatively higher inflation rates are observed in the first part of the year

compared to the latter. The exception is Australia where the annual inflation rate hovers around a 3%

level for the whole year. In Germany, the United Kingdom, Developed portfolio and the US CRSP

Universe, the average inflation rate for January-June is twice the one recorded during July-December. A

larger relative difference is seen in Canada, Japan and the United States. It is also noticed that the

magnitude of the difference between first half (H1) and second half (H2) is smaller compared to the one

of bond returns (Table 4.1).

Table 4.4: Economic importance

CountryInflation Rate

H1 H2Australia 3.17% 3.24%

33

Canada 3.67% 1.12%Germany 2.68% 1.74%Japan 1.12% 0.19%United Kingdom 5.52% 2.93%United States 4.73% 1.83%Developed (5) 3.80% 1.74%US CRSP Universe 4.39% 2.65%

Notes: The table reports the annualised average inflation rate for the period January - June (H1) and July-December (H2) of the year for the samples mentioned in Table 3.1. The inflation rate is non-seasonally adjusted. More details about the indices used to calculate inflation rate can be found in Table A.1 in the Appendix A. The numbers in parenthesis next to Developed portfolio stand for the number of countries in the portfolio. The Developed portfolio is based on equally-weighting five countries (Canada, Germany, Japan, United Kingdom and United States). Australian data is not included as the frequency of inflation data for Australia is quarterly.

According to dummy regression results displayed in Table 4.5, the H1 H2 effect is more

pronounced in case of inflation rate compared to government bond returns. The effect is statistically

significant at 1% level for all countries with the exception of Germany (which is significant at 5% level).

The signs of the coefficients are negative and consistent across countries, indicating lower inflation rates

in the second part of the year.

Table 4.5: Seasonality tests for Inflation Rate

Inflation Rate January H1 H2 SAD Inverted Halloween

Monthly frequency        AustraliaCanada 1.24 -5.17 -4.27 -0.99Germany 0.76 -2.54 -4.30 -4.12Japan -1.02 -2.69 0.53 1.92United Kingdom -4.66 -3.97 -4.01 -2.85United States 4.33 -5.14 -3.08 -0.18Developed (5) -0.50 -5.28 -3.82 -1.58

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression: Yt = α + βXt + εt

where Y are inflation rate for sample Jan 1980 – Dec 2013 at the monthly frequency. X depends on the seasonal pattern tested. In case of January effect, X is a dummy that takes the value of 1 for January and 0 otherwise. In case of H1 H2, X is a dummy that takes on the value of 1 for July to December and 0 otherwise. For SAD, X is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. And for Inverted Halloween, X is a dummy that takes on the value of 1 for May to October and 0 otherwise. The Developed portfolio is based on equally-weighting five countries (Canada, Germany, Japan, United Kingdom and United States). Australian data is not included as the frequency of inflation data for Australia is quarterly. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The SAD variable records statistical significance for four countries out of the five countries for

monthly inflation rates (Japan is the exception). As in the case of nominal bond excess returns, the

34

January and Inverted Halloween effect do not explain the difference in the inflation rates across the year

and countries.

From the dummy regression results we can conclude that H1 H2 effect is present in both nominal

bond excess returns and inflation rate with opposite signs for all analyzed countries. In case of bond

returns, the SAD factor loads in case of a limited number of countries (US, Canada and Germany). I will

further investigate the interaction between inflation rate and SAD in Section 4.4.

4.2.2 The link between bond returns and inflation rate

4.2.2.1 Monthly analysis

As shown in Section 2.3, the inflation rate is relevant for nominal bond returns dynamics and the

relationship is negative.

We have seen evidence of a complementary effect in nominal bond returns and inflation rate (the

first half of the year is characterized by lower bond returns and higher inflation rates compared to the

second half). The next step is to test if there is a contemporaneous time-series correlation between the two

variables. I use contemporaneous inflation rate: the increase in prices which takes places in the same

month when bond returns are recorded. Usually, the inflation rate of month n is published in the first half

of the month n+1. In line with evidence from TIPS market (Huberman and Schwert (1985), Chu, Pittman

and Yu (2011)) I assume that bond prices incorporate most of the consumer price dynamics rate before

the official release and that there is a marginal adjustment in bond prices when inflation data are actually

released.

Table 4.6: The relationship between Bond Returns and National Inflation Rate

Nominal Bond Excess Returns

National Inflation Rate R2

β t-statMonthly frequency      AustraliaCanada -0.261 -1.06 0.004Germany -0.630 -2.85 0.031Japan -0.162 -1.08 0.004United Kingdom -0.212 -1.05 0.003United States -0.978 -3.69 0.048Developed (5) -0.676 -2.29 0.024

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β in the regression Yt = α + βXt + εt

35

where Y are nominal bond excess returns (based on Datastream Indices) at the monthly frequency and X is the country’s own inflation (national inflation). Australia has only quarterly inflation and hence at the monthly frequency there are no national inflation results. The number in parenthesis next to Developed portfolio stands for the number of countries from the portfolio, five as inflation data for Australia is available at a quarterly frequency. The analysis is conducted on the samples of nominal bond excess returns depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

From Table 4.6, the negative sign of inflation coefficient is consistent with economic theory.

Accordingly, an increase in inflation rate leads to lower bond returns as a higher inflation rate implies a

higher discount factor and thus a lower price of the bond ceteris paribus. The relationship between bond

returns and inflation is strong, especially in case of United States - at a monthly frequency, the beta of -

0.98 is highly significant with a t-statistic of -3.69 and an R-squared of 4.8%. A significant coefficient at

5% level is also visible in case of Germany and the portfolio of five developed countries. However, the

results are not consistent across countries. One reason for this could be that investors do not pay attention

to the local (national) inflation rate, but they are focusing on the dominant economy whose monetary

policy decisions influence other countries. U.S. economy is dominant since Second World War.

Therefore, the worldwide financial markets are under the influence of the actions of United States.

Several papers indicate the importance of U.S. macroeconomic data releases for other bond

markets. Goldberg and Leonard (2003), Ehrmann and Fratzscher (2005), Andersson, Overby and

Sebestyen (2009) and Andersen, Bollerslev, Diebold and Vega (2007) find that Euro area bonds react

significantly to U.S. macro surprises, and that this effect is stronger than for the equivalent euro area

surprises. As Ehrmann and Fratzscher (2005, p. 928) put it; “In recent years certain US macroeconomic

news affect euro area money markets and have become good leading indicators for the euro area”.

Similarly, Andersson et al. (2009) find that German government bond futures react more strongly to US

macro surprises compared to German and euro area announcements. They find that the effect of US

releases has become more important during the period considered (’99-’05). Goldberg and Leonard

(2003) also find that U.S. economic data releases have a direct and influential effect on German bond

market.

In order to test this hypothesis I run the same regression as before using inflation rate recorded in

the United States instead of the national inflation rate.

Table 4.7: The relationship between Bond Returns and U.S. Inflation Rate

Nominal Bond Excess Returns

U.S. Inflation RateR2

β t-statMonthly frequency      Australia -0.533 -1.92 0.015Canada -0.827 -3.93 0.029Germany -0.937 -5.04 0.084

36

Japan -0.496 -2.59 0.022United Kingdom -1.081 -3.97 0.042United States -0.978 -3.69 0.048Developed (6) -0.893 -4.95 0.074

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β in the regression Yt = α + βXt + εt

where Y are nominal bond excess returns (based on Datastream Indices) at the monthly frequency and X is the inflation rate recorded in the United States. The Developed portfolio is based on equally-weighting the six countries provided data are available. The analysis is conducted on the samples of nominal bond excess returns depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The results in Table 4.7 improve significantly when using US inflation rate instead of the national

inflation rate. With the exception of Australia (for which the coefficient is significant at 10% level), an

increase in U.S. inflation rate leads to lower nominal bond returns in all other five countries at 1%

significance level. The signs are negative and consistent across all countries. The U.S. economy is the

largest and Fed monetary policy decisions trigger reactions on bond markets all over the world. This

could be behind the stronger results when using U.S. data compared to national data. To get a better

understanding on this, both inflation rates are considered in the equation, as displayed in Table 4.845:

Table 4.8: Time series regressions of Bond Returns on National and U.S. inflation rate

Nominal Bond Excess Returns

National Inflation Rate U.S. Inflation Rate

R2

β1 t-stat β2 t-statMonthly frequency          AustraliaCanada 0.265 0.91 -0.996 -3.53 0.032Germany -0.356 -1.85 -0.843 -4.75 0.093Japan -0.048 -0.30 -0.478 -2.48 0.022United Kingdom 0.100 0.40 -1.137 -3.84 0.043United States -0.978 -3.69 -0.978 -3.69 0.048Developed (5) 0.578 1.31 -1.258 -4.58 0.084

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β1 and β2 in the regression Yt = α + β1Xt + β2Zt + εt

where Y are nominal bond excess returns (built from Datastream Indices) at the monthly frequency, while X is the national inflation and Z is the inflation rate recorded in the United States. The Developed portfolio is based on equally-weighting the five countries as Australia only has inflation data available at a quarterly frequency. The analysis is conducted on the samples of nominal bond excess returns depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

For all countries, the U.S. inflation rate negatively influences bond returns. Only in case of

Germany, national inflation rate adds value in explaining the dynamics of nominal bond returns at 10%

significance level. However, based on the correlation coefficients from Table A.5 in the Appendix A the

45 I have also formally tested for the empirical pattern found by Fridson (2000): higher Treasury returns during June-November than the rest of the year. The effect is weaker than the H1 H2 pattern, being statistically significant at 5% level only for the United States and Developed portfolio.

37

results for Canada should be seen with caution (correlation coefficient of 0.77). This also holds for the

portfolio of five developed countries as U.S. is one of the components.

The results of the two regressions show that the consumer price dynamics of United States are

important for nominal bond excess returns. To analyse to what extent the seasonality in U.S. inflation rate

captures the seasonality of nominal bond excess returns I regress the residuals of the equation from Table

4.7 on the dummies. This approach is in line with KKL (2014).

Table 4.9: Seasonality in Inflation-corrected Bond Returns

Inflation-corrected Bond Returns H1 H2 SAD

National indicator    Australia 0.97 0.33Canada 1.12 1.87Germany 0.80 0.68Japan 0.67 -0.13United Kingdom 1.05 0.75United States 0.62 2.20Developed (6) 0.90 1.18

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β in the regression Yt = α + βXt + εt

where Y are residuals of the equation from Table 4.7 (nominal bond excess returns regressed on U.S. inflation rate) at the monthly frequency and X depends on the seasonal pattern tested. In case of H1 H2, X is a dummy that takes on the value of 1 for July to December and 0 otherwise. For SAD, X is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. The Developed portfolio is based on equally-weighting the six countries provided data are available. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The results from Table 4.9 show that the seasonality of US inflation rate captures the patterns

which were visible on nominal bond excess returns (H1 H2 and SAD)46. For the United States and

Canada, SAD seasonal effect holds after taking into account inflation with a t-statistic of 2.20 and 1.87

respectively. In case of Germany, where the SAD factor was statistically significant at 10% level, the

effect disappears.

The reminiscent SAD effect in case of the United States and Canada is not surprising as the

nominal bond excess returns of these two countries displayed strong SAD effects when testing the returns

(Table 4.2). Moreover, the correlation matrix from Table 3.2 shows the highest correlation between bond

markets for these two countries (correlation coefficient of 0.77). The presence of SAD in the residuals in

the United States after taking into account macroeconomic data is in line with the conclusion of Kamstra,

Kramer and Levi (2014). The SAD factor is significant after taking into account several macroeconomic

variables. One of the models also includes U.S. non-seasonally adjusted inflation which is also used here.

46 The correlation of national inflation and U.S. inflation rate is low in case of Germany, Japan and United Kingdom. The table with the coefficients of correlation can be found in Table A.5 from Appendix A.

38

Another explanation for the lack of consistence of results concerning the influence of national

inflation rates on nominal bond excess returns could be the existence of noise in nominal bond returns and

inflation rates. The noise in inflation rate could be related to different starting points of the fiscal year

across countries47 which is usually associated to changes in administrated prices, specific events such as a

spike in oil prices or noise related to the CPI definition which might result into larger weights for volatile

prices.

Bond prices could also react to inflation at different speed. Smirlock (1985) finds that the

response of the US Treasuries to unexpected inflation took place by the end of the announcement day

during 1979-1983, while there was no effect until 1979. The applied regression assumes that bond prices

react to contemporaneous inflation (bond returns and price dynamics take place in the same month). But,

forward-looking investors could anticipate the consumer price dynamics and in this case, the bond return

in month t is related to inflation in month t+1 (lead measure of inflation). A proof of this is the

simultaneous regression of nominal bond excess returns (recorded at time t) on contemporaneous (the

inflation rate recorded at time t) and lead inflation measures (at time t bond prices incorporate inflation at

time t+1). As captured by Table 4.10, a significant loading on both contemporaneous and lead inflation is

found in case of Germany and the United States.

Table 4.10: Time series regressions of Bond Returns on Contemporaneous and Lead Inflation Rate

Nominal Bond Excess Returns

Contemporaneous Inflation Rate Lead Inflation Rate

R2

β1 t-stat β2 t-statMonthly frequency          AustraliaCanada -0.261 -1.07 -0.211 -1.04 0.007Germany -0.595 -2.86 -0.405 -2.19 0.042Japan -0.186 -1.22 0.163 0.92 0.007United Kingdom -0.165 -0.83 -0.337 -1.48 0.012United States -0.617 -1.94 -0.603 -2.13 0.055Developed (5) -0.219 -0.65 -0.842 -3.16 0.048

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β1 and β2 in the regression Yt = α + β1Xt + β2Zt + εt

where Y are nominal bond excess returns at the monthly frequency, while X is the contemporaneous inflation rate (inflation rate recorded at time t) and Z is the lead inflation measure (inflation rate recorded at time t+1 is anticipated by investors at time t). The Developed portfolio is based on equally-weighting the five countries as Australia only has inflation data available at a quarterly frequency. The analysis is conducted on the samples of nominal bond excess returns depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

In order to reduce the noise in bond returns and inflation rates and to capture the uncertain timing

when nominal bond prices incorporate inflation rate, the analysis at a lower frequency (quarterly data) is

considered. The use of quarterly data also facilitates the inclusion of results for Australia as inflation data

47 I only test for these two because they are found to be statistically significant and the most consistent across countries.

39

are published on a quarterly basis. Australia is important for our analysis as it is situated in the Southern

Hemisphere and it is considered a robustness check for SAD hypothesis as the reverse seasons should

result into a different sign of the SAD variable. Similarly, in his analysis Ogden (2003) also considers

lower frequency data (quarterly, semi-annual, annual).

The results at the monthly frequency hint that inflation rate drives the seasonality of nominal

bond excess returns. However, the inflation measure of a large and diversified economy such as the

United States seems to capture the seasonality better than the national inflation rates. The conclusion is

confirmed by the regression results displayed in Table A.6 from the Appendix A when including US

inflation rate as a control variable in the regression of nominal bond excess returns on H1 H2 dummy.

The coefficient of H1 H2 dummy becomes insignificant, U.S. inflation rate explaining the dynamics of

nominal bond excess returns. This confirms that inflation takes out the seasonal pattern of nominal bond

returns.

4.2.2.2 Quarterly analysis

An inspection of the graphs of the quarterly average of bond returns and inflation rate from

Figure 4.3 confirm the findings from the monthly frequency. A complementary pattern exists in case of

bond returns and inflation rate. The first two quarters are characterized by poorer performance of fixed-

income instruments (null or negative returns) and higher inflation rates compared to the last two. Japan is

the exception in case of bond returns and Australia for inflation rate.

Figure 4.3: Quarterly Average of Nominal Bond Returns (left panel) and Inflation Rate (right panel)

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

Australia - Bond Returns

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

Australia - Inflation Rate

40

Q1 Q2 Q3 Q4

-1.0%

0.0%

1.0%

2.0%

Canada - Bond Returns

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

Canada - Inflation Rate

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

Germany - Bond Returns

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

Germany - Inflation Rate

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

Japan - Bond Returns

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

Japan - Inflation Rate

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

United Kingdom - Bond Returns

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

United Kingdom - Inflation Rate

41

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

United States - Bond Returns

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

United States - Inflation Rate

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

Developed - Bond Returns

Q1 Q2 Q3 Q4-1.0%

0.0%

1.0%

2.0%

Developed - Inflation Rate

Notes: The graphs depict the average of nominal bond excess returns and non-seasonally adjusted inflation rate for each quarter for the six considered countries and the Developed portfolio. The sample period for the two indicators is the same for comparison purposes (the same as in case of Nominal Bonds as depicted in Table 3.1). Details about the indices considered to measure inflation can be found in Table A.1 from the Appendix A. The Developed portfolio is based on equally-weighting the six countries provided the data are available.

I conduct the dummy regression tests for the H1 H2 and SAD seasonal patterns. The results are

centralised in Table 4.11. Both H1 H2 and SAD patterns are statistically significant for nominal bond

excess returns and inflation rates at quarterly frequency and they are opposite. In line with the results

from the monthly frequency (from Table 4.2 and 4.5), Japan and Australia are the exceptions. Japanese

nominal bond returns do not display the H1 H2 or the SAD effect. The same happens in case of

Australian inflation rate. Moreover, the effects are stronger at quarterly frequency compared to those at

monthly frequency.

Table 4.11: Seasonality tests for Nominal Bond Returns and Inflation Rate

CountryNominal Bond Excess Returns Inflation Rate

H1 H2 SAD H1 H2 SADQuarterly frequency      Australia 1.88 2.32 1.12 1.36Canada 2.45 2.53 -5.93 -6.41Germany 2.94 2.78 -2.83 -3.5Japan 1.62 1.06 -3.6 -1.9United Kingdom 2.26 1.72 -4.46 -3.24

42

United States 2.03 2.59 -4.92 -4.87Developed (6) 2.66 2.61 -5.27 -4.92

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression: Yt = α + βXt + εt

where Y are nominal bond excess returns at the quarterly frequency (left panel) and non-seasonally adjusted inflation rates (right panel). X depends on the seasonal pattern tested. In case of H1 H2, X is a dummy that takes on the value of 1 for Q3 and Q4 and 0 otherwise. The SAD factor is built from the 12 monthly values from Kamstra, Kramer, and Levi (2014) paper as the three-month average corresponding to each quarter. The Developed portfolio is based on equally-weighting the six countries provided data are available. The analysis is conducted on quarterly data for the samples of nominal bond excess returns depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The SAD factor was built from the 12 monthly values from Kamstra, Kramer, and Levi (2014)

paper as the three-month average corresponding to each quarter. Nominal bond returns and inflation rate

have opposite loadings on SAD. Interestingly, the SAD factor is statistically significant in case of

Australian bond returns at 5% level, but the sign of the coefficient is not in line with expectations. As

Australia is located in the Southern Hemisphere, the seasons are opposite to those from Northern

Hemisphere and the change in the number of hours of daylight is reversed. The positive sign implies thus

that the risk appetite of the investors deteriorates during the spring-summer of Southern Hemisphere

(September-January), which comes against the intuition.

The results of the analysis which investigates the relationship between nominal bond excess

returns and inflation rate at a quarterly level (from Table 4.12) are also stronger than at monthly

frequency. Accordingly, there is a clear improvement in t-statistic and R 2 values across all countries. In

case of national inflation rate regressions, Japan and the United Kingdom gain statistical significance,

while in case of Germany and the United States, the R2 is more than doubled (from 3.1% to 11.6% and

from 4.8% to 12.2% respectively). In case of U.S. inflation rate, the negative coefficient of inflation rate

is statistically significant at 1% significance level in case of all analyzed countries. Moreover, R2

increased significantly and ranges from 8% in case of Japan to 20% in Germany.

Table 4.12: The relationship between Bond Returns and Inflation

Nominal Bond Excess Returns

National Inflation Rate   U.S. Inflation Rateβ t-stat R2 β t-stat R2

Quarterly frequency              Australia -0.393 -1.05 0.010 -0.954 -2.87 0.085Canada -0.781 -1.71 0.039 -1.184 -5.12 0.114Germany -1.383 -3.20 0.116 -1.120 -6.02 0.199Japan -1.039 -3.40 0.070 -0.792 -2.82 0.080United Kingdom -0.747 -2.15 0.046 -1.373 -3.77 0.128United States -1.260 -4.73 0.122 -1.260 -4.73 0.122Developed (6) -1.036 -2.58 0.069   -1.145 -5.25 0.180

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β in the regression Yt = α + βXt + εt

43

where Y are nominal bond excess returns at the quarterly frequency and X is the country’s own inflation (national inflation) in the left panel and U.S. inflation rate in the right panel. The regression is conducted separately. The Developed portfolio is based on equally-weighting the six countries provided data are available. The analysis is conducted on quarterly data for the samples of nominal bond excess returns depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

After taking into account inflation, the nominal bond excess returns generally do not display the

seasonal patterns of H1 H2 and SAD. In case of national inflation rate (results depicted on the left panel

of Table 4.13), however, there are some remaining H1 H2 effects significant at 5% level in case of

Australia and Germany. Australia also displays a SAD effect at 1% significance level. This could be due

to the fact that the inflation rate does not exhibit a seasonal pattern in this country. As seen in Figure 3,

inflation rate hovers around 1% in quarterly terms all year long. This seems to slightly accentuate the

SAD and H1 H2 effects on nominal bond returns.

When U.S. inflation rate is considered (results depicted on the right panel of Table 4.13), there is

no evidence of remaining effects in the residuals from regressing bond returns on inflation rate. The t-

statistics are close to zero and lower in absolute terms than those when considering national inflation

rates.

Table 4.13: Seasonality in Inflation-corrected Bond Returns

Inflation-corrected Bond Returns

National Inflation   U.S. InflationH1 H2 SAD   H1 H2 SAD

Quarterly frequency          Australia 1.91 2.37 0.50 0.85Canada 1.38 1.45 0.64 0.77Germany 1.93 1.49 0.46 0.52Japan 0.99 0.87 0.08 -0.32United Kingdom 1.41 1.20 0.62 0.32United States 0.24 0.75 0.24 0.75Developed (6) 1.50 1.67   0.41 0.53

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression Ye t = α + βXt + εt

where Ye are residual bond excess returns from the regression of quarterly nominal bond excess returns on (national or US) inflation (Table 4.12). X depends on the seasonal pattern tested. In case of H1 H2, X is a dummy that takes on the value of 1 for Q3 and Q4 and 0 otherwise. The SAD factor is built from the 12 monthly values from Kamstra, Kramer, and Levi (2014) paper as the three-month average corresponding to each quarter. The Developed portfolio is based on equally-weighting the six countries provided data are available. The analysis is conducted on quarterly data for the samples of nominal bond excess returns depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The results of the conducted regressions show that after accounting for the possible noise in bond

and inflation data as well as possible time-varying response times of bond prices to inflation, the

seasonality in bond returns is largely driven by seasonality in inflation.

44

4.3 ILB – Comparator analysis

The analysis which was focused so far on nominal bonds brings the following conclusions. There

is a statistically significant seasonal pattern in nominal bond returns which is consistent with higher

returns in the second half of the year compared to the first one (H1 H2). A complementary effect was

documented on inflation rates (higher inflation rates in the first half of the year). Tests have shown that

seasonality in inflation rate captures the seasonality in bond returns and that SAD hypothesis of KKL

does not hold across the six considered countries. The results suggest that nominal bond investors do not

properly take into account seasonal variation in inflation. A possible explanation is that market

participants focus on the seasonally-adjusted inflation figures which capture the underlying inflationary

trends.

Taken into account the above conclusions, a close investigation of the seasonal pattern of ILBs is

important as it can validate or invalidate previous results. As the cash-flows (coupon payments and

principal) of these instruments are indexed to the growth of a non-seasonally adjusted official price index

over the life of the bond, the inflation-linked bond market should automatically adjust to consumer price

dynamics. As ILB prices constantly incorporate inflation rates, these prices should not react to the

inflation rate, contrary to nominal bonds. Expected inflation and inflation risk are components of nominal

bond returns. The construction of nominal bond indices with similar characteristics as inflation-linked

bonds by Barclays called comparators facilitates the analysis as it offers the possibility to investigate if

real and nominal bond indices with similar constituents display a seasonal pattern in returns for the same

sample period.

A disadvantage of analysing inflation-linked bonds is the limited data as shown in Table 3.1.

Table 4.14: Seasonality in Comparator and Inflation-Linked Bond Returns

Country January H1 H2 SADInverted Hallowee

nPanel A:Comparator Excess Returns - Monthly frequency  Australia -1.03 1.37 1.52 1.30Canada -2.21 1.90 1.65 1.07Germany -0.47 1.94 1.37 0.93Japan -0.52 1.85 1.08 0.63United Kingdom -1.16 2.46 1.36 0.84United States -0.66 2.03 3.05 2.04Developed (6) -0.90 1.91 1.23 0.77Panel B:Infl-link (ILB) Excess Returns - Monthly frequencyAustralia 1.35 0.20 0.56 0.69

45

Canada -1.40 0.24 -0.89 -0.43Germany -0.46 1.48 -0.76 -0.64Japan 1.27 0.10 -0.70 -0.93United Kingdom -0.35 1.87 0.98 0.00United States 1.62 -0.04 0.16 0.17Developed (6) 0.33 1.24 0.87 0.06

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression: Yt = α + βXt + εt

where Y are comparator bond excess returns (panel A) or inflation-linked bond excess returns (Panel B) at the monthly frequency. X depends on the seasonal pattern tested. In case of January effect, X is a dummy that takes the value of 1 for January and 0 otherwise. In case of H1 H2, X is a dummy that takes on the value of 1 for July to December and 0 otherwise. For SAD, X is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. And for Halloween X is a dummy that takes on the value of 1 for May to October and 0 otherwise. The Developed portfolio is based on equally-weighting the six countries provided data are available. The analysis is conducted on the samples of inflation-linked bond excess returns as depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The results in Table 4.14 show in the top panel that despite the reduced sample size shown in

Table 3.1, the H1 H2 seasonal pattern is significant across nominal bond markets with the exception of

Australia. SAD effect is visible in the case of Canada and the United States, but not for Germany for this

specific comparator sample. As expected, the bottom panel of Table 4.14 shows that inflation-linked

bond returns do not have any seasonal pattern with the exception of the H1 H2 seasonal for the UK. In

case of the United States, the country on which most of the analyses focus on, comparator bond excess

returns still have a significant loading on the H1 H2 and SAD seasonal with t-statistics of 2.03 and 3.05,

respectively. Yet inflation linked bond returns have insignificant loadings on these seasonals with t-

statistics of -0.04 and 0.16, respectively.

Hence, the results which show that the inflation-linked bonds do not display seasonality confirm

the finding that the nominal bond seasonal is driven by the seasonality in inflation. Unless there is a link

between inflation and SAD, the conclusion that SAD is not a good explanation for seasonality in bond

returns can be drawn. In the next section I will formally investigate the interaction between inflation rate

and SAD.

4.4 Interaction with SAD

There are two competing explanations for the seasonality found in bond markets: inflation

seasonality and the SAD factor introduced by KKL (2014). I investigate their interaction to determine

whether both are relevant or not. I conduct thus a joint regression by adding the SAD factor besides the

inflation rate in the equation (5). The SAD variable is made up from 12 values as defined by KKL, while

46

the inflation rate is a time-series. The correlation between the two is quite small as depicted in Table A.7

from the Appendix A, so there are no multicollinearity problems.

The results of the joint regression for monthly and quarterly frequency can be found in Table

4.15. At monthly level, the U.S. inflation rate is statistically significant across the six considered countries

at 1% significance level with the exception of Australia and Japan (where it is significant at 10% and 5%

level respectively). The SAD factor has explanatory power in case of Canada and the United States, the

specific markets from which it comes from. The weak significance of the SAD effect in Germany is not

visible anymore, in line with the residual tests of inflation-adjusted bond returns from Table 4.13 (right-

side panel).

Table 4.15: Interaction of US inflation rate with SAD

Nominal Bond Excess Returns

US Inflation Rate SADR2

β1 t-stat β2 t-statPanel A: Monthly frequency      Australia -0.508 -1.77 0.001 0.35 0.015Canada -0.704 -2.99 0.008 1.90 0.040Germany -0.917 -4.87 0.002 0.70 0.085Japan -0.501 -2.51 0.000 -0.13 0.022United Kingdom -1.037 -3.45 0.004 0.72 0.044United States -0.889 -3.15 0.008 2.23 0.057Developed (6) -0.854 -4.49 0.003 1.19 0.078Panel B: Quarterly frequencyAustralia -0.805 -2.03 0.016 0.99 0.093Canada -1.057 -3.53 0.014 0.80 0.119Germany -1.084 -5.47 0.005 0.58 0.200Japan -0.831 -2.61 -0.004 -0.33 0.081United Kingdom -1.325 -3.16 0.007 0.32 0.129United States -1.177 -3.82 0.012 0.77 0.126Developed (6) -1.100 -4.41 0.007 0.55 0.181

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β1 and β2 in the regression Yt = α + β1Xt + β2Zt + εt

where Y are nominal bond excess returns at the monthly frequency (Panel A) and quarterly frequency (Panel B), while X is the inflation rate recorded in United States and Z is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. At the quarterly frequency Z is built as the average of the 3 monthly values in each quarter. The Developed portfolio is based on equally-weighting the six countries provided data are available. The analysis is conducted on the samples of nominal bond returns as depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The results at the quarterly frequency reinforce the hypothesis that the seasonality in bond returns

is driven by the seasonality in inflation rate. The U.S. inflation rate gains statistical significance at 5%

level for all countries and SAD factor does not have explanatory power for the considered bond markets.

47

The results of residual tests from Table 4.16 show that at monthly frequency SAD adds value to US

inflation rate compensating for the noise behavioural of inflation rate and the uncertain reaction of bond

prices to inflation rate. There is no seasonality in the residuals. The same conclusion holds at the quarterly

frequency, but the rejection of the null hypothesis that the dummy coefficient is zero is stronger. This is

due to the fact that the t-statistic are close to zero, lower than at monthly frequency.

Table 4.16: Seasonality in SAD and inflation-corrected bond returns

SAD and U.S. Inflation-corrected Bond Returns H1 H2

Panel A: Monthly frequencyAustralia 0.73Canada -0.25Germany 0.33Japan 0.76United Kingdom 0.45United States -0.70Developed (6) 0.10Panel B: Quarterly frequencyAustralia -0.28Canada -0.10Germany -0.02Japan 0.38United Kingdom 0.29United States -0.40Developed (6) -0.08

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression Ye t = α + βXt + εt

where Ye are residual bond excess returns from the regression of nominal bond excess returns on US inflation and SAD factor (from Table 4.15). X is a dummy to capture for H1 H2 effect. Accordingly, X takes on the value of 1 for July to December and 0 otherwise at monthly frequency and 1 for Q3 and Q4 and 0 for Q1 and Q2 at quarterly frequency. The Developed portfolio is based on equally-weighting the six countries provided data are available. The analysis is conducted on the samples of nominal bond returns as depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The analysis carried above was focused on an international sample in order to check the validity

of results on six liquid and large bond markets. This section is dedicated to the SAD factor introduced by

KKL as there were signs that the factor is relevant for some countries (Canada, Germany and the United

States). Given that the interaction of SAD hypothesis and inflation rate was tested on samples which start

in January 1980 the earliest, the investigation of a longer data set as the one used by KKL(2014) which

covers 1952-2007 is an additional robustness check. The recent data sample is characterized by falling

interest rates, while the period before 1980s by rising yields and inflation, as shown in Figure A.2 from

the Appendix A. Accordingly, I conduct the same analysis on the bond returns with the maturities chosen

by KKL (20Y, 10Y, 7Y and 5Y) as in section 4.1 and 4.2.

48

I first test the existence of seasonality in bond returns at both monthly and quarterly frequency.

Table 4.17: Seasonal tests on U.S. CRSP Bond Returns

U.S. CRSP Bond Excess Returns 1952-2007 H1 H2 SAD

Panel A: Monthly frequency  20-year 1.30 2.2310-year 1.57 2.397-year 2.38 2.875-year 1.88 2.78Average 1.76 2.58Panel B: Quarterly frequency  20-year 1.36 1.4510-year 1.59 1.327-year 2.47 2.575-year 1.85 1.97Average 1.81 1.80

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression: Yt = α + βXt + εt

where Y are US CRSP Bond Excess Returns for the sample 1952-2007, as considered by Kamstra, Kramer and Levi (2014) at the monthly frequency (Panel A) and quarterly frequency (Panel B). X depends on the seasonal pattern tested. In case of H1 H2, X is a dummy that takes on the value of 1 for July to December and 0 otherwise. For SAD, X is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. Average stands for an equally-weighted portfolio made up of four maturities: 20Y, 10Y, 7Y and 5Y. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The average portfolio exhibits both H1 H2 and SAD patterns at both monthly and quarterly level.

The SAD factor is stronger than inflation at monthly frequency.

In what concerns H1 H2 effect, 5Y and 7Y US Treasuries display higher returns in the second

part of the year, while the difference in returns between January-June and July-December in case of 10Y

and 20Y Treasuries is not statistically significant. However, the t-statistics are positive in line the other

maturities. The weaker results for long maturities could be due to moves in the curve (steepening or

flattening) which seem to be stronger in the first part of the sample. As depicted in Figure A.2 from the

Appendix A, this could be due to lower volatility in bond returns during 1952-1979 compared to 1980-

2013. The weaker results in case of 10Y and 20Y are interesting for further research.

The results of regressions of US CRSP Bond Excess Returns on U.S. inflation rate from Table

4.18 confirm that a higher level of inflation leads to lower bond returns. The coefficients are statistically

significant at both monthly and quarterly frequency, and an improvement in the power of t-test and R 2 is

visible at the lower frequency. For example, for the average portfolio the t-statistics increases in absolute

terms to -4.23 from -2.65 recorded at monthly frequency. R2 also goes up from 1.3% to 6.4%.

Table 4.18: The relationship between U.S. CRSP Bond Returns and Inflation Rate

U.S. CRSP Bond Excess U.S. Inflation Rate R2

49

Returns 1952-2007 β t-statPanel A: Monthly frequency    20-year -1.040 -3.15 0.01810-year -0.572 -2.24 0.0087-year -0.520 -2.43 0.0105-year -0.401 -2.11 0.009Average -0.633 -2.65 0.013Panel B: Quarterly frequency    20-year -1.613 -4.50 0.07610-year -1.095 -3.99 0.0557-year -0.916 -4.00 0.0565-year -0.741 -3.63 0.050Average -1.091 -4.23 0.064

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β in the regression Yt = α + βXt + εt

where Y are US CRSP Bond Excess Returns for the sample 1952-2007, as considered by Kamstra, Kramer and Levi (2014) at the monthly frequency (Panel A) and quarterly frequency (Panel B). X is the inflation rate which was recorded in United States. Average stands for an equally-weighted portfolio made up of four maturities: 20Y, 10Y, 7Y and 5Y. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

For both frequencies, the magnitude of the coefficient is positively related with the maturity of

the fixed-income instrument. Accordingly, for monthly returns, the coefficient increases in absolute terms

from -0.401 for 5-year to -1.040 for 20-year US Treasuries. This is also observed by Balduzzi, Elton and

Green (2001) when investigating the reaction of US T-bills and Treasuries on 26 economic

announcements. The outcome could be explained by the fact that the duration (the sensitivity of bond

prices to interest rate changes) increases with the maturity.

Table 4.19: Seasonality in Inflation-corrected Bond Returns

Inflation-corrected bond returns H1 H2 SAD

Panel A: Monthly frequency  20-year 0.76 2.0010-year 1.22 2.217-year 1.98 2.685-year 1.52 2.60Average 1.33 2.37Panel B: Quarterly frequency  20-year 0.47 0.7310-year 0.91 0.747-year 1.71 1.925-year 1.17 1.36Average 1.03 1.14

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression Ye t = α + βXt + εt

50

where Ye are residual excess bond returns from the regression of monthly US CRSP bond excess returns (Panel A) or quarterly US CRSP bond excess returns (Panel B) on US inflation (Table 4.18). X depends on the seasonal pattern tested. For H1 H2 X is a dummy that takes on the value of 1 for July to December and 0 otherwise. For SAD it is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. At the quarterly frequency I take the average of the 3 monthly values in each quarter. Average stands for an equally-weighted portfolio made up of four maturities: 20Y, 10Y, 7Y and 5Y. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

According to results from Table 4.19, at monthly frequency the SAD effect is significant for the

average and all four maturities of inflation-corrected bond returns. At a quarterly frequency the SAD

effect disappears, except for a significant result for the 7-year maturity. This is in line with the results

based on the international data set from Table 4.9 and 4.13 (right-side panel).

The same conclusion can be drawn when considering the joint regression with U.S. inflation rate

and SAD as explanatory variables for US Bond Excess Returns. As shown in Table 4.20, at the monthly

frequency both U.S. inflation and the SAD factor are statistically significant. Interestingly, for the long

maturity of 20Y and the average portfolio, the t-statistic is higher for inflation rate compared to the SAD

factor in absolute terms.

The inflation rate gains statistical significance when decreasing the frequency to quarterly data.

The SAD factor does not have explanatory power at a quarterly frequency with the exception of 7Y U.S.

Treasuries. This analysis confirms the results when using US Datastream indices that in case of the U.S.,

the SAD effect seems to explain the seasonality of monthly bond returns, but is subsumed by the inflation

seasonal on a quarterly basis.

Table 4.20: Interaction of US inflation rate with SAD

US CRSP Bond Excess Returns 1952-2007

US Inflation Rate SADR2

β1 t-stat β2 t-statPanel A: Monthly frequency          20-year -0.994 -2.92 0.009 1.98 0.02410-year -0.528 -2.02 0.009 2.22 0.0167-year -0.478 -2.19 0.008 2.69 0.0205-year -0.367 -1.90 0.007 2.60 0.018Average -0.592 -2.41 0.008 2.37 0.021Panel B: Quarterly frequency          20-year -1.574 -4.26 0.013 0.72 0.07810-year -1.060 -3.86 0.011 0.76 0.0577-year -0.848 -3.70 0.022 1.97 0.0675-year -0.698 -3.38 0.014 1.39 0.056Average -1.045 -4.00 0.015 1.15 0.068

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β1 and β2 in the regression Yt = α + β1Xt + β2Zt + εt

51

where Y are US CRSP Nominal Bond Excess Returns for the sample 1952-2007, as considered by Kamstra, Kramer and Levi (2014) at the monthly frequency (Panel A) and quarterly frequency (Panel B), while X is the inflation rate recorded in United States and Z is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. At the quarterly frequency I take the average of the 3 monthly values in each quarter. Average stands for an equally-weighted portfolio made up of four maturities: 20Y, 10Y, 7Y and 5Y. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

Given the above results, when accounting for the noise in inflation rate and the uncertain timing

of the incorporation of the inflation rate in bond prices, I can conclude that the seasonal pattern in the

consumer price index can explain the seasonal pattern in US Treasuries at a quarterly frequency as shown

before. Moreover, the results are consistent across maturities.

Even though KKL tests models in which they also include inflation rate, they find seasonality in

the residuals and thus conclude that the seasonality in bond returns is related to the cycle in risk aversion

triggered by the daylight fluctuations. There are four reasons which can explain the different conclusion

of this analysis from the one of Kamstra, Kramer, and Levi (2014).

First, the analysis of KKL (2014) is based on monthly data and it focuses on the U.S. government

bond market, while the current analysis considers six large bond markets including the U.S. both at a

monthly and a quarterly data frequency. Considering a lower frequency helps smoothing the noise in

inflation rate which is visible in Figure 4.1 (due to different specific events such as spikes in oil prices,

different weights of prices of volatile goods).

Second, even though they consider inflation rate as a candidate for the drivers in seasonality, the

specified models do not purely focus on the inflation rate, but include several macroeconomic variables at

the same time (GDP growth, industrial production, unemployment rate, inflation based on PPI).

Third, they only look at the contemporaneous link between monthly inflation rate and bond

returns. As shown in section 4.2.2.1, both contemporaneous and lead inflation have an impact on nominal

bond prices.

Fourth, the seasonal variable developed by Kamstra, Kramer, and Levi (2014) comprises only 12

values, while I use the time series of the inflation rate. It would be interesting to study the relationship

between the SAD effect and bond returns through time. In case of the 12-value SAD variable, the

statistical significance can be the result of a coincidence of outliers of the SAD variable and bond returns

in the same month. Potentially there could also be other variables with a similar pattern for which we

could find statistical significance without a real link between bond returns and those variables. Jacobsen

and Marquering (2009) point out such examples: ice cream consumption or airline travel patterns. Also

related to the construction of the SAD variable is the fact that it is North America based and it is difficult

to use the same measure for Southern Hemisphere countries for which the seasons are reversed. One

might argue that the current analysis also uses a U.S. based inflation measure. The reason for this is that

U.S. inflation rate is relevant for U.S. monetary policy which influences markets worldwide given its size

52

and relation to the largest economy of the world. Evidence from the literature on this is available in

Section 4.2.2.1.

4.5 Other considered explanations

The literature puts forward alternative hypotheses for seasonality, but only a few papers also

empirically test these explanations. I have analysed three of these alternatives and present the key results

in this section. As the studies focus on stock return patterns, the explanations have been adapted from the

equity literature.

First, as there is no January effect, the explanations for government bond returns associated with

this pattern can be ruled out (parking the proceeds hypothesis of Clayton, Delozier and Ehrhardt (1989),

agency problems explanation of Athanassakos (2006)48).

4.5.1 Annual cycle of economic activity

The hypothesis of Ogden (2003) regarding the existence of an annual cycle of economic activity

has been tested using variables which display a seasonal pattern and are representative for economic

trends such as: Gross Domestic Product (GDP), industrial production, unemployment rate. These

indicators are also used in the literature (Ogden (2003), Gerlach (2007)) as they are closely monitored by

central banks for their monetary policy decisions which in turn can affect bond prices. Goldberg and

Leonard (2003) also showed that US indicators capturing labor market conditions (payrolls,

unemployment rate and initial jobless claims), output (GDP growth), and consumer confidence (Michigan

and Conference Board consumer confidence) had the strongest effects on US and German yield changes.

The impact of Producer Price Index (PPI – another measure of inflation which captures the prices charged

by producers) and employment announcements on the volatility of the bond market is highlighted by

Jones, Lamont and Lumsdaine (1998). Ang and Piazzesi (2003) discovered that GDP data surprises affect

bond prices for all maturities and has an impact on both the level and the shape of the bond yield curve.

This supports the hypothesis that real economy indicators affect bond prices.

The gross domestic product which tracks the dynamics of the economy displays recurrent

movements across the year. Ogden (2003) documents such an annual cycle for the US economy.

48 Fiscal year starts in January in Canada, Germany, the United States. For Japan and the United Kingdom it starts in April, while for Australia in July.

53

Accordingly, the peak of investment and industrial production growth is recorded at mid-year, while

personal consumption growth attains its maximum in October-December, probably caused by the holiday

season. However, Ogden (2003)’s analysis is different from the one considered in this paper. I am

focusing on the contemporaneous relationship, while he investigates the predictive power of stock market

returns for macroeconomic conditions (the link between stock returns and the macroeconomic indicators

for the subsequent six months).

Unemployment rate also displays seasonality due to temporary fluctuation in employment in

different sectors of the economy. Cook and Korn (1991) and Krueger and Fortson (2003) underline the

importance of employment data for US bond market (nonfarm payrolls report) starting with 1980. The

choice of the indicators is reinforced by the conclusion of Fleming and Remolona (1999) that labour and

inflation data trigger a reaction on US bond market.

Industrial production is a business cycle indicator which is taken into consideration for

forecasting GDP dynamics (given that it is available at a higher frequency) and for monetary policy

decisions49. For GDP and industrial production, I use volume indices which capture the changes in

economic and industrial output respectively after adjusting for the price fluctuations.

The expectation is that there is a negative relationship between economic growth rates and bond

returns as good economic performance is consistent with rising interest rates. Given that industrial output

is a component of the GDP, a negative sign is also expected for the coefficient which captures the impact

of industrial production growth on bond returns.

Inversely, the unemployment rate is positively correlated with the bond returns. A higher

unemployment rate is consistent with poor economic conditions and decreasing interest rates in an

attempt of central banks to stimulate the economy with loose monetary policy. A lower discount rate

results in higher bond prices and thus higher returns. Thus, a positive coefficient is expected from the

regression.

I will apply the same methodology as I have used for the inflation rate. I will first look at the

seasonal pattern in indicators and then analyse whether they can explain the seasonality of bond returns.

The results of these analyses are based on JP Morgan total return indices for the period January 1986 –

December 2013 extracted from Bloomberg. The data set is extended for another eleven years in the past,

considering Thompson Financial Datastream source for January 1980 – December 1985 and a broker for

January 1975 – December 1979. While the key results of the paper are based on public data (Datastream),

here I use an extended sample as it is interesting to investigate the ‘70s given accentuated volatility during

that period50.

49 Details about this can be found in Table B.2 in Appendix B.50 http://epp.eurostat.ec.europa.eu/statistics_explained/index.php/Industrial_production_(volume)_index_overview

54

Table 4.21: Seasonality in Economic Indicators

H1 H2 Effect GDP Change in Unemployment Rate

Industrial Production

Quarterly frequency    Australia 13.10 -4.27 6.64Canada 6.62 -7.26Germany 6.34 -1.04 3.69Japan 12.56 -6.19 -1.68United Kingdom 21.71 -0.44 9.95United States 0.38 -4.30 0.98Developed (6) 14.56 -5.40 7.62

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression: Yt = α + βXt + εt

where Y are non-seasonally adjusted real GDP QoQ growth rates (left panel), the change in non-seasonally adjusted unemployment rates (middle panel) and industrial output QoQ growth (right panel) at quarterly frequency. The unemployment rates are constructed as the 3-month average of monthly rates. Details about the data and the sample period can be found in Table A.9, A.10 and A.11 in the Appendix A. X is the dummy variable to capture the H1 H2 effect which takes on the value of 1 for Q3 and Q4 and 0 otherwise. The Developed portfolio is based on equally-weighting the six countries provided data are available. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

A look at the seasonal tests performed on growth rates (displayed in Table 4.21) shows that GDP

QoQ rates are statistically significant higher in the second part of the year (with the exception of the US

GDP). This is in line with the pattern observed on bond returns, but not in line with economic theory

which suggests that high bond returns take place during poor economic conditions. This means that

instead of removing the seasonal pattern, the GDP variable would exacerbate the seasonality pattern.

An inspection of the stationarity of the unemployment data using an ADF test indicates that the

null hypothesis of the series containing a unit root cannot be rejected. Thus, the analysis will be based on

the change in unemployment rate. The unemployment rate is available at a monthly frequency, so I use

the three-month change consistent with the regressions on the inflation rate.

The results of the seasonal tests displayed in Table 4.21 show that with the exception of Germany

and United Kingdom, the changes in unemployment rates display significant H1 H2 effect. The changes

in unemployment rates are lower in the second half of the year, a pattern which is complementary with

the one observed in bond returns.

The seasonal pattern of industrial production is not consistent and statistically significant across

countries (different sign in case of Japan and not statistically significant for United Kingdom).

The results centralized in Table 4.22 show that the coefficients when regressing bond returns on

each of the macroeconomic indicators (GDP growth, unemployment rate change and industrial

production51) are often not significant and carry mixed signs. Thus, the hypothesis that the seasonal

pattern in bond returns is explained by the cycle of the considered economic indicators is rejected. This

51 The results are in line with those when using the shorter sample of Datastream indices.

55

suggests that the macroeconomic indicators are less important for government bonds than inflation. This

is explained by the fact that changes in the inflation rate may trigger direct actions from central banks in

order to stabilise inflation around the assumed target, while economic dynamics are envisaged, but the

chance of a direct reaction from the central bank is lower as most central banks have a unique mandate to

support a stable level of consumer prices.

Table 4.22: The relationship between Bond Returns and Economic Indicators

Nominal Bond Excess Returns

GDP Change in Unemployment Rate Industrial Production

β t-stat β t-stat β t-statNational indicator          Australia 0.064 1.47 -0.005 -1.10 0.073 1.39Canada -0.088 -0.75 -0.002 -0.33Germany -0.009 -0.14 0.002 0.67 -0.042 -0.93Japan 0.030 0.67 0.004 0.52 0.010 0.34United Kingdom -0.081 -0.64 0.016 2.47 0.113 2.23United States -1.817 -4.59 -0.002 -0.41 -0.616 -2.31Developed (6) 0.055 0.91 0.001 0.20 -0.129 -1.12

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β in the regression Yt = α + βXt + εt

where Y are Nominal Bond Excess Returns based on an extended sample of JP Morgan total returns indices for the period 1975-2013, while X is the non-seasonally adjusted GDP growth rate (left panel), the change in non-seasonally adjusted unemployment rate (middle panel) or the non-seasonally adjusted industrial production (right panel) for each country. The analysis is carried out at a quarterly frequency. The results for Canada are missing in case of the industrial production as a similar volume index was not found. Developed stands for an equally-weighted portfolio made up of all six countries provided that the data are available. Details about the sample of macroeconomic indicators can be found in Table A.9, A.10 and A.11 from the Appendix A. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

4.5.2 The Optimism cycle

The second tested hypothesis is related to a cycle of optimism which influences investment

decisions (Doeswijk (2008) and Shigeki, Takashi, Katsuhiko (2011)). Doeswijk (2008) uses specific

measures to capture the sentiment of equity analysis and investors: earnings growth estimates for the

MSCI World index and monthly average initial returns of public offerings. Shigeki, Takashi, Katsuhiko

(2011) do not empirically test the “Dekansho-bushi effect”. In these conditions, the current research

brings a novel approach as it is based on sentiment proxies coming from two different methodologies:

surveys and market related data.

I use consumer confidence data and a measure of implied volatility for stock options, the VIX

index52, in order to gauge investor sentiment53. The use of the former measure has the advantage of being

52 The analysis is based on national measures as US GDP does not display a seasonal pattern, while the change in unemployment rate does not have explanatory power for US bond market.53 Chicago Board options Exchange Volatility Index (VIX)

56

based on survey data which is not related to market dynamics. The VIX index measures the implied

volatility of S&P 500 index options and it is seen as a global proxy for risk appetite54. Low(er) consumer

sentiment values and high(er) volatility are perceived as a low(er) appetite for risk which favours

government bond returns. Accordingly, the sign of the consumer sentiment measure should be negative.

The link between the VIX and bond returns should be positive. Anderson, Krylova and Vahamaa (2008)

show that when implied volatility (as measured by the VIX) is high, then stock and Treasury bond returns

tend to become more negatively correlated. Connolly, Stivers and Sun (2005) find similar findings and

argue that if periods with high stock uncertainty – and thus high volatility – tend to be characterised by

more frequent investor revisions of stock risk and the relative attractiveness of stocks versus bonds, then

higher stock market uncertainty is likely to fuel a negative stock-bond correlation. In this way, increased

stock market volatility decreases stock returns (as shown by Antonakakis, Chatziantoniou and Filis

(2013)) and increases bond returns (Jubinski and Lipton (2012)) – a response that is consistent with a

flight-to-quality.

Based on the evidence from the literature, I expect that accentuated volatility (high VIX levels

and a rising VIX) is positive for bond returns.

As both indicators of consumer confidence and volatility are not stationary, I use the change in

their levels. This does not change the expected relationship between bond returns and sentiment

indicators.

As expected, consumer optimism tends to increase in the first half of the year, favouring high

returns of risky assets and low bond returns. The pattern observed on the changes in VIX (shown in Table

4.23) is also consistent with theory. Accordingly, stock volatility is more accentuated in the second part of

the year which increases the interest of investors in fixed income instruments55 and translates into higher

bond returns.

Table 4.23: Seasonality in Sentiment Indicators

H1 H2 Effect Change in Consumer Confidence Change in VIX

Quarterly frequency    Australia -0.15Canada -1.52Germany -1.92Japan -2.91United Kingdom -2.60United States -2.49 2.64Developed (6)    

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression:

54 Employing the Baker and Wurgler (2007) sentiment measure or the lag indicator did not give conclusive results. 55 Given the popularity of VIX indicator as “the world's premier barometer of investor sentiment” (http://www.cboe.com/micro/VIX/vixintro.aspx), I rely on this indicator and not use the national equivalents. The VIX is also acomponent of four sentiment indexes surveyed by Illing and Aaron (2012)

57

Yt = α + βXt + εt

where Y are differences in Consumer Confidence indicators (left panel) and Chicago Board Options Exchange Volatility Index (VIX - right panel) at quarterly frequency. These sentiment indicators are constructed as the 3-month average of monthly rates. Details about the data and the sample period can be found in Table A.12 and A.13 in the Appendix A. X is the dummy variable to capture the H1 H2 effect which takes on the value of 1 for Q3 and Q4 and 0 otherwise. There are no results for the Developed portfolio (average of all six countries) given inconsistent measures for consumer confidence. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

A further investigation of the link between bond returns and sentiment indicators show that these

sentiment indicators carry the expected sign (negative in case of consumer sentiment and positive for

VIX). Table 4.24 also shows that the change in VIX is statistically significant at 1% in all countries with

the exception of Japan. The results of the change in consumer sentiment are less strong. The coefficient

carries a negative sign, as expected, which is consistent across countries, but it is statistically significant

at 5% level only in case of United States and Developed portfolio.

Table 4.24: The relationship between Bond Returns and Sentiment Indicators

Nominal Bond Excess Returns

Change in Consumer Confidence Change in VIX

β t-stat β t-statUS indicator      Australia -0.0002 -0.56 0.0020 4.52Canada -0.0018 -1.83 0.0014 2.80Germany -0.0008 -1.62 0.0017 4.16Japan -0.0010 -1.89 0.0007 1.58United Kingdom -0.0005 -0.88 0.0020 3.50United States -0.0022 -2.65 0.0024 6.16Developed (6) -0.0011 -2.03 0.0017 4.60

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β in the regression Yt = α + βXt + εt

where Y are Nominal Bond Excess Returns based on an extended sample of JP Morgan total returns indices for the period 1975-2013, while X is the change in US consumer confidence (left panel) and change in VIX (right panel). The analysis is conducted at quarterly frequency. Developed stands for an equally-weighted portfolio made up of all six countries, provided data are available. Details about the sample can be found in Table A.12 and A.13 from the Appendix A. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The seasonality in consumer confidence changes and VIX changes are not able to fully explain

the seasonality in bond returns, as depicted in Table 4.25 below. Thus, the explanation that the seasonality

in sentiment indicators is the driver of H1 H2 pattern is ruled out. Nevertheless, the bond returns

corrected for the seasonal pattern by each sentiment indicators loose the seasonal pattern for some

countries and show in general lower t-stats.

58

Table 4.25: Seasonality in Corrected Bond Returns

Bond Returns corrected by

Change in Consumer Confidence Change in VIX

H1 H2 H1 H2 Quarterly frequency  Australia 1.63 1.03Canada 1.56 1.99Germany 2.35 1.33Japan 1.33 0.60United Kingdom 1.63 2.54United States 0.96 0.97Developed (6) 1.94 1.77

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression Ye t = α + βXt + εt

where Ye are residual bond excess returns from the regression of quarterly JP Morgan bond excess returns on the change in US consumer confidence (left panel) and on change in VIX (right panel) (Table 4.24). These sentiment indicators are constructed as the 3-month average of monthly rates. Details about the data and the sample period can be found in Table A.12 and A.13 in the Appendix A. X is a dummy that captures H1 H2 effect, taking on the value of 1 for Q3 and Q4 and 0 otherwise. Developed stands for an equally-weighted portfolio made up of all six countries, provided data are available. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

4.5.3 Macroeconomic data surprises

Inspired by the discovery of Gerlach (2007) that higher stock returns during autumn are explained

by relatively large price movements on announcement days of economic data, I use the Citi Economic

Surprise Index (CESI) extracted from Bloomberg to capture economic data surprises. This CESI index is

defined as weighted historical standard deviations of data surprises where the weights of economic

indicators are derived from the impact that these data surprises have on foreign exchange markets. Given

that relative surprises might be important, I also consider the difference in CESI.

The analysis of an index of economic data surprises is supported by the findings of Balduzzi,

Elton and Green (2001). They show that the prices of US T-bills and Treasuries are influenced by the

surprise in eight economic announcements: e.g. Nonfarm Payrolls (which capture the employment state of

the economy), Consumer Confidence and Durable Goods Orders (which shows the prospects of the

industrial component of durable goods).

One of the disadvantages of this analysis is the short sample period as CESI is available only

starting with the beginning of 2003. The intuition is that a higher CESI is consistent with positive

surprises in macroeconomic data and thus with higher interest rates and lower bond returns.

An investigation of the seasonal pattern in the CESI level and the change in CESI (Table 4.26)

shows the rejection of the hypothesis as none of the measures displays an H1 H2 seasonal.

59

Table 4.26: Seasonality in CESI

Country CESI Change in CESIH1 H2 H1 H2

Quarterly frequency  Australia 0.10 -0.18Canada -0.85 -1.01Germany -0.33 0.33Japan -0.90 0.34United Kingdom 1.28 0.44United States 0.80 0.39Developed (6) -0.12 0.12

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression: Yt = α + βXt + εt

where Y are CESI values (left panel) and changes in CESI (right panel) for each country at quarterly frequency. In case of Germany, I use the Euro Area CESI. X is the dummy variable to capture the H1 H2 effect which takes on the value of 1 for Q3 and Q4 and 0 otherwise. The sample of the analysis is 2003-2013. Developed stands for an equally-weighted portfolio made up of all six countries. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

Following the same approach used in Section 4.2 for the inflation analysis, I have investigated

three hypotheses which have been used in the literature to explain the seasonality of stock returns: an

annual cycle of economic activity, a cycle of optimism and macroeconomic data surprises. While the

indicators used to capture economic dynamics were also employed in the literature, the choice of

indicators to capture investor sentiment proved challenging. A novel aspect of this research is the formal

testing of sentiment proxies (based on two different methodologies: surveys and market related data). To

my knowledge, CESI was also not employed in the literature before. The used indicators (centralised in

Table 4.26) did not manage to explain the seasonality in bond returns. However, I cannot conclude that

the hypotheses are not valid as I have not exhausted all available indicators.

Table 4.26: Other hypotheses for the seasonal patterns

Hypotheses How Valid

Explanations for January Effect No January effect No

Seasonal Affective Disorder (SAD) Regression with SAD factor Partly

Cycle of economic activities and risk conditions

Inflation Rate Yes

GDP No

Unemployment rate No

60

Industrial Production No

Optimism CycleConsumer Sentiment Surveys Partly

Implied Volatility Measures (VIX, MOVE) Partly

Seasonality of Macroeconomic Data Surprises Citi Economic Surprise Index (CESI) No

5. Robustness checks

5.1 Persistence over time

After analysing a long sample of UK stock returns which spans for 317 year, Zhang and Jacobsen

(2013) conclude that seasonal anomalies can be highly dependent on the sample considered. They also

fail to find a persistent January effect through time. In this context, I check the validity of the results

based on a long US sample which covers 62 years of data from 1952 to 2013. I extend the sample used in

Section 4.4 in both time horizon (from 56 years to 62 years) and the range of maturities (from four

maturities to six). I thus consider the whole universe of US bonds – with maturities between one year and

thirty years.

The results of the seasonality tests from Table 5.1 confirm the results based on the short sample

from 1980-2013 (Table 4.2). Accordingly, January and Inverted Halloween effects are not relevant for US

bond market. The SAD factor is also more pronounced at a monthly frequency than the H1 H2 effect. The

SAD factor becomes weaker at a quarterly frequency, the value of the t-statistic decreases to 1.90 from

2.72 at a monthly frequency.

The statistical significance of the H1 H2 effect is robust. The pattern is statistically significant at

10% level compared to 5% previously56 (for both a monthly and a quarterly frequency).

Table 5.1: Seasonality tests for U.S. CRSP Universe Bond Returns

Nominal Bond Excess returns January H1 H2 SAD Inverted

HalloweenMonthly frequency        U.S. CRSP Universe -0.38 1.86 2.72 1.58Quarterly frequencyU.S. CRSP Universe   1.82 1.90  

Notes: This table shows t-values for the β in the regression:

56 A similar analysis on Merrill Lynch Option Volatility Estimate MOVE Index has lead to conclusion that MOVE does not display an H1 H2 or SAD effect.

61

Yt = α + βXt + εt

where Y are US nominal bond excess returns (calculated based on CRSP indices). CRSP Universe stands for an equally-weighted portfolio of US Treasuries with maturities of 1Y, 2Y, 5Y, 7Y, 10Y, 20Y and 30Y. X depends on the seasonal pattern tested. In case of January effect, X is a dummy that takes the value of 1 for January and 0 otherwise. In case of H1 H2, X is a dummy that takes on the value of 0 for January to June and 1 otherwise. For SAD, X is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. Inverted Halloween effect is the opposite of the one discovered by Bouman and Jacobsen (2002) on the stock market. To capture the Inverted Halloween effect, X is a dummy which takes on the value of 1 for May to October and 0 otherwise. At the quarterly frequency we take the average of the 3 monthly values in each quarter. January and Inverted Halloween cannot be translated to quarters and hence at that frequency there are no results. At monthly frequency, the t-values are based on Newey-West standard errors, while at quarterly frequency, as the residuals do not exhibit autocorrelation, the t-values are based on White's heteroskedasticity corrected standard errors. Using Newey-West standard errors for quarterly frequency leads to similar results (t-stats of 1.88 for H1 H2 and 2.08 for SAD). The sample ranges from 1952 to 2013. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

When verifying the link between US bond returns and the inflation rate for the period 1952-2013,

the relationship remains strong (as depicted in Table 5.2). The inflation coefficient is statistically

significant at a 1% level and the magnitude is in line with the previous values (Table 4.12).

Table 5.2: The relationship between US bond returns and inflation

Nominal Bond Excess Returns

U.S. Inflation Rate R2

β t-statMonthly frequency    U.S. CRSP Universe -0.756 -3.02 0.026Quarterly frequencyU.S. CRSP Universe -1.123 -4.38 0.095

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β in the regression: Yt = α + βXt + εt

where Y are US nominal bond excess returns at the monthly frequency and at quarterly frequency respectively. U.S. CRSP Universe stands for an equally-weighted portfolio of US Treasuries with maturities of 1Y, 2Y, 5Y, 7Y, 10Y, 20Y and 30Y. X is the U.S. non-seasonally adjusted inflation rate. Sample period for the analysis is 1952-2013. The numbers in Bold show statistical significance at a 5% significance level, while those in Blue at a 10% significance level.

After accounting for the influence of inflation rate, the residuals display a SAD effect only at

monthly frequency, while at a quarterly frequency there is no significant seasonal variation in the

residuals (as shown in Table 5.3). These results are in line with the previous results discussed in Section

4.2.2.

Table 5.3: Seasonality in Inflation-corrected Bond Returns

62

Inflation corrected - Bond Returns H1 H2 SAD

Monthly frequencyU.S. CRSP Universe 1.08 2.21Quarterly frequencyU.S. CRSP Universe 0.70 1.00

Note: This table shows t-values based on Newey-West standard errors for the β in the regression Ye t = α + βXt + εt

where Yet are residual bond excess returns from the regression of (monthly or quarterly) US CRSP bond excess returns on US inflation (Table 5.2). U.S. CRSP Universe stands for an equally-weighted portfolio of US Treasuries with maturities of 1Y, 2Y, 5Y, 7Y, 10Y, 20Y and 30Y. X depends on the seasonal pattern tested. For H1 H2 X is a dummy that takes on the value of 1 for July to December and 0 otherwise. For SAD it is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. At the quarterly frequency I take the average of the 3 monthly values in each quarter. Sample period for the analysis is 1952-2013. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

Based on the above results, I conclude that the H1 H2 effect is persistent over time and that the

seasonality in the inflation rate can explain this pattern. Only at a monthly frequency the SAD factor

compensates for the noise in inflation rate, but its importance decreases at a quarterly frequency.

5.2 Stock returns patterns

5.2.1 Seasonal patterns of stock excess returns

Nominal government bonds are not the only asset with a seasonal pattern of its returns. For stock

markets several seasonal patterns have been studied and are documented in the literature. The Halloween

indicator, the January effect, the SAD factor and even the new bond seasonal (H1 H2) are discussed in the

literature. I investigate the existence of these seasonal patterns for the same six countries and try to

explain these as well with the seasonal pattern in inflation.

I run regression (1) with the dummies defined based on the stock literature findings and on the

opposite H1 H2 pattern discovered on bond market. Accordingly, I check if stock returns are higher in the

first month of the year (January effect), if they record a better performance during January-June compared

to July-December (H1 H2), if they are higher during January-March compared to October-December

(SAD) or if stock exhibit relatively higher returns in November-April than during May-October

(Halloween Indicator). The results of the tests shown in Table 5.4 indicate that the January effect is not

visible on stock market. H1 H2 effect is statistically significant at 10% level in Japan. This confirms the

“Dekansho-bushi” effect of Shigeki, Takashi, Katsuhiko (2011). The SAD factor is statistically

significant across countries (with the exception of Australia) and the sign of the coefficient is negative as

63

expected. When people recover from SAD (which is consistent with a decrease in the SAD

onset/recovery variable), their appetite for risk increases and translates into higher stock returns starting

with January.

Table 5.4: Seasonality in Stock Returns

Stock Excess Returns January H1 H2 SAD Halloween

Monthly frequency        Australia 0.59 0.07 -1.26 1.57Canada 0.97 0.79 -2.01 2.72Germany -0.24 0.66 -2.00 2.80Japan 0.77 1.65 -2.68 3.67United Kingdom 1.17 0.65 -2.41 3.35United States 0.96 0.83 -1.73 2.87Developed (6) 1.00 1.05 -2.53 3.75

Notes: This table shows t-values based on Newey-West standard errors for the β in the regression: Yt = α + βXt + εt

where Y are stock excess returns (calculated based on MSCI total return indices and the same cash rates used to calculate bond excess returns) at the monthly frequency. X depends on the seasonal pattern tested. In case of January effect, X is a dummy that takes the value of 1 for January and 0 otherwise. In case of H1 H2, X is a dummy that takes on the value of 1 for January to June and 0 otherwise. For SAD, X is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. Halloween effect is in line with the effect discovered by Bouman and Jacobsen (2002). To capture the Halloween effect, X is a dummy which takes on the value of 1 for November to April and 0 otherwise. Developed stands for an equally-weighted portfolio of six countries. The sample ranges from 1975-2013. More details on the data and calculations are described in respectively Chapter 2 and Chapter 3. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The Halloween Indicator of Bouman and Jacobsen (2002) is also pronounced in the analysed

countries. As in case of SAD, this is relevant only for countries from Northern Hemisphere. This confirms

the findings of Bouman and Jacobsen (2002) that the Halloween effect manifests itself in the same way in

the Northern and Southern Hemisphere (evidence from Argentina, Australia, Brazil, Chile, New Zealand

and South Africa).

The fact that the seasonal pattern from the stock market (Halloween effect) is different from the

one from the bond market (H1 H2 pattern) hints that the drivers of the seasonal variation also differ. I will

investigate if the inflation hypothesis holds in the next section.

5.2.2 The relationship between stock returns and inflation

Following the same approach as in case of bond returns, I check if the seasonality in the inflation

rate drives the seasonal variation in stock returns. The hypothesis is that the relationship between the

inflation rate and stock returns is mixed. On a long-term stocks could offer protection against inflation (if

the companies manage to increase the prices of the offered goods or services) which implies a positive

64

relationship (when inflation rises stock prices rise too), but on short-term unexpected inflation can

negatively affect stock returns.

The regression results in Table 5.5 show that there is no clear link between the inflation rate and

stock returns as the coefficient is not statistically significant across countries.

Table 5.5: The relationship between Stock Returns and Inflation

Stock Excess Returns

National Inflation Rate R2

β t-statPanel A: Monthly frequency    AustraliaCanada 0.073 0.12 0.000Germany 0.343 0.40 0.000Japan 0.311 0.82 0.001United Kingdom 1.154 1.36 0.018United States -0.936 -1.08 0.006Developed (5) 0.321 0.41 0.001Panel B: Quarterly frequency    Australia 0.725 1.11 0.008Canada 0.001 0.00 0.000Germany 0.304 0.20 0.000Japan 0.963 0.99 0.006United Kingdom 1.349 2.52 0.040United States -0.569 -0.84 0.005Developed (6) 0.982 1.26 0.010

Notes: This table shows coefficients and t-values for the β in the regression Yt = α + βXt + εt

where Y are stock excess returns at the monthly frequency (Panel A) and at quarterly frequency (Panel B) and X is the country’s own inflation (national inflation). At monthly frequency, t-values are based on Newey-West standard errors, while at quarterly frequency, the errors are not corrected as the residuals do not exhibit autocorrelation and heteroskedasticity. Australia has only quarterly inflation and hence at the monthly frequency there are no national inflation results. Developed stands for an equally-weighted portfolio of five countries at monthly frequency (as inflation data for Australia are not available at a monthly frequency) and of six countries at quarterly frequency. Sample period for the analysis is 1975-2013. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

The investigation of the seasonal pattern of stock returns has shown that the stock market exhibits

a different pattern. Stock returns are higher during November-April compared to May-October period.

The seasonality in inflation cannot explain this pattern. The different nature of the two assets suggests that

the drivers of seasonality could also be different. Another hypothesis is that the two-month lag between

the patterns could be a delayed reaction of the bond market. In line with Doeswijk (2008)’s explanation,

the optimism of investors in the last quarter of the year could be visible first in the stock market and

afterwards in the bond market. Also, Ilmanen (1995) formally shows that stock market returns can predict

government bond market returns. This result has recently been confirmed by Duyvesteyn and Martens

65

(2014). A theory or explanation behind the difference between the seasonal patterns of stocks and bonds

is an interesting subject for further research.

5.3 Economic Significance

In this section I investigate the performance of two strategies: one exploiting the H1 H2 effect

and a simple buy and hold strategy that always has a long position in bonds. I also test the statistical

significance of the returns.

5.3.1 Trading Strategies

As hinted in Section 3.3.4, I define a Long-Short strategy based on the observed H1 H2 effect.

The strategy assumes that the investor buys the government bonds from the index in July and holds this

exposure until the start of January when he enters into a Short position on the constituents of the index. I

compare this strategy with a Long position in the bond market (buy and hold) portfolio for January-

December.

Table 5.6 contains the average annual excess returns, standard deviation and information ratio for

each country. As the Information Ratio measures the excess return per unit of risk, a higher Information

Ratio is preferred. The Long Short strategy outperforms the benchmark by displaying a higher

Information Ratio for Australia, Germany and United Kingdom. In case of Canada and Japan, the

underperformance of the Long-Short strategy can be explained by the large positive returns recorded in

May and March respectively. The difference between the Information ratios is the largest for Japan – the

IR for the Long strategy is twice the IR recorded for the Long-Short strategy. Interestingly, Japan is also

the country for which the H1 H2 effect is least pronounced as the H1 H2 dummy coefficient records the

lowest t-statistic of 1.69 (as shown by Table 4.2). The results also show that the standard deviation differs

marginally across countries.

However, the results do not favour the Long-Short strategy which exploits the seasonal pattern.

For the other three analysed countries (Canada, Japan, United States) and at aggregate level (Developed

portfolio), the benchmark strategy records better results.

Table 5.6: Performance of different strategies

Country Annualised IndicatorsBenchmark Long-ShortL Jan-Dec L Jul-Dec S Jan-Jun

Australia Excess Return 1.8% 1.9%

66

Standard Deviation 4.8% 4.8%

Information Ratio 0.38 0.41

CanadaExcess Return 2.9% 2.6%

Standard Deviation 4.9% 4.9%

Information Ratio 0.59 0.53

GermanyExcess Return 1.8% 1.9%

Standard Deviation 3.9% 3.9%

Information Ratio 0.46 0.47

JapanExcess Return 2.3% 1.1%

Standard Deviation 3.7% 3.7%

Information Ratio 0.62 0.31

United KingdomExcess Return 1.9% 2.7%

Standard Deviation 6.4% 6.4%

Information Ratio 0.30 0.42

United StatesExcess Return 2.1% 2.0%

Standard Deviation 5.5% 5.5%

Information Ratio 0.39 0.37

Developed (6)Excess Return 2.1% 1.9%

Standard Deviation 4.0% 4.0%

Information Ratio 0.52 0.48Notes: This table shows performance indicators of different strategies: the Benchmark strategy is consistent with a long exposure on the bond index for the whole year, while Long-Short strategy considers that the investor has a Long exposure on the index during July-December and a Short exposure for January-June. All the performance indicators are annualised. The numbers highlighted in Bold represent the best performer for each indicator: the maximum in case of Excess Return and Information Ratio and minimum in case of Standard Deviation. The calculations are based on Datastream data for the sample from Table 3.1 with the exception of Australia where the sample starts in January 1988 in order to have full-year data.

5.3.2 Statistical Significance

Given mixed results of the performance of the two strategies, I run regression (7) to investigate if

the Long-Short strategy generates abnormal results compared to the benchmark strategy and to see if

there are any diversification benefits. The results are centralised in Table 5.7 below.

Table 5.7: Strategy statistical significance

Nominal Bond Excess Returns

α β

value* t-stat value t-statMonthly frequency  Australia 1.9% 1.87 0.01 0.07Canada 2.4% 2.23 -0.04 -0.28Germany 2.2% 3.01 -0.16 -1.28Japan 1.0% 1.36 0.05 0.32United Kingdom 2.5% 2.15 0.12 1.04United States 2.0% 1.98 0.01 0.03

67

Developed (6) 2.0% 2.60 -0.03 -0.21Notes: This table shows estimation results: estimated value of the coefficient (value) and t-values (t-stat) based on Newey-West standard errors for α and β in the regression:

Yt = α + βXt + εt

where Y are bond excess returns of the Long-Short Strategy (Long exposure during July-December and Short exposure for January-June) at the monthly frequency. X represents the bond excess returns for the benchmark (buy and hold strategy during the whole year). Developed stands for an equally-weighted portfolio made up of all six countries provided that the data are available. The analysis is based on Datastream data for the sample from Table 3.1 with the exception of Australia where the sample starts in January 1988 in order to have full-year data. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level. *For an easier interpretation, the values reported for α coefficient are annualised (multiplied by 12).

With the exception of Japan, the Long-Short strategy generates significantly higher returns

compared to the simple buy and hold strategy as the null hypothesis that α equals 0 is ruled out at 10%

level. The magnitude of Jensen’s alpha ranges from 1.9% in Australia to 2.5% for United Kingdom in

annual terms. In what concerns β, the estimated coefficient is not statistically significant, thus the null

hypothesis that β=0 cannot be rejected. This means that the strategies are not correlated with the bond

market portfolio and that there are diversification benefits. Therefore, a government bond market investor

can actively improve the return of his or her portfolio by actively applying the long-short strategy based

on the bond seasonal.

6. Conclusion

The current study focuses on the discovery and explanation of the annual seasonal patterns in six

government bond markets. It rejects the existence of a January effect in line with Schneeweis and

Woolridge (1979), Smirlock (1985), Chang and Pinegar (1986) and Chan and Wu (1993). An Inverted

Halloween effect which is the opposite pattern found by Bouman and Jacobsen (2002) on stock markets,

is also weak and inconsistent across countries. The research discovers a new pattern for government

bonds – H1 H2 effect which implies higher bond returns in the second half of the year (July-December)

compared with those recorded in the first half (January-June). This complements the “Dekansho-bushi”

effect documented by Shigeki, Takashi, Katsuhiko (2011) on the Japanese stock market.

The H1 H2 effect is economically significant and robust to outliers. Moreover, the effect is also

persistent over time and countries. As pointed out by Lakonishok and Smidt (1988) and Sullivan,

Timmermann and White (2001), it is important to analyse if the seasonal patterns are related to data-

mining problems by considering new and long data samples. Accordingly, the analysis verifies the

68

validity of the H1 H2 effect on a longer sample period (1952-2013) and across six low-correlated bond

markets.

This paper provides evidence for the existence of seasonality in the inflation rate: inflation

displays higher rates during January-June compared to July-December. The seasonality of the inflation

rate is driven by its volatile components (food prices, apparel prices, energy prices etc) and explains the

discovered pattern in government bond returns. The intuition behind this is that market players are

perhaps more focused on seasonally adjusted figures which capture the underlying trend of consumer

price dynamics from which the seasonal pattern has been removed.

It is important to consider the data on a quarterly basis to avoid noise on a monthly basis and the

misalignment between actual data releases and the moment when the market reacts on inflation data. US

inflation data also capture the seasonal pattern better than national inflation data, particularly for smaller

markets like Australia. This could be explained by the fact that U.S. economic data releases have a direct

and influential effect on other bond markets given the dominance of the US economy. Goldberg and

Leonard (2003), Ehrmann and Fratzscher (2005), Andersson, Overby and Sebestyen (2009) and

Andersen, Bollerslev, Diebold and Vega (2007) show that this is the case for Euro area bonds.

The hypothesis is reinforced by the fact that inflation-linked bonds do not exhibit seasonal

variation as non-seasonally adjusted inflation is directly incorporated in inflation-linked bond prices.

Three explanations from the equity literature have also been tested to explain the bond seasonal:

the hypothesis of an annual cycle of economic activity of Ogden (2003), the optimism cycle explanation

of Doeswijk (2008) and another one inspired from Gerlach (2007) on the link between the seasonality in

bond returns with macroeconomic data surprises. The optimism cycle hypothesis (based on two proxies:

consumer survey data and VIX) can partially explain the seasonal pattern for some countries, while the

other two are not valid in the tested form. However, a clear conclusion cannot be drawn as I have not

exhausted the indicators that can be used to test the hypotheses.

The analysis showed that the SAD factor introduced by KKL(2003) and “Dekansho-bushi” effect

of Shigeki, Takashi, Katsuhiko (2011) are limited to the markets where they were discovered. The SAD

variable has explanatory power for bond seasonality at a monthly frequency in the United States and

Canada, while at a quarterly frequency this factor is subsumed by the inflation rate. The existence of the

H1 H2 effect on the Japanese stock market is confirmed by the results of the conducted analysis, but the

effect is not consistent for other stock markets.

When investigating the seasonality in inflation-linked bonds, the limited sample in case of some

countries (93 observations for Germany) constitutes one drawback of the analysis. Also, the time-series of

SAD variable is not available to investigate the role of SAD for the seasonal variation in government

bond returns over time.

69

The empirical research shows the role of the U.S. inflation rate for the seasonal variation of bond

returns. There are several aspects which could receive more attention in further studies: a deeper

understanding of the inflation dynamics (differences between countries, noise, when does it affect the

bond markets and which components cause a seasonal pattern), the investigation of the relevance of

surprises in inflation data (the difference between the actual release and market consensus) and the

robustness of results for emerging markets, including large countries from the Southern Hemisphere like

Indonesia, South Africa and Brasil.

This study finds two different patterns for government bonds and stock returns: H1 H2 and the

Halloween Indicator respectively. It puts forward two hypotheses for the two-month lag between the

patterns without formally testing them: different drivers of the patterns or the delayed reaction of the bond

market. It would thus be interesting to further investigate why the patterns are different.

The analysis has also shown that the optimism cycle hypothesis of Doeswijk (2008) partly

explain the bond seasonal in some countries. The investigation of the potential added value of using this

explanation in addition to the inflation rate could be considered as a further step.

70

References

Aggarwal, R., & Rivoli, P. (1989). Seasonal and Day‐of‐the‐Week Effects in Four Emerging Stock Markets. Financial review, 24(4), 541-550.

Andersen, T. G., Bollerslev, T., Diebold, F. X., & Vega, C. (2007). Real-time price discovery in global stock, bond and foreign exchange markets. Journal of International Economics, 73(2), 251-277.

Andersson, M., Overby, L. J., & Sebestyén, S. (2009). Which news moves the euro area bond market?. German economic review, 10(1), 1-31.

Andersson, M., Krylova, E., & Vähämaa, S. (2008). Why does the correlation between stock and bond returns vary over time?. Applied Financial Economics, 18(2), 139-151.

Andrade, S. C., Chhaochharia, V., & Fuerst, M. E. (2013). “Sell in May and Go Away” Just Won’t Go Away. Financial Analysts Journal, 69(4), 94-105.

Ang, A. (2012). Real assets

Ang, A., & Piazzesi, M. (2003). A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables. Journal of Monetary economics, 50(4), 745-787.

Antonakakis, N., Chatziantoniou, I., & Filis, G. (2013). Dynamic co-movements of stock market returns, implied volatility and policy uncertainty. Economics Letters, 120(1), 87-92.

Athanassakos, G. (2008). Seasonal Patterns in Canadian Financial Markets and the Impact of Professional Portfolio Rebalancing: Evidence of Profitable Opportunities. Journal of Financial and Economic Practice, 9(1), 73-96.

Baker M. & Wurgler J., (2007). "Investor Sentiment in the Stock Market," Journal of Economic Perspectives, American Economic Association, vol. 21(2), pages 129-152, Spring

Balduzzi, P., Elton, E. J., & Green, T. C. (2001). Economic news and bond prices: Evidence from the US Treasury market. Journal of Financial and Quantitative Analysis, 36(04), 523-543.

Baur, D. G., & Lucey, B. M. (2010). Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. Financial Review, 45(2), 217-229.

Bellio, R., & Ventura, L. (2005, October). An Introduction to Robust Estimation with R Functions. In Proceedings of the 1st International Workshop on Robust Statistics and R. Treviso: Department of Statistics, Ca’Foscari University (Venezia).

Berges, A., McConnell, J., & Schlarbaum, G. G. (1984). The Turn‐of‐the‐Year in Canada. The Journal of Finance, 39(1), 185-192.

71

Bouman, S., & Jacobsen, B. (2002). The Halloween indicator," Sell in May and go away": Another puzzle. American Economic Review, 1618-1635.

Brandt, M. W., & Wang, K. Q. (2003). Time-varying risk aversion and unexpected inflation. Journal of Monetary Economics, 50(7), 1457-1498.

Brooks, C., 2002. Introductory Econometrics for Finance. Cambridge University Press

Brondolo, A., & Giani, G. (2005). Seasonality in Price Indices. Fixed Income Strategies Lehman Brothers.

Bryan, M. F., & Cecchetti, S. G. (1995). The seasonality of consumer prices (No. w5173). National bureau of economic research.

Campbell, J. Y. (1991). Measuring the persistence of expected returns (No. w3305). National Bureau of Economic Research.

Campbell, J.Y., Shiller R.J., & LM Viceira, L.M. (2009). Understanding Inflation-Indexed Bond Markets. In Brookings Paper on Economic Activity, April 2009, edited by D Romer and J Wolfers

Cao, M., & Wei, J. (2005). Stock market returns: A note on temperature anomaly. Journal of Banking & Finance, 29(6), 1559-1573.

Chan, K. C., & Wu, H. K. (1993). Bond market seasonality and business cycles. International Review of Economics & Finance, 2(4), 377-386.

Chang, E. C., & Pinegar, J. M. (1986). Return seasonality and tax-loss selling in the market for long-term government and corporate bonds. Journal of Financial Economics, 17(2), 391-415.

Chu, Q., Pittman, D., & Yu, L. (2011). When Do TIPS Prices Adjust to Inflation Information?. Financial Analysts Journal, 67(2), 59-73.

Ciccone, S. J. (2011). Investor optimism, false hopes and the January effect. Journal of Behavioral Finance, 12(3), 158-168.

Clayton, R., Delozier, J., & Ehrhardt, M. C. (1989). A note on January returns in the US government bond market: The term effect. Journal of Financial Services Research, 2(4), 307-318.

Cook, T., & Korn, S. (1991). The reaction of interest rates to the employment report: The role of policy anticipations, Economic Review, Federal Reserve bank of Richmond, 77/5, 3-12.

Connolly, R., Stivers, C., & Sun, L. (2005). Stock market uncertainty and the stock-bond return relation. Journal of Financial and Quantitative Analysis, 40(01), 161-194.

Dowling, M., & Lucey, B. M. (2008). Robust global mood influences in equity pricing. Journal of Multinational Financial Management, 18(2), 145-164.

Darrat, A. F., Li, B., Liu, B., & Su, J. J. (2011). A Fresh Look at Seasonal Anomalies: An International Perspective. International Journal of Business & Economics, 10(2).

Dichev, I. D., & Janes, T. D. (2003). Lunar cycle effects in stock returns. The Journal of Private Equity, 6(4), 8-29.

Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American statistical association, 74(366a), 427-431.

72

Doeswijk, R. Q. (2008). The optimism cycle: sell in May. De Economist, 156(2), 175-200.

Doran, J. S., Jiang, D., & Peterson, D. R. (2012). Gambling preference and the new year effect of assets with lottery features. Review of Finance, 16(3), 685-731.

Dudley, W. C., Roush, J., & Ezer, M. S. (2009). The case for TIPS: an examination of the costs and benefits. Federal Reserve Bank of New York Economic Policy Review, 15(1), 1-17.

Duyvesteyn, J., & Martens, M. (2014). Emerging Government Bond Market Timing. The Journal of Fixed Income, 23(3), 36-49.

Ehrmann, M., & Fratzscher, M. (2005). Equal Size, Equal Role? Interest Rate Interdependence Between the Euro Area and the United States*. The Economic Journal, 115(506), 928-948.

Ejsing, J., García, J. A., & Werner, T. (2007). The term structure of euro area break-even inflation rates: The impact of seasonality.

Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, 987-1007.

Fabozzi, F. J., Martellini, L., & Priaulet, P. (Eds.). (2006). Advanced bond portfolio management: best practices in modeling and strategies (Vol. 143). John Wiley & Sons.

Fleming, M. J., & Remolona, E. M. (1999). What moves bond prices?. The Journal of Portfolio Management, 25(4), 28-38.

Fridson, M. S. (2000). Semiannual seasonality in high-yield bond returns. The Journal of Portfolio Management, 26(4), 102-111.

Frühwirth, M., & Sögner, L. (2014). Weather & SAD Related Mood Effects on the Financial Market.

Gerlach, J. R. (2007). Macroeconomic news and stock market calendar and weather anomalies. Journal of Financial Research, 30(2), 283-300.

Global Inflation-linked Products: A User's Guide. Barclays Capital, 2012.

Goldberg, L., & Leonard, D. (2003). What moves sovereign bond markets? The effects of economic news on US and German yields. Current issues in economics and finance, 9(9), 1-7.

Grinold, R. C., & Kahn, R. N. (2000). The efficiency gains of long-short investing. Financial Analysts Journal, 40-53.

Gulko, L. (2002). Decoupling. The Journal of Portfolio Management, 28(3), 59-66.

Gultekin, M. N., & Gultekin, N. B. (1983). Stock market seasonality: International evidence. Journal of Financial Economics, 12(4), 469-481.

Gürkaynak, R. S., Sack, B., & Wright, J. H. (2010). The TIPS yield curve and inflation compensation. American Economic Journal: Macroeconomics, 70-92.

Haggard, K. S., & Witte, H. D. (2010). The Halloween effect: trick or treat?. International Review of Financial Analysis, 19(5), 379-387.

73

Hampel, F. R. (1974). The influence curve and its role in robust estimation. Journal of the American Statistical Association, 69(346), 383-393.

Hirshleifer, D., & Shumway, T. (2003). Good day sunshine: Stock returns and the weather. The Journal of Finance, 58(3), 1009-1032.

Ho, Y. K. (1990). Stock Return Seasonalities in Asia Pacific Markets*. Journal of International Financial Management & Accounting, 2(1), 47-77.

Hoaglin, D. C., Mosteller, F., & Tukey, J. W. (Eds.). (1983). Understanding robust and exploratory data analysis (Vol. 3). New York: Wiley.

Hong, H., & Yu, J. (2009). Gone fishin’: Seasonality in trading activity and asset prices. Journal of Financial Markets, 12(4), 672-702.

Huber, P. J. (1973). Robust regression: asymptotics, conjectures and Monte Carlo. The Annals of Statistics, 799-821.

Huberman, G., & Schwert, G. W. (1985). Information aggregation, inflation, and the pricing of indexed bonds. The Journal of Political Economy, 92-114.

Illing M., & Aaron, M. (2012). A brief Survey of Risk-Appetite Indexes. Financial System Review. Bank of Canada

Ilmanen, A. (1995). Time‐Varying Expected Returns in International Bond Markets. The Journal of Finance, 50(2), 481-506.

Ilmanen, A. (2011). Expected returns: an investor's guide to harvesting market rewards. John Wiley & Sons.

Jacobsen, B., & Marquering, W. (2008). Is it the weather?. Journal of Banking & Finance, 32(4), 526-540.

Jones, C. M., Lamont, O., & Lumsdaine, R. L. (1998). Macroeconomic news and bond market volatility. Journal of Financial Economics, 47(3), 315-337.

Jubinski, D., & Lipton, A. F. (2012). Equity volatility, bond yields, and yield spreads. Journal of Futures Markets, 32(5), 480-503.

Kamstra, M. J., Kramer, L. A., & Levi, M. D. (2003a). Winter blues: A SAD stock market cycle. American Economic Review, 324-343.

Kamstra, M. J., Kramer, L. A., & Levi, M. D. (2003b). SAD investors: Implications of seasonal variations in risk aversion. In Atlanta Federal Reserve Bank, University of British Colombia, refereed conference proceedings.

Kamstra, M. J., Kramer, L. A., & Levi, M. D. (2014). Seasonal Variation in Treasury Returns, Critical Finance Review, forthcoming

Kato, K., & Schallheim, J. S. (1985). Seasonal and size anomalies in the Japanese stock market. Journal of Financial and Quantitative Analysis, 20(02), 243-260.

Keim, D. B. (1983). Size-related anomalies and stock return seasonality: Further empirical evidence. Journal of Financial Economics, 12(1), 13-32.

74

Kelly, P. J., & Meschke, F. (2010). Sentiment and stock returns: The SAD anomaly revisited. Journal of Banking & Finance, 34(6), 1308-1326.

Kim, S. J., McKenzie, M. D., & Faff, R. W. (2004). Macroeconomic news announcements and the role of expectations: evidence for US bond, stock and foreign exchange markets. Journal of Multinational Financial Management, 14(3), 217-232.

Krueger, A. B., & Fortson, K. N. (2003). Do markets respond more to more reliable labor market data? A test of market rationality. Journal of the European Economic Association, 1(4), 931-957.

Kwiatkowski, D., Phillips, P. C., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?. Journal of econometrics, 54(1), 159-178.

Lakonishok, J., & Smidt, S. (1988). Are seasonal anomalies real? A ninety-year perspective. Review of Financial Studies, 1(4), 403-425.

Lakonishok, J., Shleifer, A., Thaler, R., & Vishny, R. (1991). Window dressing by pension fund managers (No. w3617). National Bureau of Economic Research.

Lean, H. H. (2011). The Halloween puzzle in selected Asian stock markets. International Journal of Economics and Management, 5, 216-225.

Maberly, E. D., & Pierce, R. M. (2004). Stock market efficiency withstands another challenge: Solving the “sell in May/buy after Halloween” puzzle. Econ Journal Watch, 1(1), 29-46.

Matsui, K. (2011). Accounting year-end dispersion and seasonality in the Japanese corporate bond market. Applied Economics, 43(26), 3733-3744.

Mirani, C., Pond M., & Skeoch, H. (2012). “Seasonality: Estimation and adjustment”. Global Inflation Linked Products: A user’s Guide, 57-79

Newey, W. K., & West, K. D. (1994). Automatic lag selection in covariance matrix estimation. The Review of Economic Studies, 61(4), 631-653.

Ogden, J. P. (2003). The calendar structure of risk and expected returns on stocks and bonds. Journal of Financial Economics, 70(1), 29-67.

Reinganum, M. R. (1983). The anomalous stock market behavior of small firms in January: Empirical tests for tax-loss selling effects. Journal of Financial Economics, 12(1), 89-104.

Ritter, J. R. (1988). The buying and selling behavior of individual investors at the turn of the year. The Journal of Finance, 43(3), 701-717.

Rozeff, M. S., & Kinney Jr, W. R. (1976). Capital market seasonality: The case of stock returns. Journal of Financial Economics, 3(4), 379-402.

Saunders Jr, E. M. (1993). Stock prices and Wall Street weather. American Economic Review, 83(5), 1337-45.

Schneeweis, T., & Woolridge, J. R. (1979). Capital market seasonality: The case of bond returns. Journal of Financial and Quantitative Analysis, 14(05), 939-958.

75

Sharpe, W. F. (1966). Mutual fund performance. Journal of business, 119-138.

Shigeki, S., Takashi, Y., & Katsuhiko, O. (2011). The Calendar Structure of the Japanese Stock Market:“Sell in May Effect” versus “Dekansho-bushi Effect”. Kobe University, Discussion Paper Series 2011-8.

Smirlock, M. (1985). Seasonality and bond market returns*. The Journal of Portfolio Management, 11(3), 42-44.

Smith, K. L. (2002). Government bond market seasonality, diversification, and cointegration: international evidence. Journal of Financial Research, 25(2), 203-221.

Sooben, K., & James, A. (2012). “Euro Area”. Global Inflation Linked Products: A user’s Guide, 163 – 182

Sullivan, R., Timmermann, A., & White, H. (2001). Dangers of data mining: The case of calendar effects in stock returns. Journal of Econometrics, 105(1), 249-286.

Swinkels, L. (2012). Emerging Markets Inflation-Linked Bonds. Financial Analysts Journal, Vol 68, Issue 5, pp. 38-56.

Swinkels, L., & van Vliet, P. (2012). An anatomy of calendar effects. Journal of Asset Management, 13(4), 271-286.

Van den Bergh, W. M., & Wessels, R. E. (1985). Stock market seasonality and taxes: an examination of the tax-loss selling hypothesis. Journal of Business Finance & Accounting, 12(4), 515-530.

Yuan, K., Zheng, L., & Zhu, Q. (2006). Are investors moonstruck? Lunar phases and stock returns. Journal of Empirical Finance, 13(1), 1-23.

Yang, J., Zhou, Y., & Wang, Z. (2009). The stock–bond correlation and macroeconomic conditions: one and a half centuries of evidence. Journal of Banking & Finance, 33(4), 670-680.

Wachtel, S. B. (1942). Certain observations on seasonal movements in stock prices. The Journal of Business, 15.

Worthington, A. C. (2010). The decline of calendar seasonality in the Australian stock exchange, 1958–2005. Annals of Finance, 6(3), 421-433.

Abu Zarour, B. (2007). The Halloween effect anomaly: evidence from some Arab countries equity markets.

Zhang, C. Y., & Jacobsen, B. (2013). Are monthly seasonals real? A three century perspective. Review of Finance, 17(5), 1743-1785.

76

Appendix A

Figure A.1: SAD Onset/Recovery Variable

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0tan27aa566027

0tan27aa566027

0tan28aa566028

0tan28aa566028

0tan28aa566028

SAD Onset/Recovery Variable

Notes: The graph depicts the dynamics of the SAD onset/recovery variable constructed by Kamstra, Kramer and Levi (2014) based on the clinical incidence of SAD symptoms among patients from Northern America.

Table A.1: Inflation Rate Data Description

Inflation Rate Bloomberg/Datastream code Description Modification

Australia AUCPI Index AU CPI ALL Groups Goods Component (Q3 2011-Q2 2012=100), NSA % QoQ

Canada CACPI Index CA STCA CPI (2002=100), NSA % MoM

Germany GRCPI Index, GRCP2000 Index

West Germany CPI for 1975-1991 and DE CPI (2010=100) after 1991, NSA % MoM

Japan JPCONPRCF JP CPI, National Measure (2010=100), NSA % MoMUnited Kingdom UKRPI Index/UKCHAW.. UK RPI All Intems (Jan 1987=100), NSA % MoM

United States CPURNSA Index US CPI Urban Consumers (1982-1984=100), NSA % MoM

Notes: The table reports the price indices used to capture inflation dynamics. The sample starts in January 1980 and ends in December 2013. In case of Germany, a price index for West Germany was used until the beginning of 1991. All indices are non-seasonally adjusted (NSA).

77

Table A.2: Normality and Stationarity Tests

Asset Country Country Jarque-Bera Test Augmented Dickey-Fuller Test KPSS Test

Statistic P-value Statistic P-value Statistic P-valueInflation Australia 18.5 0.00 -3.8 0.00 0.8 0.01

Canada 237.6 0.00 -11.3 0.00 0.3 0.01Germany 123.8 0.00 -15.0 0.00 0.1 0.10

Japan 187.6 0.00 -16.8 0.00 0.1 0.06United Kingdom 1210.1 0.00 -11.6 0.00 0.2 0.02

United States 372.0 0.00 -8.5 0.00 0.1 0.06Developed 150.1 0.00 -8.1 0.00 0.2 0.02

Nominal Australia 17.2 0.00 -17.1 0.00 0.2 0.10Canada 27.3 0.00 -18.2 0.00 0.0 0.10

Germany 35.0 0.00 -16.8 0.00 0.1 0.10Japan 196.2 0.00 -16.2 0.00 0.1 0.10

United Kingdom 12.3 0.01 -18.7 0.00 0.1 0.10United States 84.9 0.00 -17.3 0.00 0.1 0.10

CRSP Universe 232.5 0.00 -24.3 0.00 0.4 0.06Developed 12.9 0.01 -16.7 0.00 0.1 0.10

Infl-link Australia 7.6 0.03 -15.7 0.00 0.2 0.10Canada 130.6 0.00 -14.6 0.00 0.1 0.10

Germany 65.0 0.00 -10.3 0.00 0.2 0.10Japan 1279.8 0.00 -9.3 0.00 0.1 0.10

United Kingdom 98.5 0.00 -19.8 0.00 0.8 0.01United States 160.2 0.00 -13.7 0.00 0.1 0.10

Developed 153.1 0.00 -19.6 0.00 0.9 0.01Comparator Australia 17.7 0.00 -13.4 0.00 0.1 0.10

Canada 8.8 0.02 -14.4 0.00 0.1 0.10Germany 1.5 0.40 -8.3 0.00 0.1 0.10

Japan 23.5 0.00 -10.1 0.00 0.1 0.10United Kingdom 17.4 0.00 -18.2 0.00 0.0 0.10

United States 9.2 0.02 -13.3 0.00 0.1 0.10Developed 37.0 0.00 -18.0 0.00 0.0 0.10

Equities Australia 2201.9 0.00 -20.7 0.00 0.1 0.10Canada 154.1 0.00 -20.1 0.00 0.0 0.10

Germany 122.7 0.00 -20.0 0.00 0.0 0.10Japan 36.2 0.00 -19.4 0.00 0.1 0.10

United Kingdom 6609.3 0.00 -22.0 0.00 0.4 0.08United States 90.1 0.00 -20.4 0.00 0.1 0.10

  Developed 576.8 0.00 -19.0 0.00 0.1 0.10Notes: The table reports the test statistic and P-value for Jarque-Bera Test (H0: the series is Normal), Augmented Dickey-Fuller Test (H0: the series contains a unit root) and KPSS Test (H0: the series is stationary). KPSS test is conducted without including a trend term in case of returns as they are mean-reverting and with a trend term in case of inflation rate. The number of lags is the square root of the sample size as suggested by Kwiatkowski et al. (1992). The numbers in bold indicate the rejection of the null hypothesis at 5% significance level.

78

Table A.3: Autocorrelation and Heteroscedasticity Tests

Asset Class CountryLjung-Box Q-test

ARCH TestReturns Squared returns

Statistic P-value Statistic P-value Statistic P-valueInflation Australia 176.6 0.00 120.4 0.00 44.8 0.00

Canada 138.2 0.00 78.2 0.00 43.8 0.00Germany 16.7 0.01 12.2 0.03 11.1 0.05

Japan 53.6 0.00 17.4 0.00 17.5 0.00United Kingdom 59.6 0.00 26.4 0.00 13.0 0.02

United States 143.1 0.00 198.1 0.00 86.0 0.00Developed 225.0 0.00 296.9 0.00 114.4 0.00

Nominal Australia 5.3 0.38 12.8 0.03 15.4 0.01Canada 3.4 0.64 32.8 0.00 21.7 0.00

Germany 15.0 0.01 33.5 0.00 9.6 0.09Japan 22.6 0.00 48.3 0.00 34.2 0.00

United Kingdom 3.3 0.65 32.1 0.00 22.6 0.00United States 14.5 0.01 47.5 0.00 29.2 0.00

CRSP Universe 13.0 0.02 105.0 0.00 65.2 0.00Developed 12.0 0.04 29.4 0.00 24.0 0.00

Infl-link Australia 3.9 0.56 3.9 0.57 2.6 0.76Canada 4.9 0.43 33.1 0.00 30.0 0.00

Germany 12.0 0.03 12.8 0.03 15.3 0.01Japan 9.4 0.09 24.8 0.00 20.1 0.00

United Kingdom 3.3 0.65 36.6 0.00 32.9 0.00United States 6.6 0.25 22.0 0.00 18.6 0.00

Developed 3.5 0.62 20.5 0.00 17.5 0.00Comparator Australia 2.3 0.81 4.2 0.53 5.1 0.40

Canada 8.6 0.13 2.2 0.82 1.9 0.86Germany 4.5 0.48 3.1 0.69 2.8 0.73

Japan 5.0 0.42 7.7 0.17 6.4 0.27United Kingdom 5.0 0.42 45.8 0.00 30.1 0.00

United States 13.3 0.02 9.7 0.08 10.0 0.08Developed 7.6 0.18 63.2 0.00 37.6 0.00

Equities Australia 11.3 0.05 6.6 0.25 6.8 0.24Canada 6.5 0.26 16.9 0.00 16.5 0.01

Germany 5.7 0.34 32.6 0.00 21.9 0.00Japan 7.2 0.20 20.4 0.00 16.1 0.01

United Kingdom 11.6 0.04 19.7 0.00 15.0 0.01United States 5.6 0.35 12.8 0.03 10.6 0.06

  Developed 10.8 0.05 3.7 0.60 2.9 0.71Notes: The table reports the test statistic and P-value for Ljung-Box Q-test (H0: there is no autocorrelation up to lag i), Engle’s ARCH test (H0: the series exhibits no conditional heteroscedasticity (ARCH effects)). The test statistic and p-values are computed for 5 lags. The numbers in bold indicate the rejection of the null hypothesis at 5% significance level.

79

Table A.4: Robust Regressions of Monthly Nominal Bond Returns

Nominal Bond Excess

ReturnsDummy

Newey-West Huber Tukey Hampel

β t-stat β t-stat β t-stat β t-stat

Australia H1 H2 0.0030 1.73 0.0030 2.00 0.0032 2.10 0.0031 2.02SAD 0.0036 0.84 0.0045 1.25 0.0053 1.44 0.0046 1.28

Canada H1 H2 0.0038 2.28 0.0031 2.00 0.0028 1.79 0.0031 1.96SAD 0.0104 2.58 0.0083 2.22 0.0073 1.95 0.0083 2.20

Germany H1 H2 0.0031 2.67 0.0025 2.30 0.0022 2.04 0.0025 2.28SAD 0.0048 1.75 0.0032 1.24 0.0025 0.97 0.0031 1.22

Japan H1 H2 0.0019 1.69 0.0020 2.20 0.0020 2.30 0.0021 2.31SAD 0.0012 0.42 0.0020 0.92 0.0025 1.17 0.0022 1.05

United Kingdom

H1 H2 0.0045 2.37 0.0048 2.72 0.0050 2.82 0.0049 2.75SAD 0.0072 1.45 0.0087 2.06 0.0092 2.17 0.0089 2.11

United States H1 H2 0.0034 1.99 0.0034 2.37 0.0034 2.34 0.0035 2.38SAD 0.0105 3.10 0.0108 3.14 0.0107 3.12 0.0109 3.16

Developed (6) H1 H2 0.0032 2.58 0.0033 2.98 0.0032 2.89 0.0033 2.99SAD 0.0061 2.16 0.0061 2.33 0.0061 2.31 0.0062 2.33

Notes: This table shows the estimated values and t-values based on different techniques: OLS, Newey-West standard errors, M-estimation based on the proposal of Huber, Tukey and Hampel respectively, for the β in the regression:

Yt = α + βXt + εt

where Y are bond excess returns (calculated based on Datastream bond indices) at the monthly frequency. X depends on the seasonal pattern tested. In case of H1 H2, X is a dummy that takes on the value of 1 for July to December and 0 otherwise. For SAD, X is set equal to the 12 monthly values from the Kamstra, Kramer, and Levi (2014) paper. Developed portfolio is equally-weighted on six countries. Huber M-estimation is performed with k=1.5, Tukey’s estimation with k=4.685. Hampel estimation is performed with a=1.5, b=3.6 and c=8. The analysis is based on the sample of nominal bond excess returns as depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

Table A.5: Correlation between National and U.S. Inflation Rate

Correlation Coefficient between National Inflation Rate and U.S. Inflation

Monthly frequency  AustraliaCanada 0.58Germany 0.29Japan 0.30United Kingdom 0.39United States 1.00Developed (5) 0.76

Notes: This table shows correlation coefficient between time-series of National inflation rate and U.S. inflation rate. Australia has only quarterly inflation and hence the correlation coefficient is missing.

80

Table A.6: Time series regressions of Bond Returns on U.S. inflation rate and H1 H2 dummy

Nominal Bond Excess Returns

U.S. Inflation H1 H2R2

β1 t-stat β2 t-statMonthly frequency          Australia -0.419 -1.37 0.002 1.08 0.018Canada -0.705 -2.93 0.002 1.19 0.033Germany -0.890 -4.61 0.001 0.90 0.086Japan -0.447 -2.10 0.001 0.69 0.024United Kingdom -0.977 -3.09 0.002 1.03 0.045United States -0.922 -3.30 0.001 0.69 0.049Developed (6) -0.835 -4.27 0.001 0.97 0.077

Notes: This table shows coefficients and t-values based on Newey-West standard errors for the β1 and β2 in the regression Yt = α + β1Xt + β2Zt + εt

where Y are nominal bond excess returns (based on Datastream indices) at the monthly frequency, while X is the inflation rate recorded in United States and Z is a dummy which takes value of 1 during July-December and 0 during January-June. Developed portfolio is equally-weighted on six countries. The analysis is based on the sample of nominal bond excess returns as depicted in Table 3.1. The numbers in Bold show statistical significance at 5% significance level, while those in Blue at 10% significance level.

Table A.7: Correlation between Contemporaneous and Lead Inflation rate

Correlation Coefficient between Contemporaneous and Lead Inflation rate

Monthly frequency  AustraliaCanada 0.31Germany 0.06Japan 0.16United Kingdom 0.31United States 0.55Developed (5) 0.53

Notes: This table shows correlation coefficient between time-series of contemporaneous and lead inflation measures. Australia has only quarterly inflation and hence at the monthly frequency there are no national inflation results.

Table A.8: Correlation between U.S. inflation rate and SAD

Correlation Coefficient between U.S. inflation rate and SAD

Monthly -0.12Quarterly -0.21

Notes: This table shows correlation coefficient between U.S. inflation rate and SAD variable of Kramer, Kamstra and Levi (2014) over 1952 – 2013.

81

Figure A.2: U.S. Inflation and Bond yield dynamics

01/31/1952 07/31/1958 01/29/1965 07/30/1971 01/31/1978 07/31/1984 01/31/1991 07/31/1997 01/30/2004-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

10Y yield US inflation rate (annualised)

Notes: The graph depicts the dynamics of the yield of 10Y U.S. Treasuries and U.S. non-seasonally adjusted inflation rate for the period 1952 – 2007.

Table A.9: GDP Non-Seasonally Adjusted Data Description

Real GDP non-seasonally adjusted (NSA)

Bloomberg/Datastream code Description Source Sample

Australia AUNAGDCV Index AU GDP NSA by Expenditure, Chain Linked Prices (mn AUD), NSA Bloomberg 1975-2013

Canada CNGDP...CCA GDP Income Approach, Total at market prices, Constant Prices (mn CAD 2007 prices), NSA

Datastream 1981-2013

Germany WGGDP.95C, GDPB00E Index

West Germany GDP, Expenditure Approach, Constant Prices (mn EUR 1995 prices) until 1991, then DE GDP Chain Linked Pan German level Index (2005=100), NSA

Datastream, Bloomberg 1975-2013

Japan JPGDP...C JP Expenditure Approach, GDP, Constant Prices (bn JPY 2005 chnd prices), NSA Datastream 1980-2013

United Kingdom UK GDP at market prices, Volume index (2005=100), NSA Eurostat 1975-2013

United States USXGDPR.D US real GDP, Constant Prices (bn USD 2005 prices) NSA Datastream 1980-2013

Notes: The table reports the source and details of NSA GDP data used to capture the dynamics of economic activity. In case of Germany, GDP for West Germany was used until the beginning of 1991. All indices are non-seasonally adjusted (NSA).

82

Table A.10: Industrial Production Non-Seasonally Adjusted Data Description

Industrial production non-seasonally adjusted (NSA)

Bloomberg/Datastream code Description Source Sample

Australia AUIPTOL Index AU Industrial Production Index Total NSA (Volume Q3 2009-Q2 2010=100) Bloomberg 1975 - 2013

Germany BDI66..IG/since 1991 Eurostat DE Industrial Production (Volume Index) Datastream 1975 - 2014

Japan JNIPNSA Index JP Industrial Production Index (Volume), NSA Bloomberg 1978 - 2013

United Kingdom UK Volume Index of Production, NSA Eurostat 1986 - 2013

United States USIPTOT.G US Industrial Production (Total Index Volume) Datastream 1975 - 2013

Notes: The table reports the source and details of NSA Industrial Production data used to capture the dynamics of economic activity. In case of Germany, GDP for West Germany was used until the beginning of 1991. All indices are non-seasonally adjusted (NSA).

Table A.11: Unemployment Rate Non-Seasonally Adjusted Data Description

Unemployment Rate non-seasonally adjusted (NSA)

Bloomberg/Datastream code Description Source Sample

Australia AUUN%TOTRAU Unemployment Rate Labour Force Survey Estimate (as percentage of labour force), NSA

Datastream 02/1978-12/2013

Canada CAUNCUB5 Index/CNUN%TOTR

CA Unemployment Rate (15 years and over), household labour force survey NSA Datastream 01/1976-12/2013

Germany GCUETOTL Index/BDUN%TOTR

DE Registered Unemployed (15-65 years) as a percentage of the civilian labour, NSA Datastream 01/1975-12/2013

Japan JPUN%TOTR JP Unemployment Rate (as percentage of labour force), NSA Datastream 01/1975-12/2013

United Kingdom UKESUNEMR UK Unemployment rate Labour Force Survey, NSA Datastream 01/1983-12/2013

United States USURTOTN Index/USUN%TOTR

US Unemployment Rate Total in Labor Force NSA Datastream 01/1975-12/2013

Notes: The table reports the source and details of NSA Unemployment Rate data used to capture the dynamics of labour market.

Table A.12: Consumer Confidence Data Description

83

Consumer Confidence Bloomberg code Description Sample

Australia WMCCCONN Index Westpac-Melbourne Institute Consumer Confidence Consumer Sentiment, (NSA, % Balance/Diffusion Index) 01/1975-12/2013

Canada OECAA037 Index OECD Canada Comp Leading Indic Cons Conf Stock (SA, Index) 01/1975-12/2013

Germany EUCCDE Index European Commission Consumer Confidence Indicator (NSA, % Balance/Diffusion Index) 01/1985 - 12/2013

Japan JCOMHCF Index Japan Consumer Confidence Households Confidence (NSA, % Balance/Diffusion Index) 06/1982 - 12/2013

United Kingdom EUCCUK Index European Commission Consumer Confidence Indicator UK (NSA, % Balance/Diffusion Index) 01/1985 - 12/2013

United States CONSSENT Index University of Michigan Index of Consumer Sentiment 01/1978 - 12/2013Notes: The table reports the details of Consumer Sentiment data used as a proxy for investor sentiment. The data is extracted from Bloomberg.

Table A.13: Implied Volatility Measures Description

Implied Volatility Bloomberg code Description Sample

United States VIX Index Captures market expectations of near-term volatility conveyed by S&P 500 stock index option prices. 01/1990 - 12/2013

United States MOVE IndexAverage implied volatility across a wide range of outstanding options on the two-year, five-year, 10-year, and 30-year U.S. Treasury securities.

04/1988 - 12/2013

Notes: The table reports the details of implied volatility indices used as a proxy for risk appetite. The data is extracted from Bloomberg.

84

Appendix B

Table B.1: Explanations for stocks seasonal pattern

No. Empirical studies

Data period used

Country/Index Reason given for seasonality

Description Agents Seasonal pattern for stocks

Seasonal pattern for bonds

1. Wachtel (1942) 1972 - 1942 US/DJIA Tax-loss selling Investors sell losing stocks before the end of the tax year to avoid paying capital gains taxes and reinvest at the turn of the year. Abnormal returns in January represent only a recovery from depressed levels.

Individuals and corporations

Lower returns in December and higher returns in January

Not applicable

2. Lakonishok, Shleifer, Thaler and Vishny (1991)

1985 - 1989 US/769 equity pension funds; CRSP data on NYSE, American and NASDAQ stocks

“Window-dressing”

To impress sponsors, fund managers sell off losing stocks prior to the end-of-the-year reporting date and then repurchase them in January57.

Institutional investors

Better performance of small stocks at the beginning of the year.

The selling of risky bonds by bond funds put downward pressure on price in December and upside pressure in in January. Low risk bonds face the opposite effects.

3. Rozeff and Kinney (1976)

1904 - 1974 US, AU/CRSP NYSE

Accounting information

Without formally testing the advanced hypothesis, they suggest that the beginning of the tax and accounting year for most companies and also the period of accounting earnings announcements could be related to the seasonality pattern.

Non-specific January58 records higher mean of returns in US and July in case of Australia.

Not applicable

4. Ogden (1990) 1969 - 1986 US/CRSP data Liquidity hypothesis

Cash inflows in December-January (profits of privately owned businesses, bonuses for

Individuals and corporations

Higher returns than average in January

Abundant liquidity could also imply demand for bonds and thus higher

57 As shown in Table 4.2.58 They find evidence of buying losers and selling both extreme winners and losers in the last quarter.

85

individuals etc.) explain higher demand for stocks in January. The liquidity is also inversely related to the stringency of the monetary policy

returns at the beginning of the year.

5. Ritter (1988) 1971 – 1985 US/ buy/sell ratio of individual investors at Merrill Lynch

Parking the proceeds hypothesis

Some of the proceeds from the sale of losers in December are “parked” until January. The focus is on the behaviour of individual from net sellers to net buyers.

Individuals Small stocks outperform large stocks in January and other months

The price of bonds faces upside pressure in December and downward pressure in January as investors might invest the proceeds in fixed income instruments.

6. Ciccone (2011) 1983 - 2007 US/CRSP Optimistic expectations

Renewed optimism related to the beginning of the calendar year makes investors to buy stocks in January. “False hope syndrome” which assumes hopes about a correction of their failure next time explains the persistence of the effect after being discovered.

Individuals Superior performance of stocks in January compared to the other months. High dispersion firms outperform low dispersion firms inJanuary.

Optimistic investors are likely to ignore bonds at the beginning of the year, resulting in lower bond returns in January.

7. Wachtel (1942),Zhang and Jacobsen (2013)

1972 – 1942, 1693 - 2009

US, UK Christmas optimism

Positive feeling around Christmas and outlook for the new year could be visible in the equity market at the beginning of January.

Individuals Higher returns than average in January

Relatively lower bond returns at the beginning of the year.

8. Sullivan, Timmermann and White (2001)

1897 - 1996 US/DJIA Data-mining problems

The patterns were found by chance, especially as data with outliers are subjected to data-mining biases59.

Researchers When controlling for outliers, when testing out-of-sample or using new data, the calendar effects disappear.

When controlling for outliers, when testing out-of-sample or using new data, the calendar effects disappear.

59 They also note relatively high returns in July, November and December and low returns in February and June for US. In case of Australia, July and January tend to outperform the other months.86

9. Bouman and Jacobsen (2002)

1970 - 199860 19 countries/MSCI Reinvestment Indices

Holiday effect A lower number of investors during summer or an increase in risk aversion suggest a contemporary decrease in price and higher expected returns. Higher returns during winter could be the result of overspending during the holiday (higher liquidity premium).

Individuals Higher returns for stocks during November-April compared to May-October.

May-October bond returns will exceed those from November-April.

10. Doeswijk (2008) 1970 - 2003 US/MSCI World Index

Optimism cycle The outlook for earnings and economy changes during the calendar year. The Investors are overly optimistic in the last quarter and the first part of the new year and as we advance in the year, their optimism softens.

Individuals The relative performance of stocks is better in November-April than during May – October.

Bonds record higher returns during May – October than in the period November – April.

11. Hong and Yu (2009)

Different samples (the oldest starting with 1962 and the latest 1999) up to 2003, 2005

51 countries “gone fishin’ ” hypothesis

Investors are “gone fishin’ ” and the trading volume declines during summer.

Non-specific (individual and institutional investors)

Lower average stock returns during summer (July–September for Northern Hemisphere countries and January–March for Southern Hemisphere countries).

Bond returns are relatively lower during summer.

12. Ogden (2003) 1947 - 2000 US/NYSE An annual cycle of economic activities and risk conditions

There are complementary seasonalities in economic activity and stock returns; Expectations of poor macroeconomic conditions for October through March translate into lower returns during April – September and make the investors require a premium for holding stocks during

Non-specific October – March equity returns surpass those recorded in April – September.

Bonds record higher returns during April – September than in the period October – March.

60 Two practices generate data mining: several hypotheses are tested using the same data (individual) or a wide number of papers are based on the same databases and the results are not relevant when looked in isolation (collective).

87

October – March (equity market has forecasting power for dynamics of economic activity).

13. Gerlach (2007) 1980 - 2003 US/S&P 500, CRSP EW

Days of macroeconomic announcements are characterised by unusual high returns.

Higher returns during fall are explained by relatively large price movements on announcement days of economic data.

Non-specific (individual and institutional investors)

Returns during fall (October – December) are on average higher than the mean return for the rest of the year.

Fall months display lower than average bond returns .

14a. Kamstra, Kramer and Levi (2003a)

Different sample periods – Jan 1928 – Dec 2001

9 countries (4 US indices)61

Seasonal Affective Disorder (SAD)

A depression related to the decreasing daylight during autumn which influences the mood translates into risk aversion during fall and as the day becomes longer, the risk appetite of the investors recovers.

Individuals Below average returns in the fall and relatively higher returns in the winter62,63.

Higher bond returns during fall and below average bond returns during winter

14b. Kamstra, Kramer and Levi (2003b)

1941 – 200164

1962 – 20011992 - 2002

US CRSP 1-10Y TR indexesUS CRSP decile returnsUS CRSP mutual funds database

The magnitude of SAD effect increases with the risk of stocks.Equity mutual funds flows are below average in the fall and rose at the beginning of the year.

Investors’ risk aversion drives up returns in fall and decrease returns in the winter65 as the day lengthens. Bond mutual funds flows outperform in fall compared to winter.

15. Shigeki, Takashi, Katsuhiko (2011)

1950 - 2008 JP/Nikkei 225, TOPIX

“Dekansho-bushi effect”

The “fresh start” feeling related to the new year (“Oshogatsu”), fiscal year and spring lift the optimism of the investors until June.

Individuals The first half of the year (January-June) outperforms the latter (July-December).

Superior returns for bonds in the second half of the year compared to the first one.

61 With the exception of ZA which starts in 197362 Similar results using CRSP data (equal-weighted indices and total return indices)63 For Northern Hemisphere, fall is defined as September 21 to December 20 and winter from December 21 to March 20. For Southern Hemisphere, fall is considered from March 21 to June 20 and winter from June 21 to September 20. 64 The trough is recorded in September and the peak is recorded in January.65 Different start of the sample: Jan-May

88

Table B.2: Explanations for seasonality of fixed income instruments

No. Empirical studies

Data period used

Country/Index Reason given for seasonality

Description Agents Seasonal pattern for bonds

1. Clayton, Delozier and Ehrhardt (1989)

1966 - 1985

US/CRSP Parking the proceeds hypothesis

When investors sell their stocks in December, they put their proceeds into bonds.

Individuals The price of bonds faces upside pressure in December and downward pressure in January. Impact visible for long-term bonds as it is a less liquid market.

2. Athanassakos (2006)

1957 - 2003

CA Agency problems, “window-dressing”, portfolio rebalancing

The annual portfolio disclosure cycle and the one of performance evaluation of portfolio managers put upside pressure on risk assets price at the beginning of the year and on safe assets towards the end of the year respectively.

Institutional investors

Complementary bond-stock seasonal patterns: the returns of bonds are higher in the May-October period than the November-April period, while the opposite holds for stocks.

3. Matsui (2011) 1995 - 2005

JP/secondary market data

Tax-loss selling, “window-dressing”

Risky Japanese corporate bonds face upside pressure starting with April as the accounting year starts (“window-dressing”), while the end of tax year in December puts downward pressure on these assets (tax-loss selling).

Individuals (Tax-loss selling), institutionals (“window-dressing”)

The end of the accounting year in December or March explains a wider spread of Japanese corporate bonds above the Nikkei government bond index from September to December compared to April - August period.

4. Kamstra, Kramer and Levi (2014)

1952 - 2007

US/CRSP TR indices

Seasonal Affective Disorder (SAD)

The increased risk aversion during fall leads to higher bond returns and once the day becomes longer, the returns of bonds are likely to be below average.

Individuals Bond returns from October-December outperform those from January-March.

89