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A Critical Analysis of the Impact of Macroeconomic Conditions on the Relationship between Stock and Bond Returns: An Empirical Study Module: Finance Research Methods Group Members: Tian Liu (1402592) Seki Park (1402997) Josselin Williams (1403248) Albert Wilson (1204785) Date: June 5, 2015

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Page 1: Analysis of the Relationship Between Stocks and Bonds

A Critical Analysis of the Impact of Macroeconomic Conditions on the

Relationship between Stock and Bond Returns: An Empirical Study

Module: Finance Research Methods

Group Members: Tian Liu (1402592)

Seki Park (1402997)

Josselin Williams (1403248)

Albert Wilson (1204785)

Date: June 5, 2015

Page 2: Analysis of the Relationship Between Stocks and Bonds

Abstract

This study investigates the relationship between stock and bond returns with evidence from the

UK market. As this relationship is influenced by macroeconomic factors, this study also included

the influence of GDP growth, expected inflation, changes in the money supply, and changes in

sovereign bond yields. The paper finds that there is a positive correlation between bond and

stock returns. Furthermore, GDP has a positive impact on stock returns, but not on bond returns.

Also, changes in the money supply does not influence stock and bond returns. In addition,

expected inflation negatively influences bond returns but do not influence stock returns. Finally,

changes in sovereign bond yields have an influence on stock returns but not on bond returns. Our

results are similar to previous studies.

1.0 Introduction

Understanding the intrinsic relationship amongst financial assets is critical when implementing

effective investment strategies. One particular relationship that has been a focal point for finance

literature for years is the relationship between the returns of stocks and bonds. The general

consensus is that there is an inverse relationship between the returns of stocks and bonds which

is subject to the influence of macroeconomic factors such as economic growth, expected

inflation, and the money supply. Implicit in this notion is the tendency of investors to adjust their

asset allocations, relative to stocks and bonds, based on macroeconomic and microeconomic

conditions. Given the dynamic nature of macroeconomic factors, the relationship between stocks

and bonds remains ambiguous.

This paper critically analyses the impact of macroeconomic conditions on the relationship

between stocks and bonds. The remainder of this paper is divided into four sections. Section two

reviews of the existing literature regarding the relationship between stocks and bonds. Section

three explains the data and section four presents the methodology used in this study. In section

five, the findings are presented. Section six offers a brief conclusion and a discussion.

Page 3: Analysis of the Relationship Between Stocks and Bonds

2.0 Literature Review

The intrinsic relationship between stock and bond returns was first examined by Benjamin

Graham in The Intelligent Investor, published in the 1950’s, who concluded that stock and bond

returns are negatively correlated (Barksby, 1989). However, Graham’s analysis lacked empirical

support (Barksby, 1989). Markowitz (1952), in his theory on Portfolio Selection, confirmed that

assets returns are fundamentally correlated. This discovery induced a new field of enquiry into

the causal relationship between stock and bond returns.

In analysing the variability of stock prices, Shiller (1982) concluded that there is no

significant correlation between stock and bond prices. However, his analysis was limited due to

insufficient data. As such, Shiller’s conclusion (1982) was challenged by Summers (1983) who

analysed the relationship between the interest rate and the stock market during 1973 - 1980.

Summers (1983) suggested that there is a negative correlation between stock and bond prices

subject to interest rates. In other words, lower interest rates induce an increase in bond prices and

an associated decline in stock prices.

According to Barksby (1989), the relationship between stocks and bonds is determined

by macroeconomic conditions such as productivity growth and market risk, which ultimately

influence the profits of firms and the real interest rate. As such, Barksby concurs that bonds and

stocks are negatively correlated. This concept was further augmented by Gulko (2002) who

concluded that financial distress also affects the relationship between stock and bond returns. Li

(2002) examined the effects of inflation and the real interest rate on the relationship between

bond and stock returns and concluded that uncertainty regarding long-term expected inflation

causes significant negative correlation between bond and stock returns. Andersson et al (2008)

concluded that the relationship between bond and stock returns varies over time, subject to

uncertainty. This gave credence to the notion of a dynamic relationship between stock and bond

returns, which explains why understanding this particular asset relationship remains elusive.

This discussion accentuates the significance of macroeconomic factors on the relationship

between stock and bond returns.

Page 4: Analysis of the Relationship Between Stocks and Bonds

3.0 Data

3.1 Variable Selection

Based the above discussion, the three primary variables observed in this study are GDP, expected

inflation, and the money supply (M4). Needless to say, this set of variables are not

comprehensive as there are other macroeconomic factors such as unemployment and savings and

investment which may also influence the relationship between the returns of stocks and bonds.

The intuition for using GDP to test the relationship between the returns of stocks and

bonds is that both stock and bond returns are influenced by GDP. Relative to stocks, changes in

stock prices reflect the expectations of investors regarding future corporate earnings, which is

influenced by economic growth. Bond yields are also affected by GDP as economic growth

influences the demand for corporate bonds and the equilibrium between the supply and demand

for corporate bonds determines the bond yield. In this study, UK GPD growth is used which was

calculated by dividing the difference of the total GDP at market prices for each quarter, as shown

in the following formula:

GDP Growth = ln(GDPt/ GDPt-1).

Furthermore, expected inflation (CPI) is also used to examine the relationship between

the returns of stocks and bonds. There is a general consensus that expected inflation impacts the

returns of stocks either positively or negatively. Relative to bonds, rising inflation depletes the

real rate of interest, which is significant because nominal interest rates are usually fixed upon

issue. In this study, expected inflation is assumed to be equal to the prevailing rate for simplicity.

Since the data collected was non-stationary, the difference in the inflation for each month was

calculated using the following formula:

Inflation Rate = ln(Inflation Ratet/ Inflation Ratet-1).

In addition, the money supply is also presumed to influence the relationship between

stocks and bonds. In a general equilibrium analysis, an increase in the money supply should

increase consumption and consequentially increase savings and investment. However, financial

intermediation can impede an increase in the money supply as banks may simply increase their

reserves following injections of money by central banks (Joyce, et al., 2012). As such, the

Page 5: Analysis of the Relationship Between Stocks and Bonds

optimum indicator for the money supply is M4 which the most comprehensive measure of the

money supply and includes the following: notes and coins, short and long-term deposits, bonds

and similar instruments, claims from repos, and estimated holdings of sterling bank bills

(Hussain and Gilhooly, 2010). Similar to inflation, since the data collected was non-stationary,

the difference in M4 for each month was calculated using the following formula:

M4 = ln(M4t / M4t-1).

To account for the preferences of investors relative to the yield curve, this study also

analyses the effect of the risk-free rate on the relationship between the returns of stocks and

bonds. This study uses the yield of 3-Month or 90-Day Sovereign Bonds traded in the UK. Since

the data collected was the annual yield, it had to be adjusted to a monthly yield in order to be

used in our analysis. The data was also non-stationary, so the difference in the sovereign bond

yields for each month was calculated using the following formula:

Yield = ln(Yieldt/ Yieldt-1).

3.2 Sample

The sample for stocks and bonds is based on the UK corporate securities market. Relative to

stocks, the data was obtained from an index produced by Reuters, which included all UK traded

shares. As for bonds, the data was obtained from an index produced by iBoxx, which contained

all UK traded corporate bonds of all maturities. To make the data stationary, the following

formula was used:

Return = ln(Pricet/ Pricet-1).

All data in this study are collected using DataStream from a number of sources including

the Office for National Statistics, the OECD, Reuters, and iBoxx. The time period observed in

this study is May 2000 - May 2015, which is selected to account for the recession in 2008.

4.0 Methodology

In testing the relationship between the returns of stocks and bonds, we employed multiple linear

regressions supplemented with descriptive statistics, mean comparison, and correlation tests.

Page 6: Analysis of the Relationship Between Stocks and Bonds

First, a primary analysis was conducted where we tested the impact of stock and bond

returns on each other. The linear regression takes the following forms:

RE = α + βRB + e

RB = α + βRE + e

Where, RE is stock returns, RB is bond returns, α is the constant, β is the sensitivity of the

dependent variable to the independent variable, and e is the regression error.

We then introduced each macroeconomic factor into the multiple linear regressions

individually to observe their impact on the relationship between stock and bond returns in

isolation. The multiple linear regressions take the following forms:

RE = α + βRB + β1F1 + e

RB = α + βRE + β1F1 + e

Where RE is stock returns, RB is bond returns, α is the constant, β is the sensitivity of the

dependent variable to the independent variable, β1 is the sensitivity of the dependent variable to

the macroeconomic factor, F1 is the specific macroeconomic factor, and e is the regression error.

5.0 Findings

In analysing the impact of macroeconomic factors on the relationship between stock and bond

returns, we have found varying results, which can be found in detail in the Appendix.

In conducting our primary analysis, we found insightful results. The average stock return

was 0.152% and the average bond return was 0.089%. In terms of skewness, both returns were

skew to the left, which indicates that most of the returns of stocks and bonds are on the lower

range. As for kurtosis, the distribution pattern of stock returns is significantly more peaked than

that of bond returns. No significant difference was found in in the average returns of stocks and

bonds, which suggests that there was little or no arbitrage opportunity. There was also significant

positive correlation between bond and stock returns. We also found that the sensitivity of stock

returns to bond returns is 0.681, meaning that for every 1-unit increase in bond returns, stock

Page 7: Analysis of the Relationship Between Stocks and Bonds

returns increased by 0.681. On the other hand, the sensitivity of bond returns to stock returns is

0.086, meaning that for every 1-unit increase in stock returns, bond returns increased by 0.086.

Next, we observed the influence of GDP growth on the relationship between bond and

stock returns. The average GDP growth was 0.991%, which reflects the 2008 recession. In terms

of skewness, GDP growth was also skew to the left. On the kurtosis measure, GDP growth

followed a normal distribution pattern (below three). Furthermore, there was significant

correlation between stock returns and GDP growth, but there was no significant correlation

between bond returns and GDP growth. We also found that the sensitivity of stock returns to

GDP growth is 2.551. This suggests that GDP growth significantly influences stock returns

through its direct impact on the future earnings of the firm. On the other hand, we found that

bond returns are not influenced by GDP growth. Introducing GDP growth into the model did not

significantly increase the sensitivity of stock returns to bond returns. However, with GDP growth

in the model, the sensitivity of bond returns to stock returns increased to 0.109.

As for the money supply, we also found insightful results. The average change in the

money supply was 0.511%. Relative to skewness, the change in the money supply was skew to

the right, which reflects expansionary monetary policies. As for kurtosis, the distribution pattern

of changes in the money supply was significantly peaked. Furthermore, there was no significant

correlation between the money supply and stock returns. However, at an 89.1% confidence

interval, there is significant negative correlation between the money supply and bond returns.

Though this is an inadequate confidence interval, it suggests that the money supply negatively

influences bond prices. After conducting the multiple linear regressions, we found that at a 95%

confidence interval, changes in the money supply had no significant impact on the returns of

stocks and bonds or on the relationship between stock and bond returns. A possible explanation

for this is that banks increased their reserve ratios and reduced their lending which hindered the

effectiveness of the expansionary monetary policy.

We then observed the influence of inflation on the relationship between stock and bond

returns. The average inflation rate was 2.204%, which is slightly above the inflation target of the

Bank of England. As for skewness, the inflation rate was skew to the right, which reflects

moderate levels of inflation. In terms of kurtosis, the distribution pattern of the inflation rate had

a very low peak, which confirms the previous intuition. Furthermore, there was no significant

Page 8: Analysis of the Relationship Between Stocks and Bonds

correlation between the inflation rate and stock returns. However, at a 95% confidence interval,

the inflation rate and bond returns were positively correlated. After conducting the multiple

linear regressions, we found that the inflation rate had no significant influence on stock returns.

On the other hand, the inflation rate negatively influences bond returns, as the sensitivity of bond

returns to the inflation rate is -0.003. Introducing inflation into the model reduces the sensitivity

of stock returns to bond returns to 0.673.

Finally, we introduced the yield of sovereign bonds as an ancillary factor. The average

change in sovereign bond yields was 1.481%. Furthermore, the change in sovereign bong yields

was skewed to the left, indicating that the change in yield was mostly low. As for the kurtosis,

the distribution pattern of the change sovereign bond yields had a very high peak. In addition,

there was positive correlation between stock returns and the change in sovereign bond yields, but

there was no correlation between bond returns and changes in the yield. The sensitivity of stock

returns to changes in sovereign bond yields was 0.086. Also, introducing changes in sovereign

bond yields into the model had no influence on the relationship between stocks and bonds.

6.0 Conclusion

In summary, there is an inherent relationship between stock and bond returns. Unlike the general

consensus, our results show that stock and bond returns are positively correlated. The intuition

behind this is that previous studies examined the short-term relationship between stocks and

bonds, and the negative correlation reflects fluctuations in investor preferences and temporary

economic conditions. Whereas, our study examined the long-term relationship between stocks

and bonds, where these fluctuations are smoothened. Of the primary macroeconomic factors

examined in this study, only GDP growth and the inflation rate influenced stock and bond returns

and relationship between stocks and bonds returns.

Relative to future research, further analyses should be done on the announcement effects

of expansionary monetary policy on the relationship between stock and bond returns. In addition,

investors’ preferences should also be quantified and added to the analysis.

Page 9: Analysis of the Relationship Between Stocks and Bonds

References

Andersson M., Krylova, E., and Vähämaa, S., 2008. Why Does the Correlation between Stock and Bond

Returns Vary over Time?,Applied Financial Economics, 18(2), pp.139-151.

Barsky, R. B., 1989. Why Don’t the Prices of Stocks and Bonds Move Together?,American Economic

Review, 79, pp.1132-1145.

Giilhooly, R., and Hussain, F., 2014.Seasonal adjustment of M4 excluding intermediate OFCs (M4ex) - an

update, Monetary & Financial Statistics, Bank of England.

Gulko, L., 2002. Decoupling, Journal of Portfolio Management, 28(3), pp.59-66.

Joyce, M., Miles, D., Scott, A., and Vayanos, D., 2012.Quantitative Easing and Unconventional Monetary

Policy - An Introduction, The Economic Journal, 122 (November), pp.271-289.

Li, L., 2002. Macroeconomic Factors and the Correlation of Stock and Bond Returns. Yale ICF Working

Paper No. 02-26.

Markowitz, H.M., 1952, Portfolio Selection, Journal of Finance, 7(1), pp.77-91.

Shiller, R., 1982. Consumption, Asset Markets, and Macroeconomic Fluctuations, Carnegie Rochester

Conference Series on Public Policy, (Autumn 1982)17, pp.203-238.

Summers, L., The Nonadjustment of Nominal Interest Rates: A Study of the Fisher Effect in J. Tobin, ed.,

Macroeconomic Prices and Quantities: Essays in Memory of Arthur Okun, Washington: The Brookings

Institution, 1983.

Page 10: Analysis of the Relationship Between Stocks and Bonds

Appendix

1.0 Primary Analysis

1.1 Descriptive Statistics of Stock and Bond Returns

Descriptive Statistics

N Minimum Maximum Mean

Std.

Deviation Skewness Kurtosis

Statistic Statistic Statistic Statistic Statistic Statistic

Std.

Error Statistic

Std.

Error

RE 179 -.2783 .09979 .0014927 .049435 -1.596 .182 5.687 .361

RB 179 -.0733 .07027 .0004447 .017436 -.431 .182 3.226 .361

Valid N

(listwise) 179

1.2 Independent Sample Test Relative to Stock and Bond Returns

Independent Samples Test

Levene's Test

for Equality of

Variances t-test for Equality of Means

F Sig. t df

Sig.

(2-

tailed)

Mean

Difference

Std. Error

Difference

95% Confidence Interval of

the Difference

Lower Upper

Returns Equal

variances

assumed

66.873 .000 .315 358 .753 .0012295 .003899 -.006439 .008898

Equal

variances

not assumed

.315 223.472 .753 .001229 .003899 -.006454 .008913

For the test with equal variances assumed, the significant figure (0.00) is less than 0.05, so we

disregard this line. For the test with equal variances not assumed, the significant figure (0.753) is

greater than 0.05 so we accept the H0 and conclude that there is no significant difference in the

average returns of stocks and bonds.

Page 11: Analysis of the Relationship Between Stocks and Bonds

1.3 Correlation between Stock and Bond Returns

Correlations

RE RB

RE Pearson Correlation 1 .242**

Sig. (2-tailed) .001

N 180 180

RB Pearson Correlation .242** 1

Sig. (2-tailed) .001

N 180 180

**. Correlation is significant at the 0.01 level (2-tailed).

The significant figure (0.001) is less than 0.05, so we reject the H0 and conclude that there is

positive correlation between stock and bond returns.

1.4 Linear Regression with Stock Returns as the Dependent Variable

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .242a .059 .053

.04796702733946

7

a. Predictors: (Constant), RB

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) .001 .004 .370 .712

RB .681 .205 .242 3.328 .001

a. Dependent Variable: RE

The significant figure (0.001) is less than 0.05, so we reject the H0 and conclude that the

sensitivity of stock returns to bonds returns is 0.681.

Page 12: Analysis of the Relationship Between Stocks and Bonds

1.5 Linear Regression with Bond Returns as the Dependent Variable

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .242a .059 .053

.01704033105541

7

a. Predictors: (Constant), RE

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) .000 .001 .125 .901

RE .086 .026 .242 3.328 .001

a. Dependent Variable: RB

The significant figure (0.001) is less than 0.05, so we reject the H0 and conclude that the

sensitivity of bond returns to stock returns is 0.086.

2.0 Analysis of the Influence of GDP Growth on the Relationship between Stock and Bond

Returns

2.1 Descriptive Statistics

Descriptive Statistics

N Minimum Maximum Mean

Std.

Deviation Skewness Kurtosis

Statistic Statistic Statistic Statistic Statistic Statistic

Std.

Error Statistic

Std.

Error

RGDP 58 -.02263 .028419 .0099 .0091 -1.040 .314 2.217 .618

Valid N

(listwise) 58

Page 13: Analysis of the Relationship Between Stocks and Bonds

2.2 Correlation amongst Stock Returns, Bond Returns, and GDP Growth

Correlations

RE RB RGDP

RE Pearson Correlation 1 .321* .335*

Sig. (2-tailed) .014 .010

N 58 58 58

RB Pearson Correlation .321* 1 .204

Sig. (2-tailed) .014 .125

N 58 58 58

RGDP Pearson Correlation .335* .204 1

Sig. (2-tailed) .010 .125

N 58 58 58

*. Correlation is significant at the 0.05 level (2-tailed).

Relative to stock returns and GDP growth, the significant figure (0.010) is less than 0.05, so we

reject the H0 and conclude that there is positive correlation between stock returns and GDP

growth. As for bond returns and GDP growth, the significant figure (0.125) is greater than 0.05,

so we accept the H0 and conclude that there is no correlation between bond returns and GDP

growth.

2.3 Multiple Linear Regressions with Stock Returns as the Dependent Variable

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .423a .179 .149

.0767242747899

76

a. Predictors: (Constant), RGDP, RB

Page 14: Analysis of the Relationship Between Stocks and Bonds

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) -.022 .015 -1.468 .148

RB .686 .325 .264 2.112 .039

RGDP 2.551 1.131 .282 2.256 .028

a. Dependent Variable: RE

Relative to bond returns, the significant figure (0.039) is less than 0.05, so we reject the H0 and

conclude that the sensitivity of stock returns to bonds returns is 0.686. As for GDP growth, the

significant figure (0.028) is less than 0.05, so we reject the H0 and conclude that the sensitivity of

stock returns to GDP growth is 2.551.

2.4 Multiple Linear Regressions with Bond Returns as the Dependent Variable

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .337a .114 .081

.0306495997979

45

a. Predictors: (Constant), RGDP, RE

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) -.004 .006 -.573 .569

RE .109 .052 .285 2.112 .039

RGDP .378 .469 .109 .806 .424

a. Dependent Variable: RB

Page 15: Analysis of the Relationship Between Stocks and Bonds

Relative to stock returns the significant figure (0.039) is less than 0.05, so we reject the H0 and

conclude that the sensitivity of bonds returns to stock returns is 0.109. As for GDP growth, the

significant figure (0.424) is less than 0.05, so we accept the H0 and conclude that bond returns

are not influenced by stock returns

3.0 Analysis of the Influence of Changes in the Money Supply on the Relationship between

Stock and Bond Returns

3.1 Descriptive Statistics of Changes in the Money Supply

Descriptive Statistics

N Minimum Maximum Mean

Std.

Deviation Skewness Kurtosis

Statistic Statistic Statistic Statistic Statistic Statistic

Std.

Error Statistic

Std.

Error

RE 178 -.278 .09979 .00147 .04957 -1.591 .182 5.637 .362

RB 178 -.0733 .070274 .00048 .017477 -.437 .182 3.207 .362

RM4 178 -.0237 .080995 .0051 .00945 2.668 .182 22.980 .362

Valid N

(listwise) 178

3.2 Correlation amongst Stock Returns, Bond Returns, and Changes in the Money Supply

Correlations

RE RB RM4

RE Pearson Correlation 1 .245** -.059

Sig. (2-tailed) .001 .430

N 178 178 178

RB Pearson Correlation .245** 1 -.121

Sig. (2-tailed) .001 .109

N 178 178 178

RM4 Pearson Correlation -.059 -.121 1

Sig. (2-tailed) .430 .109

N 178 178 178

**. Correlation is significant at the 0.01 level (2-tailed).

Page 16: Analysis of the Relationship Between Stocks and Bonds

Relative to stock returns, the significant figure (0.430) is greater than 0.05 so we accept the H0

and conclude that there is no correlation between stock returns and changes in the money supply.

As for bond returns, the significant figure (0.109) is greater than 0.05 so we accept the H0 and

conclude that there is no correlation between bond returns and changes in the money supply.

3.3 Multiple Linear Regressions with Stock Returns as the Dependent Variable

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1 Regression .026 2 .013 5.673 .004b

Residual .409 175 .002

Total .435 177

a. Dependent Variable: RE

b. Predictors: (Constant), RM4, RB

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) .002 .004 .473 .637

RB .684 .209 .241 3.269 .001

RM4 -.159 .387 -.030 -.412 .681

a. Dependent Variable: RE

As for stock returns, the significant figure (0.681) is greater than 0.05 so we accept the H0 and

conclude that changes in the money supply do not influence stock returns.

Page 17: Analysis of the Relationship Between Stocks and Bonds

3.4 Multiple Linear Regressions with Bond Returns as the Dependent Variable

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .267a .071 .061

.016939201994

093

a. Predictors: (Constant), RM4, RE

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1 Regression .004 2 .002 6.714 .002b

Residual .050 175 .000

Total .054 177

a. Dependent Variable: RB

b. Predictors: (Constant), RM4, RE

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) .001 .001 .945 .346

RE .084 .026 .239 3.269 .001

RM4 -.197 .135 -.106 -1.458 .147

a. Dependent Variable: RB

Relative to bond returns, as suggested by the correlation test, the significant figure (0.147) is

greater than 0.05 so we accept the H0 and conclude that changes in the money supply do not

influence bond returns.

Page 18: Analysis of the Relationship Between Stocks and Bonds

4.0 Analysis of the Influence of the Inflation Rate on the Relationship between Stock and

Bond Returns

4.1 Descriptive Statistics of the Inflation Rate

Descriptive Statistics

N Minimum Maximum Mean

Std.

Deviation Skewness Kurtosis

Statistic Statistic Statistic Statistic Statistic Statistic

Std.

Error Statistic

Std.

Error

RE 179 -.2783 .09979 .00149 .0494 -1.596 .182 5.687 .361

RB 179 -.0733 .07027 .0004447 .01743 -.431 .182 3.226 .361

RCPI 179 -.10000 5.2000 2.20391 1.09889 .626 .182 .043 .361

Valid N

(listwise) 179

4.2 Correlation amongst Stock Returns, Bond Returns, and the Inflation Rate

Correlations

RE RB RCPI

RE Pearson Correlation 1 .245** -.084

Sig. (2-tailed) .001 .266

N 179 179 179

RB Pearson Correlation .245** 1 -.212**

Sig. (2-tailed) .001 .004

N 179 179 179

RCPI Pearson Correlation -.084 -.212** 1

Sig. (2-tailed) .266 .004

N 179 179 179

**. Correlation is significant at the 0.01 level (2-tailed).

Relative to bond returns and inflation rates, the significant figure (0.001) is less than 0.05, so we

reject the H0 and conclude that there is positive correlation between returns of inflation and bond

returns, but not between stock returns and inflation. The result shows that there is significant and

negative relation between them.

Page 19: Analysis of the Relationship Between Stocks and Bonds

4.3 Multiple Linear Regressions with Stock Returns as the Dependent Variable

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .247a .061 .050

.0481782335121

59

a. Predictors: (Constant), RCPI, RB

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1 Regression .026 2 .013 5.705 .004b

Residual .409 176 .002

Total .435 178

a. Dependent Variable: RE

b. Predictors: (Constant), RCPI, RB

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) .004 .008 .544 .587

RB .673 .212 .238 3.178 .002

RCPI -.001 .003 -.033 -.445 .657

a. Dependent Variable: RE

Relative to stock returns, the significant figure (0.657) is greater than 0.05 so we reject the H0

and conclude that the inflation rate does not influence stock returns.

Page 20: Analysis of the Relationship Between Stocks and Bonds

4.4 Multiple Linear Regressions with Bond Returns as the Dependent Variable

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .311a .097 .087

.0166648805494

13

a. Predictors: (Constant), RCPI, RE

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1 Regression .005 2 .003 9.433 .000b

Residual .049 176 .000

Total .054 178

a. Dependent Variable: RB

b. Predictors: (Constant), RCPI, RE

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) .007 .003 2.519 .013

RE .081 .025 .228 3.178 .002

RCPI -.003 .001 -.193 -2.685 .008

a. Dependent Variable: RB

Relative to bond returns, the significant figure (0.008) is less than 0.05, so we reject the H0 and

conclude that the inflation rate influences bond returns. The sensitivity of bond returns to the

inflation rate is -0.003. However, the adjusted R square is only 0.087 that means 8.7% of bond

returns can be explained by stock returns and inflation.

Page 21: Analysis of the Relationship Between Stocks and Bonds

5.0 Analysis of the Influence of Changes in Sovereign Bond Yields on the Relationship

between Stock and Bond Returns

5.1 Descriptive Statistics of Changes in Sovereign Bond Yields

Descriptive Statistics

N Minimum Maximum Mean

Std.

Deviation Skewness Kurtosis

Statistic Statistic Statistic Statistic Statistic Statistic

Std.

Error Statistic

Std.

Error

RE 179 -.27832 .09979 .00149 .0494 -1.596 .182 5.687 .361

RB 179 -.07333 .07027 .00044 .0174 -.431 .182 3.226 .361

RT 179 -.74533 .40546 -.0148 .1189 -1.376 .182 11.326 .361

Valid N

(listwise) 179

5.2 Correlation amongst Stock Returns, Bond Returns, and Changes in Sovereign Bond Yields

Correlations

RE RB RT

RE Pearson Correlation 1 .245** .204**

Sig. (2-tailed) .001 .006

N 179 179 179

RB Pearson Correlation .245** 1 -.014

Sig. (2-tailed) .001 .851

N 179 179 179

RT Pearson Correlation .204** -.014 1

Sig. (2-tailed) .006 .851

N 179 179 179

**. Correlation is significant at the 0.01 level (2-tailed).

Relative to stock returns and sovereign bond yields, the significant figure (0.006) is less than

0.05, so we reject the H0 and conclude that there is positive correlation between returns of T-bill

and stock returns. As for bond returns and sovereign bond yields, the significant figure (0.851) is

Page 22: Analysis of the Relationship Between Stocks and Bonds

greater than 0.05 so we accept the H0 and conclude that there is no correlation between bond

returns and sovereign bond yields.

5.3 Multiple Linear Regressions with Bond Returns as the Dependent Variable

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .253a .064 .053

.0169638157892

95

a. Predictors: (Constant), RE, RT

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1 Regression .003 2 .002 6.030 .003b

Residual .051 176 .000

Total .054 178

a. Dependent Variable: RB

b. Predictors: (Constant), RE, RT

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) .000 .001 .128 .899

RT -.010 .011 -.067 -.899 .370

RE .091 .026 .258 3.467 .001

a. Dependent Variable: RB

As for bond returns, the significant figure is (0.370) so we accept the H0 and conclude that

sovereign bond yields do not influence bond returns.

Page 23: Analysis of the Relationship Between Stocks and Bonds

5.4 Multiple Linear Regressions with Stock Returns as the Dependent Variable

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .321a .103 .093

.0470839964763

20

a. Predictors: (Constant), RB, RT

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1 Regression .045 2 .022 10.111 .000b

Residual .390 176 .002

Total .435 178

a. Dependent Variable: RE

b. Predictors: (Constant), RB, RT

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) .002 .004 .694 .489

RT .086 .030 .208 2.913 .004

RB .702 .202 .248 3.467 .001

a. Dependent Variable: RE

As for stock returns, the significant figure (0.004) is less than 0.05 so we reject H0 and conclude

that sovereign bond yields have an influence on stock returns. The sensitivity of stock returns to

bond returns is 0.086. Both bond returns and T-bill have a positive relation with stock returns,

i.e., stock and bond returns, and T-bill move the same direction. However, the adjusted R square

is only 0.093, which means 9.3% of stock returns can be explained by bond returns and changes

in the sovereign bond yields.