evaluating the efficiency of frontier equity markets in ... o. morrell, sean... · web...

2015 Cambridge Business & Economics Conference ISBN : 9780974211428

Evaluating the Efficiency of Frontier Equity Markets in Caribbean Economies: Equity Market Efficiency in Barbados, Jamaica and Trinidad

and Tobago

Stephen O. Morrell, Ph.D.Professor of Economics and Finance

Andreas School of BusinessBarry University

Miami Shores, Florida USA 33161

Sean CooneyAnalyst

Energy Investment BankingCapital Markets Division

Bank of Montreal Calgary, Alberta Canada T2P 1G1

_____________________Corresponding author: Stephen O. Morrell, Ph.D., Professor of Economics and Finance, Andreas School of Business, Barry University, 11300 N.E. Second Avenue, Miami Shores, Fl. USA 33161. Phone: 305 899 3513; Fax: 305 892 6412; Email: [email protected]

July 1-2, 2015Cambridge, UK 1

mailto:[email protected]


Abstract

Professional investors have only recently turned their attention to so-called Frontier equity markets. Academic researchers have been even later in starting to research Frontier equity markets. Asset pricing, the distributions of returns and risks, and potential diversification benefits of Frontier equity markets have been the primary topics of investigation among professional investors and academic researchers.

However, the informational/pricing efficiency of Frontier equity markets and its evolution over time have not been systematically analyzed and evaluated by either professional investors or academic researchers – although this issue is seemingly the essence of market valuation assessments as well as broader issues associated with capital market effectiveness and economic development.

Our research seeks to begin to fill this void. We employ a variety of empirical techniques to ascertain the efficiency of equity markets in the three Caribbean Frontier market countries of Barbados, Jamaica, and Trinidad and Tobago, and to determine if these markets have become more efficient over time. The empirical techniques include analyzes, assessments, tests and evaluations of return autocorrelations; adjusted Dickey-Fuller tests for unit roots; runs tests; and Lo-MacKinlay, Chow-Demming and Wright variance ratio tests as well as rolling Lo-Mackinlay variance ratio tests for dynamic changes to market efficiency.

Our empirical techniques indicate pricing and valuations in all three frontier markets are inefficient and predictable. Additionally, the evidence is weak that any of the three markets have become more efficient over time. However, thin trading, illiquidity and non-linearities may be influencing our results.

JEL classification: F37; G14; G15Keywords: Frontier markets; Market Efficiency, Forecasting Returns



I. Introduction

Frontier equity markets have quite recently started to attract attention from the professional investment community as well as from academic researchers. This heightened interest reflects a variety of factors, including economic, investment and capital market growth prospects in so-called frontier countries.

The United Nations(2011),for example, notes that from 2000 – 2009 real output increased at an annual average rate of 3.3 percent in countries classified as developed versus 6.9 percent in those classified as developing (including frontier), and also that 2012 – 2015growth is forecasted to average 1.6 percent for developed countries compared to 5.7 percent for developing ones. Speidell (2011) reports that while Frontier countries account for 22 percent of the world’s population and 7 percent of its nominal GDP they only represent approximately 3 percent or roughly $1.9 trillion of 2010 world equity market capitalization. Emerging markets, in contrast, accounted for 63 percent of global population, 42 percent of nominal GDP and 42 percent or about $26 trillion of 2010 global equity market capitalization. Moreover, equity market capitalization relative to GDP in early 2011 totaled only 17 percent in frontier markets versus 45 percent for emerging and 72 percent for developed markets, respectively.

The heightened attention directed to frontier equity markets from the professional investment community can be seen in the following activities:

The establishment of criteria for classifying markets as frontier. The design and development of frontier stock market indices. The subsequent design, development and marketing of investable

products tied to frontier stock market indices. The growth in the market capitalization and number and asset sizes

of the investable products.

Four organizations at present, S&P/IFC, MSCI/Barra, the Frank Russell Company and the Financial Times have been primarily responsible for establishing and defining criteria for classifying equity markets as Frontier, and then designing and developing indices to measure market performance. While the criteria and the weight given to each criterion vary somewhat across organizations they include:



Liquidity screens for individual companies; Minimum free float adjusted market capitalizations relative to

emerging markets. The extent of any investment restrictions. Qualitative evaluations of a nation’s capital market development,

governance and informational transparency Exposure to each of the world’s five global regions.

S&Ps Aye Soe (2007) and Speidell (2011) offer even more basic definitions of Frontier markets. As Soe notes, “Frontier markets are the subset of emerging markets deemed to be relatively small and illiquid, even by emerging markets standards.” Speidell notes that of the 211 countries covered in the World Bank’s World Development Indicators 117 have independent stock markets. Morgan Stanley Capital International (MSCI) places 24 of the 117 in the Developed group and classifies 22 as Emerging. The remaining 71 equity markets are then categorized as Frontier.1

Table 1 summarizes basic features of the four primary Frontier equity market indices:

Table 1: Frontier Equity Market Indices

InceptionNumber of:2013Equity Market IndexIndex Date Countries Companies Capitalization Construction

S&P/IFC 2007 37 563 $296 billion MVW

MSCI/Barra 2009 25 371 $228 billion MVW

Russell 2008 41 209 $941 billionMVW

FTSE 50 2010 25 50 $ 48 billion MVW

MVW = market value weighted

Sources: All accessed August 11, 2014S&P/IFC:https://www.spindexdata.com/idpfiles/emdb/prc/active/factsheets/Factsheet_SP_Frontier_BMI.pdfMSCI/Barrahttp://www.msci.com/products/indices/country_and_regional/fm/performance.html

1 See, for example, World Bank World Development Indicators, 2013 http://data.worldbank.org/indicator/CM.MKT.INDX.ZG?display=graphAccessed August 11, 2014


http://www.msci.com/products/indices/country_and_regional/fm/performance.html

https://www.spindexdata.com/idpfiles/emdb/prc/active/factsheets/Factsheet_SP_Frontier_BMI.pdf


http://data.worldbank.org/indicator/CM.MKT.INDX.ZG?display=graph


Russellhttp://www.russell.com/indexes/data/Frontier/russell_frontier_indexes.aspFTSE 50http://www.ftse.com/Indices/FTSE_Frontier_Indices/Index_Rules.jsp

As an illustration of the growth in Frontier markets Morningstar (2012) currently provides research on nine separate Frontier open-end funds and five Frontier exchange traded funds (ETFs). Total assets of the nine open-end funds were approximately $900 million as of June 30, 2014 while total assets of the five exchange traded funds were about $400 million. The open-end funds ranged in size from Franklin Templeton’s $500 million Frontier Market Fund to Nile Capital’s $4million Nile Pan Africa Fund. With regard to exchange traded funds Guggenheim – Bank of New York/Mellon’s Frontier Market fund of $142 million in assets is the largest and Market Vector’s Gulf States Index with assets of $11 million is the smallest in the Morningstar universe. All of these funds date from mid-to-late 2008. The median compound annual return over the three year period June, 2009 – June, 2012 for the open-end funds is 5.22 percent, while it is 6.56 percent for the exchange traded funds.2

The scant academic research on frontier markets has focused on topics such as their integration with developed and emerging markets, their portfolio diversification potential, and the distributions of their returns and risks. Berger, et.al. (2010) found extremely low levels of integration between frontier and developed markets and, hence, significant diversification benefits. Speidell (2011) contends frontier markets offer higher Sharpe ratios than either developed or emerging markets – based on higher returns with about the same amount of risk as those found in emerging markets.

The pricing efficiency of Frontier equity markets and its evolution over time, however, have not been systematically analyzed and evaluated by either professional investors or academic researchers – although this issue is seemingly the essence of market valuation assessments as well as broader issues associated with capital market effectiveness and economic development. Our research seeks to begin to fill this void.

We employ a variety of empirical techniques to ascertain the efficiency of equity markets in the three Caribbean Frontier market countries of Barbados, Jamaica, and Trinidad and Tobago, and to determine if these markets have become more efficient over time. The empirical techniques include analyzes, assessments, significance tests and evaluations of return autocorrelations; adjusted Dickey-Fuller tests for unit roots; runs tests; and Lo-MacKinlay, Chow-Demming and Wright variance ratio tests as well as rolling Lo-MacKinlay variance ratio tests for relative comparison as well as dynamic changes to market efficiency.2 See, for example. http://library.morningstar.com/fund/quote?t=TFMAX&region=USASite accessed August 12, 2014


http://library.morningstar.com/fund/quote?t=TFMAX&region=USA

http://www.ftse.com/Indices/FTSE_Frontier_Indices/Index_Rules.jsp

http://www.russell.com/indexes/data/Frontier/russell_frontier_indexes.asp


Our choice of researching the efficiency of equity markets in Barbados, Jamaica and Trinidad and Tobago is based on four factors. First, these three Caribbean nations have the closest geographic proximity to the U.S. of all the 47 nations contained in the above Frontier market indices. The second reason is these three countries are the only predominately English speaking ones among the Latin America and Caribbean Region components of the above Frontier market indices. The third factor is that each country obtained its independence from Great Britain in the early –to-mid 1960s and possessed similar, shared and inherited British institutions.3 The fourth reason is that all three nations are members of CARICOM and thus, in addition to inherited British institutions, share similar trade and financial regulatory structures.

The contribution of our research is thus twofold. First, to initiate the examination of market efficiency in Frontier markets and, in the second instance, to focus on the efficiency of Frontier equity markets in countries geographically and – in some dimensions – institutionally and culturally close to the United States.

The remainder of the paper is organized as follows. Section 2 reviews the literature on the efficient markets hypothesis. However, as this literature is voluminous reflecting its status as one of the most widely researched and debated topics in all of financial economics our focus in Section 2 is on research that has a bearing on the efficiency of Frontier equity markets. Section 3 discusses the statistical techniques we employ to test for the presence and evolution over time of equity market efficiency in the three Caribbean countries. Section 4 presents the data we employed in the research and an overview of each nation’s equity market. Section 5 presents results of a battery of statistical techniques that test for market efficiency. Section 6 presents our conclusions and suggestions for further research.

II. The Efficient Markets Hypothesis and the Evolution of Market Efficiency in Frontier Equity Markets

The debate about the Efficient Markets Hypothesis is undoubtedly one of the most widely researched topics in all of financial economics. In their survey of the empirical literature on the evolution of stock market efficiency Lim and Brooks (2011) cite 320 journal articles, monographs and books dating from 1955 through 2009 in the References section of their paper. However, even their extensive reference list is not exhaustive as it excludes Kendall’s (1953) seminal article which launched the empirical research on 3 Jamaica and Trinidad and Tobago obtained their independence in August and September, 1962, respectively. Barbados obtained its independence in November, 1966



the efficient markets hypothesis. LeRoy’s (1989) survey article focusing on efficient markets and martingale stochastic processes had 167 References, while dueling, back-to-back articles by Shiller and Malkiel (2003) on the validity of the efficient markets hypothesis and behavioral finance cite a combined 112 distinct references in their respective bibliographies.

In the broadest sense,the efficient markets hypothesis is the theory of equilibrium in competitive markets applied to security markets - most notably equity markets. As in the theory of competitive equilibrium, the ongoing quest for economic profits in equity markets causes investors to allocate resources and incur costs up to the point where the net marginal returns are zero. At this point equity prices will fully reflect the marginal valuations and marginal risk-adjusted opportunity costs of the marginal investor.

Information, knowledge and technology are the critical resources to which investors allocate resources and incur costs in their efforts to consistently earn economic profits in equity markets. Any information that can be used to indicate whether or not the existing level of stock prices provides an opportunity for economic profit will be seized upon by investors, and quickly incorporated into prices until the economic profit is dissipated. The same behaviors would be true about knowledge regarding such things as the processes of price formation, trading rules, patterns, cycles and trends in equity prices. Technologies, especially to the extent they lower the costs of acquiring information and executing trades, are also resources investors highly value and will quickly acquire, again to the point where economic profit from so-doing becomes zero.4

The lessons of market efficiency emerge directly from the perspective that equity prices reflect equilibrium outcomes in competitive markets populated by rational investors. These lessons include:

Equity prices reflect all relevant, publicly available information (also known as ‘weak-form’ efficiency).

Investors cannot consistently earn economic profits (excess risk-adjusted returns) in efficient equity markets.

Active investment management strategies cannot consistently succeed.

Since equities are correctly priced and not consistently mis-priced scarce capital and savings will not be wasted but instead efficiently allocated to markets/countries, sectors and firms offering the highest expected risk-adjusted returns/ value added.

4 Grossman and Stiglitz (1980) important insight that in equilibrium efficient information gathering activities should be value-creating is relevant here. Their point also implies the degree of market efficiency can vary over time and across markets.



As equities are not consistently mis-priced and fully embed all relevant publicly available information then it is new, relevant information which drives equity price changes. Moreover, changes in stock prices will be complete and rapid in response to the release of new information.

By definition, new information must be non-forecastable and therefore unpredictable. Consequently, stock price changes in efficient markets should also be unpredictable and non-forecastable.

Evolution and progress towards increasing market efficiency are especially vital for Frontier equity markets in light of the research which has clearly demonstrated the key contributions of more efficient markets to a nation’s development. Levine and Zervos (1998) find financial institutions and stock markets with high liquidity positively predict capital accumulation, productivity improvements and greater economic growth.

Bekaert and Harvey (1997) set out numerous arguments and evidence supporting the idea that efficient markets increase economic growth in emerging economies and, by implication, in frontier economies as well. They demonstrate that the cost to investors of diversifying decreases as equity market efficiency improves and in the process corporations find it less expensive to raise equity capital since investors can more easily reduce firm-specific risk. Bekaert and Harvey (1997) further argue that countries lacking efficient capital markets force companies, not stock markets, to provide this diversification. Companies accomplish this by concentrating investments in low-risk projects that may conflict with the firm’s comparative advantages. In contrast, as equity markets become more efficient investors may achieve greater diversification through lower costs of investment in multiple companies and issuing companies can focus on higher risk and more specialized projects that will increase economic growth for the home country. More efficient equity markets can also aid in the management of moral hazard issues by holding firm executives accountable for the long-term value of a firm as evidenced by its share price. As executives are held to higher standards of accountability for the value of the firms they lead economy-wide productivity can increase boosting a nation’s economic growth in the process. Moreover, the greater ease of change in ownership as equity market efficiency progresses serves as a deterrent to executives from engaging in productivity decreasing behaviors.

Both Levine and Zervos (1998) and Bekaert and Harvey (1997) argue persuasively that rising liquidity and the degree of ‘fair pricing’ are of paramount importance to improving equity market efficiency in emerging and frontier equity markets. They view liquidity as the extent to which trades of large size can me made instantaneously and continuously without



moving price significantly. Fair pricing is a situation where neither sellers sell “too cheaply” nor buyers pay “too much” for shares.The notion that stock price changes in efficient markets should be unpredictable requires elaboration as it is the basis for empirical tests of market efficiency. This notion is frequently interpreted, represented and tested as a requirement that, in efficient markets, equity prices follow a random walk stochastic process. However, as authors such as Bodie, Kane and Marcus (2013) state and LeRoy (1989) demonstrates this is being loose and inaccurate with terminology leading to misdirected conclusions about market efficiency.

In markets that are weak form efficient prices (and returns) follow martingale, martingale difference and submartingale stochastic processes. A stochastic process Pt is a martingale with respect to a sequence of information sets Φt where next period’s expected price (or return) conditional on this period’s information set is equal to this period’s actual price (or return) under the assumption that this period’s information set includes this period’s prices (or returns). Equation 1 depicts a martingale process. It simply says that the best forecast for next period’s price (or return) based on current information is this period’s price (or return).

(1) E(Pt+1 |Φt) = PtEquation 2 shows a martingale difference process, also known as a fair game. It states that the best prediction for the change in next period’s price (or return) conditional on this period’s information set is equal to zero. If Pt+1- Pt is a fair game then Ptis a martingale.

(2) E(Pt+1- Pt|Φt) = 0(3) E(Pt+1 |Φt) ≥PtEquation 3 depicts a submartingale process. It simply says that next period’s expected price can be greater than this period’s. LeRoy (1989) shows this is the case when investors have positive time preference and therefore require compensation for the loss of current period consumption.

In contrast to martingales, random walks are more restrictive stochastic processes than martingales. Equations 4 and 5illustrate a random walk



with drift process. The assumption that successive price (or return) changes should be independently and identically distributed makes random walk processes more stringent and restricted than martingales. Nonetheless, for reasons that are not clear the term “random walk” is commonly used rather than the correct martingale one.

(4) Et(Pt ) = Pt-1 + β +µt;

Or

(5) Rt =Et(Pt ) - Pt-1 x 100 Pt-1

(6) Rt = β +µt; where β is arbitrary drift term; µt =iid (o,б2)

If Kendall’s 1952 paper is used as the starting point for the evidentiary research on the efficient markets hypothesis then for approximately the next thirty years the bulk of the research seemed to have supported it. Research by, among others, Fama (1965, 1970, 1991), Malkiel (1973), Merton (1973), Lucas (1979), Breeden (1979) andFama and French (1988) appeared to indicate returns in equity markets (at least U.S. large capitalization ones) were consistent with the efficient markets hypothesis.

Over the last roughly thirty years, however, the consensus of research seems to have shifted. Research inconsistent with equity market efficiency has appeared with increasing frequency, and a growing number of factors have been identified as prospective causes of equity market inefficiencies. These include market microstructure issues and other market imperfections, noise trading and limits to arbitrage, and the psychological biases identified by behavioral finance researchers. Additionally, the thorny issue that empirical tests for market efficiency are essentially joint tests for efficiency and asset/security pricing models remains unresolved. In other words it may or may not be market efficiency that is confirmed or rejected by the data as much as the underlying pricing model. Research showing excess volatility in actual equity returns Shiller (1981), momentum in returns over short horizons Lo and MacKinlay (1988),predictable patterns in stock returns Campbell (1991) all started to increase doubts about the validity of the efficient markets hypothesis. Moreover, by the start of the 21st Century behavioral finance research



emphasizing psychological aspects of investor behavior was consistently indicating current and future equity returns could be predicted on the basis of past returns. Barberis’ and Thaler’s (2003) survey of behavioral finance summarized, synthesized and integrated the broad and deep scope of research in this field. Their summary indicated investors do not always process information correctly and at times make inconsistent or suboptimal decisions. Investor characteristics including overconfidence, conservatism, narrow framing and regret avoidance have led toa mispricing of equities, generating renewed interest in technical analysis and the development of new investment strategies such as those based on fundamental indexing.

The shifting professional consensus noted above, however, has not necessarily been completely supported by relatively recent, on-going empirical research. Recent years have witnessed empirical research on equity market efficiency in an expanding number of developed and, especially, emerging markets. We have reviewed six published papers which tested for equity market efficiency in a total of forty-four separate countries. Eighteen of these markets were classified as being in developed nations while the remaining twenty-six were categorized as being emerging markets. The authors of these studies applied a variety of statistical techniques in analyzing these forty-four equity markets, with the observational frequency of the data ranging from daily to monthly, and the number of price/return observations varying from a low of approximately 300 to a high of roughly 4,000.

Recognizing that the sample periods and sizes as well as methodologies varied widely we have nonetheless summarized in Table 2 the overarching results of these research papers.



Table 2: A Summary of Six Recent Research Papers on Equity Market Efficiency

Markets Data Market EfficiencyAuthor(s) Examined Freq.N/Mkts.Tests Yes/ No

Worthington, et al.16 developed Daily 2700 - 40001,2,3,4 No: 11 of 16 developed(2003) (2005) 11 emerging No: 11 of 11 emerging

Islam, et al. 1 emerging Monthly 312 1, 2 No(2005) Daily 2500 1, 2No

Hamid, et al. 2 developed Monthly 72 1,2, 3, No: 2 of 2 developed(2010) 12 emerging Monthly 72 1,2,3,4 No: 12 of 12 emerging

Tabak 1 emerging Daily 3,000 1,2,3,4, 7 Mixed: Varies over time(2002)

Lock 1 emerging Weekly 850 1,2,3,4 Yes(2007)

Totals 44 markets 18 developed 5 efficient; 13 inefficient 26 emerging 1 efficient; 24 inefficient; 1

mixed

Tests: 1 = Autocorrelations of Returns; (2) = Runs Test; (2) Unit Root Test; (4) Lo-MacKinlay Multiple Variance Ratio Tests; (5) Chow – Deming Multiple Variance Ratio Tests; (6) Wright Rank and Sign Multiple Variance Ratio Test; (7) Rolling Multiple Variance Ratio Tests.

The information summarized in Table 2 indicates that researchers have been overwhelmingly finding evidence not consistent with market efficiency. From a simple, unweighted point of view the return data in 37 of the 44 markets researched (84 percent) were found to be inconsistent with the efficient markets hypothesis. Return data in five of the eighteen developed and twenty-four of the twenty six emerging markets were found to be inconsistent with market efficiency.

In contrast to the six papers we reviewed, Lim and Brooks (2011) report on twenty six recent studies of market efficiency (10 on China alone) covering twenty four emerging equity markets. They report that the research results remain mixed regarding the efficiency of the two stock exchanges in Shanghai and Shenzhen, China. But otherwise, however, the studies they



report on indicate eighteen of the remaining twenty two markets (82 percent) do show evidence of weak form efficiency. 5

Research by Griffin, Kelly, and Nardari (2006) add to the inconclusive status of the debate on market efficiency. They examine and test fifty six markets around the world, twenty three of which are classified as developed and thirty three classified as emerging,and find, via the Lo-MacKinlay variance ratio test about 60 percent of 33 emerging markets do not pass the test for lack of autocorrelated returns while about 40 percent of developed markets fail the test for serial dependence in returns. Overall, however, based on a battery of tests they findemerging markets are by and large as efficient as developed markets.

Do the studies of the 112 equity markets reported above hint that, after about thirty years, the consensus of research might be shifting back ever so slightly to support for the efficient markets hypothesis? Recall eighty three of these equity markets were categorized as emerging, thirty two of which (39 percent) exhibited evidence of weak form efficiency. A major “intellectual innovation” may be at work in this regard - namely Lo’s (2005) pathbreaking foray into neuroscience – the Adaptive Markets Hypothesis.

For our purposes the salient points of Lo’s excursion into evolutionary dynamics are twofold: First, the implications of the efficient markets hypothesis and behavioral finance can co-exist. Investors may indeed have behavioral biases resulting in profitable trading patterns remaining embedded in past price data while other investors discern these profitable trading patterns, exploit them, and in the process erode the residual profits and propel markets to efficiency. The second implication is that market efficiency is not an all-or-none state – though the vast majority of research on the subject has treated it as such – but, instead, is a characteristic of equity markets that can and should vary continuously over time. An important implication, discussed in the next section, is that empirical techniques used in testing for market efficiency need to be dynamic in nature and attempt to measure efficiency on a relative basis over time rather than on a static all-or-none basis.

III. Statistical Techniques and Tests for Market Efficiency

Daily equity market returns, discussed in more detail in Section 4, are the basic unit of analysis for each country’s stock market. Daily returns are measured as the successive differences in the natural logarithms of the

5 See Lim and Brooks (2011) pages 74-75.



daily closing values of each nation’s equity market index, as depicted in equation 7.

(7) Rti = (lnPt

i - lnPt-1i) where:

Rti = return in equity market i at time t

Pti =value of stock market index i at time t

Pt-1i= value of stock market index i at time t-1.

For each of our three Frontier equity markets, Barbados, Jamaica, and Trinidad and Tobago, we apply seven statistical techniquesto test whether or notequity prices and returns conform to the martingale stochastic processes consistent with the efficient markets hypothesis. The seven statistical techniques are;

1. Return autocorrelations;2. Augmented Dickey Fuller unit roots test;3. Runs test; 4. Lo-MacKinlay Multiple Variance Ratio test; 5. Chow-Denning Multiple Variance Ratio test; 6. Wright ‘Rank and Sign’ Multiple Variance Ratio test; 7. Rolling/Time Varying Lo-MacKinlay Multiple Variance Ratio test.

Each of these techniques is briefly described below.

1. Return Autocorrelations Examining the serial (auto) correlations of returns is one of the older and most widely usedtests in the efficient markets hypothesis literature, first employed by Fama (1965). The concept is straightforward. Namely, if prices and returns are determined in efficient markets, then successive price changes and returns are unpredictable and the best forecast of next period’s return, given available information, is zero. The clear implication is that return autocorrelations should be zero in efficient markets.

2. Augmented Dickey Fuller Test for Unit Roots The Augmented Dickey Fuller (ADF) test is a test for a unit root in the equity market returns data series. Data series, such as the equity market returns in our three countries, that possess a unit root also have the property of being non-stationary. A non-stationary data series, in turn, is one where the order of the observations in the series, for example the



sequencing of the data, does not affect the value of the observation. Non-stationary data series follow random walks and are therefore consistent with efficient equity markets.Equation 8 illustrates a Dickey-Fuller test regression augmented for both a constant and trend in the underlying data series.

(8) ΔRt = α + βT + γRt-1 + δΔRt-1 +…+ δp-1ΔRt-p+1 +εt

Where: α = constant; β = coefficient on time trend; P = lag order of autoregressive process.

3. Runs Test A runs test is a non –parametric test for the randomness of the number of series of successive return changes of the same sign within an entire sample of return changes. A run is defined as a series of successive return changes of the same sign. Positive runs are defined as series of successive return changes where each return is greater than the sample mean return, while negative returns are defined as series of successive return changes where each return change is less than the sample mean return.

Let NAbe the number of positive runs and NB be the number of negative runs. The test statistic is N, the total number of runs. Where NA and NB are sufficiently large the test statistic is approximately normally distributed:

(9) Z = N - µ N

σN

(10) where µN = 2NANB +1; σN = [ 2N ANB (2NANB-N)] 1/2 N [N2 (N-1)]1/2

The key issue is whether or not the total number of runs actually observed in the entire sample of returns is statistically significantly different from the number that would be observed if the number of runs was randomly distributed.

4. Variance Ratio (VR) Tests Generation 1: Lo- MacKinlay VR Tests (1988,1989)The variance ratio test, as pioneered by Lo and MacKinlay (1988, 1989), has become the workhorse statistical technique for testing whether or not equity returns are autocorrelated.The test is based on the property that the variance of increments of a martingale difference process Xt is a linear



process of the sampling interval of the data time series. This implies that the variance of the q period return (Xt – Xt-q) is q times the variance of the one period return (Xt – Xt-1). Whether or not returns follow a martingale difference process can then be estimated by comparing 1/qtimes the variance of (Xt – Xt-q) to the variance of (Xt – Xt-1).

Let Pt represent the numerical value of a frontier stock market index for a country at time period t, and let Xt equal the natural logarithm of Pt. The variance ratio (VR) is theratio of the variance of the q-period return to qtimes the variance of the one-period return, as illustrated in equation 11.

(11)V Rq=σ 2(q)σ2(1)

where σ2 (q) is 1/q times the variance of (Xt – Xt-q) and σ2 (1) is the variance of (Xt – Xt-1). VR should be equal to one for any holding period q, under the nullhypothesis of serially uncorrelated stock returns. The equations to calculate σ2 (1) and σ2 (q) are given in expressions (12) – (15).

(12)σ2= 1nq−1∑t=1

nq

(X t−Y t−1−u)2

(13) u= 1nq∑t=1

nq

(Y t−Y t−1)=1nq

(Y nq−X0)

(14)σ 2(q)= 1m∑

t=q

nq

(X t−Y t−q−q u)2

Where:

(15)m=q (nq−q+1 )(1− qnq )

(16) Z(q)=(VR (q )−1)√θq ~ N (0, 1)



(17) Z¿ (q )= (VR (Q )−1 )√θ¿ (Q )

N (0 ,1)

Where:

(18) θ (q )=2 (2q−1 )(q−1)

3q(nq)

(19)θ¿ (q )=∑j=1

q−1 [2 (q− j )q ]

2

б ( j )

(20) б j=∑t= j+1

nq

(Y t−Y t−1−u)2(X t−Y t− j−u)

2

[∑t=1

nq

(Y t−Y t−1−❑u)2]2

Xnqis the last observation ofthe time series of data. X0 is the first observation and there are nq + 1 total observations. It has become customary to examine the VRs for several holdingperiods, and the verdict of non-random walk is proclaimed when one of theestimated VR statistics is significantly different from unity. However, this multiplecomparison across all pre-selected holding periods can lead to over-rejection of the null hypothesis.

The standard normal test statistics used to test the null hypothesis of a martingale difference process under the assumptions of homoscedasticity, Z(q), and heteroscedasticity, Z(q*), respectively are calculated using equations 16 through 20 respectively.

(16) Z(q)=(VR (q )−1)√θq ~ N (0, 1)

(17) Z¿ (q )= (VR (Q )−1 )√θ¿ (Q )

N (0 ,1)

Where



(18) θ (q )=2 (2q−1 )(q−1)

3q(nq)

(19)θ¿ (q )=∑j=1

q−1 [2 (q− j )q ]

2

б ( j )

(20) б j=∑t= j+1

nq

(Y t−Y t−1−u)2(X t−Y t− j−u)

2

[∑t=1

nq

(Y t−Y t−1−❑u)2]2

5. Variance Ratio (VR) Tests Generation 2: Chow- Denning VR Test 1993 The multiplecomparison of VR across all pre-selected holding periods has been found to result in type 1 errors; that is, the over-rejection of the null hypothesis that the returns series follows a martingale difference process. Chow and Denning’s extension of the Lo – MacKinlay VR methodology solves this problem by using the Lo-MacKinlay test statistics as given in equations (16) and (17) as the studentized maximum modulus (SMM) statisticsfor a number of lags set equal to the number of observations minus 1. Rejecting the null hypothesis that the process is a martingale difference process for any lag length leads to the rejection of it for all lag lengths. The values of the test statistics are given by equations (21) and (22).

(21) Z1≤i≤ L

1(q)=Max|Z (q i)|

(22) Z1≤i≤ L

z(q)=Max|Z ¿(qi)|

Where Z(qi) and Z*(qi) are defined in equations (16) and (17).

6. Variance Ratio (VR) Tests, continued Generation 3: Wright Rank and Sign VR Test(2000)A notable recent innovation of theVR test includes non-parametric tests designed and developed by Wright (2000) based on signsand ranks of returns that follow exact distributions. Wright’s rank and sign VR tests are thought to be more powerful ones than those discussed above, and are more robust when the data are non-normally distributed and non-stationary.



Formally for the ranks-based tests, let r(rt)be the rank of the returns among r1, r2 ,..., rT. Then, r1t and r2tare the ranks of the returns, defined per equations 23 and 24:

(23)r1 t=(r (r−T+1

2))

√ (T−1 )(T+1)12

(24)r2 t=Ф−1(r (r 1)T +1

)

Where Ф-1 is the inverse of the standard normal cumulative distribution function.The series r1t in equation (23) is a simple linear transformation of the ranks, standardized to have a sample mean 0 and a sample variance 1. The series r2tin equation (24) known as the inverse normal orvan der Warden score has a sample mean 0 and a sample variance approximately equal to one. Wright substitutes r1t and r2t for the return (Xt – Xt-q) in the definition of the Lo-MacKinlay variance ratio test statistic Z(q) in equation (16) above, giving his test statistics R1 and R2 (not shown here).

By using the signs of the differences instead of the ranks, Wright demonstrates that it may be possible to apply a variance ratio test that is exactin case of conditional heteroscedasticity. Hence u (rt, 0) is0.5 if rt is positive and -0.5 otherwise. Let St = 2u(rt, 0) = 2u(εt,o). Clearly, st is an i.i.d. series with zero mean and variance equal to one. Each st is equal to 1with a probability 0.5 and is equal to -1 otherwise. The test statistic based on signs is S1 (not shown here).In Monte Carlo experiments and empirical tests, Wrightshowed that this test could be exact and more powerful than other VR tests under both homoscedastic andheteroscedastic conditions.

7. Rolling Variance Ratio Tests As previously noted, Grossman and Stiglitz seminal paper on market efficiency and Lo’s pathbreaking Adaptive Markets Hypothesis imply that market efficiency may be time varying. Technological advances, changing regulatory frameworks, introduction of electronic trading systems, learning over time by market participants, and structural changes in the price setting process can all cause return predictability to evolve through time. Indeed, in frontier markets which are newer and as a result smaller, less liquid and more thinly traded we might expect, a priori, that such markets will initially be highly inefficient but may evolve to become more efficient over time.



Rolling VR test, that is VR tests in rolling estimation windows of set lengths, can capture the persistence of equity market return departures from the martingale difference benchmark over time. Moreover, the time varying framework of rolling VR tests let the data detect such things as structural breaks where market efficiency has either improved or diminished, and then researchers can proceed to identify the associated events. Additionally, the rolling VR approach permits examinations of relative market efficiency where efficiency may be compared across markets. This approach, in turn can be used to assess factors which have and have not contributed to improved market efficiency.

IV. Overview of the Three Frontier Markets: Barbados, Jamaica and Trinidad and Tobago

As noted in the introductory section our research focuses on Frontier equity markets in Barbados, Jamaica and Trinidad and Tobago for four reasons. The fourth reason was that all three nations have been members of CARICOM since its inception – a point meriting additional discussion.

CARICOM, an acronym for Caribbean Community, was preceded by the Caribbean Free Trade Association (CARIFTA). CARICOM was first established in 1973 and substantially revised between 1993 and 2000 to form the CARICOM Single Market and Economy. CARICOMs common trade policy and harmonization of laws have allowed for the free movements of capital, labor, goods and services, products, and rights of establishment.

We would expect that, owing to CARICOM there should be scant artificial barriers affecting equity investment flows (trading, listing of securities, IPOs, etc.) across and between the three equity exchanges that would affect pricing across borders.6The CARICOM Single Market Economy clearly intends to foster economic growth and our tests for market efficiency will help determine if equity markets have either supported or hindered this goal.

BarbadosThe Barbados Stock Exchange (BSE) is a non-profit association of member broker/dealers. Originally established in 1987 as the Securities Exchange of Barbados, the organization was reincorporated and renamed in 2001 concurrent with the Securities Act of 2001 and a month after the exchange transitioned from the manual open auction outcry method to an electronic trading system (BSE, 2012). 6This provides an additional factor for why the three countries provide a unique and effective sample of frontier markets for analysis.



The Barbados Central Securities Depository Inc. (BCSDI) manages clearing and settlement of trades, is a subsidiary of the BSE, and like its parent company, is a self-regulatory organization that is monitored by the Securities Commission. Since inception, the market is open and trading has occurred three days per week.

JamaicaThe Jamaica Stock Exchange (JSE) was incorporated as a private limited company in 1968 and officially opened on February 3, 1969 to become the first equity market in the CARICOM region (JSE, 2012). The JSE is a self-regulated exchange made up of independent directors and member broker/dealers, but it is, however, overseen by the Financial Services Commission (FSC). Since 2000, the Exchange has had an electronically automated trading system with back office operations handled by the Jamaica Central Securities Depository Ltd. (JCSD) (JSE, 2012).

Trinidad and TobagoThe Trinidad and Tobago Stock Exchange Ltd. (TTSE) formally opened on October 26, 1981 under the aegis of the Ministry of Finance and the provisions of the Securities Industry Act of 1981 (TTSE, 2012). The TTSE was the second exchange in the CARICOM region to open after the JSE.

The Securities Industry Act of 1995 replaced the original 1981 Act. A Securities and Exchange Commission (SEC) was formed to regulate the equity market. All market participants are currently required to register with the (SEC), which is charged with ensuring fair and equitable dealings in securities, while the Exchange self- regulates trading on the secondary market .

On March, 2005 the TTSE replaced the original manual outcry system with an Electronic Trading System. Beginning in April 1, 2008, trading days for the exchange were set for Monday through Friday excluding holidays (TTSE, 2012). The Trinidad and Tobago Central Depository (TTCD) is charged with operating a safe, prompt and efficient electronic clearing system (TTSE 2012). With regard to ownership structure, the TTSE is owned equally by listed companies and members of the exchange.

Data: Sources and Frequency



Daily closing values for the equity market indices for the BSE and TTSE were obtained directly from the respective exchanges, while daily closing values for the stock market index for the JSE were obtained from Bloomberg Financial.

The starting and ending dates for the daily closing values of the respective equity market indices as well as the number of observations for each market is presented in Table 3 below:

Table 3: Time periods and number of observations for TTSE, JSE and BSE equity markets

Country Start Date Finish Date # ObservationsTrinidad & Tobago 1/1/1983 12/30/2011 4369Jamaica 6/11/1987 11/25/2011 5119Barbados 1/5/1999 1/13/2012 2236

The market index data for Trinidad and Tobago is from approximately two years after the TTSE opened, when the index was recalibrated to 100, until the end of 2011. The market index data for Jamaica covers less of the market’s history as it starts about 18 years after inception. The JSE data nonetheless covers approximately 24 years of the exchange (a very substantial time period). Market index data for Barbados is from the inception of electronic tracking of the market index until the beginning of 2012.

Trading days, the number of days of the week when the markets are open for trading, have evolved over their respective histories. Table 4 indicates the number and specific week days each respective market was open from the start of our daily stock market index data for each respective frontier market until each market was opened for trading from Monday through Friday.

Table 4: The Evolution of Trading Dates on the BSE, JSE and TTSE

BSE JSEDates Trading Days Date Trading Days

1/5/1999 - 2/3/2003

Tuesday & Friday 6/11/1987 - 1/09/1990

Tuesday and Thursday

2/4/2003 2/28/2007

Tuesday, Wednesday, Friday

1/10/1990 - 10/6/1991

Tuesday, Wednesday,Thursday



3/1/2007 - present

Monday through Friday 10/7/1991 - 12/31/2000

Monday through Thursday

1/2/2001- present Monday through Friday

TTSEDate Trading Days1/1/1983 -12/31/1985

Friday

1/02/1986-3/6/1989

Monday, Wednesday, Friday

3/7/1989 - 3/31/2008

Tuesday,Wednesday,Friday

4/1/2008 - present

Monday through Friday

Sources: Barbados Stock Exchange, Jamaica Stock Exchange, Trinidad and Tobago Stock Exchange.

As can be seen in Table 4 continuous week - day trading for each market did not occur until the early 2000s.As will be discussed in the next section, statistical tests for market efficiency may be biased against efficiency in equity markets where trading is not continuous.

Table 5 below presents a number of economic and especially financial market indicators for Barbados, Jamaica and Trinidad and Tobago for 1990, 2000, and 2010. Several points stand out:

While Barbados is the wealthiest of the three nations with a purchasing power parity real per capita GDP of almost $30,000, income growth over the last twenty years has been strongest in Trinidad and Tobago. Trinidad’s compound annual growth rate of real GDP per person has been 5.4 percent, considerably above Barbados’1.9 percent and Jamaica’s 2.3 percent. Convergence may indeed be occurring in the English speaking Caribbean countries.

The TTSE, by a substantial margin, has become the largest of the three equity markets as measured by market capitalization and the total value of trades. However, both Barbados and Jamaica witnessed spikes in their respective equity markets in 2010 raising the size of



their equity market capitalizations to sizes roughly 50 percent above and equal to, respectively, their GDPs.

Despite considerable growth in all three equity markets from 1990 to 2010 the markets remain relatively illiquid and thinly traded. Barbados may be the exception here as liquidity and turnover jumped in 2010.7

In a relative sense all three markets are quite small. While the TTSE is the largest market of the three in comparison to developed markets it is extremely small. For example, compared in size to Ireland - the smallest developed market in the Morgan Stanley Capital International (MSCI) Developed Market Index (MSCI, 2012) the TTSE is less than 37 percent of its size in regards to capitalization and less than 1 percent of the largest developed market, the U.S (World Bank, 2012).

Following Table 5 Figures 1, 2 and 3 present two graphs for each frontier market. The first graph depicts the daily closing value of the stock market index for each frontier market over the period of our time series, while the second figure presents the daily return for each frontier market based on Equation (7) above. 8

Several observations are worth noting from a visual inspection of Figures 1-3:

Positive time trendsexist in the levels/values of all three frontier markets indices.This can also be seen in the data in Table 5 for the current U.S. dollar value of the three markets respective equity market capitalizations; equity market capitalizations relative to GDP; and the current dollar values of equity market trades.

Volatility clustering, that is successive time periods when the volatility of returns is either especially high or low, can be seen in the returns graphs for the three frontier markets. Clustering of risks appears especially notable in Jamaica and Trinidad and Tobago.9

Volatility clustering appears to have diminished in all three frontier markets over time.

7Market Liquidity is measured as the ratio of the Total Value of Equity Trades to GDP. Equity Market Turnover is the ratio of the Total Value of Equity Trades to Equity Market Cap.8 For the BSE and TTSE the horizontal axes in Figures 1 and 3 respectively are the observation number rather than date. For the JSE the horizontal axes in Figure 2 show the dates.9 Engle (2004) presents an informative discussion of the concept and modeling of volatility clustering.



Table 5: Selected Economic and Financial Market Indicators for Barbados, Jamaica and Trinidad and Tobago. 1990, 2000, 2010.

COUNTRY

Trinidad &

Barbados Jamaica Tobago__

PPP RGDP/Capita ($ US)1990 $20,289 $6,354 $9,091

2000 $27,487 $7,903 $13,549

2010 $29,736 $9,989 $25,883

Equity Market Cap ($ US B)1990 $0.282B $0.911B

$o.696B2000 $1.690B $3.582B $4.330B2010 $4.366B $6.626B $12.158B

Equity Market Cap/GDP (%)



1990 16.50% 19.80%13.70% 2000 66.00%39.80% 53.10%

2010 136.00% 47.30%60.00%

Total Value Equity Trades ($ US millions) 1990 $10.00M $32.00M $55.00M

2000 $6.48M $75,62M $135.80M2010 $16.00M $211.00M $136.00M

Market Liquidity (%)1990 0.6% o.7% 1.1%2000 0.3% 0.8% 1.7%

2010 0.5% 1.5% 0.7%

Equity Market Turnover (%)1990 0.3% 3.4% 9.9%2000 0.4% 2.5% 3.1%2010 0.4% 3.3% 1.2%

Number of Listed Domestic Firms

1990 14 44 302000 17 46 27

2010 20 39 37

Sources: The World Bank. www.worldbank.org/programs/finance Accessed August 14, 2013 Penn World Tables. www.pwt.econ.upenn.edu Accessed August 14, 2013

Figure 1: Daily Closing Values and Daily Returns of the Barbados Stock Exchange Index, January 1999 – January 2012

BSE Daily Closing Value


http://www.pwt.econ.upenn.edu/

http://www.worldbank.org/programs/finance


1,500

2,000

2,500

3,000

3,500

4,000

4,500

250 500 750 1000 1250 1500 1750 2000

A_INDEX_VALUE_GRAPH

BSE Daily Return

BSE Daily Return

Figure 2: Daily Closing Values and Daily Returns of the Jamaica Stock Exchange Index, June, 1987 – November, 2011

JSE Daily Closing Value


-.3

-.2

-.1

.0

.1

.2

.3

500 1000 1500 2000

Daily Return


JSE Daily Return

Figure3: Daily Closing Values and Daily Returns of the Trinidad and Tobago Stock Exchange Index, January, 1983 – December, 2011

TTSE Daily Closing Value

Trinidad


0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

90 95 00 05 10

A_INDEX_VALUE_GRAPH

-.15

-.10

-.05

.00

.05

.10

.15

88 90 92 94 96 98 00 02 04 06 08 10

Daily Return

0

200

400

600

800

1,000

1,200

1,400

500 1000 1500 2000 2500 3000 3500 4000

A_INDEX_VALUE_GRAPH


TTSE Daily Return

Table 6 depicts the distributions of returns for the three Caribbean equity markets. Several noteworthy facts stand out:


-.08

-.06

-.04

-.02

.00

.02

.04

.06

.08

1000 2000 3000 4000

Daily Return


Unpredictable returns. In absolute value mean daily returns per trading day in all three frontier markets are essentially zero. Assuming a year has 250 trading days annualized returns are approximately 1.7 percent, 19.5 percent, and 13.3 percent in Barbados, Jamaica and Trinidad and Tobago.

Relative to their standard deviations the mean daily returns per trading day on the TTSE and JSE are approximately 9.5 and 6.7 percent, respectively. For the BSE the ratio of mean return to standard deviation is about 0.7 percent.

The standard deviation of returns, the typical measure of risk, is highest on the JSE followed by the TTSE and then the BSE. Indeed risk per trading day return on the JSE is roughly one hundred percent (twice) that on the TTSE and about 24 percent higher than on the BSE. Annualized standard deviations, assuming again a year has 250 trading days, are 18.4% for the JSE, 14.9% for the BSE and 8.9% for the TTSE.

Returns are positively skewed on the BSE, while they are small on the JSE and TTSE. The positive skewness on the BSE indicates more daily returns lie above the mean daily return than if the return distribution was normal. The positive skewness also implies that the standard deviation of returns over-states the actual risk in the BSE.

The kurtosis statistics, which measure the magnitude of the extreme returns, clearly show that returns in all three markets exhibit “fat tails,” that is periods of boom and bust. Moreover, if returns are normally distributed then the kurtosis statistics should be three. One can see in Table 6 kurtosis statistics many magnitudes larger than three for each of the frontier equity markets. The kurtosis statistic is a whopping 323 for Barbados, 32 for Trinidad and 18 for Jamaica. Moreover, the absolute values of the sums of the maximum and minimum daily returns are 45 percent for the BSE, 23 percent for the JSE and 14 percent for the TTSE.

The Jarque-Berra statistics for each of the three frontier equity markets offer additional confirmation that returns are not normally distributed in any of the three markets. The Jarque-Berra statistics suggest daily returns on the BSE are least normally distributed followed by the TTSE and then the JSE.

Return correlations among the three Caribbean frontier equity markets and the U.S. equity market as represented by the S&P 1500 were calculated for the period from the first quarter, 1999 through the third quarter, 2011. The positive signs of all the correlations



indicate returns in all markets co- move together with the closest co-movements of returns, based on the size of the correlation coefficients, existing between the TTSE and the other two Caribbean markets. The correlations between the TTSE , JSE and BSE are sizable and solid at 75 and 56 percent, respectively, while the correlation between the JSE and BSE is a more modest 32 percent. Common factors may be more prevalent and important between and among Trinidad and Tobago and Jamaica than either nation – especially – Jamaica shares with Barbados. Finally, return correlations betweenall three Caribbean frontier equity markets and a broad index of the U.S. equity market are small, with perhaps the exception of the JSE and S&P 1500.

Table 6: Descriptive Statistics for BSE, JSE and TTSE10

Market BSE JSE TTSE

Statistic

Number of Daily Return Observations 2237 5120 4369

Mean Return 6.75e-05 0.000780.00053

Median Return 0.00033 0.674e-05 0.00021

Maximum Return 0.2397 0.10850.0599

Minimum Return -0.2094 -0.1245 -0.0760

Standard Deviation 0.0094 0.011640.0056

Skewness 3.5918 0.88124 -0.3857

Kurtosis 323.0128 18.30731.731

Jarque-Berra 9550108 50648150378

Return Correlations

10 All the descriptive statistics above as well as the statistical tests reported in Section 5 were performed using E-Views software, versions 5 and 7.



TTSE JSE BSE S&P 1500

TSE 1JSE 0.74641

21

BSE 0.563432

0.320489

1

S&P 0.214907

0.303909

0.122637

1

V. Results of Tests for Market Efficiency

The results of the seven separate empirical tests for weak form market efficiency for each of the three Caribbean frontier equity markets are reported in this section. Ex ante we should expect the evidence to be inconsistent with weak form efficiency - especially during the earlier years when these markets were in their respective infancies.

Recall from Tables 3 and 4 that our data on daily closing values of the respective stock markets starts as long ago as 1983 (TTSE) and as recently as 1999 (BSE), while the market openings date from 1969 (Jamaica) to 1987 (Barbados). In all three frontier equity markets we should expect that the near instantaneous, low cost access to reliable information on factors necessary to determine if prices are efficient as well as the market and institutional structures necessary and sufficient to support efficiency would not be adequately present in these markets nascent years. The resources economic profit seeking investors require to drive markets towards competitive equilibrium evolve over time, and likely depend on, among other things, the size of the markets and associated economic profits. The implication, also supported by Lo’s Adaptive Market Hypothesis, is that we should look for evidence that market efficiency is improving over time.

The discussion in the previous section also alludes to potential structural breaks in each market – such as adding to the number of days when the equity markets are open and trading - that could, in concept, change the respective degrees of market efficiency. However, as discussed earlier we follow the approach of letting the data detect such things as structural breaks where market efficiency has either improved or diminished.

Test 1: Return AutocorrelationsTable 7 presents the autocorrelations of returns for each of the three equity markets. Autocorrelations are presented for each market for up to eighteen successive trading days.

As can be seen in Table 7 return autocorrelations are statistically significant at the 1 percent level for each market for at least eighteen successive



trading days. Moreover, most of the autocorrelations carry a negative sign – indicating mean reversion in equity returns for each of the three frontier markets.

The statistically significant return autocorrelations are inconsistent with market efficiency as they imply returns do not follow a martingale difference process. Returns on current trading days are related to prior trading days returns. Additionally, as can be seen at the bottom of Table 7 the absolute sum of the eighteen return autocorrelations is smallest for the TTSE and largest for the BSE, suggesting the TTSE is (relatively) less inefficient than either the JSE or BSE.

Test 2: Augmented Dickey-Fuller Test for Unit RootsTable 8 illustrates the results of the Augmented Dickey-Fuller tests for each of the three Frontier equity markets. Though the number of estimated lagged returns varies from sixteen in the TSSE to twenty-two for the BSE they all tell the same story; namely that no unit root exist in the return series of the respective markets, the coefficients on the lagged return and changes in lagged returns are all statistically significant at the 1 percent level and we can reject the null hypothesis that the return series in either any or all of the Frontier markets under study follow a martingale difference process. None of either the constants or time trends terms are statistically significant. As was the case with the return autocorrelations tests the absolute sum of the coefficients is smallest for the TTSE and largest for the BSE, again suggesting the TTSE is (relatively) less inefficient than either the JSE or BSE.

Test 3: Runs TestTable 9 presents the results of the Runs Test for the three Frontier equity markets. The negative Z- values for all of the markets indicates that the actual number of runs is less than the expected number under the null hypothesis of return independence at the 1 percent level of significance. In other words the fewer number of runs than expected if runs were randomly distributed shows persistence, which is positive serial correlation, in returns and is inconsistent with the efficient markets hypothesis.

However, unlike the previous two tests the runs test suggest that the TTSE is relatively less efficient in terms of the persistence of the sign and number of returns than either the JSE or BSE. On the TTSE the number of runs is approximately 36 percent less than the number expected if runs were randomly distributed, while the corresponding figures are 23 percent and 11 percent, respectively, for the JSE and BSE.



Test 4: Lo-MacKinlay Variance Ratio TestTable 10 gives the results of the multiple variance ratio tests of returns for each of the three Frontier equity markets. The sampling intervals for all the markets are 2, 5, 10, and 20 days corresponding roughly to one-day, one week, two week and one month calendar periods of trading days when markets are open and trading occurs five days per week.

For each interval Table 10 presents the estimated variance ratio under the null hypothesis of heteroskedastic Z*(q) martingale difference process. An inspection of the data in Table 10 shows that all of the variance ratios at all of the intervals for all of the markets are statistically significantly different at the 1 percent level from 1. That is, the sampling interval does affect the variances of the returns and, by implication, the returns themselves. Again, this evidence is not consistent with the efficient markets hypothesis. Moreover, the Z(q) statistics for all markets for all sampling intervals are negative indicating, as was the case with the return autocorrelations and the one-period lagged return term in the Augmented Dickey Fuller regression, that return processes are mean reverting ones.

Additionally, Lo and MacKinlay (1988) also show that for Q=2 the estimated Variance Ratio minus one (VR -1) should equal the first-order return autocorrelation. If this is the case then the two tests reinforce conclusions about the presence or absence of market efficiency. For the three Caribbean Frontier equity markets the Variance Ratios for Q=2 from Table 10 and the one day lagged autocorrelation coefficients from Table 7 are presented below:

Market VR -1 One day lagged autocorrelationTrinidad -0.40 -0.40Jamaica -0,32 -0.32Barbados -0.49 -0.49

The data above demonstrate that the implications of the Return Autocorrelations test and Lo-Mackinlay tests are indeed reinforcing - specifically that the evidence does not support weak form market efficiency for any of the three Frontier Caribbean equity markets.

Finally, the magnitudes of the variance ratios relative to one for each market over different sampling periods do not appear to provide any information about the relative efficiency of the three Caribbean equity markets.

Test 5: Chow – Denning Multiple Variance Ratio TestTable 11 reports test statistics based on the Chow-Denning advances to the Lo-Mackinlay multiple variance ratio test. Recall from the discussion in Section III that the Chow – Denning test is designed to correct for the



potential problem of over rejection of the null hypothesis that return series follow a martingale difference process in the LO-MacKinlay version of the test. Chow – Denning also offer the innovation thatrejecting the null hypothesis that the process is a martingale difference process for any lag length leads to the rejection of it for all lag lengths.

The Z(q) statistics reported in Table 11 are significant at the 1 percent level for the TTSE and JSE and at the 5 percent level for the BSE. The Chow – Denning statistics reject the null hypothesis of a martingale difference process and market efficiency at Q = 5 for the TTSE and JSE and at Q = 2 for the BSE.

Test 6: Wright Rank and Sign Variance Ratio TestThe Wright rank and sign based variance ratio tests are, as discussed in Section III, considered to be the most robust and powerful of all such tests. The test statistics for each country are presented in Table 12. They reveal the same results, with minor exceptions, as the Lo-MacKinlay and Chow-Denning variance ratio tests.

The Wright rank based tests, the R1 and R2 statistics in Table 12, are statistically significant at the 1 percent level for all sampling periods for all three Caribbean Frontier equity markets. The evidence here does not allow us to accept the null hypothesis of that return in these markets follow a martingale difference process and that the markets are weak form efficient.

The sign based test statistics tell a similar story, with a minor exception. The sign based tests provide evidence that permit rejection of the null hypothesis of returns following a martingale difference process and that weak form efficiency exists. The only exceptions are for the BSE at sampling period lags of 15 and 20 days where the null hypothesis of returns following a martingale difference process cannot be rejected at high levels of confidence.

Test 7: Rolling, Fifty Day Window Multiple Variance Ratio Tests As discussed previously more emphasis in the analysis, assessment and evaluation of the informational and allocative efficiency of Frontier markets should be placed on the evolution of their efficiency over time and on comparisons of their relative efficiency rather than all-or-none, full sample tests for efficiency. Our last of seven empirical test is designed for these purposes.

Specifically, we employ an overlapping, rolling Lo-MacKinlay type multiple variance ratio test to examine the evolution of market efficiency in our three Caribbean Frontier markets over time and to compare their relative efficiency. We use a rolling window of 50 days, assuming that overlapping



periods of fifty days should be sufficient to readily detect structural changes and/or trends in efficiency. 11 The rolling 50 day window produces 3,120 variance ratios for each sampling interval (Q= 2, 5, 10, 20 as before) for the TSE, 3,871 for the JSE and 988 for the BSE.

Figures 4, 5 and 6 show a graph of the rolling variance ratios for each of the three Caribbean, Frontier equity markets for Q = 5 and then a chart of the probability of accepting the null hypothesis that the respective return series follows a martingale difference process consistent with weak form efficiency.

Overall, the rolling multiple variance ratios indicate throughout that returns in the three Caribbean, Frontier equity markets are not consistent with weak form efficiency. There are some signs, however, of movements towards greater efficiency.

In Trinidad and Tobago, the variability of the variance ratios drops substantially after window 2977 and the probability of accepting the null hypothesis increases substantially at about the same time. In Jamaica, variance ratio variability falls considerably, but not as much as in Trinidad and Tobago, after window 2611 and the probability of accepting the null hypothesis starts to rise somewhat about this time. Spikes in the variance ratios for the BSE appear to distort any trends towards greater or lesser efficiency, In the absence of these spikes, the rolling variance ratios are more stable for Barbados than either Trinidad and Tobago or Jamaica.

VI. Conclusions and Directions for Future Research

Seven separate though obviously related tests for weak form market efficiency have been performed for the three Caribbean Frontier equity markets of Barbados, Jamaica and Trinidad and Tobago. These three countries share a number of similarities and therefore present appealing cases as a starting point for research into the allocative and informational efficiency of Frontier equity markets.

All seven tests proved inconsistent with the statistical process underlying the weak form version of the efficient markets hypothesis. Rolling variance ratio tests, however, provide a glimmer of optimism that market efficiency is gradually improving in each country. Additionally, the seven tests generally pointed toward the Trinidad and Tobago Stock Exchange being relatively more efficient than the other two.

11 Fifty days rolling windows seem popular for such tests with daily return data series, See, for example Tabak (2002), Kim and Shamsuddin (2008), and Hung (2009)



Evaluating market efficiency in these three Frontier markets in particular and all Frontier markets in general is fraught with unique challenges not found in such studies of developed and, perhaps, emerging markets. One such challenge arises from infrequent trading and stale prices as, for much of their respective lives, our three Frontier markets were open only two to three days per week. We need to adjust for the possible existence of stale prices in future research. Thin markets with low levels of liquidity present another, albeit similar, challenge.

Finally, as we have noted, these are small equity markets with small numbers of listed companies in economies whose GDPs in absolute – though not necessarily at all in per capita terms – are also small. A regional market rather than three nation-based ones may provide greater liquidity, breadth and efficiency.



Table 7: Return Autocorrelations for TTSE, JSE and BSE

Lags AC PAC Prob AC PAC Prob AC PAC Prob1 -0.4000 -0.4000 0.0 -0.3234 -0.3234 0.0 -0.4916 -0.4916 0.02 -0.0082 -0.2002 0.0 -0.0604 -0.1843 0.0 -0.0696 -0.4106 0.03 -0.0396 -0.1533 0.0 -0.0850 -0.1940 0.0 0.1246 -0.1992 0.04 -0.0489 -0.1684 0.0 -0.0134 -0.1531 0.0 -0.0621 -0.1679 0.05 0.0239 -0.1101 0.0 -0.0161 -0.1385 0.0 -0.0026 -0.1334 0.06 0.0128 -0.0630 0.0 -0.0038 -0.1244 0.0 0.0141 -0.1102 0.07 -0.0164 -0.0679 0.0 -0.0206 -0.1359 0.0 -0.0273 -0.1260 0.08 -0.0069 -0.0694 0.0 0.0064 -0.1193 0.0 0.0119 -0.1168 0.09 -0.0126 -0.0735 0.0 0.0163 -0.0926 0.0 0.0006 -0.1121 0.010 0.0025 -0.0632 0.0 0.0234 -0.0587 0.0 0.0028 -0.0927 0.011 0.0100 -0.0448 0.0 -0.0098 -0.0634 0.0 -0.0073 -0.0961 0.012 -0.0043 -0.0441 0.0 -0.0148 -0.0735 0.0 0.0150 -0.0705 0.013 -0.0078 -0.0508 0.0 -0.0178 -0.0885 0.0 0.0012 -0.0496 0.014 -0.0038 -0.0515 0.0 0.0269 -0.0507 0.0 -0.0146 -0.0555 0.015 0.0072 -0.0376 0.0 -0.0298 -0.0878 0.0 0.0047 -0.0574 0.016 0.0002 -0.0342 0.0 0.0102 -0.0763 0.0 -0.0038 -0.0664 0.017 -0.0193 -0.0597 0.0 -0.0009 -0.0750 0.0 0.0147 -0.0394 0.018 0.0070 -0.0518 0.0 0.0132 -0.0630 0.0 -0.0121 -0.0411 0.0

Absolute Sum: 0.6315 1.7436 0.6923 2.1026 0.8808 2.4367

Jamaica BarbadosTrinidad and Tobago

Auto-Correlations



Table 8: Augmented Dickey – Fuller Test for Unit Root in TTSE, JSE and BSE Return Series

Trinidad and Tobago Jamaica Barbados Coefficient T-Stat Prob Coefficient T-Stat Prob Coefficient T-Stat Prob

Lags 0 -4.9120 -24.6932 0.0000 -7.4702 -29.3056 0.0000 -9.0996 -13.8809 0.00001 3.2969 16.9856 0.0000 5.8869 23.5689 0.0000 7.1820 11.0504 0.00002 2.8611 15.3097 0.0000 5.3758 22.1971 0.0000 6.3144 9.8925 0.00003 2.4766 13.8981 0.0000 4.8431 20.8061 0.0000 5.6188 9.0392 0.00004 2.1157 12.5628 0.0000 4.3390 19.5735 0.0000 4.9561 8.2441 0.00005 1.8311 11.6109 0.0000 3.8523 18.4070 0.0000 4.3269 7.4897 0.00006 1.5927 10.8870 0.0000 3.3861 17.3077 0.0000 3.7257 6.7551 0.00007 1.3612 10.1355 0.0000 2.9332 16.1957 0.0000 3.1383 6.0018 0.00008 1.1441 9.3897 0.0000 2.5202 15.1982 0.0000 2.5961 5.2755 0.00009 0.9466 8.6773 0.0000 2.1531 14.3617 0.0000 2.0987 4.5676 0.0000

10 0.7786 8.1046 0.0000 1.8257 13.6762 0.0000 1.6617 3.9069 0.000111 0.6326 7.6377 0.0000 1.5082 12.9068 0.0000 1.2806 3.2849 0.001012 0.4879 7.0516 0.0000 1.2018 11.9855 0.0000 0.9633 2.7262 0.006513 0.3469 6.2697 0.0000 0.9176 10.9179 0.0000 0.6937 2.1930 0.028414 0.2268 5.4315 0.0000 0.6871 10.0644 0.0000 0.4509 1.6152 0.106415 0.1367 4.8145 0.0000 0.4612 8.6643 0.0000 0.2478 1.0224 0.306716 0.0623 4.1491 0.0000 0.2834 7.2578 0.0000 0.0805 0.3904 0.696317 0.1459 5.5859 0.0000 -0.0363 -0.2120 0.832218 0.0526 3.7556 0.0002 -0.1283 -0.9312 0.351819 -0.1906 -1.8039 0.071420 -0.1699 -2.2591 0.024021 -0.0855 -1.8523 0.064122 0.0644 3.0224 0.0025

Constant 0.0000 0.0458 0.9635 0.0000 0.0825 0.9342 0.0000 0.0737 0.9412@ Trend 0.0000 -0.0254 0.9797 0.0000 -0.0807 0.9357 0.0000 -0.0777 0.9380

Absolute

Sum: 25.2100 49.8435 55.1101

Table 9: Runs Test for TTSE, JSE and BSE



Trinidad and Tobago Jamaica BarbadosNumber of observations 4369 5120 2237

Number above mean 1865 2281 730Number below mean 2504 2839 1507

Number of runs 1372 1945 872

E(R) 2138.77 2530.59 984.56Stdev(R) 32.34 35.35 20.79

Z-value -23.71 -16.57 -5.41p-value (2-tailed) 0.00 0.00 0.00

% of E(R): 64.1% 76.9% 88.6%

Runs Test



Table 10: Lo-MacKinlay Variance Ratio Test for Q = 2, 5, 10, 20 lags

Q = Var. Ratio Z-Stat Prob Var. Ratio Z-Stat Prob Var. Ratio Z-Stat Prob2 0.5983 -4.6241 0.0000 0.6767 -8.7209 0.0000 0.5087 -2.5131 0.01205 0.2925 -4.8266 0.0000 0.3369 -9.4335 0.0000 0.2052 -2.4221 0.015410 0.1666 -4.8210 0.0000 0.1606 -8.8893 0.0000 0.1014 -2.3126 0.020720 0.0863 -4.7218 0.0000 0.0789 -7.6585 0.0000 0.0511 -2.2399 0.0251

Trinidad and Tobago Jamaica Barbados

Table 11: Chow-Denning Variance Ratio Test (Q= 2, 5, 10, 20 lags)

Z-Stat Prob Z-Stat Prob Z-Stat ProbMax Z (Chow & Denning) 4.8266 0.0000 9.4335 0.0000 2.5131 0.0470

Jamaica BarbadosTrinidad and Tobago

Max Z at Q = 5 for TTSE and JSE and Q= 2 for BSE.



Table 12: Wright Rank and Sign Variance Ratio Test for Q = 2, 5, 10, 20 lags

-----------------------------------------------------------------------------------------------------------------------------Number of Lags (Q)

__________________________________________________

Trinidad and Tobago Q=2 Q=5 Q=10 Q=20

R1 o.635* 0.383* 0.278*0.208*

R2 0.627* 0.347* 0.228*0.149*

S1 0.744* 0.568* 0.501*0.506*

*Significant at 1% level

______________________________________________________________________

Jamaica Q=2 Q=5 Q=10 Q=20

R1 0.504* 0.394* 0.246*0.186*

R2 0.652* 0,361* 0.195*0.122*

S1 0.711* 0.542* 0.450*0.424*


________________________________________________________________________

Barbados Q=2 Q=5 Q=10 Q=20

R1 0.557* 0.319* 0.224*0.196*

R2 0.527* 0.279 0.179*0.141*



S1 0.789* 0.736* 0.8671.189


Figure 4: Rolling 50 Day Window MVR Test for TSE. 1 – Probability of Accepting Null Hypothesis

Rolling 50 Day Variance Ratios for TSE (Q=5)


0

0.2

0.4

0.6

0.8

1

1.2

R1R1

25R2

49R3

73R4

97R6

21R7

45R8

69R9

93R1

117

R124

1R1

365

R148

9R1

613

R173

7R1

861

R198

5R2

109

R223

3R2

357

R248

1R2

605

R272

9R2

853

R297

7R3

101

R322

5R3

349

R347

3R3

597

R372

1R3

845

R396

9R4

093

R421

7


0

0.5

1

1.5

2

2.5

3

R1R1

25R2

49R3

73R4

97R6

21R7

45R8

69R9

93R1

117

R124

1R1

365

R148

9R1

613

R173

7R1

861

R198

5R2

109

R223

3R2

357

R248

1R2

605

R272

9R2

853

R297

7R3

101

R322

5R3

349

R347

3R3

597

R372

1R3

845

R396

9R4

093

R421

7

Figure 5: Rolling 50 Day Window MVR Test for JSE. 1 – Probability of Accepting Null Hypothesis

0

0.2

0.4

0.6

0.8

1

1.2

R1R1

46R2

91R4

36R5

81R7

26R8

71R1

016

R116

1R1

306

R145

1R1

596

R174

1R1

886

R203

1R2

176

R232

1R2

466

R261

1R2

756

R290

1R3

046

R319

1R3

336

R348

1R3

626

R377

1R3

916

R406

1R4

206

R435

1R4

496

R464

1R4

786

R493

1

Rolling 50 Day Variance Ratios for JSE (Q=5)



0

0.5

1

1.5

2

2.5

R1R1

46R2

91R4

36R5

81R7

26R8

71R1

016

R116

1R1

306

R145

1R1

596

R174

1R1

886

R203

1R2

176

R232

1R2

466

R261

1R2

756

R290

1R3

046

R319

1R3

336

R348

1R3

626

R377

1R3

916

R406

1R4

206

R435

1R4

496

R464

1R4

786

R493

1

Figure 6: Rolling 50 Day Window MVR Test for BSE. 1 – Probability of Accepting Null Hypothesis

0

0.2

0.4

0.6

0.8

1

1.2

R1 R62

R123

R184

R245

R306

R367

R428

R489

R550

R611

R672

R733

R794

R855

R916

R977

R103

8R1

099

R116

0R1

221

R128

2R1

343

R140

4R1

465

R152

6R1

587

R164

8R1

709

R177

0R1

831

R189

2R1

953

R201

4R2

075

R213

6

Rolling 50 Day Variance Ratios for BSE (Q=5)



REFERENCES

Akash, R.S.I., Hamid, K. Shah, S.Z.A., and Suleman, T.M. (2010) Testing the Weak Form of Efficient Markets Hypothesis: Empirical Evidence from Asia-Pacific Markets. International Research Journal of Finance and Economics.58, January, 2010, 121- 133

Barnett, W.A. and Serletis, A. (2000) Martingales, nonlinerity, and chaos. Journal of Economic Dynamics and Control 24: 703-724.

Basu, P., Kawakatsu, H. and Morey, M.R. (2000) Liberalization and stock prices in emerging markets. Emerging Markets Quarterly 4(3): 7-17

Bekaert, G., & Harvey, C. (1997). Capital Markets: An Engine for Economic Growth. Duke University Working Paper, 1, 1-18.



Berger, Dave, Kuntara Pukthuanthong, and J. Jimmy Yang. 2011. “International Diversification with Frontier Markets.” Journal of Financial Economics

Black, F. (1986) Noise. Journal of Finance 41: 529-543

Blake, A.P. and Kapetanios, G. (2007) Testing for ARCH in the presence of nonlinearity of unknown for in the conditional mean. Journal of Econometrics 137 : 472-488

Bodie, Z., Kane, A., & Marcus, A.J. (2011). The Efficient Market Hypothesis. Essentials of Investments (Eighth ed., pp. 228-259). New York: McGraw-Hill Irwin.

Box. G.E.P. and Jenkinds, G.M. (1970) Times and Series Analysis, Forecasting and Control. San Francisco, CA: Holden-Day.

Brooks, R. and Lim, Kian-Ping. (2011) The Evolution of Stock Market Efficiency Over Time: A Survey of the Empirical Literature. Journal of Economic Literature 25 (1): 69-108

Campbell, J.Y. (1991). A Variance Decompositionfor Stock Returns. The Economic Journal. 101(405): 157-179

Campbell, J.Y., Lo, A. W. and MacKinlay, A.C. (1997) The Econometrics of Financial Market. Princeton, NJ: Princeton University Press.

CARICOM. (2012). The Caribbean Community. Caribbean Community (CARICOM) Secretariat. Retrieved April 8, 2012, from http://www.caricom.org/jsp/community/community_index.jsp? menu=community

Chen, L. (2008). Variance Ratio Tests Of Random Walk Hypothesis Of The Euro Exchange Rate. International Business and Economics Journal. 7(12): 97 - 105



Fama, E.F. (1965) The behavior of stock-market prices. Journal of Business 38: 34-105

Fama, E.F. (1970) Efficient capital markets: a review of theory and empirical work. Journal of Finance 25: 383-417

Fama, E.F. (1991) Efficient capital markets: II. Journal of Finance 46: 1575-1617

Fama, E.F. (1998) Market efficiency, long-term returns, and behavioral finance. Journal of Financial Economics 49: 283-306

Financial Times. (2012). Cross Listing. Financial Times Lexicon. Retrieved March 31, 2012, from http://lexicon.ft.com/Term?term=cross-listing

FTSE Frontier Markets. (2012). FTSE Frontier 50 Index. Retrieved August 11, 2012,


Griffin, J., Kelly, P., & Nardari, F. (2006). Measuring Short-Term International Stock Market Efficiency. Working Paper, 1, 1-59.

Grossman, S.J. and Stiglitz, J.E. (1980) On the impossibility of Informationally efficient markets. American Economic Review 70: 393-408

Gu, A.Y. and Finnerty, J. (2002) The evolution of market efficiency: 103 years daily data of the Dow. Review of Quantitative Finance and Accounting 18: 219-237

Hargis, K. (1999). International Cross-Listing and Stock Market Development in Emerging Economies. International Review of Economics and Finance, 9, 101-122.

Hinich, M.J. and Patterson, D.M.(1985) Evidence of nonlinearity in daily stock returns. Journal of Business and Economics Statistics 3: 69-77



http://lexicon.ft.com/Term?term=cross-listing


Islaom, K.N. Pro-Cyclicality of Consumer Spending and the Financial Crisis of Thailand. The Journal of Developing Areas. 38(2): 41-54

Islam, S., Sethapong, W., & Clark, C. (2007). Are Emerging Financial Markets Efficient? Some Evidence from the Models of the Thai Stock Market. Journal of Emerging Market Finance, 6(3), 291-302.

Ito, M. and Sugiyama, S. (2009) Measuring the degree of time varying market inefficiency. Economic Letters 103: 62-64

JSE. (2012). About Us. JSE : Jamaica Stock Exchange. Retrieved April 4, 2012, from http://www.jamstockex.com/controller.php?action=about_exchange

King, R., & Levine, R. (1993). Finance and Growth: Schumpeter Might be Right. The Quarterly Journal of Economics, 108(3), 717-737. Retrieved April 8, 2012, from the JSTOR database.

King, M., & Segal, D. (2006). The Long-Term Effects of Cross-Listing, Investor Recognition, and Ownership Structure on Valuation. The Review of Financial Studies, 22(6), 2393-2421.

Leroy, S. F. (1989) Efficient Capital Markets and Martingales. Journal of Economic Literature. 27 (4): 1583-1621

Levine, R., & Zervos, S. (1998). Stock Markets, Banks, and Economic Growth. The American Economic Review, 88(3), 537-558. Retrieved June 4, 2012, from the JSTOR database.

Lim, K. (2011). The Evolution of Stock Market Efficiency Over Time: A Survey of the Empirical Literature. Journal of Economic Surveys. 25(1): 69-108

Lo, A.W. (2005) Reconciling efficient markets with behavioral finance: the adaptive markets hypothesis. Journal of Investment Consulting 7(2): 21-44

Lo, A.W. and MacKinlay, A.C. (1988) Stock market prices do not follow random



walks: evidence from a simple specification test. Review of Financial Studies 1: 41-66.

Lo, A.W. and MacKinlay, A.C. (1999) A Non-Random Walk Down Wall Street. Princeton, NJ: Princeton University Press.

Lock, D. B. (2007). The Taiwan Stock Market Does Follow a Random Walk. Econometric Bulletin - Feng Chia University, 7(3), 1-8.

Malkiel, B.G. (2003) The efficient market hypothesis and its critics. Journal of Economic Perspectives 17: 59-82.

Malkiel, B.G., Mullainathan, S. and Stangle, B. (2005) Market efficiency verses behavioral finance. Journal of Applied Corporate Finance 17(3): 124-136.

MSCI. (2012). MSCI Developed Markets Indices. MSCI. Retrieved April 7, 2012, from http://www.msci.com/products/indices/country_and_regional/dm/

MSCI Emerging. (2012). MSCI Frontier Markets Indices. MSCI. Retrieved April 1, 2012, from http://www.msci.com/products/indices/country_and_regional/fm/performance.html

Russell Investments. (2012).Russell Frontier Indices. RFI. Retrieved August 11, 2012, from http://www.russell.com/indexes/data/Frontier/russell_frontier_indexes.asp

S&P Emerging Market. (2011). S&P Global BMI. S&P Indices, 1, 1-5.

S&P Frontier BMI. (2011). S&P Frontier BMI. S&P Indices, 1, 1-2. Retrieved April 5, 2012, from https://www.spindexdata.com/idpfiles/emdb/prc/active/factsheets/Factsheet_SP_Frontier_BMI.pdf

Shiller, J.R. (2003). From Efficient Market Theory to Behavioral Finance. Journal of Economic Perspectives 17(1): 83-104




http://www.russell.com/indexes/data/Frontier/russell_frontier_indexes.asp




Speidell, L. (2011). Frontier Market Equity Investing: Finding Winners of the Future. Research Foundation of CFA Institute. Retrieved April 9, 2012 from

http://www.cfainstitute.org/learning/products/publications/rf/Pages/rf.v2011.n2.1.aspx

Tabak, B.M. (2003) The random walk hypothesis and the behavior of foreign capital portfolio flows: the Brazilian stock market case. Applied Financial Economics 13: 369-378.

TTSE. (2012). About Trinidad and Tobago Stock Exchange. The Trinidad and Tobago Stock Exchange. Retrieved April 5, 2012, from http://www.stockex.co.tt/index.php

World Bank. (2012). World Databank. Databank. Retrieved April 6, 2012, from http://databank.worldbank.org/ddp/home.do

Worthington, A., & Higgs, H. (2003). Tests of Random Walks and Market Efficiency in Latin American Stock Markets: An Empirical Note2003. School of Economics and Finance Discussion Papers and Working Papers - Queensland University of Technology, 157, 1-12.

Wright, J.H. (2000) Alternative variance-ratio tests using ranks and signs. Journal of Business and Economics Statistics 18: 1-9




evaluating the efficiency of frontier equity markets in ... o. morrell, sean... · web...

Documents