1.1 Background of Research
For over 30 years academics and practitioners have been debating the merits of the CAPM, focusing on whether beta is an appropriate measure of risk (Estrada 2002). A crucial input parameter for using the model is the equity risk premium, the return earned by a broad market index in excess of that earned by a relative risk-free security (Mehra and Prescott 2008).
Equity risk premiums are a central component of every risk and return model in finance and are a key input into estimating cost of equity and capital in both corporate finance and valuation. The equity risk premium reflects fundamental judgments about how much risk we see in a economy/market and what price we attach to that risk. Particularly, it affects the expected return on every risky investment and the value that we estimate for that investment (Damodaran 2009). Given their importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice (Damodaran 2009). The term “equity risk premium puzzle” coined by Mehra and Prescott (1985) originally referred to the inability of standard neoclassical economic theory to reconcile the historically large realized premium of stock market return over the risk-free rate, with its low covariability with aggregate consumption growth (Constantinides 2008). Particularly, Mehra and Prescott (1985) showed that historical equity premium in the U.S. with risk-free Treasury bills was much larger than could be justified as a risk premium on the basis of standard theory (6.2% compare to 0.35%) (Dimson et al. 2008).
However, there is little agreement among practitioners or academics about how best to measure ERP, and the estimate results end up with can vary a lot depending on the approach that is taken (Soenen and Johnson 2008). This is especially true when estimating the ERP in emerging markets (EMs), where expected returns are widely understood to be affected by variables other than those specified by the CAPM such as country-specific political, economic and financial risk factors (Soenen and Johson 2008). Moreover, emerging markets are also known with high expected returns and high volatile, low correlations of equity returns with developed countries and the world market; and thus emerging market returns are influenced by local rather than global information variables (Harvey 1995). Furthermore, there is little attention paid on equity risk premium estimates in emerging markets (Aggarwal and Goodell 2008) while these markets are becoming more importance participants in the world market. In order to estimate ERP in such developing countries, different approaches were exploited either on CAPM-based or dividend yield based. Yet, the latter approach is thought to be difficult to apply due to the lack and inconsistency of dividend information in these markets. Therefore, historical CAPM-based method is to be further discussed as means to estimate ERP in emerging markets.
Nonetheless, there is by now a growing literature arguing against the use of the CAPM to estimate required returns on equity in emerging markets (EMs). One of the characteristics of this model is that it measures risk by beta, which follows from an equilibrium in which investors display mean-variance behavior in which risk is assessed by the variance of returns, a questionable and restrictive measure of risk (Estrada 2002). However, the specified asset pricing model is found unable to explain the cross section of expected returns in these markets (Harvey 1995).
The semivariance of returns, a concept introduced by Markowitz (1959), is believed to be a more plausible measure of risk and can be used to generate an alternative behavioral hypothesis, an alternative measure of risk for diversified investors, an alternative pricing model (Harvey, 2000; Estrada, 2002). The model that integrated downside measures with traditional CAPM (or D-CAPM) proposed by Estrada (2000) are believed to be suitable and perform better to capture expected returns in emerging markets. The notion of the D-CAPM that put more weight on the downside fluctuations is perhaps gaining attention and acceptance among academics and practitioners as it reflect investors’ preference of upside fluctuations rather than downside one.
1.2 Reasons for choosing topic
It is reasonable to choose Equity Risk Premium and Downside CAPM as the main topic of this study. First and foremost, as discussed in the background of the research, Equity Risk Premium is believed to be the single most important contemporary issue in finance, and is the key determinant of the cost of capital (Dimson et al. 2000). However, most research on the subject has focused on the developed market, especially the US equity market and with relatively little attention paid to estimates for emerging markets (Aggarwal and Goodell 2008) while capital markets in many developing markets lately have grown to become large and important. Therefore, a study on Equity Risk Premium on emerging market is thought to partly fill the gap, especially on Vietnamese Stock Market, which is found quite new-established and rarely mentioned in previous studies. Secondly, it is the unique characteristic of such under-developed market as Vietnam that should have caught the attention of researchers; thus, there would be no reason to neglect the market.
Another reason that highly motivates studying in this topic is my main taught subject at the university. The course that I am tracking on is Finance with Risk Management; hence, choosing this topic is believed to be most suitable as I would have chances to enlarge and apply my knowledge of managing risk as well as improve skills of research. Besides, the dissertation would be helpful for my future pursuing career in corporate finance.
1.3 Research purposes and key research questions
The study aims to provide general knowledge of Equity Risk Premium in a perspective of Emerging Markets, particularly apply two suggested models on the Vietnamese Stock Market and nine stocks which are considered to be industrial representatives in Vietnam’s economy. The two models suggested in the dissertation are (i) the standard capital asset pricing model (CAPM) and (ii) the downside risk measuring model based on standard CAPM (D-CAPM for short), in order to assess the significance of asymmetric risk in Vietnam. Therefore, the two main purpose and key questions of the research are identified as follow:
The first purpose is to find out Vietnam’s Equity Risk Premium and estimate the risk premiums of nine chosen stocks using two mentioned models to answer key research questions: How many percent of Vietnam’s ex post Equity Risk Premium is calculated What are differences between risk premiums estimated by CAPM and D-CAPM of industry cross-section stocks The second purpose is using statistical methods to test the significance and efficiency of risk variables computed base on the CAPM and the D-CAPM, in order to answer the key research questions: Whether or not risk measures of these models are correlated and able to explain the cross-sectional variation of the stocks returns Which model is better in measuring risk in Vietnamese Stock Market1.4 Structure of the dissertation
The study is to be organized as follows:
Chapter 1 is an introduction which provides the research’s general background about equity risk premium as well as the use of the CAPM and D-CAPM in estimating risk in emerging markets. It sets stages for what will contain in later chapters.
Chapter 2 is literature review which discusses previous research that relevant to the topic and its objectives, which is included of four parts. The chapter will start by discuss the foundation of related body of knowledge which is the relationship between risk and return as the first part. Next, the second part will identify the matters of Equity Risk Premium in a perspective of emerging markets. The third one provide descriptions of the two models, the standard CAPM and the Downside CAPM (or D-CAPM), that are used in the later empirical analysis. Part four is a review of several statistical methods to conduct a hypothesis test.
Chapter 3 identifies the research paradigms as well as appropriate research philosophy; and based on which, proper method for conducting the research will be presented and illustrated.
Chapter 4 is an analysis of dissertation’s issue and answers to the research’s key questions. It demonstrates all the main findings and analysis. The results will be organized and formed in a system of tables, graphs along with the detailed discussion upon these calculations. This section will first provide estimate outcomes and adhered by in depth discussion. In the next part, the test on the hypothesis assumption will be conducted as well as thorough evaluations of the models efficiency will be furnished.
The last section is Chapter 5, which is a main conclusion and recommendation for a further research on the related topic. By reviewing all arguments and analysis made in previous chapter, this part will conclude the significance of integrating downside risk in the CAPM and applying it in the case of Vietnam. Besides, recommendations of using the models will be given for practisers as well as for further research.
Chapter 2: Literature review
In this chapter, a critical evaluation of the existing body of knowledge on the dissertation topic will be presented. Divided into four parts, the chapter will start with mentioning the relationship between risk and return which is the foundation of financial theories in order to, then, come up with the discussion of Equity Risk Premium issues in emerging market perspective in the second part. The third one will provide two models which are Capital Asset Pricing Model (CAPM for short) and Downside risk measures in Downside CAPM (D-CAPM for short) to estimate risk premiums in emerging markets and particularly in Vietnamese Stock market. In order to assess the efficiency and reliability of the two models, statistic testing models are established and reviewed in the last part.
2.1 Market risk – an emerging market view point
The relationship between risk and return is considered to be a fundamental idea in finance. There always is possibility of losing some or all of the original investment because of risk. Yet, the greater the amount of risk that an investor is willing to take on, the greater the potential return is expected as compensation for investors for taking on additional risk (Elton et al., 2007). However, the expected return is not the return investors believe they necessarily will earn. It is, indeed, the result of averaging across all possible outcomes or the average rate of return across possible economic scenarios E(r) (Brealey et al., 2008). The measure of risk is based on the variance of the rate of return or the standard deviation (?) (Bodie et al., 2009). Hence, risk includes not only the bad outcomes such as returns that are lower than expected (downside risk), but also good outcomes, returns that are higher than expected (upside risk).
The risk of any stock can be broken down into two parts which are unique risk that is atypical to that stock and market risk that is associated with market-wide variations. Investors can eliminate unique risk by holding a well-diversified portfolio, but they cannot eliminate market risk such as interest rate fluctuation, inflation or global economic crisis. All the risk of a fully diversified portfolio is market risk. A stock’s contribution to the risk of a fully diversified portfolio depends on its sensitivity to market changes. This sensitivity generally known as beta (?) is the main component of the Capital Asset Pricing Model (CAPM). In the model, beta is computed based on covariance of the stock and the market expected return over the variance of the market returns (Elton et al., 2007) and is thought to be useful way to assess relationship between risk and return in stock markets. As stated by Fama, 1991. E. Fama , Efficient capital markets: II. Journal of Finance 46 (1991), pp. 1575–1617. Full Text via CrossRefFama (1991), market professionals and academics still think of risk in terms of beta as long as the asset is correlated with the underlying benchmark. Yet, while the variance has traditionally been accepted among practitioners and academics as a measure of risk in financial markets, using beta to compute rate of return is very controversial (Chen and Chen, 2004) and has several problems especially in measuring risk of emerging markets as these markets do not necessarily have a strong correlation with a world market benchmark (Girard et al., 2001). Furthermore, beta and stock returns in these markets are largely found uncorrelated (Estrada, 2000) that the use of CAPM, argued by Hwang and Pedersen (2004), is not to be appropriately described. Indeed, they highlight emerging markets characteristics where “data are sparse, liquidity low, or huge price changes” (p.110). This study points out problems of CAPM when applying to emerging markets, which are the assumptions that investors have mean-variance preferences and that emerging markets are fully integrated with the world market (Hwang and Pedersen, 2004). However, this is supported by empirical evidence as beta and equity returns are far less correlated in emerging markets. Fama and French (1992) also proclaimed the lack of empirical evidence during the past three decades to support the CAPM and thus, searching for more appropriate risk measures is rising amongst economists (Chen and Chen, 2004).
Hwang and Pedersen (2004), in their study, suggested an optimal strategy for quantitative risk management and asset pricing for emerging markets that should develop a mixture of approaches depending upon the current economic, political climate and historical price movements. Jacobsen and Liu (2008) stress the difficulty of extrapolating results from developed markets to emerging market since returns in emerging capital markets are very different from developed ones. The International CAPM version is also suggested to apply to these markets as large capital inflows from industrial economies caused pricing in emerging markets to reflect covariance risk with the world portfolio.
On the other hand, the variance of returns, according to Estrada (2002), is an appropriate measure of risk and can be applied straightforwardly only when the underlying distribution of returns is symmetric and normal. Semivariance of returns is considered to be more plausible measure of risk rather than the variance when the underlying distribution of returns is asymmetric (in emerging markets). These markets are much more sensitive to differences in downside beta than to equal differences in beta (Estrada, 2000; 2001).
2.2 Equity risk premium – an emerging market perspective
As a central component of every risk and return model, equity risk premium is regarded as the most important number in finance (Dimson et al., 2000). The risk premium matters because it is essential in estimating costs of equity capital in both corporate finance and valuation (Mayfield, 2004) yet remains debated issues. From the notion of risk – return trade-off that riskier investments should have higher expected returns than safer investments, the expected return on any investment can be written as sum of the risk-free rate and a risk premium to compensate for the risk (Damodaran, 2009). The CAPM states that in a competitive market the expected risk premium on each investment is proportional to its beta. This relationship can be written as:
Expected risk premium on stock = beta x expected risk premium on market
r –rf = ?(rm – rf)
where expected risk premium on market or market risk premium is the difference between the return on the market and the interest rate (Brealey et al., 2008). On the other hand, Dimson et al. (2000) suggests taking the geometric difference between the equity return and the risk-free return as a formula to measure equity risk premium, which is:
In both ways ERP represents the price that investors demand for the average risk investment. When equity risk premium rise, investors are charging a higher price for risk and will therefore pay lower prices for the same set of risky expected cash flows (Damodaran, 2009).
2.2.1 Determinants of Equity Risk Premium
As one of important concept in risk-return relationship, risk aversion of investors in market is believed to be a key determinant of equity risk premium and its “reasonable” level is centered in the equity premium puzzle which is first suggested by Mehra and Prescott (1985) (Siegel, 2005). Damodaran (2009) states in his study that the more risk averse investors become, the higher ERP will be. Siegel (2005) also highlights the increasing of ERP in recessionary period when risk aversion increases. This can be explained by the utility theory (Bodie et al, 2008) that investors who are risk averse reject investment portfolios that are fair games (zero risk premiums) or worse (negative risk premium). Risk aversion however, is believed to be inconsistent and most likely to change over time due to numerous variables influence such as investor age or preference for current consumption. Another determinant of ERP is economy conditions. ERP should be lower in an economy with predictable inflation, interest rates and economic growth than in one where these variables are volatile (Damodaran, 2009). This is also supported by empirical research in the United States by Lettau et al. (2008). Brandt and Wang (2003) present evidence that ERP tend to increase if inflation is higher than anticipated and decrease when it is lower than expected.
Both the quantity and quality of information available to investors over the last two decades are believed to have significant changes in investments performance (Damodaran, 2009). According to him, accessing to more information about their investments during information booming period leading to investors’ higher confidence and lower risk premiums in 2000. Yet, easy access to large amounts of information of varying reliability was making investors less certain about the future, stated Damodaran (2009). This is why investors require larger risk premiums in emerging markets where transparency and information disclosure differ widely.
In addition to the above factors, liquidity is also needed to be considered. Along with accepting high transaction costs to liquidate equity positions, investors will demand a large risk premium. Liquidity which depends on market cap magnitude, stock traded, or economy conditions might have significant effects on equity risk premiums (Constantinides, 2008). Apart from those, Damodaran (2009) also explains catastrophic risk and irrational component as other determinants of ERP.
2.2.2 The Equity risk premium puzzle
This premium has attracted academic interests after Mehra and Prescott’s article in 1985, titled “The Equity Premium: A Puzzle”. By examining the behavior of the US stock market and aggregate consumption, they argued that the observed historical equity risk premiums which were estimated at about 6% were too high, and that investors would need implausibly high risk-aversion coefficients to demand these premium (Damodaran, 2009; Mehra and Prescott, 1985; Seigel, 2005) or why average risk-free rate was so low (Mehra and Presscott, 1985). On the other hand, Dimson et al. (2008) and Constantinides (2008) agree that equity premium puzzle is indeed a quantitative puzzle about the magnitude of the risk premium and suggest two possible resolutions which are either standard models are wrong or historical premiums are misleading. In fact, the notion that the historical premium is misleading is supposed to be true from the research of Dimson et al. (2008). They found that solving the puzzle based on US evidence must start from the wrong set of belief about the past and proposed an estimation historical equity premium on assumption that it was stationary and used DMS global database. Base on analyzing components of premium which are luck and repricing from changes in underlying premium that can be used as inference about future long-term premium they inferred that investors might expect an equity premium of around 3 – 3 ? percent on geometric mean basis, and implied 4 ? – 5 percent on an arithmetic mean for the word index. Yet, equity premium will continue to be puzzle for the foreseeable future (Dimson et al., 2008).
2.2.3 Equity risk premium estimation methods
Apart from the puzzle itself, Equity risk premium one more time trigger academics and practitioners of how to measure it. As defined earlier, Equity risk premium (ERP) is the difference between the return on equities and the return on a risk-free asset (Dimson et al, 2000). The immense questions are how to determine risk-free rate and how to estimate the return on equities. Actually, there are load of researches and papers which suggest different approaches to perceive these factors. Goetzmann and Ibbotson (2004) classify methods of estimating the ERP into four categories which are: historical, demand, supply, and consensus approach. On a slightly different view point, Damodaran (2009), Hassett (2010) look at three perspectives to estimate ERP which are historical, implied (or forward-looking) and survey perspective. There are overlaps found in identifying historical and demand approach, this paper thus, will discuss ERP estimation methods base on the latter idea.
(i) The consensus/survey method
The consensus method is to survey investors to see what they think the ERP is. The theoretical foundation of this approach, according to Goetzmann and Ibbotson (2004), is that investors make up the market and that whatever they believe about expected returns should be impounded into the price of stocks and implicitly into the discount rate at which the expected cash flows are valued. Plus, Damodaran (2009) states that this is the most logical way to estimate as investors are the main acts in the markets and thus their thought would reflect the demand for investing in risky assets. However, there are only a few published surveys and this approach is believed to be heavily subjective to whom the question is directed, how the question is asked (Damodaran, 2009; Goetzmann and Ibbotson, 2004; Soenen and Johnson, 2008).
(ii)Implied/forward-looking approach
In the implied approach, according to Damodaran (2009) or supply method as defined by Goetzmann and Ibboston (2004), a forward-looking estimate of the premium is taken to account using dividend yield, book values or GDP growth, etc and is based upon the dividend discount model. While Dimson et al. (2008) looks across many countries to decompose the equity premium into dividend growth, price dividend ratio, dividend yield and real exchange rate components (Donaldson et al, 2010), estimating the equity premium using fundamentals (dividends and earnings) suggested by Fama and French (2002) is believed to help judge whether the realized average return is high or low relative to the expected value. Their computation is based upon the dividend growth model and earnings growth model and found that equity premiums estimated from 1951 to 2000 by these models are well below the estimates from the average return (Fama and French, 2002). It is suggested that these estimates are closer to the true expected value, more precise with lower standard errors than average return estimate (Fama and French, 2002; Donaldson et al., 2010).
However, this supply approach is thought to be highly sensitive because it also based on the assumptions of the analysts which would introduce a huge element of subjectivity (Soenen and Johnson, 2008). Particularly, dividends are a policy variable and any changes in policy can raise problems for the estimation (Fama and French, 2002). Plus, the absence of dividend or inaccurate of growth rate estimated in such market as emerging markets where there are paucity of quality of information, illiquidity of market and uncertainty of policy and politic (Cohen, 2009) will make it hard to generate meaningful estimate of equity premium (Dimson et al., 2008).
(iii) Historical approach
The historical approach according to Goetzmann and Ibbotson (2004) bases on historical returns and risk premia collected, looking for predictability and extrapolating the past into the future. Many other articles, however, mention historical method as including using historical stock and bond returns as sources to apply to asset pricing models that differ from Goetzmann and Ibbotson (2004) classification as this, according to them, is defined as demand method. Nonetheless, this combined historical approach is believed to be the most widely and commonly employed method in practice (Mayfield, 2004; Damodaran, 2009; Soenen and Johnson, 2008).
Also known as the most commonly approach to solve the equity puzzle, historical method is based upon the estimate actual returns earned on stock over a long time period, and compare to the actual returns earned on default-free assets which regard as government securities (Damodaran, 2009). The very early historical estimation was made in Mehra and Prescott (1985) which provide the evidence on the U.S stocks returns in excess of the riskless rate. “Reliable data to estimate the historical premiums of stocks over bonds were only collected in the mid-20th century, and more precise econometric estimates of the equity premium only came after the development of the theory that uses it as a central input – the Capital Asset Pricing Model, or CAPM which provide a theoretical foundation for estimating the magnitude of the equity risk premium directly from investor preferences”, said Goetzmann and Ibboston (2008). One of the major issues with statistical estimation of the realized ERP, according to them, is a very long time series of stationary returns required to achieve a high degree of confidence in the estimate. However, there are debates of the risk premium estimation process: different time periods for estimation, the uses risk-free rates and market indices and which average method used to calculate returns over time (Damodaran, 2009).
The first question is how long of the time period should be used to estimate premium. There is belief that historical period should be as long as possible to generate better the estimation (Soenen and Johnson, 2008). “Many financial managers and economists believe that long-run historical returns are the best measure available”, states Brealey and Myers (2000) (cited Dimson et al., 2008). The importance of this issue is also stressed by Goetzmann and Ibbotson (2008) as a requirement to achieve a high degree of confidence in the estimate and that “the longer the data series, the more accurate the equity risk premium calculation…”. Estimating the U.S equity premium is considered to be the longest possible time period and this is also thought to be the most complete data set of stock prices and dividends assemble to date (Goetzmann and Ibbotson, 2008). Emerging markets, unfortunately, are found to be established at only around year 1988 to 1995 (Estrada, 2000), which means that computing ERP using historical data in these markets will be tougher and with a quite low level of confidence. Yet, many analysts are found to use shorter time period, such as fifty, twenty or even ten years to estimate historical risk premium (Damodaran, 2009). This is due to the fact that not all markets in the world have such a long historical data set as in U.S and that estimation based only on U.S historical data is thought to be hard to avoid upward biased (Donaldson and Mehra, 2008). This also explains why Dimson et al. (2002, 2006) cover capital market history in 17 countries in DMS database to estimate the historical equity premium around the world. Back to the main question on the length of time period should be used to estimate historical premium, Damodaran (2009) suggests that using a shorter and more recent time period provides a more updated estimate due to the changes of market and average investors’ risk aversion. However, short time periods would provide fewer observations which are believed to be inadequate to process precise estimation because of the higher standard error. Therefore, for such young markets as emerging one with short time history, estimation would be more difficult and should use more frequent observed intervals.
The second estimation consideration is using the risk-free rate. There are two alternative choices which are Treasury bills (short-term government securities) and long-term government bonds. While Treasury bill is considered to be the only risk-free asset (Dimson et al., 2000) long-term government bond is found to be riskier due to its sensitivity both to changes in real interest rate and inflation expectation. Using a short term treasury bill as a proxy for the risk-free rate has been proved by Kraus and Litzenberger (1976), De Santis and Gerard (1997), Girard and Sinha (2006). For that reason, ERP estimated relative to bond might less than to bill (Dimson et al., 2000; Damodaran, 2009). Yet, using long-term bond is believed to be a benchmark which reflects today’s short-term interest rate and future expected interest rate.
The final point that needs to underpin is how to average returns on stocks in estimating historical premium, arithmetic or geometric mean. Soenen and Johnson (2008) clarify the difference between these two approaches that arithmetic mean return is a single period rate of return and therefore should be used in association with a short-term risk-free rate while geometric mean return is a multi-period rate of return and should be used in the CAPM together with the yield on a long-term government security. The market risk premium used arithmetic mean is found to exceed the geometric version (Soenen and Johnson, 2008; Mehra and Prescott, 2008). The greater the volatility of returns, the larger the amount by which the arithmetic exceeds the geometric mean. Using geometric averages is thought to significantly underestimate the expected future value of an investment (Mehra and Prescott, 2008).
2.3 Estimating Equity Risk Premium in emerging market using CAPM vs. Downside CAPM
2.3.1 Emerging market
Financial markets of developing countries, such as Mexico, Malaysia, Thailand and China are considered to be emerging markets. They have tremendous growth potential with highest volatility in the world stock markets but also pose significant risks due to the uncertainty of politic, economic policy (Deutsche Bank). Moreover, they are thought to have lower quality of governance, higher country credit risk and higher market concentration with small samples of firms accounting for large proportions of aggregate market values (Aggarwal and Goodell, 2008).
Historical data in emerging markets, stated by Damodaran (2009), tends to be limited and volatile. They are also found in research of Girard and Sinha (2006) to be characterized by low integration and correlation in the world market and thus high diversifiable risk. This is due to the fact that these markets witnessed only short-time period development and have seen substantial changes over the last few years. Estrada (2000) summarizes previous studies and concludes that even betas and stock returns in emerging markets do not seem be related. Another point made by Iqbal and Brooks (2007) as limitation of emerging market that data set is only available the closing price data to researchers.
According to Morgan Stanley Capital International’s classification, Vietnam is classified as one of “Frontier markets”, also known as pre-emerging markets, due to the lower market capitalization and liquidity than the more developed emerging markets, yet share similar limitations and conditions as identified as in emerging markets. Pre-emerging markets, therefore, are pursued by investors seeking for potentially high returns who are able to accept the higher risks exposure. Berger et al. (2011) explain that these markets have low integration with the world market and thereby offer significant diversification benefit. Overtime, Vietnam or other frontier market, is to be believed to become more liquid and exhibit similar risk and return characteristics as the larger, more liquid developed emerging markets (Berger et al., 2011) and MSCI would be expected to reclassify this group.
2.3.2 CAPM vs. Downside CAPM (D-CAPM)
Empirical finance is found mostly focuses on developed equity markets (Salomons and Grootveld, 2003) with little attention paid on equity premia estimates for emerging markets (Aggarwal and Goodell, 2008). Yet, the paucity of data in these developing economies intensifies the problems of estimation (Cohen, 2009). In order to estimates ERP in such developing countries different approaches were exploited either adjusted CAPMs based on historical data or forward-looking, the most recent methods based on dividend yield or growth rate. Forward-looking method is thought to be difficult to apply and to be meaningless without dividend related information, especially in such developing countries where stock markets do not even display the so-called “weak-form” of market efficiency (Soenen and Johnson, 2008).
Traditionally, the CAPM stems from an equilibrium in which investors display mean-variance behavior (Estrada 2002), a utility function that investors want to maximize. This utility (U) is determined by the mean (?) and variance (?2) of return of the investor’s portfolio: U= U(?, ?2). The risk of an asset i as it is one of many in a fully diversified portfolio is measured as its covariance with respect to the market portfolio or the market index:
?iM = E[(Ri – ?i )(RM – ?M)]
A more useful and widely mentioned measure of risk is discussed beta which is obtained by:
It is also widely used in estimate required return on equity: E(Ri) = Rf + ERP.?i ; and then risk premium of an asset i: RPi = ERP.?i; where E(Ri) and Rf stand for required return on asset i and the risk-free rate; and ERP denotes equity risk premium or the risk premium of the market index and determined as ERP = E(RM) – Rf . The application of the CAPM will be further exploited later in this dissertation in order to determine the equity risk premium of the Vietnamese Stock Market, and the beta will also be used to calculated risk premiums of the chosen stocks.
However, applying the traditional CAPM which is mentioned above in emerging markets is found problematic because of the unique characteristic of the model from the developed markets. It is only an appropriate measure of risk when the underlying distribution of returns is symmetric and normal. Yet, both the symmetry and the normality of stock returns are questioned by the empirical evidence in emerging markets (Estrada 2002). Hence, many different versions of CAPM are suggested by researchers to adjust components in order to apply to emerging markets. For instance, the international version of CAPM which implicitly assumes perfect world market integration, but the existing evidence on emerging market integration is contrary to this assumption (Chen and Chen, 2004). Aggarwal and Goodell (2008) estimate annual equity premia for 16 emerging markets and find that they are generally low even compared to risk-free rates. They suggest the possibility that in many emerging markets there are non-pecuniary benefits to holding equity or that controlling ownerships have preferential access to capital.
Alternatively, Estrada (2000) suggests that an intuitively plausible downside risk measure, i.e., semideviation or semivariance, could perform much better than the traditional deviation to capture expected returns in emerging markets. Harvey (1995) and Markowitz are also found to support this measure and states that this measure somewhat preferable to those of the standard deviation (Estrada, 2006; Chen and Chen, 2004) and that the emerging markets’ historic performance provides a good test sample. Harvey (2000) and Estrada (2000, 2002) tested various risk measures and suggested the downside risk measures such as semi-standard deviation matter for analyzing emerging market equity indices (Hwang and Pedersen, 2004). Suggested by Estrada (2000), this new version of CAPM or Downside CAPM (D-CAPM for short) accesses the downside risk of investment with two measures which are semi-deviation or semi-variance and downside beta. This approach bases upon the fact that risk include upside and downside risk and apparently investors want to avoid downside volatility in return (Estrada, 2006; Chen and Chen, 2004). Secondly, semivariance is believed to be more useful when the underlying distribution of asymmetric and just as useful when the underlying distribution is symmetric (Estrada 2002). Furthermore, this model can be applied both at the market level and at the company level (Estrada 2006).
According to Estrada (2000; 2001), investor’s utility is given by U=U (µp, ?p2) where ?p2 denotes the downside variance of returns (or semivariance for short) of the investor’s portfolio, the risk of an asset i taken individually is measured as relative-to-mean-return semideviation (?i), which is given by:
?i =
This equation can be more generally expressed with respect to any benchmark return B (?Bi) as
?Bi =or ?Bi =
It measures downside volatility which below the benchmark return B with time i and n observations, and thus, semivariance or semideviations could estimate the average loss that an asset or a portfolio could incur.
The second measure of downside risk as formulized in Estrada (2000; 2001; 2006) is the downside beta with respect to benchmark B (?BD) is defined as:
?BD =
These two measures are believed to provide better estimation required returns of cost of capital model (Estrada, 2006) and therefore better risk premium estimate. These downside risk measures can be used as proxies for the firm’s sensitivity and thus replace ?i by ?BD in the Downside CAPM (or D-CAPM for short) as follow:
E(R)i= Rf + ?BiD ERP or E(R)i= Rf + ERP(?Bi / ?Bm )
if firm-specific risk is measured by the semideviation of a company (?Bi) relative to the semideviation of the market (?Bm ); and thus, risk premium of a stock i will be estimated as proportional of the market’s equity risk premium to firm-specific risk:
RPi = ?BiD ERP or RPi = (?Bi / ?Bm )ERP
The equity risk premium and risk-free rate, in Estrada’s (2000; 2001; 2006) studies, are based on the U.S market as these studies stand on perspective of U.S investors who can internationally diversify investment portfolio. Yet, using these inputs to estimate equity risk premium can be varied depending on perspective of each researcher or beholder. Therefore, latter in this study, the D-CAPM will be used to calculate risk premiums of each chosen stocks and compare them to those computed traditionally by the CAPM.
2.4 Statistical Testing methods
Statistical testing methods are generally used in finance to test mathematical models of the relationship between one dependent variable and one or more independent variables (Parramore and Watsham, 2004). Among those is the linear regression which is thought to be important application, for example, in testing a theory or the well-know capital pricing model, estimating the sensitivity of the asset returns to variations in the market return (Parramore and Watsham, 2004), or examining the empirical behavior of financial markets (Alexander, 2008) in the form:
Simple linear regression: Yi = ? + ?Xi + ?i ;
Multiple linear regression: Yi = ? + ?1iX1i + ?2iX2i + … + ?kiXki + ?i;
where parameter ? is called the regression constant or intercept, ? and ?ki are accordingly regression coefficients in simple linear and multiple linear regression, ?i is the error process (Alexander, 2008). Many reported studies such as Estrada’s (2000; 2001; 2002), Chen and Chen’s (2004) and Harvey’s (2000) are found to use cross-sectional regression to estimate the coefficient of risk measures to see if the risk measure is important in explaining the variation of the return across different assets. Particularly, Estrada’s (2000; 2001; 2002) studiesuse cross-sectional regression models test the superiority of the downside risk measures over standard ones in emerging markets. The first model is cross-sectional simple linear regression, which is presented as:
MRi = ?0 + ?1RVi + ?i ,
where MRi and RVi stand for mean return and risk variable, respectively, ?0 and ?1 are coefficients to be estimated, ?i is an error term, and i asset/index. This allows assessing correlation between risk variables and mean of returns in the market, thus reveal the ability of each risk measure in explaining the variation of stock returns.
The next ones are cross-sectional multiple regression models, which are grouped in pairs and groups of four risk measures:
MRi = ?0 + ?1RV1i + ?2RV2i + ?i , and MRi = ?0 + ?1RV1i + ?2RV2i + ?3RV3i + ?4RV4i + ?i
where RV1i, RV2i, RV3i, and RV4i stand for the variables in the model which are ?, ?, ?, ?D. These models will pinpoint the variables with the highest results which help validate the model accuracy and the risk measures’ superiority. Similarly, Chen and Chen (2004); Harvey (2000) are also found to use regression models to assess the importance of downside risk variables. However, the dependent variable used in these studies is the excess return of an asset over risk-free rate (known as the risk premium) instead of the mean return in Estrada’s (2000; 2001; 2002) studies.
The estimates of ?k (with k ? 0) in those above described models are used to test the general hypothesis of if the estimated risk measure is significant in explaining the cross-section returns, that is:
Null hypothesis (H0): H0: ?k (k ? 0) = 0
Alternative hypothesis (HA): ?k (k ? 0) ? 0.
Indeed, regression analysis cannot “prove” a hypothesis; it can only support it statistically or reject it if the evidence is strong enough (Parramore and Watsham, 2004). In this test, it means that the estimated risk measure is able to explain the variation of the mean return. However, according to Rawlings et al. (1998) a useful starting point in any multiple regression analysis is to compute the matrix of correlations among all variables including the dependent variable. This is believed to provide a first look at the simple linear relationships among the variables (Rawlings et al, 1998). Correlation is the most common measure of dependency between two random variables. It always lies between -1 and + 1. The absolute value of correlation infers the strength of an association. If movements in independent variable have no association with movements in dependent variable, their correlation is zero. Furthermore, the use of correlation as a measure of dependence will be difficult unless the two variables have a bivariate normal distribution (Alexander, 2008). Estrada (2000; 2001; 2002), Chen and Chen (2004) and Harvey (2000) are also found to analyze correlation matrices between risk variables in emerging markets before linear regression analysis; and that these correlation results do support their testing using regression models.
Chapter 3: Research MethodologyResearch is defined as a search for knowledge in a scientific and systematic way (Saunders et al., 2009; Lancaster, 2005) for many purposes such as discovering new facts, confirming existing phenomena or clarifying perspective on an issue. “Scientific and systematic way” is suggested by Saunders et al. (2009), Veal (1997), O’Leary (2004) as the logical relationship on which a research based on, which is believed to be essentially carried out in methodical processes, logically evidence examination to draw rational and unbiased conclusions. Therefore, it is critical to provide a coherent and persuasive explanation of the way in which a research in general and this dissertation in particular will be processed. Furthermore, Adams et al. (2007) distinguishes the two terms which are research methodology and research method. Research methodology is the science and philosophy behind all study while research method is a way of conducting and implementing a study which guided by the chosen research philosophy and approach.
It is noted that there would be no perfect research methods for any research topic, but choosing the most suitable among the available ones is the key point for the successful research. This section of the study includes identifying research paradigm as well as research methods in both theoretical and practical manners in order to answer the main research questions. Besides, possible limitations due to the research design are also advised in this dissertation.
3.1 Research Philosophy and Research Approach
A research paradigm which is believed to be linked to researcher’s views on the development of knowledge (Wilson, 2010), is a philosophical framework that guides how scientific research should be conducted (Collis and Hussey, 2009). People’s ideas about reality and the nature of knowledge have changed over time and, therefore, new research paradigms emerge in response to the perceived inadequacies of earlier paradigms. Epistemology, which refers to the nature of knowledge, raises the key question of what acceptable knowledge is. It is also stressed by Bryman and Bell (2007, p.16) that “A particularly central issue in this context is the question of whether or not the social world can and should be studied according to the same principles, procedures and ethos as the natural sciences”.
Positivism and interpretivism are perhaps the two most well-known research philosophies (Wilson, 2010). Positivism, which has its roots in the philosophy of realism, “rests on the assumption that social reality is singular and objective, and is not affected by the act of investigating it” (Collis and Hussey, 2009, p.56). It is, according to Bryman and Bell (2003) and Wilson (2010), an epistemological position that advocates the application of the methods of the natural sciences to the study of social reality and beyond. The carrying out of this research is therefore usually linked to a deductive approach, known as top-down reasoning (Horn, 2009), starting with a theory and hypothesis, then design a research strategy to test the hypothesis using observations (Wilson, 2010; Saunders et al., 2009; Horn, 2009). Deductive approach also relies on the fact that universal laws remain so until one or more of their predictions are found to be false – in which case the theoretical framework, from which predictions derived, needs to be revisited (Adams et al., 2007). On the hold of empirical research, it is usually believed to associate with quantitative methods of analysis (Collis and Hussey, 2009).
Based on the principles of idealism, alternatively, interpretivism is underpinned by the belief that social reality is not objective but highly subjective because it is shaped by our perceptions; and it, therefore, requires the social scientist to grasp the subjective meaning of social action (Bryman and Bell, 2003). The carrying out of this research is usually relied on an inductive approach or bottom up reasoning (Horn, 2009) which starts with using observations as collected data to develop a theory (Wilson, 2010). Whereas positivism focuses on measuring social phenomena, interpretivism focuses on exploring the complexity of social phenomena with a view to gaining interpretive understanding. Therefore, interpretive research is any type of research where the findings are not derived from the statistical analysis of quantitative data (Strauss and Corbin, 1990).
With regard to current literature review of this dissertation, positivism is thought to be a more appropriate epistemological position as the study provides explanatory theories of risk – return tradeoff to understand Equity Risk Premium phenomena in such developing countries as Vietnam. Developed from the theoretical concept of risk-return relationship, the paper then discusses the use of two asset pricing models, CAPM and D-CAPM, and evaluates whether CAPM or D-CAPM is a more plausible model to apply in the case of Vietnam Stock Market by quantifying risk variables and then testing by empirical observations. Thus, the study seems to be deduced from general inferences with regard to the point made by O’Leary (2004).
Based on a chosen research philosophy, a researcher can come up with his/her own research methodology which either is qualitative or quantitative. Due to the fact that this study will adopt a positivist paradigm, a quantitative approach is to be taken to draw conclusions and hypothesis testing on the representative sample in Vietnam Stock Market. Quantitative approach, according to Hype (2000), relates to measuring the behavior and characteristics of the sample representing the population of interest, and attempt to construct generalizations regarding the population as a whole. Analysis is usually statistical and involves analyzing the results following theoretical application (Wilson, 2010). Therefore, this dissertation starts with a discussion of existing literature of Risk-Return relationship and Equity Risk Premium issues in Emerging markets perspective; then it will test the models which are used to estimate risk measures in the case of Vietnam Stock Market.
3.2 Research Method
While methodology is concerned with the overall approach to the research process, research methods, according to Collis and Hussey (2009), Wilson (2010) and Saunders et al. (2007), refer to different techniques for collecting and/or analysis data. Since this paper aims to study financial models on a case study of Vietnam Stock Market in general and leading stocks in particular, it will be composed principally by secondary research, for example, literatures review, secondary information and data analysis.
3.2.1 Conducting Literature review
The literature refers to all sources of published data on a particular topic (Collis and Hussey, 2009). Hence, literature review is thought to be an essential part of academic research since it is basically an acknowledgement of what has already been written that is relevant to the chosen subject (Wilson, 2010). Literature review, according to Hart (1998, p. 9), “not only demonstrates the skills to search and compile accurate and consistent bibliographies, but also summarizes your key ideas, showing a critical awareness”. Indeed, conducting literature review can provide inspiration for research topic idea, identification of new and emerging research areas as well as further this knowledge (Wilson, 2010). Link to this dissertation, risk-return relationship has been foundation of financial models; and thus, identifying relevant studies and notions in this field inspired the specific subject of equity risk premium. The literature review in this study reviews previous literature on equity risk premium at a standpoint of emerging markets. Many financial models, which mainly depend on quantitative approach, are suggested to explain risk-return tradeoff issue and estimate risk premium in these markets yet remain both pros and cons. Among those is D-CAPM that is found to be more plausible to apply in special conditions in emerging markets. However, the model merely mentions applying in classified emerging markets to which Vietnam Stock market does not belong. Therefore, by reviewing previous literature, it able the study to come up with method and similar approach to Estrada’s (2000; 2001) researches in measuring risk premium of stocks in Vietnam Stock Market.
3.2.2 Collecting secondary data
Data are known facts or things used as a basis for inference or reckoning (Collis and Hussey, 2009). Base on source classification, data can be either collected from existing source – secondary data or generated from an original source such as experiment or surveys – primary data. Typical sources of secondary data include commercial databases, published books, articles, reports and statistics that can be published in hard copy or in digital form (Collis and Hussey, 2009; Wilson, 2010). Secondary data are widely used in research because in general, it is a convenient and cost-effective source of information for the student researcher (Stewart and Kamins, 1993). By focusing on secondary data, a researcher may be able to collect and analyze much larger data sets as well as coming up with cross-culture or international comparative research which is limitations associated with primary data collection (Wilson, 2010). Due to objectives and specific conditions, this dissertation is conducted by exploiting the secondary data sources with careful consideration and evaluation.
In order to develop literature review, the study consults a growing literature on Equity Risk Premium and risk measures estimation base upon a wide range of text books and academic journals and articles. Although text books are considered to be one of the most reliable sources of basis knowledge they are becoming less up-to-date rather than academic journals and articles which are published quarterly or even monthly. As a result, academic journals and articles especially in finance area are accessed as the main sources of data for a more comprehensive and comparative analysis and more valuable citation and reference in this dissertation.
For the later purpose of this study which is estimating Vietnam stock market ERP and stocks’ risk premiums using CAPM and D-CAPM, the data are mainly chosen as the historical closing price, which indices the monthly returns of nine leading companies’ stocks, representing the nine major industries in Vietnam economy in a period of about five years depend on each stock history. The statistic is accurately obtained from the databases of FPT Securities JSC (http://fpts.com.vn/VN/Home/), Hochiminh City Stock Exchange (http://www.hsx.vn/hsx/Default.aspx) and Hanoi Stock Exchange (http://bond.hnx.vn/default.aspx?tabIndex=1&tabid=35) under the websites permission.
3.2.3 Analyzing data
With adoption of positivism and quantitative research approach, the study comes up with the next step of quantitative data analysis to answer key research questions (Sharp et al., 2002). According to Wilson (2010), Collis and Hussey (2009), statistics is widely applied to quantitative data in order to draw conclusions and make predictions. A statistic “enables us to recognize and evaluate the errors involved in quantifying our experience, especially when generalizing from what is known of some small group (a sample) to some wider group (the population)” (Rowntree, 1991, p.186 cited Collis and Hussey, 2009, p.221). Quantitative analysis is grouped as descriptive statistics and inferential statistics. The former is used to summarize and describe data, while the latter is used to make inferences in relation to a wider population (Wilson, 2010; Collis and Hussey, 2009).
As the study’s aim is estimating stocks’ risk premium using different risk measures which formulized from CAPM and D-CAPM, then validating of each model’s efficiency in the case of Vietnam Stock Market, inferential statistics is believed to be applicable. Several methods of inferential statistics will be taken to validate models and their estimations, namely hypothesis testing, correlation coefficient, and regression analysis. Hypothesis testing involves making a statement about some aspect of the population, and then generating a sample to see if the hypothesis can or cannot be rejected (Wilson, 2010). In this paper, the hypothesis testing assesses whether or not the existence relationship between the risk variables estimated from the models and the stocks’ returns, thus, validate applicability of the model in Vietnam Stock Market. Correlation coefficient is “a measure of the linear dependence of one numerical random variable on another” (Upton and Cook, 2006, p.101 cited Collis and Hussey, 2009, p.267). Yet, it only offers additional information about an association between two quantitative variables. Regression analysis is used for further investigating the strength of a relationship between variables (Wilson, 2010). Linear regression is a measure of the ability of an independent variable to predict an outcome in a dependent variable where there is a linear relationship between them (Collis and Hussey, 2009). In the case of this dissertation, applying both simple and multiple linear regressions allows us to measure the ability of risk measures generated from CAPM (which are standard deviation and beta) and D-CAPM (which are semideviations and downside betas) in explaining the variation of cross-sectional returns in Vietnamese Stock Market.
The process of quantitative analysis is supported by Microsoft Office Excel software Data Analysis Tools. This application helps calculating risk measures from CAPM and D-CAPM of nine stocks’ historical returns. Moreover, the outcomes of running regression analysis by using Data Analysis Tool are fundamental to make a verdict of the significance of adhering downside betas of D-CAPM to measure market risk in Vietnamese Stock Market.
3.2.4 Possible limitations
First of all, this study faces the constraint of time due to the submission deadline which makes it difficult for researcher to completely estimate and analyze the effects of downside risk to every stock in the market. It, therefore, is suggested that more time should be needed to generate more comprehensive outcomes which help providing more accurate and thorough verdict.
Second of all, exploiting completely secondary data based is thought to come up with some possible deficiencies due to trustworthy and accuracy of the data. Though such numerical data as historical closing price is obtained from the database of FPT Securities and official site of VN-Index Hochiminh City Stock Exchange, the numbers cannot avoid imprecision of information provided. This is due to the fact that Vietnam Stock Market is classified as pre-emerging market by MSCI, where stock market is newly established and regulations are uncompleted.
Another limitation of the research is the sample size, which ranges from 170 to 263 weekly returns for each stock and 462 weekly observations for VN-Index. This is believed to be quite small sample to produce high reliable and qualified research. Moreover, due to the effort to collect as much historical data as possible, the time period in each stock’s estimation is slightly different as the difference in the start trading date. Choosing the risk-free rate for the Equity Risk Premium is also problematic due to the variety of Government bonds with various benchmarks regarding to each code of Government bond.
Chapter 4: Empirical Findings and Data AnalysisThis chapter will demonstrate the findings and results which cover the main research questions; and starts with a description of collected data. In the next part, a summary as well as detailed analysis of estimating results which answer the main research questions is to be presented. The main findings include (i) calculations of the Vietnamese Stock Market’s CAPM-based Equity Risk Premium, (ii) risk premiums of each stock that represent nine main industries in the Vietnam economy using risk variables which are estimated base upon applications of the CAPM and D-CAPM. The last part is to provide statistical tests of the use of various risk measures in Vietnamese Stock Market as well as an evaluation on the strength and efficiency of each model in explaining the variations of the market and stocks returns.
4.1 Data Descriptions
As mentioned in Chapter 1, the main purposes of this dissertation is to calculate Vietnam’s Equity Risk Premium and using Downside CAPM which suggested and developed by Estrada (2000; 2001; 2006) to estimate downside risk measures and risk premiums of stocks in Vietnamese Stock Market. For the first aim, the main Vietnam stock market index, namely VN-Index will be used along with the Vietnam’s 2–year Government bond (Bond code: CPB0911001) interest rate of 8% (issued at 14 January 2009) as the risk-free rate[1]. The VN-index is a capitalization-weighted index of all the companies listed on the Hochiminh City Stock Exchange. The index was created with a base index value of 100 as of July 28, 2000. However, only after March 1st 2002, the market trade on continuous working days[2]. Therefore, the time priod for ERP estimation will start on 1st March 2002 to 11th March 2011. This estimation will base upon 463-week trading data and historical method using traditional CAPM: ERP = E(RM) – Rf, where E(RM) is expected return (or historical mean return) of the market index, Rf is the rate of return of default-free asset which is generally designated with Government bond.
The later aim is to estimate risk premiums of stocks in Vietnamese stock market using downside risk measures proposed by Estrada (2000; 2001; 2006) which are semideviation and downside beta. The list of chosen stocks consists of nine leading Vietnam companies’ stocks traded in Hochiminh City Stock Exchange (HoSE), representing nine main sectors in Vietnam’s economy. The list of nine chosen stocks is presented in the below Table 1.
Table 1: List of companies
Company Code Industry Start date Number of observations Vietnam Dairy Products JSCVNM Food Producers Jan 2006 263 Hoa Phat Group JSCHPG General Industrials Nov 2007 170 Tan Tao Industrial Park Corp.ITA Real Estate Nov 2006 221 Petrovietnam Fertilizer & Chemical JSCDPM Chemicals Nov 2007 172 Financing & Promoting TechnologyFPT Fixed Line & Telecommunications Dec 2006 217 SaiGon Thuong Tin Commercial JSBSTB Banks Jul 2006 239 PhaLai Thermal Power JSCPPC Electricity May 2007 211 Petrovietnam Drilling & Well Services JSCPVD Oil Equipment & Services Dec 2006 218 Saigon SecuritiesSSI General Financial Dec 2006 174Note: Companies are classified base on the Industry Classification Benchmarkt (FactSheet, July 2008, FTSE The Index Company[3]). Data Sources: FPT Securities, http://priceboard.fpts.com.vn/user/stock/lich-su/ [Accessed 11th March 2011]. Hochiminh City Stock Exchange http://www.hsx.vn/hsx_en/default.aspx [Accessed 11th March 2011].
The data were obtained from FPT Securities and Hochiminh City Stock Exchange historical database, comprising weekly closing prices for approximately five years, from January 2006 until March 2011 in Vietnam Dong. The estimation also uses weekly returns of the nine stocks yet varies on the historical period. The different time periods used for computing risk premiums bases on the trading history of each stock, from the first traded week in HoSE ends at the moment of this study (11th March 2011). Using data in different time period on each stock is due to the fact that VN-Index is a very new-established stock index, and hence, each stock contained within has a quite short historical time period. Therefore, using as long observed period as possible is believed to generate more reliable estimations on each stock. These nine stocks, moreover, are chosen based on FTSE Group validation as in top 10 constituents of FTSE Vietnam All-Share Index that account for 72.36% of the Index Weight[4]. The observations weekly returns are log returns computed with the following formula:
Ri = ; where Ri is log return at time i, Pi and Pi-1 are closing prices at time i and (Alexander, 2008). These estimated log returns will be used in estimating risk measures of each stock by applying Downside CAPM proposed by Estrada (2000; 2001; 2006) and then to identify risk premium of each one. Estimating each stock risk variables with respect to VN-Index allows us to test the relationship and cross-sectional correlation between these stocks and Vietnamese stock market, which help assessing the efficiency of the applied model.
4.2 Main estimates and Analysis
4.2.1 Vietnam Equity Risk Premium
According to CAPM, the market equity risk premium is defined as the expected excess return of the market index to the rate of return of riskless asset (Rf), as follow:
With 462 historical weekly returns of VN-Index, we obtain the market mean return, total risk or standard deviation (?) and the Equity Risk Premium in Table 2 below:
Table 2: VN-Index Equity Risk Premium Total observations462 462 Weekly Mean E(RM) 0.20Annualized Mean E(RM) 10.95 Standard deviation 4.31 2-year Gov. bond (%/week)0.152-year Gov. bond8 ERP (%/week)0.05 Annual ERP 2.63Annual ERP2.95Note: All values are stated in percentage.
The study applied two ways to calculate Vietnam’s ERP. One way is changing risk-free rate from 8% annually into 0.15% weekly, and thus obtaining the weekly ERP of 0.05%. Based on the VN-Index weekly data, we consider that there are 52 trading weeks in a year. The annual ERP is then calculated as: . The other is to annualized the weekly mean return as: , and minus 8% risk-free rate to generate annualized ERP of 2.95%. There is slightly different between two ways due to the minor errors from rounding numbers. Results attained from the first way will be used in the study’s analysis and to calculate stocks’ risk premiums and risk variables later in this section.
The results show that the ERP in Vietnamese Stock market of 2.63% is very low in comparison to the local risk-free rate 8%. This low result is also found in the study of Aggarwal and Goodell (2008) that the risk premia in emerging markets are “surprisingly low” compared to the risk-free rates and is much lower than ERP of developed countries which are generally ranged from 6 to 8% (Aggarwal and Goodell, 2008). This low ERP can be explained that due to the hit of the recent world financial crisis. At this time, Vietnamese stock market saw unavoidable downside trend which was believed to the reach starting point of the market sometimes. Moreover, Vietnamese stock market total risk of 4.31% a week is quite high in comparison to its weekly returns 0.20%. Nonetheless, due to the fact that Vietnamese stock market is newly established and still partly controlled by authorities institutions in trading which is known as limited fluctuation interval of +/- 5%[5], the market is believed not to be able to fully reflect investors’ demand, behavior and aversion level. This also means that the required return and ERP estimated for the market is thought to be biased and incomprehensive; and thus, imprecise. However, it is unavoidable due to the nature characteristics and conditions of the market. Another reason that is believed to cause the low Vietnamese ERP is choosing the local risk-free rate. The chosen risk-free rate in this study is 2-year Government bond, which is relatively long-term in comparison to a quite short-term interval of data.
4.2.2 Risk measures and risk premiums: CAPM vs. D-CAPM
By applying the CAPM and the downside risk model advocated by Estrada (2000) in VN-Index and other nine leading stocks in Vietnam stock market we obtain risk variables with respect to the average returns, which are summarized in Table 3. Estimating ?i and ?BiD are based on linear regression model for stock i’s returns with respect to the market return in CAPM, and conditionally respect to benchmark B in D-CAPM.
Table 3: Mean Return and Risk Measures
Stock??????f?0??D?fD?0DSkew VNM 0.21% 6.91% 0.80 5.36% 5.34% 5.28% 0.78 0.77 0.77 -2.77 HPG -1.52% 10.87% 1.15 8.04% 8.91% 8.83% 1.16 1.25 1.25 -0.44 ITA -0.63% 9.01% 1.09 6.61% 7.00% 6.92% 1.13 1.18 1.25 -0.50 DPM -0.46% 6.30% 0.95 4.17% 4.53% 4.44% 0.89 0.91 0.90 0.42 FPT -0.97% 7.94% 1.05 6.01% 6.55% 6.47% 1.13 1.21 1.21 -0.86 STB -0.72% 8.27% 0.97 6.54% 6.91% 6.84% 1.08 1.17 1.17 -2.38 PPC -1.08% 6.85% 0.97 4.53% 5.25% 5.16% 0.94 1.04 1.04 0.48 PVD -0.34% 8.29% 1.10 6.10% 6.34% 6.27% 1.06 1.08 1.08 -0.69 SSI -1.39% 10.86% 1.47 8.29% 9.03% 8.95% 1.40 1.50 1.50 -1.29 VN-Index 0.20% 4.31% 1.00 2.99% 2.96% 2.89% 1.00 1.00 1.00 0.001 Average -0.77% 8.37% 1.06 6.18% 6.65% 6.57% 1.06 1.12 1.13?: Mean return; ?: standard deviation; ?:systematic risk with respect to Vietnam stock market (VN-index); ??, ?f, ?0: Semideviation with respect to mean (?), risk-free rate (Rf = 0.15%/week) and zero; ??D, ?fD, ?0D: downside beta with respect to mean (?), risk-free rate (Rf = 0.15%/week) and zero.
In general, only downside betas with respect to risk-free rate and to zero are found higher than traditional one (1.12 and 1.13 respectively to 1.06 in average) account for particularly about 63% of higher downside betas. Sensitivity of stocks returns to changes in market return that below zero is found highest. Meanwhile, the table also shows that volatility in VN-Index can be explained more by downside risk rather than the upside one as the ratio between semideviations (with respect the mean return, risk-free rate, and zero) and total risk are found more than half (69.4%, 68.7% and 67%). This means that investors in the market should expose more probability of loss than gain especially investing in financial, technology and general industrials sectors, which are mainly crashed after the 2007 Credit crunch.
Base on the estimated risk measures and Vietnamese stock market’s ERP, we can find risk premium of each stock in the market using either CAPM or D-CAPM. The risk premium (RP) estimation of a stock i, according to CAPM, is formulized as:
RP = ?i . ERP;
whereas, the D-CAPM-based estimation is presented either by the semideviation of an asset i relative to the semideviation of the market M, as follow:
RPi = (?Bi /?BM) . ERP,
where ?Bi and ?BM denote the semideviation for stock i and for the market with respect to the benchmark B or by the downside beta:
RPi = ?BiD. ERP,
where ?BiD denotes the downside beta of stock i with respect to the benchmark B. Table 4a, 4b show risk premiums estimated base on the two asset pricing models.
Table 4a: Weekly risk premium of stocks: CAPM vs D-CAPM
? ?µ ?f ?0 ?µD ?f D ?0D VNM 0.04% 0.09% 0.09% 0.09% 0.04% 0.04% 0.04% HPG 0.06% 0.13% 0.15% 0.15% 0.06% 0.06% 0.06% ITA 0.05% 0.11% 0.12% 0.12% 0.06% 0.06% 0.06% DPM 0.05% 0.07% 0.08% 0.08% 0.04% 0.04% 0.04% FPT 0.05% 0.10% 0.11% 0.11% 0.06% 0.06% 0.06% STB 0.05% 0.11% 0.12% 0.12% 0.05% 0.06% 0.06% PPC 0.05% 0.07% 0.09% 0.09% 0.05% 0.05% 0.05% PVD 0.05% 0.10% 0.11% 0.11% 0.05% 0.05% 0.05% SSI 0.07% 0.14% 0.15% 0.15% 0.07% 0.07% 0.07% Average 0.05% 0.10% 0.11% 0.11% 0.05% 0.06% 0.06% Dif. CAPM N/A 0.05% 0.06% 0.06% 0.00% 0.01% 0.01%?: systematic risk with respect to Vietnam stock market (VN-index); ??, ?f, ?0: Semideviation with respect to mean (?), risk-free rate (Rf = 0.15%/week) and zero; ??D, ?fD, ?0D: downside beta with respect to mean (?), risk-free rate (Rf = 0.15%/week) and zero.
Table 4b: Annual risk premium of stocks: CAPM vs D-CAPM
? ?µ ?f ?0 ?µD ?f D ?0D VNM 2.05% 4.61% 4.62% 4.69% 2.01% 1.99% 1.98% HPG 2.95% 6.91% 7.72% 7.84% 2.97% 3.22% 3.22% ITA 2.79% 5.68% 6.06% 6.15% 2.89% 3.04% 3.22% DPM 2.44% 3.58% 3.93% 3.94% 2.28% 2.33% 2.32% FPT 2.70% 5.16% 5.67% 5.75% 2.90% 3.11% 3.12% STB 2.50% 5.62% 5.99% 6.08% 2.77% 3.00% 3.00% PPC 2.50% 3.89% 4.55% 4.58% 2.42% 2.67% 2.67% PVD 2.84% 5.24% 5.49% 5.57% 2.72% 2.79% 2.78% SSI 3.76% 7.12% 7.82% 7.95% 3.58% 3.85% 3.86% Average 2.73% 5.31% 5.76% 5.84% 2.73% 2.89% 2.91% Dif. CAPM N/A 2.59% 3.04% 3.11% 0.00% 0.16% 0.18%?: systematic risk with respect to Vietnam stock market (VN-index); ??, ?f, ?0: Semideviation with respect to mean (?), risk-free rate (Rf = 8%) and zero; ??D, ?fD, ?0D: downside beta with respect to mean (?), risk-free rate (Rf = 8%) and zero.
As can be seen in the table above, risk premiums calculated by downside risk measures are higher than those estimated by traditional beta. In average, annualized results from semideviations with respect to the mean return, risk-free rate and to zero are found significant higher than from beta (2.59%, 3.04% and 3.11%), while downside betas only generate slight differences (0.00%, 0.16% and 0.18%). This can be explained that in some particular industries such as the Food Producers (VNM), Chemicals (DPM) and Oil equipments and services (PVD), downside betas generate rather low risk premiums compare to standard betas despite the relatively high negative skewness (Table 3).
4.3 Test results and Analysis
In order to validate efficiency of the two asset pricing models, the study is aimed to examine whether the risk measures used in the model can explain the variation in the returns. Therefore, performing hypothesis test on the true value of a coefficient is believed to be useful for determining whether the explanatory variable is significant enough to be included in the regression model: ; where MR is mean return and RV is risk variable used in the estimation. The null and alternative hypotheses of the study are:
H0: The downside risk variable estimated is unable to explain cross-section of returns in Vietnamese stock market
HA: The downside risk variable estimated is correlated with and is able to explain cross-section of returns in Vietnamese stock market
Or for short:
H0: ?k (k ? 0) = 0
HA: ?k (k ? 0) ? 0.
Risk variables tested will be both from CAPM and D-CAPM which are standard deviation (?), beta (?), semideviations (?) and downside beta (?D) with respect to benchmarks mean return, risk-free rate of 2-year Government Bond 0.15% a week and zero.
4.3.1 Correlation Matrix
By building Correlation Matrix, the relationship between the mean return and risk measures using both models, CAPM and D-CAPM, is to be assessed. This partly lets us compare the industry cross-sectional correlation level of each risk variable to the mean returns. Particularly, as shown in Table 5, downside betas, especially downside beta with respect to risk-free rate 0.15% and to 0, are strongest correlated to the average return (-0.82 and -0.79 respectively). It means that the relationship between return and risk in Vietnam stock market might have explained largely by downside risk. Moreover, the very high correlation between total risk (?) and semi-deviations (0.98, 0.99, 0.99) reveals the higher probability of downside volatility rather than the upside one in Vietnamese market. Similarly, downside betas are also found high correlated to classic beta (0.94, 0.92, 0.91).
Table 5: Cross-Section Analysis. Correlation Matrix
µ ? ? ?µ ?f ?0 ?µD ?f D ?0D µ1.00 ?-0.68 1.00 ?-0.71 0.82 1.00 ?µ-0.58 0.98 0.77 1.00 ?f-0.70 0.99 0.81 0.99 1.00 ?0-0.70 0.99 0.80 0.99 1.00 1.00 ?µD-0.75 0.87 0.94 0.84 0.88 0.88 1.00 ?f D-0.82 0.85 0.92 0.82 0.87 0.87 0.99 1.00 ?0D-0.79 0.85 0.91 0.82 0.87 0.86 0.99 0.99 1.00?: Mean return; ?: Systematic risk (beta); ?: standard deviation; ??, ?f, ?0 : Semideviation with respect to ?, risk-free rate, and zero; ??D, ?fD, ?0D: downside beta with respect to mean, risk-free rate (0.15%), and zero.
4.3.2 Linear regression
This test will start with simple linear regressions. Eight variables are considered in the analysis: total risk which is measured by standard deviations of returns, systematic risk measured by beta, three downside risk measures – semideviations of returns with respect to three targets which are arithmetic mean return of each stock, 0.15% risk-free rate and 0, three downside betas with respect to the three targets above, defined as the sensitivity of each industry-representative stock with respect to the whole Vietnamese Stock Market return, symbolized by VN-Index.
By running a cross-sectional simple linear regression model relating mean returns to each of the risk variables, the study is believed to be able to examine whether each of these risk measures is significantly correlated to the mean returns, and hence, their ability to explain cross-sectional variation of stock return statistically. This model is formulized as follow:
;
where MR is average return, RV is tested risk variable, u1 is error of the test. At confidence level of 95%, Table 6 illustrates the test results that all risk measures (apart from semideviation with respect to the mean return) are significantly correlated to stock returns as their p-values are less than 0.05 significance level, which is small enough to reject the null hypothesis. In general, with p-value is less than 0.05 significance level, it is said to have strong enough evidence to reject the null hypothesis (Alexander, 2008). It means that those tested risk variables except semideviation with respect to mean return, generate significant statistics values in explaining the industry cross-sectional mean return variation individually.
Table 6: Cross-section analysis (simple linear regressions)
MRi = ?0 + ?1 RVi + u1 RV?0p-value?1p-valueR2Adj- R2 ?0.010.19-0.220.040.470.39 ?0.010.13-0.020.030.500.43 ??0.010.43-0.230.100.340.25 ?f0.010.21-0.250.030.500.42 ?00.010.23-0.240.040.490.42 ??D0.020.08-0.020.020.560.50 ?fD0.020.04-0.020.010.670.50 ?0D0.020.06-0.020.010.630.57MR: Mean return; RV: risk variables; ?: standard deviation; ?: beta; ??, ?f, ?0: semideviation with respect to mean, risk-free rate and zero; ?? D, ?f D, ?0 D: downside beta with respect to mean, risk-free rate and zero. Confidence level of the test: 95%.
Moreover, with R square values calculated from these variables, they can be seen as also explain no less than 47% of the variation of return around its mean return. R square values also provide further interesting judgment on which variable is best fit in the model (Alexander, 2008; Parramore and Watsham, 2004). Thus, downside betas with respect to risk-free rate and to zero with R2 = 0.67 and 0.63 seem to be more superior to others. This statement is also strengthened when we consider higher confidence level. With 99% confidence, these two variables are still significant correlated to the mean return (p-values are both 0.01).
The figures in the table reveal controversy from previous studies by Estrada (2000), Soenen and Johnson (2008) and Cohen (2009) that systematic risk measured by beta in emerging markets, is not significantly related to stock returns and thus CAPM is thought to be impossible to explain the market behavior. In this study, systematic risk does significantly correlate to mean returns; thus, industry representative betas also do explain the cross-section of stock returns, which is in harmony with Estrada’s (2001) report. According to this simple linear regression model, we can conclude that the obtained evidence is strong enough to reject the null hypothesis and that risk measures from both models are able to explain the industry cross-section of return in Vietnamese stock market. Yet, in order to answer the question of whether D-CAPM do generate better estimations of risk measures and thus, a more plausible risk premium of stocks in Vietnam stock market we need to implement further inspections.
To examine the outperforming of whether risk variables from CAPM or D-CAPM, we run multiple regression models. The first tests groups of two measures and the second is jointed with four variables, which are:
;
;
where MR is average return, RVs are risk variables are tested, ui is error term of the test. Table 7.1 and 7.2 below show statistical results of these cross-sectional regressions.
Table 7.1: Cross-section analysis (multiple regressions with two variables)
Panel A: MRi = ?0 + ?1 RV1i + ?2 RV2i + u1 RV1/RV2?0p-value?1p-value?2p-valueR2 ?/ ??0.020.07-0.850.070.760.150.63 ?/ ?f0.010.650.250.72-0.510.500.51 ?/ ?00.010.630.170.81-0.420.570.49 ?/ ??D0.020.11-0.050.81-0.020.290.56 ?/ ?fD0.020.060.010.93-0.020.110.67 ?/ ?0D0.020.09-0.010.95-0.020.160.63 ?/ ??0.010.16-0.020.21-0.040.830.50 ?/ ?f0.010.17-0.010.42-0.130.440.55 ?/ ?00.010.17-0.010.44-0.130.450.55 ?/ ??D0.020.110.000.99-0.020.400.56 ?/ ?fD0.050.060.000.77-0.060.130.67 ?/ ?0D0.010.110.000.93-0.020.200.63Table 7.2: Cross-section analysis (multiple regressions with four variables)
Panel B: MRi = ?0 + ?1 RV1i + ?2 RV2i + ?3 RV3i + ?4 RV4i + u1 RV1/RV2/RV3/RV4?0p-value?1p-value?2p-value?3p-value?4p-valueR2 ?/ ??/ ?/ ??D0.020.05-0.930.111.050.110.030.33-0.040.180.79 ?/ ?f/ ?/ ?fD0.020.29-0.160.870.180.870.010.71-0.030.340.68 ?/ ?0/ ?/ ?0D0.010.400.120.89-0.150.880.001.00-0.020.480.63As the table 7.1 shows, when jointly considered, none of these risk measures come out significant. This may due to the high correlations between these pairs of explanatory variables, especially ?/ ?f and ?/ ?0 which are 0.99 (see Table 5). Yet, downside beta with respect to the risk-free rate seems perform better than others due to higher fitness R-square (0.67) and lower probability true of the null hypothesis (p-value is lower). Similarly, the second multiple regression test does not provide strong outcomes to acquire reliable conclusion when four variables are jointed together (see Table 7.2).
4.3.3 Empirical Test
The last testing method used in this dissertation is empirical test which will buttress the results from the above tests of the effectiveness and outperforming of these models. By calculating every weekly return of each stock using ? for CAPM and semideviations and downside betas for D-CAPM and looking at the difference between actual weekly returns and estimated numbers from the two models, we might be able to identify the more appropriate model for Vietnamese stock market. Estimated returns of each stock are computed as the followings:
Based on ?: ;
Based on semideviation ?B : ;
Based on downside betas ?BD:
Where, all at time i, Ri is estimated return, RMi is actual market return, B stands for each of the benchmark average return, risk-free rate and zero. Table 8 shows the difference of stocks’ returns generate from different estimated betas and risk measures.
Table 8: Empirical test
Dif. CAPM (%)Dif. D-CAPM (%) ????f?0??D?fD?0D meanSdmeansdmeanSdMeanSdmeansdmeansdmeansd VNM0.23 5.49 -1.09 7.61 -1.10 7.63 -1.13 7.72 0.25 5.49 0.26 5.49 0.26 5.50 HPG0.84 8.92 -2.09 12.26 -2.69 13.50 -2.78 13.69 0.82 8.92 0.64 8.93 0.64 8.93 ITA0.42 6.82 -1.34 9.17 -1.57 9.72 -1.62 9.85 0.36 6.82 0.27 6.84 0.16 6.88 DPM0.13 3.64 -0.72 4.37 -0.98 4.81 -0.99 4.84 0.56 3.66 0.21 3.65 0.22 3.65 FPT0.67 5.68 -0.96 7.62 -1.30 8.35 -1.35 8.47 0.55 5.69 0.41 5.74 0.40 5.74 STB0.76 6.45 -1.08 9.16 -1.29 9.72 -1.35 9.87 0.60 6.48 0.46 6.54 0.46 6.54 PPC0.81 4.64 -0.18 5.44 -0.65 6.23 -0.67 6.27 0.86 4.65 0.69 4.66 0.69 4.66 PVD0.01 5.86 -1.55 7.71 -1.71 8.06 -1.76 8.16 0.08 5.87 0.04 5.86 0.04 5.86 SSI0.03 7.46 -2.53 10.29 -3.06 11.35 -3.16 11.56 0.17 7.47 -0.03 7.46 -0.04 7.47 Average0.43 6.11 -1.28 8.18 -1.59 8.82 -1.65 8.94 0.47 6.12 0.33 6.13 0.32 6.14As it is shown in the table, downside betas with respect to risk-free rate and to zero generate better estimations of required return due to the smaller average differences (0.33 and 0.32 respectively) to the actual return and similar standard deviation of these differences (6.13% and 6.14%) as the whole, which enhances the argument of above regression tests. However, 90% of the results which is computed by semideviations are found cannot outperform standard beta due to the higher differences and standard deviations to observed returns; and in those which are computed by downside betas, there is about 36% that generates better estimations for each stocks. These results can be explained by the findings that many of stocks returns in the chosen list are distributed relatively symmetric (see Appendix 3). Consequently, in comparison to the CAPM, the D-CAPM does not seem to produce better-quality estimations. Besides, in terms of applying the D-CAPM, downside betas, especially with respect to risk-free rate and to zero, seem to be superior to semivariances or semideviations.
This is surprised that Vietnamese Stock market, which is considered to be under-developed financial market and was believed to share similar characteristics with other emerging markets, behaved differently. While Estrada (2002) mentions both the symmetry and the normality of stock returns are challenges to apply CAPM in emerging markets, Vietnamese stock market’s returns performs as symmetric and normal distributed (see Figure 1) when it has very low skewness of 0.001 and kurtosis of 2.7 (see Appendix 3).
This result also challenges the applicability of the D-CAPM in Vietnam which is known as more plausible to measure risk variables in asymmetric conditions happen in most of emerging markets as in previous studies (Harvey, 2000; Estrada, 2000; 2001; 2002; Chen and Chen, 2004). Findings of this study are believed to explain the appropriateness of using CAPM to estimate the Vietnam Stock Market Equity Risk Premium rather than the downside version. In the case of particular stocks, however, with those which perform asymmetrically and abnormally, the D-CAPM can prove its strength with better estimations. Chapter 5: ConclusionThis chapter will provide an overview of the dissertation. By reviewing critical discussions of relevant literature on the subject as well as analysis made in the previous section, this chapter will start with a summary of the main findings and conclude the significance of using the CAPM and D-CAPM in estimating risk and risk premiums in Vietnamese Stock Market, which will provide answers to the key research questions presented. However, the study is thought to face limitations that will be brought up in the next part in order to advise considerations for users in applying the models practically as well as suggestions for further research.
5.1 Summary of main findings and conclusions
The study discusses the matters of Equity Risk Premium on the perspective of emerging markets, base on which to apply in the case of Vietnam. ERP is thought to be the most important number in finance yet there remains controversies on much was it in the past and how much should investors and researchers expect in the future. ERP matters on how it could be estimated and how far data back in time to use for the calculation. Calculating ERP using historical data in emerging markets is thought to be tougher and with a quite low level of confidence due to their relatively short period of trading time. Moreover, betas and stock returns in these markets are found unrelated in Estrada’s (2000) study and that applying CAPM is impropriate due to the markets’ returns asymmetric and non-normal distributions. Therefore, the application of D-CAPM is being widely accepted among academics and practitioners due to the notion that standard deviation and beta give equal weight to upside and downside fluctuations while investors do not. Semideviations in many studies are found capturing the downside volatility that investors want to avoid; and downside beta is believed to isolate the downside potential of an asset’s returns relative to that of the market’s returns (Estrada 2006). Thus, the downside risk measures are believed to be plausible in explaining risk-return relationship in emerging markets. Nevertheless, it is neglecting of research on such developing market as Vietnam and potential applicability of the model that motivate this study.
First, the study’s calculation exhibit annualized Vietnam’s ERP of 2.63% which is believed to be too low compare with the risk-free rate of 8% and much lower than ERP estimated in developed countries. Besides, the total risk of the market 4.31% is also noted to be too high compare with its average returns 0.20%. Second, by applying the CAPM and the D-CAPM suggested in Estrada’s (2000) study, the paper shows that downside betas, in average, are higher than traditional one particularly downside beta with respect to risk-free rate (1.12) and zero (1.13). Moreover, based on the semideviations calculated, the study also finds that probability investors’ exposure to losses is higher than to gains in Vietnam because of the large volatility that below risk-free rate 0.15% (6.65%) and zero (6.57%) in total volatility of 8.37%. As a result, industry cross-section risk premiums calculated by downside risk measures especially semideviations are significant higher than those calculated by beta.
In order to assess the significance of the risk variables of the two models as well as find out the model that better fit in the case of Vietnam, the study implements several statistical tests which result the following outcome:
First, due to (i) industry cross-sectional downside betas, especially with respect to risk-free rate 0.15% and to zero, are strongest correlated to average returns (-0.82 and -0.79 respectively) and (ii) the very high correlation between total risk (?) and semideviations (0.98, 0.99, 0.99), the study can conclude that Vietnamese stock market’s volatility is more likely downward and fall below either risk-free rate or zero rather than upward.
Second, downside betas and semideviations are found individually significant in simple linear regression models with 95% confidence. Especially, downside betas with respect to risk-free rate and zero are even significant correlated the mean returns at 99% confidence. These strongly indicate that downside risk measures from the D-CAPM do explain industry cross-sectional returns on the market and we can reject the null hypothesis. Moreover, systematic risk or beta in Vietnam is also related to stocks returns; distribution of the market returns is found symmetric and normal, which is different from other studies that those in developing countries should be asymmetric and non-normal. This means that applying the CAPM in Vietnamese stock market might also attainable.
Third, using multiple regressions to examine the outperforming of whether risk variables from CAPM or D-CAPM does not come out significant. The findings are not strong enough to reach decisions. Yet, R-squares and p-values do imply that downside beta with respect to risk-free rate and to zero might generate better outcomes. Besides, empirical test shows that downside beta with respect to zero produce the best calculation of cross-section required returns with smallest average difference to observed returns (0.32%) while semideviations cannot outperform standard beta. The study, hence, can conclude that the D-CAPM does not produce better-quality estimations than the traditional CAPM in the case of Vietnam and only downside beta with respect to risk-free rate and to zero are superior if we use the D-CAPM in this market.
5.2 Recommendations and suggestions for further research
The recommendations and suggestions are given based on limitations as well as benefits of this study in order to help investors and financial institutions in examining cost of equity, evaluating risk of their investments.
First and foremost, thanks to the finding of this study that Vietnam stock market return distribution is currently symmetric and normal, the CAPM can be suggested to use in estimating historical ERP of the market. The ERP estimated is believed to be crucial not only for investors, but also for Vietnamese Government as it is yardsticks for judging the worth of public sector projects, for raising and managing government debt, which are troublesome in Vietnam. Yet, as explained by some previous studies, such a developing economy or a financial market as Vietnam, it is thought to be significant to consider variables like politics or inflations as additional determinants of country risk, thus affect ERP. Due to the research time allowance, the study could not take these factors into account. Another benefit of the study is providing a new look of measuring risk which help pricing investments in Vietnamese market; and thus, companies’ managers will understand what their principals (shareholders) require of returns and ensure raising and using capital best effectively. The D-CAPM is thought to be more useful for those want to look at a particular stock or portfolio as it does a better job when returns’ distribution is skewed or the benchmark is any return other than the mean; and thus, investors who pursue different benchmark of return can apply this model more flexibly. Moreover, both the semideviation and the downside beta could be calculated easily in Excel as guided by Estrada (2006). Along with using the model, backtesting and statistical tests are recommended to examine the efficiency and accuracy of the model.
Yet, there is existence of several drawbacks in the study due to limited researching time, research design and the author’s insufficient understanding of the related body of knowledge. Choosing Vietnamese Stock Market is believed to be challenged due to the lack of previous studies on the market; plus, with about-10-year-old established with relatively small capital magnitude, the case could not provide good and sufficient quality of data and observations as expected. While reviewing limitations of this study, thus, the author came to awareness of possible further study on the related topic. As this research has computed semideviations and downsides beta for a group of stocks that representing key sectors in the Vietnam’s economy, it would be logical and practical adjust the model in a whole particular industry in order to assess its impacts on the stock market. Additionally, comparing the significance of downside risk measures in the D-CAPM with Value-at-risk method in valuing loss-gain of investments is also suggested to validate efficiency and reliability of the model. Apart from semideviations and downsides beta, there are also others indicators to measure asymmetric risk-return that should be taken to account to generate more comprehensive conclusion. Furthermore, the research can be extended by integrating country-specific risk factors such as politics, consumptions, inflations or even culture in the model to explain more thoroughly Equity Risk Premium in the Vietnamese Stock Market endogenously; and it could be placed in the theme of international integration theme to consider attractiveness and prosperity of the market.
BibliographyAdams, J., Khan, H., Reaside, R., and White, D., 2007. Research Methods for Graduate Business and Social Science Students. London: Sage.
Aggarwal, R. and Goodell, J., 2008. Equity premia in emerging markets: National characteristics as determinants. Journal of Multinational Financial Management, 18(4), 389-404 Available from: http://www.sciencedirect.com/ [Accessed 13 February 2011].
Alexander, C., 2008. Market risk analysis. v. 1: quantitative methods in finance. Chichester: Wiley-Blackwell.
Berger, D., Pukthuanthong, K. and Yang, J., 2011. International diversification with frontier markets. Journal of Financial Economics. Article in Press, Accepted Manuscript. Available from: http://www.sciencedirect.com/ [Accessed 17 February 2011].
Bodie, Z., Kane, A. and Marcus, A.J., 2009. Investment. 8th ed. Boston: McGraw-Hill/Irwin.
Brandt, M.W. and Wang, K.Q., 2003. Time-varying risk aversion and unexpected inflation, Journal of Monetary Economics, 50(7), 1457-1498 Available from: http://www.sciencedirect.com/ [Accessed 8 February 2011].
Brealey, R.A., Myers, S.C. and Allen, F., 2008. The principles of corporate finance. 9th ed. London: McGraw-Hill.
Bryman, A. and Bell, E., 2003. Business research methods. Oxford: Oxford University Press Inc.
Bryman, A. and Bell, E., 2007. Business research methods. 2nd ed. Oxford: Oxford University Press Inc.
Campbell, S. D., 2005. A review of Backtesting and Backtesting Procedures. Finance and Economics Discussion Series. Available from: http://www.federalreserve.gov/pubs/feds/2005/200521/200521pap.pdf [Accessed 20 February 2011].
Chen, J. and Chen, D., 2004. The Downside Risk and Equity Evaluation: Emerging Market Evidence, Journal of Emerging market finance, 3(1), 77-93 Available from: British Library Document Supply Centre Inside Serials & Conference Proceedings, http://ejournals.ebsco.com/ [Accessed 8 February 2011].
Cohen, M.B., 2009. Estimating the Equity Risk Premium for Economies in the Asian Region, Asian Journal of Finance & Accounting, 1(1), 23-33 Available from: http://ehis.ebscohost.com/ [Accessed 13 February 2011].
Collis, J. and Hussey, R., 2009. Business Research: A Practical Guide for Undergraduate and Postgraduate Students. 3rd ed. Basingstoke: Palgrave Macmillan.
Constantinides, G.M., 2008. Understading the Equity Risk Premium Puzzle. In: Mehra, R., eds. Handbook of the Equity Risk Premium. Oxford: Elsevier, 331-359.
Damodaran, A., 2009. Equity Risk Premium (ERP): Determinants, Estimation and Implications – A Post-Crisis Update. Financial Markets, Institutions & Instruments, 18(5), 289-370 Available from: http://ehis.ebscohost.com/ [Accessed 8 February 2011].
De Santis, G. and Gerard, B., 1997. International Asset Pricing and Portfolio Diversification with Time-Varying Risk. Journal of Finance, 52(5), 1881-1912 Available from: http://ehis.ebscohost.com/ [Accessed 13 February 2011].
Dimson, E., Marsh, P. and Staunton, M., 2000. Risk and Return in the 20th and 21st Centuries. Business Strategy Review, 11(2), 1-18. Available from: http://ehis.ebscohost.com/ [Accessed 8 February 2011].
Dimson, E., Marsh, P. and Staunton, M., 2002. Triumph of the Optimists: 101 Years of Global Investment Returns. Princeton, NJ: Princeton University Press.
Dimson, E., Marsh, P. and Staunton, M., 2006. DMS Global Returns data module. Chicago: Ibbotson Associates.
Dimson, E., Marsh, P. and Staunton, M., 2008. The Worldwide Equity Premium: A Smaller Puzzle. In: Mehra, R., eds. Handbook of the Equity Risk Premium. Oxford: Elsevier, 467-514.
Donaldson, G.R., Kamstra, M.J. and Kramer, L.A., 2010. Estimating the Equity Premium. Journal of Financial and Quantitative Analysis, 45(4), 813-848 Available from: http://papers.ssrn.com/ [Accessed 12 February 2011].
Donaldson, J. and Mehra, R., 2008. Risk-Based Explanations of the Equity Premium. . In: Mehra, R., eds. Handbook of the Equity Risk Premium. Oxford: Elsevier, 37-99.
Elton, E.J., Gruber, M.J., Brown, S.J. and Goetzmann, W.N., 2007. Modern Portfolio Theory and Investment Analysis. 7th ed. Hoboken, N.J.: John Wiley.
Estrada, J., 2000. The cost of equity in emerging markets: A downside risk approach. Emerging markets quarterly, 4(3), 19-31 Available from: http://ehis.ebscohost.com/ [Accessed 13 February 2011].
Estrada, J., 2001. The cost of equity in emerging markets: A downside risk approach (II). Emerging markets quarterly, 5(1), 63-72 Available from: http://ehis.ebscohost.com/ [Accessed 13 February 2011].
Estrada, J., 2002. Systematic risk in emerging markets: the D-CAPM. Emerging Markets Review, 3(4), 365-379. Available from: http://ejournals.ebsco.com/ [Accessed 9 February 2011].
Estrada, J., 2006. Downside Risk in Practice. Journal of Applied Corporate Finance, 18(1), 117-125 Available from: http://onlinelibrary.wiley.com/ [Accessed 14 February 2011].
Estrada, J., 2007. Mean-semivariance behavior: Downside risk and capital asset pricing. International Review of Economics and Finance, 16(2), 169-185 Available from: http://www.sciencedirect.com/ [Accessed 8 February 2011].
Fama, E.F. and French, K.R., 1992. The cross-section of expected stock returns. Journal of Finance, 47(2), 427-465 Available from: http://ehis.ebscohost.com/ [Accessed 13 February 2011].
Fama, E.F. and French, K.R., 2002. The Equity Premium. Journal of Finance, 57(2), 637- 659.
Fama, E.F., 1991. Efficient Capital Markets: II. Journal of Finance, 46(5), 1575-1617 Available from: http://ehis.ebscohost.com/ [Accessed 8 February 2011].
Frankfurter., M., 2010. Market risk: Known and unknowns. Futures: News, Analysis & Strategies for Futures, Options & Derivatives Traders, 39 (12), 48-52 Available from: Business Source Complete, EBSCOhost [Accessed 8 February 2011].
Girard, E. and Sinha, A., 2006. Does Total Risk MatterThe Case of Emerging Markets. Multinational Finance Journal, 10(1-2), 117-151. Available from: Business Source Complete, EBSCOhost, [Accessed 9 February 2011].
Girard, E., Rahman, H. and Zaher, T., 2001. Intertemporal risk return relationship in the Asian markets around the Asian crisis. Financial Services Review, 10(1-4), 249-272 Available from: http://www.sciencedirect.com/ [Accessed 8 February 2011].
Goetzmann, W.N. and Ibbotson, R.G., 2004. The equity risk premium: essays and explorations. New York : Oxford University Press. Available from: Bournemouth University Library Catalogue, http://site.ebrary.com/lib/bournemouth/ [Accessed 12 February 2011].
Goetzmann, W.N. and Ibbotson, R.G., 2008. History and the Equity risk premium. In: Mehra, R., eds. Handbook of the Equity Risk Premium. Oxford: Elsevier, 515-529.
Hart, C. 1998. Doing a Literature review: Releasing the Social Science Research Imagination. Thousand Oaks, CA: Sage.
Harvey, C.R., 1995. Predictable Risk and Returns in Emerging Markets. Review of Financial Studies, 8(3), 773-816 Available from: http://ehis.ebscohost.com/ [Accessed 13 February 2011].
Harvey, C.R., 2000. The drivers of Expected Returns in International Markets. Emerging Markets Quarterly, 4(3), 32-49 Available from: http://faculty.fuqua.duke.edu/~charvey/Research/Published_Papers/P69_The_drivers_of.pdf [Accessed 21 January 2011].
Hassett, S.D., 2010. The RPF Model for Calculating the Equity Market Risk Premium and Explaining the Value of the S&P with Two Variables. Journal of Applied Corporate Finance, 22(2), 118-130, http://ehis.ebscohost.com/ [Accessed 13 February 2011].
Horn, R., 2009. Researching and writing dissertations: A complete guide for business student. Wimbledon: Chartered Institute of Personnel & Development.
Hwang, S. and Pedersen, C.S., 2004. Asymmetric risk measures when modeling emerging markets equities: evidence for regional and timing effects. Emerging Markets Review, 5(1), 109-128 Available from: http://ejournals.ebsco.com/ [Accessed 8 February 2011].
Hyde, K.F., 2000. Recognising deductive processes in qualitative research. Qualitative Market Research: An International Journal, 3(2), 82-89.
Iqbal, J. and Brooks, R., 2007. Alternative beta risk estimators and asset pricing tests in emerging markets: The case of Pakistan. Journal of Multinational Financial Management, 17(1), 75-93 Available from: Elsevier Science, EBSCOhost [Accessed 9 February 2011].
Iqbal, J., Brooks, R. and Galagedera, D.U.A., 2010. Testing conditional asset pricing models: An emerging market perspective. Journal of International Money and Finance.29(5), 897-918. Available from: http://www.sciencedirect.com/ [Accessed 10 Feb 2011].
Jacobsen, B.J. and Liu, X., 2008. China’s segmented stock market: An application of the conditional international capital asset pricing model. Emerging Markets Review, 9(3), 153-173 Available from: http://www.sciencedirect.com/ [Accessed 8 February 2011].
Kandel, S. and Stambaugh, R.F., 1989. A Mean-Variance Framework for Tests of Asset Pricing Models. The Review of Financial Studies, 2(2), 125-156.
Kaplanski, G., 2004. Traditional beta, downside risk beta and market risk premiums. Quarterly Review of Economics & Finance, 44 (5), 636-653 Available from: http://ehis.ebscohost.com/ [Accessed 8 February 2011].
Kraus, A. and Litzenberger, R., 1976. Skewness Preference and the Valuation of Risk Assets. Journal of Fiance, 31(4), 1085-1100 Available from: http://ehis.ebscohost.com/ [Accessed 22 February 2011].
Lancaster, G., 2005. Research methods in Management: a concise introduction to research in management and business consultancy. Oxford: Elsevier Butterworth – Heinemann.
Lettau, M., Ludvigson, S.C. and Wachter, J.A., 2008. The declining Equity Risk Premium: What role does macroeconomic risk play?. Review of Financial Studies, 21(4), 1653-1687 Available from: http://ehis.ebscohost.com/ [Accessed 8 February 2011].
Marshall, A., Maulana, T., and Tang, L., 2009, The estimation and determinants of emerging market country risk and the dynamic conditional correlation GARCH model. International Review of Financial Analysis, 18(5), 250-259 Available from: http://www.sciencedirect.com/ [Accessed 9 February 2011].
Mayfield, E.S., 2004. Estimating the market risk premium. Journal of Financial Economics, 73(3), 465-496 Available from: http://www.sciencedirect.com/ [Accessed 8 February 2011].
Mehra, R. and Prescott, E.C., 1985. The equity premium: A puzzle. Journal of Monetary Economics, 15(2), 145-161.
Mehra, R. and Prescott, E.C., 1988. The equity risk premium: A solution?. Journal of Monetary Economics, 22(1), 133-136 Available from: http://www.sciencedirect.com/ [Accessed 8 February 2011].
Mehra, R. and Prescott, E.C., 2008. The Equity Premium: ABCs. In: Mehra, R., eds. Handbook of the Equity Risk Premium. Oxford: Elsevier, 1-36.
O’Leary, Z., 2004. The Essential Guide to Doing Research. London: Sage.
Parramore, K. and Watsham, T., 2004. II.F Regression Analysis in Finance. In: Alexander, C. and Sheedy, E., eds. Professional Risk Manager’s Handbook: A comprehensive Guide to Current Theory and Best Practices. Wilmington, DE: PRMIA Publications.
Quisenberry, JR.C. and Griffith, B., 2010, Frontier Equity Markets: A Primer on the Next Generation of Emerging Markets, Journal of Wealth Management, 13(3), 50-58, Available from: http://ehis.ebscohost.com/ [Accessed 22 February 2011].
Rawlings, J.O., Pantula, S.G. and Dickey, D.A., 1998. Applied regression ananlysis: a research tool. 2nd ed. New York: Springer. Available from: Bournemouth University Library Catalogue, http://site.ebrary.com/lib/bournemouth/ [Accessed 19 March 2011].
Salomons, R. and Grootveld, H., 2003. The equity risk premium: emerging vs. developed markets. Emerging Markets Review, 4(2), 121, Available from: http://ehis.ebscohost.com/ [Accessed 20 February 2011].
Saunders, M., Lewis, P. and Thornhill, A., 2007. Research Methods for Business Students. 4th ed. London: FT/Prentice Hall.
Sharp, J., Peters, J. and Howard, K., 2002. The Management of Student Research Project. 3rd ed. Hants: Gower.
Siegel, J.J., 2005. Perspectives on the Equity Risk Premium. Financial Analysts Journal, 61(6), 61-71 Available from: http://papers.ssrn.com/ [Accessed 8 February 2011].
Smith, J.K., 1983. Quantitative v qualitative research: An attempt to classify the issue. Educational Research, March.
Soenen, L. and Johnson, R., 2008. The Equity Market Risk Premium and the Valuation of Overseas Investments’, Journal of Applied Corporate Finance, 20(2), 113-121 Available from: http://ehis.ebscohost.com/ [Accessed 13 February 2011].
Stewart, D., and Kamins, M., 1993. Secondary Research: Information Sources and Methods in the Applied Social Research Methods Series vol. 4. 2nd ed. London: SAGE
Stewart, D.W. and Kamins, M.A., 1993. Secondary research: information sources and methods. 2nd ed. Newbury Park: Sage.
Strauss, A. and Corbin, J. 1990. Basics of Qualitative Research: Grounded Theory Procedures and Techniques. Newbury Park: Sage.
Veal, A.J., 1997. Research methods for Leisure and Tourism: A practical guide. 2nd ed. London: Pearson Professional Limited.
Vivian, A., 2007. The UK Equity Premium: 1901–2004. Journal of Business Finance & Accounting, 34(9-10), 1496-1527 Available from: http://ehis.ebscohost.com/ [Accessed 17 February 2011].
Wilson, J. 2010. Essentials of Business Research: A guide to doing your research project. London: Sage.
AppendicesAppendix 1: Simple regression summary outputs
Exhibit 1-1: Simple regression analysis of standard deviation (?) to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.68 R20.47 Adj. R20.39 SE0.00 Observations9 ANOVA Df SS MS F Significance F Regression1.0000 0.0001 0.0001 6.0884 0.0430 Residual7.0000 0.0001 0.0000 Total8.0000 0.0002 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 1.44 0.19 -0.01 0.03 -0.02 0.04 ?-0.22 0.09 -2.47 0.04 -0.44 -0.01 -0.54 0.09Exhibit 1-2: Simple regression analysis of beta (?) to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.71 R20.50 Adj. R20.43 SE0.00 Observations9 ANOVA Df SS MS F Significance F Regression1 0.00 0.00 6.96 0.03 Residual7 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 1.70 0.13 -0.01 0.03 -0.02 0.04 ?-0.02 0.01 -2.64 0.03 -0.04 0.00 -0.05 0.01Exhibit 1-3: Regression analysis of semideviation with respect to mean (?? ) to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.58 R20.34 Adj. R20.25 SE0.00 Observations9 ANOVA Df SS MS F Significance F Regression1 0.00 0.00 3.60 0.09 Residual7 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 0.84 0.43 -0.01 0.02 -0.02 0.03 ??-0.23 0.12 -1.90 0.10 -0.51 0.06 -0.64 0.19Exhibit 1-4: Simple regression analysis of semideviation with respect to risk-free rate (?f ) to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.83 R20.69 Adj. R20.64 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression1 0.00 0.00 15.41 0.005 Residual7 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 1.37 0.21 0.01 0.02 -0.01 0.03 ?f-0.25 0.09 -2.62 0.01 -0.47 -0.02 -0.58 0.08Exhibit 1-5: Simple regression analysis of semideviation with respect to zero (?0 ) to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.70 R20.49 Adj. R20.42 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression1 0.00 0.00 6.71 0.04 Residual7 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 1.33 0.23 -0.01 0.02 -0.01 0.03 ?0-0.24 0.09 -2.59 0.04 -0.47 -0.02 -0.58 0.09Exhibit 1-6: Regression analysis of downside beta with respect to mean (??D ) to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.75 R20.56 Adj. R20.50 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression1 0.00 0.00 8.88 0.02 Residual7 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.02 0.01 2.02 0.08 0.00 0.04 -0.01 0.05 ??D-0.02 0.01 -2.98 0.02 -0.04 0.00 -0.05 0.00Exhibit 1-7: Simple regression analysis of downside beta with respect to risk-free rate (?fD ) to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.82 R20.66 Adj. R20.62 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression1 0.00 0.00 13.86 0.01 Residual7 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.02 0.01 2.50 0.04 0.00 0.03 -0.01 0.04 ?fD-0.02 0.01 -3.73 0.01 -0.03 -0.01 -0.04 0.00Exhibit 1-8: Simple regression analysis of downside beta with respect to zero (?0D ) to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.79 R20.63 Adj. R20.57 SE0.00 Observations9.00 ANOVA df SS MS F Significance F Regression1 0.00 0.00 11.69 0.01 Residual7 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.02 0.01 2.23 0.06 0.00 0.03 -0.01 0.04 ?0D-0.02 0.01 -3.42 0.01 -0.03 -0.01 -0.04 0.00Appendix 2: Multiple regression summary outputs
Exhibit 2-1: Multiple regression analysis of ? and ?? to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.79 R20.63 Adj. R20.51 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 5.11 0.05 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.02 0.01 2.17 0.07 0.00 0.04 -0.01 0.05 ?-0.85 0.39 -2.17 0.07 -1.82 0.11 -2.31 0.61 ??0.76 0.46 1.63 0.15 -0.38 1.89 -0.96 2.48Exhibit 2-2: Multiple regression analysis of ? and ?f to mean return
SUMMARY OUTPUT Regression Statistics Multiple R1.00 R20.99 Adj. R20.99 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 370.83 0.00 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.02 0.01 2.27 0.06 0.00 0.03 -0.01 0.04 ?0.01 0.15 0.09 0.93 -0.35 0.37 -0.53 0.56 ?f-0.02 0.01 -1.90 0.11 -0.05 0.01 -0.07 0.02Exhibit 2-3: Multiple regression analysis of ? and ?0 to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.70 R20.49 Adj. R20.33 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 2.94 0.13 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 0.51 0.63 -0.02 0.03 -0.04 0.05 ?0.17 0.67 0.25 0.81 -1.46 1.80 -2.31 2.64 ?0-0.42 0.71 -0.59 0.57 -2.16 1.32 -3.06 2.21Exhibit 2-4: Multiple regression analysis of ? and ?? to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.75 R20.56 Adj. R20.42 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 3.88 0.08 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.02 0.01 1.87 0.11 -0.01 0.04 -0.04 0.05 ?-0.05 0.18 -0.26 0.81 -0.48 0.39 -0.07 0.61 ??-0.02 0.02 -1.17 0.29 -0.06 0.02 -0.08 0.04Exhibit 2-5: Multiple regression analysis of ? and ?f to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.82 R20.67 Adj. R20.55 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 5.98 0.04 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.02 0.01 2.27 0.06 0.00 0.03 -0.01 0.04 ?0.01 0.15 0.09 0.93 -0.35 0.37 -0.53 0.56 ?f-0.02 0.01 -1.90 0.11 -0.05 0.01 -0.07 0.02Exhibit 2-6: Multiple regression analysis of ? and ?0 to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.79 R20.63 Adj. R20.50 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 5.02 0.05 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.02 0.01 2.04 0.09 0.00 0.03 -0.01 0.04 ?-0.01 0.16 -0.07 0.95 -0.39 0.37 -0.59 0.57 ?0-0.02 0.01 -1.61 0.16 -0.05 0.01 -0.06 0.03Exhibit 2-7: Multiple regression analysis of ? and ?? to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.71 R20.50 Adj. R20.34 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 3.04 0.12 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 1.58 0.16 -0.01 0.04 -0.02 0.05 ?-0.02 0.01 -1.40 0.21 -0.05 0.01 -0.07 0.03 ??-0.04 0.17 -0.23 0.83 -0.46 0.39 -0.68 0.60Exhibit 2-8: Multiple regression analysis of ? and ?f to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.74 R20.55 Adj. R20.40 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 3.67 0.09 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 1.57 0.17 -0.01 0.04 -0.02 0.05 ?-0.01 0.01 -0.86 0.42 -0.05 0.02 -0.06 0.04 ?f-0.13 0.16 -0.83 0.44 -0.53 0.26 -0.74 0.47Exhibit 2-9: Multiple regression analysis of ? and ?0 to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.74 R20.55 Adj. R20.40 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 3.64 0.09 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 1.56 0.17 -0.01 0.04 -0.02 0.05 ?-0.01 0.01 -0.88 0.41 -0.05 0.02 -0.06 0.04 ?0-0.13 0.16 -0.81 0.45 -0.53 0.26 -0.73 0.47Exhibit 2-10: Multiple regression analysis of ? and ??D to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.75 R20.56 Adj. R20.41 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 3.80 0.09 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.02 0.01 1.86 0.11 -0.01 0.04 -0.02 0.05 ?0.00 0.02 -0.02 0.99 -0.06 0.06 -0.09 0.09 ??D-0.02 0.02 -0.91 0.40 -0.08 0.04 -0.11 0.07Exhibit 2-11: Multiple regression analysis of ? and ?fD to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.82 R20.67 Adj. R20.56 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 6.07 0.04 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 1.57 0.17 -0.01 0.04 -0.02 0.05 ?-0.01 0.01 -0.86 0.42 -0.05 0.02 -0.06 0.04 ?fD-0.13 0.16 -0.83 0.44 -0.53 0.26 -0.74 0.47Exhibit 2-12: Multiple regression analysis of ? and ?0D to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.79 R20.63 Adj. R20.50 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression2 0.00 0.00 5.02 0.05 Residual6 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 1.86 0.11 0.00 0.03 -0.01 0.04 ?0.00 0.02 0.09 0.93 -0.04 0.04 -0.06 0.07 ?0D-0.02 0.01 -1.43 0.20 -0.06 0.02 -0.08 0.03Exhibit 2-13: Multiple regression analysis of ?, ??, ?, ??D to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.89 R20.79 Adj. R20.57 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression4 0.00 0.00 3.69 0.12 Residual4 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.02 0.01 2.82 0.05 0.00 0.05 -0.01 0.06 ?-0.93 0.46 -2.03 0.11 -2.21 0.34 -3.05 1.19 ??1.05 0.51 2.04 0.11 -0.38 2.47 -1.31 3.41 ?0.03 0.02 1.10 0.33 -0.04 0.09 -0.08 0.14 ??D-0.04 0.03 -1.63 0.18 -0.12 0.03 -0.17 0.08Exhibit 2-14: Multiple regression analysis of ?, ?f, ?, ?fD to mean return
SUMMARY OUTPUT Regression Statistics Multiple R1.00 R20.99 Adj. R20.99 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression4 0.00 0.00 176.1 0.00 Residual4 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.02 0.01 1.21 0.29 -0.02 0.06 -0.05 0.08 ?-0.16 0.91 -0.17 0.87 -2.67 2.36 -4.33 4.01 ?f0.18 1.01 0.18 0.87 -2.63 2.99 -4.48 4.48 ?0.01 0.03 0.39 0.71 -0.07 0.09 -0.12 0.14 ?fD-0.03 0.03 -1.08 0.34 -0.11 0.05 -0.16 0.10Exhibit 2-15: Multiple regression analysis of ?, ?0, ?, ?0D to mean return
SUMMARY OUTPUT Regression Statistics Multiple R0.79 R20.63 Adj. R20.26 SE0.00 Observations9 ANOVA df SS MS F Significance F Regression4 0.00 0.00 1.70 0.31 Residual4 0.00 0.00 Total8 0.00 Coefficients SE t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept0.01 0.01 0.95 0.40 -0.03 0.05 -0.05 0.08 ?0.12 0.82 0.14 0.89 -2.17 2.41 -3.68 3.92 ?0-0.15 0.89 -0.17 0.88 -2.63 2.33 -4.27 3.97 ?0.00 0.03 0.00 1.00 -0.07 0.07 -0.12 0.12 ?0D-0.02 0.02 -0.77 0.48 -0.09 0.05 -0.13 0.09