Further investigation on the variability of individual stock beta and portfolio size.
Beta, as a measure of systematic risk, considers the volatility of a financial asset with respect to the general market movements. The higher the beta of an asset, the greater is the asset's price variability relative to the market as a whole. Beta also measures market risk. It captures the portion of an asset's overall risk that cannot be diversified away. Modern Portfolio Theory (MPT), as articulated by Sharpe (1964) and Lintner (1965), argues that market risk, also referred to as systematic risk, is the only risk that is rewarded when an asset is held as part of a diversified portfolio. In Sharpe's representation of the Capital Asset Pricing Model (CAPM), beta is assumed stationary. Studies, such as Das (2008), Brooks et al (1997); and Chen & Keown (1981), show that the beta stability assumption holds fairly well for well diversified portfolios. Fama & French (2004) and later, Bundoo (2008), are among many that have shown that this assumption may be invalid especially for individual stocks.
Other studies presenting evidence that the beta stability assumption may be invalid include Morana (2009), Avramov & Chordia (2006), Gregory-Allen, Impson & Karafiath (2006), Ebner & Neumann (2005), and Brooks, Faff & Ariff (1998). With constant beta, Morana (2009) and Avramov and Chordia (2006) show that none of the alternative market models examined in their studies capture the true returns generating process. However when beta is allowed to vary, other factors such as firm value and past return effects, are captured.
The study by Weinraub and Kuhlman (1994) was the first to examine the effect of the variability of individual stock betas on the variability of small portfolio betas. Using undiversified U.S. equity portfolios, they find that minimization of portfolio beta variability cannot be achieved by combining stocks which, individually, have low beta variability. The study by Weinraub and Kuhlman suggests that the variability of portfolio beta may not be related with changes in the systematic risk exposure of individual stocks. This finding raises the additional question as to whether portfolio beta variability is influenced by the size of beta, regardless of how it varies. It is quite possible that portfolio managers may be motivated to seek low beta stocks in the belief that such composition would achieve a portfolio that is not as sensitive to market quirks over the horizon.
Portfolios of small beta stocks are those that hardly react to market quirks while stocks with large betas are more apt to respond to systematic risk factors. However, while portfolios of small beta stocks exhibit low systematic risk, there is no assurance that the variability of the betas themselves would be low compared to that of a portfolio of large beta stocks. It is this conjecture that provides the motivation for this study. Greater beta variability indicates greater uncertainty regarding the systematic risk exposure of the asset. This characteristic may not bode well for investors seeking greater stability in their portfolio performance.
To investigate the problem, this study examines the relationship between the variability of individual stock betas and the variability of large portfolio betas. It also compares the variability of the betas of small capitalization stocks within a portfolio to that of a portfolio of large capitalization stocks. Similar to Weinraub and Kuhlman (1994), beta variability is measured using both standard deviation and coefficient of variation. In this study however, portfolios are ranked first in terms of the standard deviation of individual stock betas and subsequently, in terms of the market capitalization of the stocks. In all the cases, portfolio size (in terms of number of stocks per portfolio) is held constant.
Results of this study show that it is possible to minimize portfolio beta variability by selecting stocks which, individually, exhibit low to moderate beta variability. Portfolios of small capitalization stocks not only possess higher betas than large cap stocks, but the betas themselves are much more variable. This characteristic causes the ultimate performance of small cap stock portfolios to be more uncertain than that of large cap stocks. These findings should be of interest to portfolio managers who select stocks based on the size of the individual stock betas as a way to mitigate exposure to market risk.
STUDIES ON BETA VARIABILITY AND ASSET RETURNS
Early studies on the stability of beta and portfolio returns were mostly concerned with the specification of the Capital Asset Pricing Model (CAPM). These studies include Morana (2009), Avramov and Chordia (2006), Gregory-Allen, Impson and Karafiath (2006), Ebner and Neumann (2005), Howton and Peterson (1998), Brooks, et al (1997), Fabozzi and Francis (1977), and Bhardwaj and Brooks (1993).
Fabozzi and Francis (1977) conduct stability tests of beta for bull and bear markets and show that small firm stocks tend to outperform large firm stocks in bull markets. Moreover, Bhardwaj and Brooks (1993) find that bull market betas are significantly larger than bear market betas, although the beta differences are much larger for small firm stocks. Later, Howton and Peterson (1998) discover that while bull market betas are positively related to stock returns, the relationship between returns and bear market betas is negative. All of this evidence led Fama and French (2004) to conclude that if the market proxy problem invalidates tests of the CAPM in these studies, it also invalidates applications that employ the market proxies used in empirical tests.
In addition to the seminal work of Black, Jensen, and Scholes (1972), some recent studies have shown evidence of a positive relation between beta and expected return. For example, Das (2008) observes such a relationship in the Indian stock market and finds that majority of stocks on the National Stock of Exchange of India appear to have stable betas. El-Shaer, Elsas, and Theissen (2003) also find a positive and significant relationship between beta and expected return in a study of the German stock market. They argue that the reason previous studies did not identify this relationship was the result of a near zero market risk premium in the sample period. However, Ebner and Neumann (2005) find that the problem of beta instability in German stocks persist over different market regimes. They then show that a time-varying estimation model fits the data considerably better than the time-invariant model of El-Shaer, Elsas, and Theissen (2003).
In a study of the performance of international stock portfolios, Tang and Shun (2003) show that skewness, but not kurtosis, plays a major role in the pricing of stocks, even after beta instability has been accounted for. Their findings are in line with the seminal work of Kraus and Litzenberger (1976) which shows that investors accept less positive returns for positively skewed portfolios.
SOURCES OF BETA VARIABILITY IN THE CAPM
Brooks et al (1997) argue that the observed beta instability in many financial studies may be the result of instability in the individual stocks. They show that beta variability increases in periods of rising economic uncertainty. Earlier, Schwert and Seguin (1990) consider the question as to how such market volatility affects stock beta. Using a heteroscedastic market model, they show that over time, betas of firms of different sizes are affected by market volatility via the following relationship:
[[beta].sub.j,t] = [[beta].sub.j] + [[delta].sub.j] / [[sigma].sub.2.sub.M, t] (1)
where [[beta].sub.j] is constant and [[sigma].sub.2.sub.M, t] is the aggregate equity market volatility. The term [[sigma].sub.j]/[[sigma].sub.2.sub.M, t], is the time-varying component of the composite beta coefficient. A positive [[delta].sub.j] indicates a negative relationship between asset beta and market volatility. On the other hand, a negative [[delta].sub.j] indicates a positive relationship between asset beta and market volatility. Schwert and Seguin find that for US stocks, [delta] is negative for small firms and positive for stocks of large firms, meaning that the difference between the systematic risk of small and large firms is greater during times of high overall stock market volatility.
Reyes (1999) re-examines the relationship between firm size and the time-variation in stock betas using UK equity indexes. The study by Reyes shows that the time-varying component identified by Schwert and Seguin (1990) is not statistically significant for both small and large firms. In these studies, time-variation in stock betas is accounted for by modifying the following traditional market model:
[R.sub.jt] = [[alpha].sub.j] + [[beta].sub.j][R.sub.M,t] + [[epsilon].sub.jt] (2)
where [R.sub.jt] is the asset return, [R.sub.Mt] is the return on the market portfolio, and [[alpha].sub.j] and [[beta].sub.j] are parameters that measure the degree of the asset's performance. Substituting Equation 1 into Equation 2 yields the Schwert and Seguin (1990) time-varying beta market model:
[R.sub.j,t] = [[alpha].sub.j] + [[beta].sub.j][R.sub.M,t] + [[delta].sub.j] + ([R.sub.M,t]/[[sigma].sup.2.sub.M,t] + [[epsilon].sub.j,t] (3)
Campbell and Vuolteenaho (2004) apply a two-beta model to show that asset betas reflect two kinds of risk, one arising from the market's future cash flows and the other reflecting news about the market's discount rates. They find that value stocks and small stocks have considerably higher cash flow betas than growth and large stocks, which probably explains the former's higher average returns. They also show that while portfolio value may fall because investors receive bad news about future cash flows, it may also decline because investors increase the discount rate attaching to these cash flows. In the first case, wealth decreases and investment opportunities are unchanged. But in the second case, wealth decreases but investment opportunities improve.
Brooks et al (1997) examine the effect of diversification on the stability of portfolio betas. They show that for a portfolio of a given size, substitution of constant beta stocks for varying beta stocks enhances the stability of the portfolio's overall beta. They also point out that as the size of a portfolio is increased, a greater proportion of constant beta stocks are needed to maintain the relative stability of the larger portfolio's systematic risk exposure. In a subsequent study, Brooks, Faff, and Ariff (1998) explore the issue of beta instability in the Singaporean stock market and find a high incidence of beta instability.
In a study on the effect of stock beta variability on the variability of portfolio betas, Weinraub and Kuhlman (1994) find that stocks with low betas exhibit greater relative beta variability. Empirical evidence in Weinraub and Kuhlman's study does not confirm whether beta instability is due to the small portfolio size used in the study (market capitalization of individual stocks) or the result of the low beta stocks themselves. For this study, the intertemporal stability of beta is examined by first forming portfolios which, individually, exhibit different levels of beta variability. Thereafter, the variability of beta is examined across portfolios of different market values but of equal number of securities. The latter construct is an attempt to plug the gap in the empirical process applied by Weinraub and Kuhlman (1994).
DATA AND EMPIRICAL METHODOLOGY
In this study, month-end stock prices and a value-weighted equity index were obtained over a 24-year period, from 1980 to 2003. The working sample consisted of 800 randomly selected stocks. To be part of the final sample, the stock must have stayed listed for the entire period. All data were generated from the University of Chicago's Center for Research in Security Prices (CRSP).
For each year in the sample period, beta was calculated for each stock by implementing the market model specified in Equation 2. The periodic return is calculated as the logarithmic price changes, thus: [R.sub.t] = ln([P.sub.t]/[P.sub.t-1]). For each of the 800 stocks, 24 annual betas were obtained from the market model regressions over the sample period.
Two measures of variability were calculated for the annual betas of each stock: standard deviation and coefficient of variation. Based on the standard deviation of the individual stock betas, four portfolios were formed in hierarchical order, each containing 200 stocks. The first portfolio contained 200 stocks with the smallest standard deviations while the fourth portfolio contained 200 stocks with the highest standard deviations.
Portfolios were also ranked based on the market values of the stocks. This latter arrangement distinguishes the process of this analysis from the method employed by Weinraub and Kuhlman (1994) in which only small portfolios were considered. With this arrangement, one is able to determine whether the variability of small beta stocks when assembled in a portfolio is influenced by the market value of that portfolio or simply by the size of the beta. In this construct, there is no presumption that the size of beta is necessarily influenced by the market value of the stock.
While the value of beta informs the investor of how a portfolio is expected to react relative to the market, it does not necessarily suggest what the outcome of the investment would be relative to market performance. Given a beta of 0.5, for example, the portfolio would be considered to be half as volatile as the market. Yet, if the market were to decline by, say 10%, the portfolio may not necessarily decline by 5% over the same horizon. The performance of the portfolio at the endpoint may be a change to a level quite different from a decline of 5% of the change in the market. This is because the ultimate systematic performance of the portfolio is guided by the variability of the portfolio beta regardless of its size (Morana, 2009; Groenewold & Fraser, 1999). The more variable the beta coefficient over the horizon, the less likely the eventual performance of the portfolio would reflect the market's impact for that value of beta. This argument underlies the import of this study, which is designed to show that the consideration of beta variability is integral in portfolio management.
The framework for understanding the structure of beta begins with the classic market model presented earlier in Equation 2. Based on this framework, the variance of each stock's return is defined as:
[[sigma].sup.2.sub.j] = [[beta].sup.2.sub.j][[sigma].sup.2.sub.M] + [[sigma].sup.2.sub.[epsilon]j] (4)
This expression splits total asset risk, [[sigma].sup.2.sub.j], into two familiar components: systematic risk ([[beta].sup.2.sub.j][[sigma].sup.2.sub.M]) and unsystematic risk or residual variance ([[sigma].sup.2.sub.[epsilon]]). For a portfolio, total risk ([[sigma].sup.2.sub.p]) is expressed as
[[sigma].sup.2.sub.P] = ([n.summation over (j=1)] [w.sup.2.sub.j][[beta].sup.2.sub.j]) [[sigma].sup.2.sub.M] + [n.summation over (j=1)] [w.sup.2.sub.j] [[sigma].sup.2.sub.[epsilon]j] (5)
where [w.sub.j] is the proportional investment in the jth asset. The first term, in parenthesis, is portfolio beta, defined as the weighted average of the individual stock betas. The last expression is the residual variance, also a weighted average of the residual variances of the individual stocks.
Chen and Keown (1981) have examined the issue of decomposing the total risk of a portfolio when beta is unstable. They show that total risk of a portfolio consists of three components: systematic risk, pure residual risk, and beta instability risk. Modern portfolio theory (MPT) suggests that systematic risk is undiversifiable and hence, rewarded with higher returns. However, Chen and Keown find that for individual stocks, the risk due to beta instability is considerably more important than pure residual risk. They therefore conclude that this element can potentially thwart efforts to reduce non-systematic risk via diversification. Using a risk-free adjusted market model, they show that the dynamic counterpart of the standard market model is
[R.sub.jt] = [[alpha].sub.j] + [bar.[[beta].sub.j][R.sub.Mt] + [[upsilon].sub.jt] (6)
where [[upsilon].sub.jt] = [a.sub.it][R.sub.Mt] + [[epsilon].sub.jt]
The decomposition of portfolio risk is then derived to be:
[[sigma].sup.2.sub.P] = [[beta].sup.2.sub.P] [[sigma].sup.2.sub.M] + [n.summation over (j)] [w.sup.2.sub.j] [[sigma].sup.2.sub.[epsilon]j] [n.summation over (i=1)] [n.summation over (j=1)] [w.sub.i][w.sub.j][[??].sub.ij] (7)
The first two terms are the familiar measures for systematic and unsystematic risks, respectively. As Chen and Keown (1981) explain, this derivation shows that the total risk of a portfolio actually consists of three components. The first two components in Equation (7) are sufficient when beta is assumed stable. The last and new component, which contains the covariance term, is due to beta instability. In effect, unsystematic risk has two components (the last two in the expression). The middle component is the 'pure residual risk' while the last is the additional risk due to the instability of beta. Brooks et al (1997) show that this additional unsystematic risk can be diversified away by combining constant and time-varying beta stocks while Ebner (2005) suggests the use of a time-varying estimation model to account for the additional beta variability.
FINDINGS OF THIS STUDY
Results of the variability of individual and portfolio betas are summarized in Tables 1 through 3. Table 4 presents results of the variability of betas when stocks are placed in portfolios according to market values of the individual stocks. Each portfolio contains 200 stocks. In Table 1, Portfolio 1 contains stocks which, individually, have the lowest standard deviation of betas. Portfolio 4 contains stocks with the highest standard deviations of betas.
In Table 1 where portfolios are ranked by the magnitude of the standard deviation of the individual stock betas, it is found that stocks with the lowest beta standard deviations (Portfolio 1) also tend to have the lowest beta coefficients, with an average beta of 0.6. In contrast, Portfolio 4, which contains stocks with the highest individual beta standard deviations, has the highest average beta of 1.10.
When only the lower and upper quartile portfolios are compared, two characteristics regarding their beta variability are apparent. The first is that stocks which individually possess low beta variability are also stocks with low average betas. Alternatively, stocks with the highest beta variability, tend to be high beta stocks. This is evident from the results shown for Portfolios 1 and 4 in Table 1.
The second characteristic is that stocks with the lowest average betas tend to be stocks which, when held in a portfolio, exhibit less beta variability than those with particularly high average betas. Stocks with the lowest average betas are those in Portfolio 1. These are also the stocks that exhibit the lowest individual beta variability in the portfolio ranking. In contrast, Portfolio 4 which features stocks with the highest individual beta variability also contains stocks with the highest average betas. Specifically, the average beta for stocks in Portfolio 1 is 0.60 and their beta standard deviation is 0.44. In contrast, the average stock beta for Portfolio 4 is 1.10 with a beta standard deviation of 0.67.
In between portfolios 1 and 4, we find an anomaly of sorts. Portfolio 2, which contains stocks with the second lowest level of individual beta variability, has a portfolio beta standard deviation of only 0.28 compared to the value of 0.30 for Portfolio 3. These two values are less than the beta standard deviation for Portfolio 1.
Results of tests of significance for the comparison of portfolio beta variability and average portfolio betas are presented in Table 2. As expected, there is a statistically significant difference between the variability of the betas of Portfolios 1 and 4. These results also show that there are no statistical differences in the variability of portfolio betas as well as in the size of the betas themselves between Portfolios 2 and 3. However, tests show that there is a statistically significant difference between either Portfolio 2 or Portfolio 3 and Portfolios 1 and 4, respectively.
Table 3 compares the standard deviation of stock betas at the beginning of the sample period (1980) to the last year (2003). This analysis enables one to determine whether there is consistency in the relationship between individual stock beta variability and the variability of portfolio beta over an extended period. As expected, the results shown in Table 3 are consistent with the results shown in Table 1. For each of the two periods, Portfolio 1 (Portfolio 4), which consists of stocks with the lowest (highest) individual beta variability, has the lowest (highest) average beta. The average beta for Portfolio 1 is 0.38 in 1980 and 0.61 in 2003. For Portfolio 4, the average beta is 1.81 and 2.60 in 1980 and 2003, respectively. Across the board, these results show in particular that the degree of systematic risk exposure of stock portfolios rose over the 23-year period. Schwert and Seguin (1990) explain that such intertemporal shifts in beta is due to either a change in the covariance of the stock's returns with market returns or because of a change in the variance of market returns.
Similar to the pattern of the overall results, the standard deviation of the beta of Portfolio 4 is greater than that of Portfolio 1 for each of the two sub periods. The two middle portfolios once again exhibit anomalous behavior in that both have lower beta variability than either Portfolio 1 or Portfolio 4.
In Table 4, stocks are ranked by market capitalization. Portfolio 1 contains stocks with the smallest market values while stocks with the largest market values are placed in Portfolio 4. Consistent with evidence presented in Avramov & Chordia (2006) and Al-Rjoub, Varela & Hassan (2005), the results show that in general, the smaller the market value of the stocks, the greater the systematic risk exposure of the portfolios, as measured by beta. Portfolio 1, which has the smallest market value, also has the highest average beta of about 1.03. Portfolio 4, the largest portfolio by market value, has the smallest beta of close to 0.82. Also, Portfolio 1 has the highest beta variability as indicated by its standard deviation of 0.70. Although Portfolio 4 has lower portfolio beta variability than Portfolio 1, its portfolio beta standard deviation is second lowest; the lowest being portfolio 2.
It is well documented that small cap stocks tend to be more reactive to market quirks than large cap stocks (see for example Bundoo, 2008). But what is additionally evident in Table 4 is that the (high) betas associated with small stocks tend to be more unstable when combined in a portfolio. In essence, while the systematic risk exposure of small stocks is expected to be high, the eventual performance of the portfolio over different market regimes is a bigger guessing game than that of large stock portfolios whose betas are both smaller and less variable.
LIMITATIONS OF THIS STUDY
This study may be improved upon by creating separate stock portfolios for different industries. Beta variability for individual stocks could then be evaluated within each industry group. By considering only diversified portfolios in this study, industry effects on beta variability may have been crowded out. Studies such as Avramov & Chordia (2006) point out that industry effects may be a significant aspect of beta instability, although this view was not confirmed. Second, in the empirical analysis of this study, portfolios were ranked solely on the basis of standard deviation of individual stock betas. While this approach has been used in other studies (for example, Weinraub & Kuhlman, 1994), it may be additionally informative to rank stocks according to coefficient of variation of the betas. Coefficient of variation has the additional advantage of discounting beta variability by the size of beta itself. Finally, this study relies exclusively on the performance of portfolios of a fixed size. By not allowing portfolio sizes to vary, it is difficult to assess whether beta variability also changes on the basis of portfolio size.
RECOMMENDATIONS FOR FUTURE RESEARCH
Future study could evaluate beta variability on three separate grounds. First, the beta variability of small stock portfolios could be compared to the beta variability of stocks held in large portfolios. For example, the beta variability for a portfolio of 20 stocks could be compared to that of 100 stocks. Second, it may prove helpful to design portfolios across different industry groups so as to capture industry effects. Finally, it may be useful to investigate the presence of volatility clustering in the beta coefficients of diversified stock portfolios. Such an inquiry would be guided by the contention that if beta changes over time then perhaps those changes embody a pattern that can best be modeled by the autoregressive conditional heteroskedasticity (ARCH).
In order to compare the variability of individual stock betas to the variability of portfolio betas, four portfolios were constructed and ranked by the standard deviation of the individual stock betas. When variability is measured by standard deviation of portfolio betas, empirical results show that in large portfolios, stocks with low beta variability are also stocks with the
lowest average beta. Also, stocks which individually exhibit the highest levels of beta variability tend to be high beta stocks. These findings came from arranging portfolios into quartiles. The lower quartile portfolio contained stocks which individually possess the lowest beta variability while the upper quartile portfolio contained stocks which individually exhibit the highest beta variability.
One conclusion of this study is that investors might be able to control their portfolio's systematic risk exposure by selecting stocks which, individually, possess less variable beta coefficients. And because the beta variability of the portfolios in the lower quartile are generally less than the top quartile, it means that an investor may be able to minimize the uncertainty associated with the market risk exposure of the portfolio by choosing stocks with low beta variability. The evidence is not universal however. When variability of portfolio beta is measured by standard deviation, it is found that portfolios in the middle quartiles actually exhibit less beta variability than either the lower or the upper quartile portfolio.
Consistent with existing evidence, this study also shows that small capitalization stocks, on average, have higher betas than large cap stocks. Also, the standard deviation of the portfolio beta in the first quartile (lowest market value) is the highest. Portfolios in the other quartiles exhibit beta variability that is in some cases, less than half the size of the beta variability of the small cap portfolio. This outcome suggests that selecting small cap stocks not only exposes the investor to greater market risk (because beta is relatively high for those stocks) but also presents the investor with greater uncertainty about the eventual performance of that portfolio. This is because the greater the variability of beta, the greater is the uncertainty about the ultimate performance of that portfolio relative to the market.
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About the Authors:
Shomir Sil received his Ph.D. in Finance from Texas Tech University. He teaches Corporate Finance and Investments at Purdue University Calumet. His scholarly publications have appeared in a number of business academic journals. He is the president of Sil Foundation for Higher Education, a not-for-profit support organization for international students and scholars.
Pat Obi earned his Ph.D. in Finance with a minor in Econometrics from the University of Mississippi. At the time of this study, he was a visiting scholar at Kyung Hee University in Seoul, South Korea. He teaches Corporate Finance and Derivatives at Purdue University Calumet. In addition to a finance textbook, he is the author of several articles in scholarly business and Finance journals.
Jeong-gil Choi is a Professor in the School of Hotel and Tourism Management at Kyung Hee University in Seoul, South Korea. He teaches courses in Business Finance and Strategic Management in the Department of Hotel Management, which he also heads. His scholarly publications have appeared in various business academic journals. He received his Ph.D. from Virginia Polytechnic Institute and State University.
Purdue University Calumet
Kyung Hee University, South Korea
Table 1 Portfolio Ranking by Standard Deviation of Individual Stock Betas Portfolio Rank + Average Stock Beta Standard Deviation of Portfolio Beta Portfolio 1 0.6044 0.4392 Portfolio 2 0.8965 0.2777 Portfolio 3 1.0477 0.2981 Portfolio 4 1.1044 0.6688 + Portfolio 1 (4) contains stocks with lowest (highest) standard deviation of stock betas Table 2 Comparison of Portfolio Beta Variability and Portfolio Beta + Comparison of Variability of Portfolio Betas ++ F P-value Portfolio 1, 2 2.5006 * 0.0263 Portfolio 1, 3 2.1713 * 0.0497 Portfolio 1, 4 2.3191 * 0.0372 Portfolio 2, 3 1.1516 0.3807 Portfolio 2, 4 5.7992 ** 0.0002 Portfolio 3, 4 5.0356 ** 0.0005 Comparison of Average of Portfolio Betas t P-value Portfolio 1, 2 2.5132 * 0.0163 Portfolio 1, 3 3.7345 ** 0.0006 Portfolio 1, 4 2.7942 ** 0.0081 Portfolio 2, 3 1.6600 0.1052 Portfolio 2, 4 1.2839 0.2069 Portfolio 3, 4 0.3463 0.7311 ** Significant at the 1% level * Significant at the 5% level + Portfolio 1 (4) contains stocks which, individually, have the lowest beta variability ++ For this test of significance, variability of portfolio beta is measured by variance of the stock betas Table 3 Portfolio Raking Between Extended Observation Periods Portfolio Rank + Average Stock Beta Standard Deviation of 1980 Portfolio Beta Portfolio 1 0.3787 0.2028 Portfolio 2 0.3821 0.1968 Portfolio 3 0.9509 0.0976 Portfolio 4 1.8062 0.5862 2003 Portfolio 1 0.6128 1.2037 Portfolio 2 0.8695 0.1261 Portfolio 3 1.3102 0.1414 Portfolio 4 2.5988 1.7931 + Portfolio 1 contains stocks with smallest standard deviation of stock betas Table 4 Portfolio Ranking by Market Value of Equity Portfolio Rank + Average Stock Beta Standard Deviation of Portfolio Beta Portfolio 1 1.0255 0.7048 Portfolio 2 0.8441 0.3008 Portfolio 3 0.9674 0.4346 Portfolio 4 0.8159 0.3961 + Portfolio 1 contains stocks with smallest market value of equity
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|Author:||Sil, Shomir; Obi, Pat; Choi, Jeong-gil|
|Publication:||International Journal of Business, Accounting and Finance (IJBAF)|
|Date:||Dec 22, 2011|
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