The Myth of Downside Risk Based CAPM: Evidence from Pakistan

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1 The Myth of ownside Risk Based CAPM: Evidence from Pakistan Muhammad Akbar (Corresponding author) Ph Scholar, epartment of Management Sciences (Graduate Studies), Bahria University Postal Code: 44000, Shangrilla Road, Islamabad, Pakistan Atta ur Rahman Assistant Professor, Institute of Management Sciences, Hayatabad, Peshawar, Pakistan Zahid Mahmood Professor, epartment of Management Sciences (Graduate Studies), Bahria University Islamabad, Pakistan Abstract Given the emergence of the downside risk based asset pricing framework, the present study investigated its empirical validity in the Pakistani equity market. For this purpose a sample of 33 stocks listed on the Karachi stock exchange (KSE) over sample period July 2000 to June 20 were analyzed. The empirical results reveal that there is no significant empirical evidence over the full and subsample periods to validate the downside risk based capital asset pricing model (CAPM) in the KSE. The results were insensitive to the choice of estimation technique i.e. the generalized least squares (GLS) and the white heteroskedasticity-consistent standard errors and covariance matrix. Keywords: ownside Risk, CAPM, Fama-MacBeth Methodology. Introduction Markowitz modern portfolio theory (Markowitz, 952) explains that the risk and return of investments are effectively measured by variance and mean of the expected return from the investment. The measure of risk i.e. variance considers deviations both below and above mean equally contributing towards the risk perceived by investors. However, it is suggested that investors are more concerned with deviations below mean than deviations above mean (Libby & Fishburn, 977). The behavior of downside risk aversion has been claimed to be theoretically consistent with Prospects Theory s S-shaped utility functions of Kahneman & Tversky (979) and Gul (99). This family of utility functions assumes that investors weight losses more heavily than gains in their utility functions. Hence investors are loss averse, not risk averse. Estrada (2002) also criticized the use of variance of returns as a measure of risk for two reasons i.e. asymmetry and normality of returns. The arguments are that variance is a good measure of risk only when returns distribution is both symmetric and normal (Estrada, 2002). Empirical evidence contradicts both the underlying requirements of variance as a measure of risk. Therefore, semivariance i.e. deviations below mean, is considered a better measure to reflect risk than variance (Estrada, 2002). As Estrada (2000) suggests that semi-variance has at least three advantages as a measure of risk: a) recognizes investors like upside risk b) more useful than variance when underlying distribution is asymmetric and otherwise at least as good as variance c) gives same information given by variance and skewness and hence is more efficient for use in asset pricing. Estrada (2002) provided evidence in support of the mean-semi-variance behavior (MSB) as an alternative for mean-variance behavior (MVB). Estrada (2002) showed that expected utility and MSB were nearly perfectly correlated. The MSB framework assumes that investors exhibit risk aversion when returns are below investors target return and investors are risk neutral when returns are above the investors target return subject to the type of underlying return distributions (Artavanis et al, 200). Markowitz (959) suggested the use of semi-variance as a measure of risk in his seminal work on the development of modern portfolio theory. The first most notable attempt in this direction was taken by Hogan and Warren (974). They developed an asset pricing model based on expected return semi-variance. Their model paralleled that of Sharpe (964) and Lintner (965) which use mean-variance framework. Following Hogan & Warren (974), Bawa & Lindenberg (977) developed a CAPM like asset pricing model using mean-lower partial moment (MLPM) framework. It uses returns below a fixed target level of returns to measure risk. COPY RIGHT 202 Institute of Interdisciplinary Business Research 860

2 2. Review of Empirical Literature Subsequently Price et al (982) found that semi-variance risk based measures of risk are different than the variance based risk measures. They used data on the U.S. stocks over sample period 927 to 968. Their findings suggest that the variance based CAPM beta overestimate the risk of high beta stock and underestimate the risk of low beta stocks. Their hypotheses were that expected return and downside risk share positive and linear relationship, borrowing and lending takes place at the risk free rate and that downside risk beta is a complete measure of risk. On the bases of their findings they held that the Bawa & Lindenberg (977) mean-lower-partial-moments (MLPM) based asset pricing model better reflects risk than the mean-variance based CAPM. Similar findings were reported by Post & Van Vliet (2006) for the U.S. market using data over sample period 926 to Harlow & Rao (989) provide a measure of downside risk (called the generalized mean-lower partial moment (MLPM)) based on downside deviations below average return of asset i and the market portfolio. The generalized MLPM measures the sensitivity of an asset s returns (below and above mean returns) to changes in market returns below mean. They suggested that the general MLPM beta performed better as a measure of risk than the regular beta of the traditional CAPM. Harlow (99) provided empirical evidence to support the MLPM framework of risk measures. Post & Van Vliet (2006) found that the value-weighted market portfolio was second-order stochastic dominance efficient to all benchmark portfolios created on the basis of size, value and momentum. They found that mean-variance criterion performed poor relative to the second-order stochastic dominance efficient criterion. They argued that the mean-variance market inefficiency is caused by only taking variance as a measure of risk. Olmo (2007) introduced mean-variance-downside-risk (MVR) CAPM to explain the statistically significant intercept terms in both the CAPM and downside risk CAPM. The MVR CAPM also explains that stocks with positive correlation with stock market require positive risk premium and stock with negative correlation with stock market require negative risk premium. Hence it suggested that investors require higher risk premium for stocks that have higher correlation with market in downturns and lower risk premium for stocks that have lower correlation with market in downturns (Olmo, 2007). Ang et al (200) analyzed the explanatory power of downside risk based risk measure to explain momentum effect using daily U.S. stock data from January 964 to ecember 999. They found that the average returns on stocks with the highest downside risk were greater by 6.5% per annum over the average returns of the stocks with the lowest downside risk neutralizing the effect of market beta, the size effect, and the value effect. They concluded that the returns from momentum strategy could partly be explained by the high exposure to downside risk. However, they failed to find any noticeable pattern in the expected returns of stocks when ranked by third-order moments as proposed by Rubinstein (973), Kraus & Litzenberger (976) and Harvey & Siddique (2000). They also found no significant pattern in expected returns of stocks when ranked by the fourth-order moment of ittmar (2002) and the downside betas or upside betas of Bawa & Lindenberg (977). Ang et al (2006) reported a 6% risk premium for downside risk and concluded that the average returns are higher on stocks that are highly correlated with the market in downturns. Another notable contribution to the theory of downside risk came from Estrada (2000). Estrada (2000) suggested using the ratios of the semideviations of the asset and market to measure systematic downside risk. This measure of risk was empirical supported as it explained the variations in the cross section of stock returns in emerging markets as well emerging market industries and the internet stocks. Estrada (2002) proposed the mean-semi-variance behavior hypothesis and provided empirical support for the downside CAPM (-CAPM). Artavanis et al (200) also found empirical support for the -CAPM using data over sample period from January 997 to ecember 2004 covering stocks listed in U.K. and France. The alternative specification of the CAPM i.e. the downside risk CAPM assumes mean-semi-variance behavior (MSB) by investors and assumes that investors give more weight to deviations below a target rate of return than deviations above a target of return. Hence stocks that are positively related with market in downturns should require higher risk premium than stocks that are negatively related with the market. A review of literature, however, suggests that downside risk based CAPM has not been put to empirical test in the Pakistani equity market. The recent international evidence on the explanatory power of downside risk based CAPM is very promising (e.g. Estrada, 2002; Olmo, 2007). This study contributes to the literature on downside risk capital asset pricing models in the context of Pakistan. The present study investigates the empirical validity of the COPY RIGHT 202 Institute of Interdisciplinary Business Research 86

3 hypotheses underlying the downside risk CAPM and establishes their utility in explaining the cross section of stock returns in the Pakistani equity market i.e. the KSE. 3. Methodology 3. Population The equity market of Pakistan consists of three stock exchanges namely, the Karachi stock exchange (KSE), the Lahore stock exchange (LSE) and the Islamabad stock exchange (ISE). The KSE is the oldest, largest and most significant of all the three stock exchanges in all pertinent aspects. Therefore, for the purpose of this study the KSE was selected as the representative of equity market of Pakistan. The total listed stocks on the KSE were 652 divided into 32 different sectors (KSE Annual Report, 20). Hence the sample was drawn from the population of 652 stocks listed on the KSE. 3.2 Sample and ata Availability of data was the main criterion that determined the inclusion or exclusion of stocks from the sample. Following this rule, a total of 33 stocks were selected from 30 different sectors on the KSE over the sample period from July 2000 to June 20. Out of the 33 stocks, there were 268 stocks with data available from July 2000 to June 20. Another 23 stocks had stock price data available from July 2003 to June 20. The stock price data of 22 stocks was only available from July 2006 to June 20. Stock prices of all the sample stocks were collected from the KSE. To proxy the market portfolio, the KSE00 index was used as market portfolio. The KSE00 index is a market value weighted index that is composed of the top 00 companies in the KSE based on market capitalization and represents a significant portion (more than 80 percent) of the total market capitalization. The six months Treasury bill rate was used as a proxy for the risk free rate. ata on this variable was obtained from the State Bank of Pakistan. For empirical analysis the monthly stock returns were calculated as: P it R it ln 4. Pit In equation 4. the monthly stock return on stock i, R is the natural log of the ratio of end of month and beginning it of month stock prices P it and Pit respectively. The monthly returns on market portfolio represented with the KSE00 index were measured as: Pm t R mt ln 4.2 Pmt In equation 4.2 the monthly portfolio returns is the natural log of the ratio of end of month and beginning of month KSE00 index values i.e. Rmt Pmt and Pmt respectively. 3.3 Portfolio Formation Procedure To form portfolios and subsequently test the empirical validity of the downside risk based CAPM, the empirical methodology of Fama and MacBeth (973) was borrowed. Javid (2008, 2009) and Iqbal and Brooks (2007b) adopted the same methodology in their studies of asset pricing models in the context of Pakistan. For each sample stock monthly downside betas were calculated using 36 months rolling regression over the sample period for which data was available for the stock. Next each month, downside-beta sorted equally weighted portfolios were formed using monthly downside betas of each stock in ascending order. The portfolios were revised and recomposed each month and the portfolio beta for each portfolio was calculated as simple average of the individual securities betas in the portfolio. Following the above procedure 27 portfolios were formed from 268 stocks (of 0 stocks each except for the 27 th portfolio which contained only eight stocks) over the sample period from July 2003 to June The number of portfolios increased to 29 from 29 stocks (of 0 stocks each except for the 29 th portfolio which contained stocks) from July 2006 to June Similarly 3 portfolios were formed from 33 stocks, where the last three portfolios were of stocks each, from July 2009 to June Econometric Specification of ownside Risk Based CAPM To estimate the downside risk beta for each stock over the sample period, a 36 month rolling window time series regression in equation 4.5 is estimated using generalized method of moments (GMM). Excess market returns and COPY RIGHT 202 Institute of Interdisciplinary Business Research 862

4 lagged excess market returns were used as instrumental variables in the GMM. The estimation model for downside risk beta is given as: it imt min[0, R } [min(0, R ] where imt mt t was the estimated downside risk beta. Equation 4.5 essentially estimates the downside beta as proposed by Estrada (2002). Given the problem of auto-correlation in error terms, where necessary, equation 4.5 is expanded to include appropriate number of ARMA terms. After estimation of monthly downside betas for each stock over the corresponding sample period for which the stock data was available, equally weighted lagged beta-sorted portfolios were formed. Hence for each portfolio there was a lagged portfolio beta which was the average of the individual stocks beta in the portfolio at the beginning of the month and excess portfolio returns which were the average of the month-end individual stock returns in the portfolio. Subsequently a monthly cross-sectional regression of the excess portfolio returns on the lagged portfolio betas was estimated as follows: Rpt 0 pmt p where 0, and pmt are the estimated intercept term, estimated market risk premium for downside risk and measure of downside risk respectively. To overcome the problem of heteroskedasticity, white heteroskedasticityconsistent standard errors and covariance was used in the estimation of equation 4.6. However, equation 4.6 was also estimated using generalized least squares as estimation technique to assess the sensitivity of the results to the choice of estimation technique. Finally the estimates of the monthly intercept terms and monthly market risk premium for downside risk are averaged and tested for significance using t-statistics. Specifically the following hypotheses were tested using t-statistic to establish the empirical validity of the downside risk CAPM: = 0 i.e. the intercept term is statistically no different than zero. 0 > 0 i.e. the market risk premium for downside risk is positive and statistically significant. 4. Empirical Results The descriptive statistics on the downside beta-sorted portfolios returns and downside betas are given in Table and Table 2. The portfolio returns and downside betas are the equally weighted averages of the individual stocks in the portfolios. The average return of all the sample portfolios is negative and hence suggests negatively skewed distributions of portfolio returns. The Jarque-Bera statistics suggests that most of the portfolios have returns that are non-normally distributed. The descriptive statistics of the downside betas of downside beta-sorted portfolios reveal that all of the portfolios, except P3 and P4, have normally distributed betas over time. This is an indication that portfolio downside betas are stable over time. Following the Fama-MacBeth methodology as adapted in this study, downside risk CAPM as specified in equation 4.6 was empirically estimated each month over the entire sample period using white heteroskedasticity-consistent standard errors and covariance. The mean of all monthly time series coefficients from the estimation of downside risk CAPM in equation 4.6 were tested for statistical significance to empirically test the embedded hypothesis of downside risk CAPM. The results of the t-tests of these time series coefficients are given in Table 3. Table 3 reveals that the mean intercept term over the full sample period was negative and marginally significant at 0 percent. This is also the case over subsample period including July 2007 to June 20, March 2006 to October 2008, November 2008 to July 20 and July 2007 to June It can be observed that most of these negative intercept terms correspond to year 2007 to year 2009, a period of high economic recession, political instability and deteriorated law and order situation in Pakistan. The mean of the time series of estimated market risk premium is positive and statistically insignificant (Table 3). Except for subsample periods including March 2006 to October 2008 and July 2009 to June 20 a positive but insignificant market risk premium is reported for all other subsample periods. A positive market risk premium is consistent with the downside risk CAPM; however, it is insignificant as well as time variant. Therefore, the empirical evidence on the downside risk CAPM reported in Table 3 is inconclusive to validate it in the KSE COPY RIGHT 202 Institute of Interdisciplinary Business Research 863

5 The downside risk CAPM in equation 4.6 was alternatively estimated using GLS to check the robustness of the results in Table 3. The results from the GLS estimation are given in Table 4. It was observed that only the intercept terms for subsample periods including March 2006 to October 2008 and July 2007 to June 2009 were both negative and statistically significant at five percent level of significance. However, the intercept terms over all other estimation periods are insignificant including the full sample period i.e. July 2003 to June 20. The results in Table 4 show that there is a positive though insignificant market risk premium for downside risk over the full sample period. Further over most of the subsample periods similar findings are reported. However, it can also be observed that not only the values of R 2 have increased significantly relative to Table 3 but most of t-values have also significantly increased in absolute terms for most of the coefficients using GLS method. For example the t-value reported for the market risk premium in Table 3 over the full sample period is.49. However, the use of GLS method results in t-value that is more than double in size i.e..0 (Table 4). Though there is improvement in terms of the values R 2 of t-value, however, overall the findings reported in this section are mixed and do not provide conclusive evidence on the status of the downside risk CAPM. Galagedera & Brooks (2005) also reported mixed and inconclusive findings on the validity of the downside risk CAPM. Cheremushkin (20) also reached similar conclusions and observed that downside beta was an unreliable measure of systematic risk of a security. 5. Conclusions The study reports the findings from the empirical estimation of the downside risk based CAPM estimated using both GLS and white heteroskedasticity-consistent standard errors and covariance matrix. The findings on the empirical validity of the downside risk based CAPM are found to be inconclusive. The intercept term has been reported to be varying in significance over sub-sample periods. This evidences that mispricing is inconsistent in the KSE. Similarly systematic downside risk has been found to be insignificantly priced in the KSE over the full and subsample periods. However, the estimated risk premium for downside risk has been found to be mostly positive though statistically insignificant. Over all the reported findings of the study are consistent with Richards (996) who argued that equilibrium based asset pricing models are ill-suited to explain the cross sectional variations in stock returns of emerging equity markets. COPY RIGHT 202 Institute of Interdisciplinary Business Research 864

6 References Ang, A., Chen, J. and Xing, Y. (200). ownside Risk and the Momentum Effect. Working Paper 8643, National Bureau of Economic Research, Massachusetts. Ang, A., Chen, J. and Xing, Y. (2006). ownside Risk. Review of Financial Studies, 9, Artavanis, N., iacogiannis, G. and Mylonakis, J. (200). The -CAPM: The Case of Great Britain and France. International Journal of Economics and Finance, 2(3), Bawa, V. and Lindenberg, E. (977). Capital Market Equilibrium in a Mean-Lower Partial Moment Framework. Journal of Financial Economics, 5(2), Cheremushkin, S. (20). Internal Inconsistencies of ownside CAPM Models. Electronic Journal of Corporate Finance, 4(20), pp ittmar, R. (2002). Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns. Journal of Finance. 57(), Estrada J. (2000). The Cost of Equity in Emerging Markets: A ownside Risk Approach. Emerging Markets Quarterly, 4, pp Estrada, J. (2002). Systematic Risk in Emerging Markets: the -CAPM. Emerging Markets Review, 3, Fama, E. and MacBeth, J. (973). Risk, Return and Equilibrium: Empirical Tests. The Journal of Political Economy, 8, Galagedera,. and Brooks, R. (2005). Is Systematic ownside Beta Risk Really Priced? Evidence in Emerging Market ata. Working Paper /05, epartment of Econometrics and Business Statistics, Monash University, Australia. Gul, F. (99). A Theory of isappointment Aversion. Econometrica, 59, 3, Harlow, W. (99). Asset Allocation in a ownside-risk Framework. The Financial Analyst Journal, 47(5), Harlow W. and Rao K. (989). Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory & Evidence. Journal of Financial & Quantitative Analysis, 24, Harvey, C. and Siddique, A. (2000).Conditional Skewness in Asset Pricing Tests. Journal of Finance, 55, Hogan, W. & Warren, J. (974). Towards the evelopment of an Equilibrium Capital-Market Model Based on Semivariance. Journal of Financial & Quantitative Analysis, 9(), -. 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, 7, Javid, A. (2008). Time Varying Risk Return Relationship: Evidence from Listed Pakistani Firms, Journal of Scientific Research, 22(), Javid, A. (2009). Test of Higher Moment Capital Asset Pricing Model in Case of Pakistani Equity Market. European Journal of Economics, Finance and Administrative Sciences, 5, Kahneman,. and Tversky, A. (979). Prospect Theory: An Analysis of ecision under Risk. Econometrica, 47, pp Kraus, A. and Litzenberger, R. (976). Skewness Preference and the Valuation of Risky Assets. Journal of Finance, 3(4), KSE Annual Report (20), Available at: Lee, W. and Rao, R. (988). Mean Lower Partial Moment Valuation and Lognormally istributed Returns. Management Sciences, 34(4), Libby, R. and Fishburn, P. (977). Behavioral Models of Risk Taking in Business ecisions: A Survey and Evaluation. Journal of Accounting Research, 5, Lintner, J. (965). The Valuation of Risk Assets and Selection of Risky Investments in Stock Portfolios and Capital Budgets. Review of Economics and Statistics, 47, Markowitz, H. (952). Portfolio Selection. The Journal of Finance, 7, Post, T. and Van Vliet, P. (2006). ownside Risk and Asset Pricing. Journal of Banking & Finance, 30(3), Richards, A. (996). Volatility and Predictability in National Markets: How do Emerging and Mature Markets iffer? IMF Staff Papers, 43 (3), Rubinstein, M. (973). The Fundamental Theorem of Parameter Preference Security Valuation. Journal of Financial and Quantitative Analysis, 8(), Sharpe, W. (964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, 9, COPY RIGHT 202 Institute of Interdisciplinary Business Research 865

7 Annexure Table Portfolio Returns: escriptive Statistics Portfolios Mean Max Min S. Skew Kurt J-B Prob Obs. P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P COPY RIGHT 202 Institute of Interdisciplinary Business Research 866

8 Table 2 Portfolio Betas: escriptive Statistics Portfolios Mean Max Min S. Skew Kurt J-B Prob Obs. P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P COPY RIGHT 202 Institute of Interdisciplinary Business Research 867

9 Table 3 ownside Risk Based CAPM (White Error) Period Rpt 0 0 pmt July/03 to June/ -0.0*** July/03 to June/ July/07 to June/ -0.03* July/03 to Feb/ Mar/06 to Oct/ *** Nov/08 to June/ -0.03** July/03 to June/ July/05 to June/ July/07 to June/ * July/09 to June/ *, **, *** indicates significance at %, 5% and 0% respectively Note: The average coefficients values are followed by the t-statistics and the corresponding p-values. p R 2 COPY RIGHT 202 Institute of Interdisciplinary Business Research 868

10 Table 4 ownside Risk Based CAPM (GLS) Period Rpt 0 pmt 0 July/03 to June/ July/03 to June/ July/07 to June/ July/03 to Feb/ Mar/06 to Oct/ ** Nov/08 to June/ July/03 to June/ July/05 to June/ July/07 to June/ ** July/09 to June/ ** indicates significance at 5% Note: The average coefficients values are followed by the t-statistics and the corresponding p-values. p R 2 COPY RIGHT 202 Institute of Interdisciplinary Business Research 869