Drivers of expected returns in Istanbul stock exchange: Fama–French factors and coskewness

Abstract

We investigate the impact of coskewness on the variation of portfolio excess returns in Istanbul Stock Exchange (ISE) over the period July 1999 to December 2005. We form portfolios according to size, industry, size and book-to-market ratio, momentum and coskewness and compare alternative asset pricing models. The traditional capital asset pricing model (CAPM) and the three-factor model of Fama and French are tested in the multivariate testing procedure of Gibbons–Ross–Shanken (1989). Coskewness is introduced as a fourth factor and its incremental effect over CAPM and Fama–French factors is examined both in multivariate tests and in cross-sectional regressions. The findings reveal that coskewness is able to explain the size premium in ISE. Hence, the basic two-moment CAPM without the coskewness factor would underestimate the expected return of size portfolios. Multivariate test results indicate that coskewness reduces the pricing bias, albeit insignificantly. Cross-sectional analysis uncovers that coskewness has a significant additional explanatory power over CAPM, especially for size and industry portfolios. However, coskewness does not have a significant incremental explanatory power over Fama–French factors in ISE.

Notes

¹Examples of evidence on the nonnormality of returns in the US market as well as in emerging markets include Bekaert et al. (1998) and Chung et al. (2006). Similarly, Harris and Kucukozmen (2001) focus on the ISE and reject the normality of daily equity returns.

²Lim (1989) tests the three-moment CAPM of Kraus and Litzenberger (1976) with GMM estimation, and finds evidence on pricing of systematic skewness in the US market.

³Based on time series regressions of portfolio excess returns on a constant and the three factors, Fama and French (1993) report 22 out of 25 portfolios with insignificant intercept terms implying the existence of pricing bias for three portfolios. Furthermore, the multivariate tests of Gibbons et al. (1989) indicate that the three-factor model outperforms CAPM and other competing multifactor models even though the pricing bias still exists.

⁴Another significant risk factor in Harvey's (2000) study is semivariance which is a downside risk measure. Other studies analysing the effect of semivariance on asset returns in emerging markets include Estrada (2000) and Hwang and Pedersen (2004).

⁵Monthly returns are available from ISE for the period July 1996 to December 2004. Adjusted closing prices for the period January to December 2005 are obtained from http://www.analiz.com, the website of IBS Yazilim, a data vendor endorsed by ISE. We calculate the monthly returns from the adjusted prices for 2005. The data are available from the authors upon request.

⁶The length of pre-estimation period in Harvey and Siddique (2000) is 60 months. We do not have a long return history and thus we have fewer observations (36 months) in the pre-estimation period. However, it is longer than 24 months used by Akdeniz et al. (2000). We find that our results are robust to using 30 months for the pre-estimation period.

⁷Book-to-market ratio data are available since December 1995. Hence, we choose July 1996 as the beginning of our sample period.

⁸The first measure, , and the second measure, beta of the squared excess market return, are related if the excess market return and the squared excess market return are orthogonal to each other.

⁹Hung (2004) also forms country portfolios to investigate the effect of the squared term for individual markets. Its coefficient is significant for Canada, the US, Belgium, Denmark, Australia and Taiwan.

¹⁰Fama and French (1998) find evidence in favour of this size effect for 11 emerging markets as well as for value-weight and equal-weight portfolios of 16 emerging markets; however their sample does not include ISE. Rouwenhorst (1999) also analyses size effect in 20 emerging markets including ISE. Although small stocks outperform large stocks in internationally diversified portfolios, he does not find a significant size effect for ISE during 1989–1997. This result can be explained by sampling bias in the data. The Emerging Markets Database (EMDB) in that study includes 64 stocks from ISE and is biased towards stocks that are larger in terms of market capitalization and that are more frequently traded. Moreover, as pointed out by Rouwenhorst there are missing values and data errors in EMDB.

¹¹This evidence is well known in the literature and documented by Fama and French (1996) for the US market and by Aksu and Onder (2000) for ISE.

¹²Momentum strategies will be taken up later in the text.

¹³GRS test the validity of CAPM for beta portfolios of Black et al. (1972) and conclude that equally weighted market portfolio is mean-variance efficient. We also form beta portfolios and test the efficiency of equally weighted market portfolio for ISE. We reject the efficiency of equally weighted market portfolio. These results are available from the authors upon request.

¹⁴Fama and French (1993) use this F-statistic to test CAPM and different combinations of multifactor models. The factors are excess market return, SMB, HML, TERM and DEF. TERM captures the term premium calculated as LG–R_f where LG is the long-term government bond return. DEF captures the corporate sector spread, calculated as CB-LG where CB is the return on a proxy for the market portfolio of corporate bonds.

¹⁵The first and the second momentum strategies are analysed by Harvey and Siddique (2000) and Lin and Wang (2003), and the third momentum strategy is analysed by Rouwenhorst (1999) and Hameed and Kusnadi (2002).

¹⁶One possible explanation for lack of application of GRS to CAPM tests in emerging markets is that GRS test rests upon the assumption that returns and explanatory variables are normally distributed, and there is substantial evidence against this assumption for emerging markets, e.g. Bekaert et al. (1998). Nonetheless, referring to simulation evidence by MacKinlay (1985), GRS argue that F-test is fairly robust to departures from normality. Lin and Wang (2003) apply GRS test to Taiwanese stock market in order to test the three factor and the four-factor models, however they do not report any result about CAPM tests.

¹⁷Additionally, we perform the GRS test for all portfolios after excluding November 2000–February 2001 financial crises period. Apart from an insignificant reduction in the F-statistics for portfolios formed according to size, size and book-to-market, our inferences do not change. Part of the pricing bias mentioned in the text may be attributed to the volatility of ISE during the crisis period.

¹⁸For example, for momentum strategy (j =6, k = 6) average return difference between prior losers and prior winners is 1.75%.

¹⁹DeBondt and Thaler (1985) find that losers in the US market outperform winners by 25%, 36 months after these portfolios are formed.

²⁰For the momentum strategy (j =12, k = 6), coefficient estimates on (R _m  − R _f ), SMB and HML are 1.025, 0.814 and 0.183, respectively, for past losers and 0.860, 0.631 and 0.078, respectively, for past winners.

²¹Moreover, as pointed out by Shanken (1992), Fama–MacBeth procedure does not fully overcome measurement errors in beta estimates, and these errors-in-variables can be important in practice. Therefore, we base our inferences on the FIML procedure.

²²Chung et al. (2006) form 50 portfolios for the US market according to book-to-market and size criteria, and run their excess returns on a set of comoments of order 3–10. It is not feasible to obtain enough sub-samples and run similar cross-sectional regressions for ISE since the total number of stocks stands at 194.