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A Firm-Level Analysis of the Cross-Sectional Relation between Expected Returns and Expected Idiosyncratic Volatility in the Korean Stock Market

  • Sangkyu Lee School of Management, Kyung Hee University
  • Young Sik Kim School of Management, Kyung Hee University
Using monthly firm-level data from the Korean stock market from January 1992 to June 2016, we examine the cross-sectional relation between expected returns and expected idiosyncratic volatility. Considering the time varying property of idiosyncratic volatility, we use EGARCH model to estimate the conditional out-of-sample expected idiosyncratic volatility to avoid the problem of look-ahead-bias. Our main results are as follows. Our equal-weighted portfolio analysis that exclude any control variables exhibits that as conditional out-of-sample expected idiosyncratic volatility increase, expected returns tend to decrease. According to the equal-weighted Fama-MacBeth cross-sectional regression that includes systematic beta, size, book-to-market ratio factor, momentum, liquidity, return reversal and asset growth on the firm level, conditional out-of-sample expected idiosyncratic volatility consistently have a significantly negative relation with expected returns. This relation is also observed in the periods after the currency crisis and the global financial crisis, in the non-January sample, and in both up-phases and down-phases. Interestingly, we observe a spurious positive relation induced by look-ahead bias between contemporaneous conditional in-sample expected idiosyncratic volatility and expected returns. Our empirical findings suggest that the significantly negative relation between conditional out-of-sample expected idiosyncratic volatility and expected returns observed in the Korean stock market may be an idiosyncratic volatility anomaly.

  • Sangkyu Lee
  • Young Sik Kim
Using monthly firm-level data from the Korean stock market from January 1992 to June 2016, we examine the cross-sectional relation between expected returns and expected idiosyncratic volatility. Considering the time varying property of idiosyncratic volatility, we use EGARCH model to estimate the conditional out-of-sample expected idiosyncratic volatility to avoid the problem of look-ahead-bias. Our main results are as follows. Our equal-weighted portfolio analysis that exclude any control variables exhibits that as conditional out-of-sample expected idiosyncratic volatility increase, expected returns tend to decrease. According to the equal-weighted Fama-MacBeth cross-sectional regression that includes systematic beta, size, book-to-market ratio factor, momentum, liquidity, return reversal and asset growth on the firm level, conditional out-of-sample expected idiosyncratic volatility consistently have a significantly negative relation with expected returns. This relation is also observed in the periods after the currency crisis and the global financial crisis, in the non-January sample, and in both up-phases and down-phases. Interestingly, we observe a spurious positive relation induced by look-ahead bias between contemporaneous conditional in-sample expected idiosyncratic volatility and expected returns. Our empirical findings suggest that the significantly negative relation between conditional out-of-sample expected idiosyncratic volatility and expected returns observed in the Korean stock market may be an idiosyncratic volatility anomaly.
Idiosyncratic Volatility Anomaly; EGARCH; Conditional Out-of-Sample Expected Idiosyncratic Volatility; Conditional in-Sample Expected Idiosyncratic Volatility; Look-Ahead-Bias