A remark on mean-semivariance behaviour: Downside risk and capital asset pricing

In the conventional capital asset pricing model (CAPM), standard deviation as a measure of risk penalizes both upward and downward movements. However, while downward movements in investments are risky, upward movements are favourable. Therefore, standard semideviation that treats only those negative differences in returns over the benchmark as risky was proposed as a measure of downside risk. Attempts have been made to obtain the formulation of beta in this context, called downside beta. In this work, CAPM in the mean-semivariance framework (D-CAPM), with semivariance measured in terms of negative deviation around expected return, is derived and established that the model proposed earlier with a version of downside beta with respect to this definition of semivaraince is invalid. The appropriate version of downside beta is obtained, and under the rectified formulation, the validity of the true D-CAPM is empirically tested during July 2013-July 2018. The solution to the tangent point is also obtained. The proportion of investment in the stocks in the tangent portfolio and the downside beta for the stocks in the tangent portfolio are determined. We find that there is no evidence to disprove that D-CAPM holds true considering either Nifty 50 or S&P BSE Sensex as market portfolio.

Automated summary

In this study, a new model called D-CAPM, which measures downside risk, is proposed along with a version of downside beta. Empirical tests on two Indian stock market indices show that D-CAPM holds true in both market portfolios.