Explanation of Capital Asset Pricing Model (CAPM) with Downside Risk in TSE

In the capital asset pricing model (CAPM), Beta () is a measure of systematic risk and explains the assets return differences. CAPM Beta comes from an equilibrium in which investors display mean-variance behavior. In other words, from an equilibrium in which investors maximize a utility function that depends on the mean and variance of returns. The variance of returns, however, is a questionable measure of risk for at least two reasons: first, it is an appropriate measure of risk only when the underlying distribution of returns is symmetric. And second, it can be applied straightforwardly as a risk measure only when the underlying distribution of returns is Normal. The semivariance of returns, on the other hand, is a more plausible measure of risk for several reasons: first, investors obviously do not dislike upside volatility; they only dislike downside volatility. Second, the semivariance is more useful than the variance when the underlying distribution of returns is asymmetric and just as useful when the underlying distribution of returns is symmetric; in other words, the semivariance is at least as useful a measure of risk as the variance. This paper investigates the relationship between risk and return by the use of three downside Beta in CAPM.