The effect of asymmetrical and leptokurtic stock market returns on security market portfolios

Although most companies listed on major stock market exchanges have normally distributed returns, financial research finds a significant minority of stocks that have skewed or leptokurtic distributions. Standard practice in equity market portfolio construction uses only mean and variance to characterize the distribution of portfolio returns. as long as the portfolio is normally distributed, this practice gives accurate measures of expected return and risk. The addition of non-normally distributed company returns to a portfolio, however, introduces the potential for inaccurate measurement of both risk and expected return. Simulations using the normal and beta distributions show that variance, symmetry, and tail thickness all diversify as the number of securities included in a portfolio increases.