Chapter 19 MEAN VARIANCE PORTFOLIO ALLOCATION. Abstract The basic rules of balancing the expected return on an investment against its contribution to portfolio risk are surveyed. The related concept of Capital Asset Pricing Model asserting that the expected return of an asset must be linearly related to the covariance of its return with the return of the market portfolio if the market is efficient and its statistical tests in terms of Arbitraging Price Theory are also surveyed. | Chapter 19 MEAN VARIANCE PORTFOLIO ALLOCATION CHENG HSIAO University of Southern California USA SHIN-HUEI WANG University of Southern California USA Abstract The basic rules of balancing the expected return on an investment against its contribution to portfolio risk are surveyed. The related concept of Capital Asset Pricing Model asserting that the expected return of an asset must be linearly related to the covariance of its return with the return of the market portfolio if the market is efficient and its statistical tests in terms of Arbitraging Price Theory are also surveyed. The intertemporal generalization and issues of estimation errors and portfolio choice are discussed as well. Keywords mean-variance efficiency covariance capital asset pricing model arbitrage pricing theory Sharpe ratio zero-beta portfolio volatility minimum variance portfolio value at risk errors of estimation . Introduction Stock prices are volatile. The more volatile a stock the more uncertain its future value. Investment success depends on being prepared for and being willing to take risk. The insights provided by modern portfolio theory arise from the interplay between the mathematics of return and risk. The central theme of modern portfolio theory is In constructing their portfolios investors need to look at the expected return of each investment in rela tion to the impact that it has on the risk of the overall portfolio Litterman et al. 2003 . To balance the expected return of an investment against its contribution to portfolio risk an investment s contribution to portfolio risk is not just the risk of the investment itself but rather the degree to which the value of that investment moves up and down with the values of the other investments in the portfolio. This degree to which these returns move together is measured by the statistical quantity called covariance which is itself a function of their correlation along with their volatilities when volatility of a stock is measured by
