Encyclopedia of Financial Models, Volume III by Fabozzi Frank J.;

Author:Fabozzi, Frank J.;
Language: eng
Format: epub
ISBN: 4789965
Publisher: John Wiley & Sons, Incorporated
Published: 2012-09-18T00:00:00+00:00

ALTERNATIVE RISK MEASURES FOR PORTFOLIO SELECTION

The goal of portfolio selection is the construction of portfolios that maximize expected returns consistent with individually acceptable levels of risk. Using both historical data and investor expectations of future returns, portfolio selection uses modeling techniques to quantify “expected portfolio returns” and “acceptable levels of portfolio risk,” and provides methods to select an optimal portfolio.

It would not be an overstatement to say that modern portfolio theory as developed by Harry Markowitz (1952, 1959) has revolutionized the world of investment management. Allowing managers to appreciate that the investment risk and expected return of a portfolio can be quantified has provided the scientific and objective complement to the subjective art of investment management. More importantly, whereas previously the focus of portfolio management used to be the risk of individual assets, the theory of portfolio selection has shifted the focus to the risk of the entire portfolio. This theory shows that it is possible to combine risky assets and produce a portfolio whose expected return reflects its components, but with considerably lower risk. In other words, it is possible to construct a portfolio whose risk is smaller than the sum of all its individual parts.

Though practitioners realized that the risks of individual assets were related, prior to modern portfolio theory they were unable to formalize how combining them into a portfolio impacted the risk at the entire portfolio level or how the addition of a new asset would change the return/risk characteristics of the portfolio. This is because practitioners were unable to quantify the returns and risks of their investments. Furthermore, in the context of the entire portfolio, they were also unable to formalize the interaction of the returns and risks across asset classes and individual assets. The failure to quantify these important measures and formalize these important relationships made the goal of constructing an optimal portfolio highly subjective and provided no insight into the return investors could expect and the risk they were undertaking. The other drawback, before the advent of the theory of portfolio selection and asset pricing theory, was that there was no measurement tool available to investors for judging the performance of their investment managers.

The theory of portfolio selection set forth by Markowitz was based on the assumption that asset returns are normally distributed. As a result, Markowitz suggested that the appropriate risk measure is the variance of the portfolio's return and portfolio selection involved only two parameters of the asset return distribution: mean and variance. Hence, the approach to portfolio selection he proposed is popularly referred to as mean-variance analysis.

Markowitz recognized that an alternative to the variance is the semivariance.2 The semivariance is similar to the variance except that, in the calculation, no consideration is given to returns above the expected return. Portfolio selection could be recast in terms of mean-semivariance. However, if the return distribution is symmetric, Markowitz (1959, p. 190) notes that “an analysis based on (expected return) and (standard deviation) would consider these … (assets) as equally desirable.” He rejected

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