subject: Efficient Portfolios [print this page] Efficient Portfolios Efficient Portfolios
Efficient Portfolios
Most portfolios are not perfectly efficient, and, consequently, theyare not perfectly correlated with the market. Thus, part of the variation in returns on such portfolios is not attributable to variation inthe market. Whereas the beta coefficient is sufficient to indicate therelative volatility (riskiness) of efficient portfolios, it may not be sufficient to indicate the relative variability (riskiness) of inefficientportfolios.
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The total variability of inefficient portfolios or of a single asset isgreater than that indicated by the beta coefficient. Thus the questionarises as to the appropriate measure of their risk. The standard answerof modern financial theory is that the proper measure oftotal riskfor a single asset is a measure of its total variability. But, the measureof risk which determines its riskpremium is its contribution tothe variability of a diversified portfolio. The answer is based on thepremise that most investors dislike risk and therefore hold diversifiedportfolios. The contribution of an asset to the riskiness of a portfolio its systematic risk is measured by the familiar beta coefficient, sincethe beta coefficient of a portfolio is simply a weighted average of thecoefficients of its component securities, each individual coefficient being weighted by the value of its security as a percent of the portfolio's total value.
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In other words, the risk premium which an asset commands dependsupon only that part of its variability which is associated with generalmarket movements and not upon its independent variability. We areled to the startling conclusion that there is no risk premium for anasset if its rate of return has no correlation with rates of return onthe market as a whole. The relationship between the beta coefficientof an asset and its correlation with the market is as follows:
The assumption of risk aversion seems quite reasonable.
