Beyond Mean-variance: Risk and Performance Measures for Portfolios with Nonsymmetric Return Distributions
نویسندگان
چکیده
Most practitioners measure investment performance based on the CAPM, determining portfolio "alphas" or Sharpe Ratios. But the validity of this analysis rests on the validity of the CAPM, which assumes either normally distributed (and therefore symmetric) returns, or mean-variance preferences. Both assumptions are suspect: even if asset returns were normally distributed, the returns of options or dynamic strategies would not be. And investors distinguish upside from downside risks, implying skewness preference. This has led to the adoption of ad hoc criteria for measuring risk and performance, such as "Value at Risk" and the "Sortino Ratio." We consider a world in which the market portfolio (but not necessarily individual securities) has identically and independently distributed (i.i.d.) returns. In this world the market portfolio will be mean-variance inefficient and the CAPM alpha will mismeasure the value added by investment managers. The problem is particularly severe for portfolios using options or dynamic strategies. Strategies purchasing (writing) fairly-priced options will be falsely accorded inferior (superior) performance using the CAPM alpha measure. We show how a simple modification of the CAPM beta can lead to correct risk measurement for portfolios with arbitrary return distributions, and the resulting alphas of all fairly-priced options and/or dynamic strategies will be zero. We discuss extensions when the market portfolio is not assumed to be i.i.d.
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Most practitioners measure investment performance based on the CAPM, determining portfolio"alphas" or Sharpe Ratios. But the validity of this analysis rests on the validity of the CAPM, whichassumes either normally distributed (and therefore symmetric) returns, or mean-variance preferences.Both assumptions are suspect: even if asset returns were normally distributed, the returns of ...
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