Portfolio Evaluation, Downside Risk and an Anomaly
Owing to the developments in portfolio theory in the 1960s, the evaluation of portfolio performance has evolved from a return-only mentality to a process that makes risk no less important than return. Earliest efforts to combine the two dimensions into a single (or composite) measure belong to Treynor (1965) and Sharpe (1966), who suggested dividing a portfolio's return in excess of the risk-free rate by the portfolio's bets and standard deviation, respectively. When Fama (1972) recommended that portfolios pay premiums that capture both market and diversification risk, he was implicitly asking whether Jensen's (1968) use of beta sufficiently measures the investor's risk. It is suggested that portfolios pay premiums that are sensitive to incomplete diversification and nonsymmetric returns.