During the 1960s, Eugene Fama developed his efficient market hypothesis and William Sharpe published his capital asset pricing model (CAPM). It might seem these were unrelated avenues of research, but the latter proved important for empirically confirming the former. CAPM states that assets' expected returns depend on their systematic risk. Assets or portfolios with greater systematic risk have higher expected returns than those with lower systematic risk. This means an investment manager can boost his returns by merely increasing the systematic risk (beta) of his portfolio. This poses a problem for anyone who wants to assess an investment manager's performance. How do you distinguish a manager who achieved high returns merely by taking high risk from one who was successful at market timing or stock picking? Early studies of investment manager performance—including Cowles (1933), Friend et al (1962) and Horowitz (1963)—failed to address this problem. They assessed investment managers' returns without any adjustment for the risks they took to achieve those returns. Not only did CAPM highlight this problem, it provided a framework for assessing—and hence adjusting returns for—a portfolio's risk. Between 1965 and 1970, a number of papers were published on investment managers' performance, primarily to support testing of the emerging efficient market theory. These suggested various risk-adjusted performance metrics (RAPM) based on CAPM. Jack Treynor (1965) proposed that managers' risk-adjusted performance be measured as
Sharpe (1966) proposed a metric with the same numerator but a different denominator. He felt it appropriate to penalize a portfolio manager for not fully diversifying, so his metric was
where the denominator is generally calculated as the standard deviation of simple return. Formulas [1] and [2] have come to be known, respectively, as the Treynor ratio and the Sharpe ratio. Both have been widely adopted by practitioners for performance assessments. The Sharpe ratio is the more popular of the two. In 1968, Michael Jensen published a RAPM that proved even more popular than the Sharpe ratio. Today, it has become more than a RAPM. For proponents of active portfolio management, it symbolizes their belief in the ability of active managers to outperform the overall market. Its name is Jensen's alpha.
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Is
it possible for the Treynor ratio to ever take on a negative
value? If so, how might we interpret such a result?.
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