I'm doing a bit of research on the Sharpe and Information ratios, and am finding loads of confusion. This may end up becoming an article, but for now I'll share with you some "facts," at least as I understand them, regarding the Sharpe ratio.
1. The Sharpe ratio was developed by William F. Sharpe (Sharpe, William F. (1966). "Mutual Fund Performance." Journal of Business), who was awarded the Nobel Prize in Economics.
1a. Sharpe's Nobel was not awarded for this risk measure, but rather for his work on CAPM.
2. Sharpe referred to his measure as "reward to variability," and to Treynor's (which was published in 1965) as the "reward to volatility."
2a. Neither terms seem to have made it into the common lexicon.
3. Sharpe introduced a revised version of his formula in 1994 (Sharpe, William. (1994). "The Sharpe Ratio." Journal of Portfolio Management). It appears, though not yet confirmed, that the earlier version dominates in our industry.
4. Although it appears that many firms use annualized values in their formula, Sharpe (1994) states that "To maximize information content, it is usually desirable to measure risks and returns using fairly short (e.g., monthly) periods. For purposes of standardization it is then desirable to annualize the results."
5. In Sharpe (1994), the author acknowledges how "The literature surrounding the Sharpe Ratio has, unfortunately, led to a certain amount of confusion." For example, he cites an article by Treynor-Black that define the ratio as "the square of the measure we describe," which, as Sharpe points out, would mean that it is always positive.
6. Although the Sharpe ratio is often criticized, from our research it remains the dominant risk-adjusted measure.
Stay tuned: more to follow!
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I think you are right to mention the fact that "the literature" has led to confusion regarding the Sharpe ratio as well as other risk statistics. I believe you are generating a bit of confusion yourself in your 4th point, which hints at some controversy over using annualized values. I believe that Sharpe is simply indicating that short measurement periods are preferable so that you have an adequate sample size from which to derive an inference, given that your confidence level is directly related to the number of observations. And, the use of annualization is simply to provide comparability, since a) it's the way we think and b) it eliminates the need for finding comparable measurement horizons. As Mary Poppins rightly said: "Why complicate things that are really simple?"
ReplyDeletePerhaps I wasn't clear enough: I believe he was saying to annualize AFTER you do the calculation; he's fine with annualization, just (apparently) not to use annualized figures in the calculation.
ReplyDeleteI think you touch on something here that is important and has not been demonstrated mathematically - at least not in any public way: does it matter if you calculate and annualize or annualize first and then calculate statistics. I know you have discussed this before, but I think it's worth a more formal presentation if something definitive has been developed.
DeleteAgreed (no, I'm not patting myself on the back). I was quite surprised when I learned of a common approach to annualize first; I never suspected this. And in seeing Sharpe's comment, I realized that he had already done so, and dismissed it. I do plan to "run some numbers" to see what the differences would be.
ReplyDelete