# Sharpe performance measure

## Sharpe Benchmark

In financial econometrics, a model for a portfolio's performance that attempts to account for a money manager's index-like tendencies. In other words, the Sharpe benchmark attempts to statistically calculate whether a portfolio's success was due to good management or the taking of excessive risk. The model measures a company's or portfolio's performance against a series of securities indices.

## Sharpe performance measure

A measure of risk-adjusted portfolio performance developed by William Sharpe. The index is calculated by dividing the risk premium return (average portfolio return less average risk-free return) divided by risk (standard deviation of portfolio returns). The Sharpe measure adjusts portfolio performance for total risk rather than market risk. Compare Treynor performance measure.
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PERF = Sharpe performance measure (i.e., reward-to-variability ratio), which is calculated as a) the difference between the daily post-recommendation return on the stock and the daily risk-free rate over the three-month period from 12/15/94 through 3/15/95 divided by b) the standard deviation of the return series.
The dividend yield for the average firm is 2.46%; the average market-value-to-book-value ratio is 2.60; the average forecasted growth rate is 13.24%; and the average industry-adjusted PE ratio is -2.84.(14) Over the ex-post analysis period from December 15, 1994 to March 15, 1995, the Sharpe performance measure has a mean level of 4.25.
Buy recommendations have a higher Sharpe performance measure (PERF).
where S[H.sub.ik,Q] = Transformed Sharpe performance measure difference between portfolios i and k for overall period Q.
First, the Sharpe performance measure was regressed on the lagged value of P/E ratio and market value, separately.
where [SH.sub.ik,Q] = Transformed Sharpe performance measure difference between portfolios i and k for overall period Q.
Multiple Regression and Simple Regression Analysis For Sharpe Performance Measure: Tests of the Relationship Between P/E Ratio and Size, and the Portfolio Performance Sharpe performance measure and average P/E, size and beta for each portfolio are measured quarterly.

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