Sharpe Ratio Versus Information Ratio for Benchmark Returns
Summary
The document distinguishes the Sharpe ratio from a benchmark-relative performance measure. A Sharpe ratio compares portfolio or asset returns with the risk-free rate and scales the excess return by its variability. When the market index or another benchmark replaces the risk-free rate, the measure is generally called the information ratio; its denominator is the variability of active returns, meaning portfolio returns minus benchmark returns.
It also mentions an ex-post Sharpe formulation that uses realized asset returns relative to a benchmark. For transparent comparisons, the benchmark should be stated clearly. The explanation is brief and does not specify details such as return frequency, annualization, or adjustments for serial correlation, so it does not provide a complete calculation protocol.
Key ideas
- The Sharpe ratio uses the risk-free rate as its return reference.
- A benchmark-relative measure is commonly called the information ratio.
- The information ratio uses the variability of active returns in its denominator.
- State the benchmark when reporting realized benchmark-relative performance.
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Full text
# Proper way to calculate the realized indiviual stock sharpe ratio # Proper way to calculate the realized indiviual stock sharpe ratio From the textbook, sharpe ratio is (return-riskfree rate)/risk However I wonder if I can use (return-index return)/risk, where the index acts as the benchmark, to calculate the sharpe ratio? I am quite confused about the difference between these two.. Thanks ## Answer by Tim (score 3) https://quant.stackexchange.com/a/22980 Indeed, the Sharpe ratio utilises the risk-free rate. When you're using another benchmark then the risk-free rate, say the market, the ratio is often referred to as the Information Ratio. In addition, the denominator becomes the standard deviation of the difference between the market return with your portfolio returns instead of standard deviation of the difference between the risk-free rate and your portfolio return ## Answer by owner (score 0) https://quant.stackexchange.com/a/21985 Sure you could use this formula so-called `Ex-post Sharpe ratio` in which you consider in `the numerator`of the formula the differential between the realized asset return and its benchmark. Using this approach always disclose for transparency purposes the benchmark under consideration, in particular if you're doing some comparison analyses. You'll consequently avoid some biases than resorting to the problematic selection of an adequate `risk-free rate` ( flat `yields` on `T-bills` or `adhoc rates` on money market instruments). Hope it helps.
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