Annualizing Sharpe, Alpha, and Beta from Monthly Fund Returns
Summary
The discussion describes common performance calculations when a fund supplies monthly returns. It says monthly observations are widely used in fund reporting, in part because many funds publish data only at that frequency. For monthly returns, annualize the Sharpe ratio by multiplying the monthly ratio by the square root of twelve, and annualize regression alpha by multiplying the monthly estimate by twelve. Beta remains unchanged because it measures the relationship to the benchmark rather than a return accumulated over time.
Benchmark selection should reflect the manager’s investment universe and the investor’s comparison needs. The S&P 500 may be suitable for a manager focused on large US equities, but may misrepresent performance for a different mandate. The answer offers a convention, not a universal rule: it does not resolve differences in return definitions, risk-free-rate treatment, estimation windows, or serial correlation, and readers should apply consistent assumptions when comparing managers.
Key ideas
- Monthly returns are a common basis for fund performance reporting.
- Annualize a monthly Sharpe ratio using the square root of twelve under the stated convention.
- Scale monthly regression alpha by twelve for an annual estimate.
- Beta is not annualized.
- Choose a benchmark that fits the manager’s investment universe and the investor’s comparison objective.
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Full text
# What is the industry standard way of calculating and annualizing performance metrics? # What is the industry standard way of calculating and annualizing performance metrics? Say I am looking at a performance report for a hedge fund manager who trades mostly equities, and they provide me a list of monthly returns for the past 5 years. What is the industry standard way to compute Sharpe ratio, alpha, and beta? Sharpe ratio: - Calculated off monthly returns and annualized by multiplying by $\sqrt 12$? - Or calculated off daily log returns and annualized by multiplying by $\sqrt 252$? Alpha & Beta: - Calculated by performing a regression on monthly returns relative to S&P 500 I assume. - Is alpha annualized by multiplying by 12? - Beta does not need to be annualized, is that correct? I am reading about a myriad of ways to compute these metrics and am wondering what most managers do. ## Answer by Tim Wilding (score 5, accepted) https://quant.stackexchange.com/a/40408 To give you an idea of industry standards for funds (although not hedge-fund specific), Morningstar and Trustnet both use monthly returns and annualize their data. See, for an example plucked at random, https://www.trustnet.com/factsheets/o/gnol/aberdeen-asia-pacific--japan-equity-i-acc. Monthly returns remain the standard because some funds only publish monthly numbers. If you are using monthly returns, Alpha is multiplied by 12 and Beta is unchanged. A Monthly Sharpe ratio is annualized by multiplying by $\sqrt[]12$ (although you might want to read How to annualize Sharpe Ratio?). Your choice of benchmark depends on what investors are looking for from the hedge fund manager. The S&P 500 is OK if you are expecting the manager to invest in large-cap US equities, but it might not be appropriate if the manager has a different universe.
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