Annualizing Active Returns and Volatility for an Ex-Post Sharpe Ratio

Summary

The document presents a proposed ex-post Sharpe calculation using daily portfolio returns and S&P benchmark returns. It subtracts the benchmark return from each portfolio return, computes the arithmetic mean and sample standard deviation of those daily differentials, compounds the mean over a 252-day year, and scales volatility by the square root of 252. The resulting ratio appears unusually high to the author.

This is a calculation question rather than a resolved analysis: no answer or verification is included. In particular, the example does not provide the daily observations or discuss how the stated annualization choices relate to the conventional Sharpe ratio, which uses excess returns over a risk-free rate and typically annualizes the arithmetic mean by the square-root-of-time convention alongside volatility. The reported figure therefore cannot be independently checked from the document alone.

Key ideas

• The proposed measure uses benchmark-relative daily returns as its numerator series.
• The author annualizes the average by compounding across a 252-day year.
• Volatility is annualized by scaling the daily standard deviation by the square root of 252.
• The document raises concern about the resulting ratio but provides no verification or underlying daily data.

Tags

# Calculating Ex-Post Sharpe Ratio


# Calculating Ex-Post Sharpe Ratio












I'm trying to calculate an Ex-Post Sharpe Ratio for my portfolio and I would appreciate verification I'm doing it correctly.

I have my portfolio's daily returns in one column and my benchmark's returns (the S&P) in another. I calculate the differential between the two (Daily_return - S&P_return). Next I find the arithmetic average of the differential, which in my case is 0.15% over 87 trading days. I annualize the average return by (avg_daily_return+1)^252-1, for a value of 46%.

I then calculate the sample standard deviation of the differential returns, for a value of 0.62%. I annualize the standard deviation by multiplying this number by the square root of 252, for a value of 9.95%.

Finally, I divide the annualized daily average return by the annualized daily standard deviation (46%/9.95%) for a Sharpe of 4.59. I believe I'm performing the calculation correctly, but this value seems unreasonably high.

Thanks!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.