Interpreting and Comparing Sharpe Ratios from Quarterly Returns

Summary

The document describes a rolling Sharpe-ratio calculation using quarterly stock returns. For each window, the author computes the arithmetic average and standard deviation of the quarterly returns, subtracts the risk-free rate from the average, and divides by the standard deviation. The calculation is then repeated on a shifted window. The central question is how to interpret these values and compare ratios calculated from windows of different lengths.

The document provides example window lengths and Sharpe values to illustrate the uncertainty, but it contains no answer or recommended annualization formula. It therefore identifies a distinction that matters in reporting: the frequency of the returns used and the amount of history used to estimate the ratio. It does not establish that different window lengths alone make the resulting ratios incomparable, nor does it discuss assumptions behind annualizing Sharpe ratios, such as return dependence.

Key ideas

• The described rolling calculation uses quarterly average returns, volatility, and a risk-free rate.
• Each successive rolling window shifts forward by one quarter.
• The question distinguishes return frequency from the number of observations in a window.
• The document does not give an annualization formula or answer the comparability question.
• Dependence among returns is not discussed as a potential limitation of annualization.

Tags

# How to annualize sharpe ratio using quarterly data?


# How to annualize sharpe ratio using quarterly data?












Say I have quarterly returns data for a stock. I am currently calculating rolling Sharpe ratios using an eight-quarter forward window. So for example, say I have quarterly returns data starting in 2000Q1, then 2000Q2, 2000Q3, 2000Q4, etc.

What I do is take the arithmetic average of the quarterly returns from 2000Q1 all the way until 2001Q4 (so basically just the average of 8 returns). Then I calculate the standard deviation of these quarterly returns (so again, just the standard deviation of 8 returns). Then I subtract the risk-free rate from the average returns and divide the whole thing by the standard deviation to get the Sharpe ratio for this window.

I then repeat the same process but using the quarterly returns from 2000Q2 to 2002Q1 to calculate the Sharpe ratio for the next window.

Now say I get a Sharpe ratio of 0.51 for the first window. How do I interpret this number? Do I say this is the quarterly Sharpe ratio? (Because it is estimated using quarterly returns?) But then, say I use a different window of 12 quarters (instead of 8), I do the exact same calculation, now the first window Sharpe ratio becomes 0.66. Is this also a "quarterly" Sharpe ratio? How would I compare between 0.51 and 0.66? Surely they can't be directly comparable because one is estimated using 8 quarters of data while another is estimated using 12 quarters of data. How can I "annualize" both so that they are comparable?

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