Choosing a Risk-Free Rate for Ex-Post Sharpe Ratio Evaluation

Summary

This discussion asks how to choose a risk-free rate when evaluating a strategy with weekly returns over a year. It considers using the one-year rate at the start of the sample, averaging weekly rates, or subtracting each week’s rate from the corresponding strategy return before calculating performance statistics.

The response ties the choice to how the strategy uses capital. For a self-financing strategy, it suggests a zero funding rate in the Sharpe calculation; for capital committed for the full year, it points to the one-year zero rate at the start. If capital is returned and reinvested weekly, it suggests using the geometric mean of weekly Treasury bill returns over the sample. These are conditional guidelines, not a detailed derivation, and the document does not discuss rate conventions, compounding alignment, or other implementation details. Its main lesson is to match the benchmark rate to the strategy’s funding horizon and cash flows.

Key ideas

• The risk-free benchmark should reflect how and when a strategy ties up capital.
• A self-financing strategy may use a zero funding rate in the Sharpe calculation.
• Capital committed for a full year can be compared with the one-year zero rate at the sample start.
• Weekly reinvestment suggests matching returns against weekly Treasury bill rates over the evaluation period.

Tags

# Risk-free rate for ex-post evaluation of investment strategy


# Risk-free rate for ex-post evaluation of investment strategy












When evaluating the strategy ex-post using e.g. Sharpe ratio, what should one use as the risk-free rate? Let's suppose I am using a 1Y sample of weekly returns, sampled between 2012-01-01 and 2012-12-31. Should I use the 1Y risk-free rate as of 2012-01-01, an average of the 1W risk-free rates as of the beginning of each week in 2012, or subtract each 1W risk-free rate from the corresponding strategy return each week before averaging/calculating variance?

My intuition was to do the last, but on the other hand with the interest rates floating, this hardly makes it the "risk-free" option?

## Answer by Vince (score 1)

https://quant.stackexchange.com/a/7926

seems to me that the rate used depends on the corresponding strategy's grip on funding: that is to say, if the strategy is self-financing, rf=0 when calculating sharpe (in the sense that your costs of funds is zero in construction of the strategy); if it requires an outlay at t_0, an amount which is tied up throughout the time frame of the year, rf should be the 1 yr zero rate as of t0; if the strategy is such that each week the outlay is returned and reinvested the following week, then the rf should be the geometric mean of the return on 1 week t-bills as of 2012-01-01 through 2012-12-31 at any rate see here: see here: http://www.edge-fund.com/Dowd00.pdf

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