Diagnosing Risk-Free Rate Sensitivity in Sharpe Ratio Calculations

Summary

The document addresses an unexpected result in a Sharpe ratio sensitivity analysis: lowering the assumed risk-free rate appears to lower the ratio for both a strategy and its benchmark. The calculation described converts an annual rate into a daily rate, subtracts it from daily returns, averages the excess returns, and scales by return volatility and the number of trading periods. The answer gives a basic diagnostic rather than recommending a new long-horizon risk-free-rate model.

If the return observations, dates, and volatility denominator remain fixed, decreasing the risk-free rate increases each excess return and therefore cannot reduce the Sharpe ratio. A reversed result suggests that some other input or processing step changes across scenarios. The suggested checks include whether the rate is entered as a percentage or decimal and whether each calculation uses exactly the same dates and observations. Scaling errors, date misalignment, missing data, or other changing inputs can explain the behavior. The response does not assess the choice of risk-free proxy or provide a full historical-rate methodology, so those questions remain outside its scope.

Key ideas

• With returns and volatility held fixed, a lower risk-free rate cannot lower the Sharpe ratio.
• Check whether annual percentage rates are entered using the correct decimal scale.
• Keep return dates and observations identical across sensitivity cases.
• Unexpected changes can arise from date alignment, missing data, scaling, or altered inputs.
• The answer diagnoses the calculation but does not prescribe a long-term risk-free-rate series.

Tags

# Application of risk-free rate in sharpe ratio over long time periods


# Application of risk-free rate in sharpe ratio over long time periods












I am working on a project that includes risk/return characteristics for a certain strategy and its benchmark (SPX). Included on the outputs is a sensitivity table, which may be showing signs of overfitting.

I tested sharpe ratio with varying risk-free rates, and while the table does show a worse sharpe for higher rates, to be expected, it also shows a worse sharpe for lower rates which I don't believe makes sense.

I am currently calculating a daily risk-free rate (effective fed funds% + 1)^(1/252)-1, then finding the spread (daily return - daily rf), taking the average of that spread, and dividing by standard deviation of returns, * sqrt(252)

While originally I thought this was a strategy specific issue, I am getting the same result of a lower sharpe on the SP500 using a lower risk free rate.

Is there a better way to calculate rf rates and/or sharpe over long time periods?

## Answer by Russlan Ramdowar (score 0)

https://quant.stackexchange.com/a/85773

One quick check: when you say “effective fed funds %,” are you plugging 5.33 or 0.0533 into the formula? And does the sensitivity table keep exactly the same return dates and observations in every case? With the returns and denominator fixed, lowering the risk-free rate cannot lower the Sharpe ratio. A non-aligned result usually means a scaling, date-alignment, missing-data issue, or another input is changing.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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