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Use Historical Risk-Free Rates When Calculating Backtest Sharpe Ratios

Article Quant Q&A · Author: Spencer Smolen
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Summary

The document considers whether Sharpe ratios for backtests spanning different historical periods should use risk-free rates from those periods or a single current rate. The answer recommends matching the risk-free rate to the period being evaluated, so the calculation reflects the investment environment at the time. It also says the rate should match the investment’s duration and suggests using an average rate over the backtest period for a multi-year evaluation.

This guidance distinguishes historical performance measurement from estimating how a strategy might compare with today’s alternatives: using today’s rate in a historical calculation would mix periods. The answer is brief and does not specify a data source, compounding convention, or how frequently to align the risk-free return with strategy returns. Comparisons across periods may still reflect differences in market conditions, so the ratio alone does not isolate a strategy’s profitability from its historical context.

Key ideas

  • A historical Sharpe ratio should use risk-free rates corresponding to the backtest period.
  • The risk-free rate should match the investment horizon being evaluated.
  • For a multi-year period, the answer suggests using the average risk-free rate over that same period.
  • Using a current rate for historical returns mixes different market environments.

Tags

BacktestingRisk managementStatistics
Full text
# when calculating sharpe ratio of a backtest, do you use the historical risk-free rate or the current one?


# when calculating sharpe ratio of a backtest, do you use the historical risk-free rate or the current one?












Say I'm running a few backtests, say 1980-now, 2000-now and 2010-2015. When I'm calculating the Sharpe ratio of these backtests, do I use the risk-free rates associated with those time periods? or should I use the current risk-free rate for all of them?

My concern is that is that it might misleading to compare the Sharpe ratios of these different backtests to assess the viability of the different trading strategies I'm backtesting, because the Sharpe will be dependent on, say, what the T-bills at the time were looking like at the time of the backtest and not necessarily how profitable the trades are. However, if I use the current risk-free rate for all of them it will (I think) suggest what their risk-adjusted returns would be in the current market.

Is this a valid concern? Or should I just be using the historical risk-free rate for the times I'm backtesting. Thanks in advance!

## Answer by user18663 (score 1)

https://quant.stackexchange.com/a/31058

You should use the historical risk free rate so that it becomes viable for you to analyse your investment. But make sure your risk free rate should match the duration of the investment which was before while performing a back test. Because if you take the current one, it is not viable to compare your investment in history with the current risk free rate because the risk free rate is the average return over the time period under evaluation. And if you are backtesting a period (say 3 years) then you can take the average of the risk free rate (over 3 year period) over the same time period.

Hope this helps!!!

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