The cash benchmark should match the period, frequency and currency of the returns being measured. Changing it can materially change a Sharpe ratio even when the investment history stays exactly the same.
Changing a reporting benchmark leaves the investment’s compounded wealth unchanged. Geometric growth remains the outcome of interest; a change in the ratio alone is not a reason to change holdings.
A historical ratio usually subtracts the cash return actually associated with each observation. A forward-looking calculation instead needs an explicit expected cash return. Mixing those questions can make a historical investment look better or worse merely by changing the comparison standard.
The main Sharpe article gives the definition. Here we quantify the benchmark choice rather than changing the underlying investment.
Key takeaways
The cash benchmark must be consistent with the return series’ currency, dates and observation frequency.
Changing the benchmark can change the Sharpe ratio without changing the investment’s compounded wealth.
A historical cash return and an assumed future cash rate serve different calculations.
Keep one stock-return history fixed
Use January 2016–December 2025, comprising 120 monthly nominal US-dollar total returns for the value-weighted US stock market. The Kenneth French Data Library supplies the market and monthly Treasury-bill series.
Over this period, 12 times the monthly stock-return mean is 15.041%, and monthly sample volatility times sqrt(12) is 15.740%. These are annualised monthly statistics, not the arithmetic mean and standard deviation of ten calendar-year returns.
First subtract hypothetical constant cash yields instead of observed bills. This holds stock returns fixed purely to measure sensitivity. It does not claim that stocks would have delivered the same returns in different interest-rate environments.
Convert the annual yield before subtracting it
For a hypothetical effective annual cash yield y, the constant monthly return is (1 + y)^(1/12) − 1. At 6%, that is about 0.4868% per month. Twelve times that monthly rate is 5.8411%, while compounding it for twelve months returns 6%.
That distinction explains why the annualised excess mean below does not simply equal 15.041% minus the stated annual effective yield.
Assumed effective annual cash yield
Annualised excess mean
Annualised Sharpe
0%
15.041%
0.956
2%
13.059%
0.830
4%
11.113%
0.706
6%
9.200%
0.584
These are original counterfactual benchmark calculations, with a sample denominator throughout. The sensitivity CSV includes the converted benchmark means, volatility and observed-bill comparison.
Because each assumed cash return is constant, subtracting it changes the mean but leaves volatility unchanged. With a changing cash series, the precise denominator is the standard deviation of the differences, which need not exactly equal stock-return volatility.
What happens with the observed cash series?
Using the actual monthly bill returns gives an annualised cash arithmetic mean of 2.090%, excess mean of 12.951%, excess volatility of 15.737%, and a Sharpe ratio of 0.823.
That is the historical calculation under our chosen method. The constant-2%-yield score of 0.830 is a nearby sensitivity, not an interchangeable estimate of the same cash history.
The primary file's header identifies a source change: bill data through May 2024 come from Ibbotson Associates; from June 2024 they come from the ICE BofA US 1-Month Treasury Bill Index. The source snapshot preserves that disclosure. A provider's series definition belongs with the result.
Cash can change the Sharpe ranking
Consider a separate annual hypothetical model: portfolio A has an 8% arithmetic mean and 10% volatility; B has an 11% mean and 20% volatility. At 0% constant cash, their ratios are 0.80 and 0.55. At 5% cash, both are 0.30. At 6%, they become 0.20 and 0.25.
The crossover follows from (8 − f)/10 = (11 − f)/20, giving f = 5%. The ranking CSV reproduces this annual example. Its cash assumption is an arithmetic annual return, distinct from the monthly conversion exercise above.
Match currency and method before comparing reports
Subtracting euro cash from unconverted US-dollar returns mixes units of economic comparison. Currency conversion changes the investment-return series too; swapping the benchmark alone does not create a euro investor's Sharpe ratio. Fees and taxes can also change the return being measured.
Methodology and sources
Definitions follow Sharpe's 1994 paper. We checked the existing inputs against the current primary download and used sample standard deviations. Sampling and annualisation explain why matching the benchmark still leaves other methodological choices.
Checked on 28 October 2026. No current cash yield or future investment return is forecast here; this is educational comparison rather than investment advice.
FAQ
Should I use today's interest rate for a historical Sharpe ratio?
A historical comparison normally subtracts the benchmark return for each matching observation. Applying today's rate throughout an older history answers a hypothetical sensitivity question. It does not reproduce the cash returns available during that period.
How is an annual cash yield converted for monthly Sharpe calculations?
For an effective annual yield y under a constant monthly compounding assumption, the matching monthly rate is (1 + y)^(1/12) - 1. A quoted simple or discount yield requires its own conventions; dividing by 12 is not universally equivalent.
Can the cash benchmark reverse two portfolios' Sharpe rankings?
Yes. With hypothetical arithmetic annual means and volatilities of 8% and 10% for A, and 11% and 20% for B, A has the higher ratio at zero cash. They tie at 5% cash, and B has the higher ratio at 6%.
