# When calculating the Sharpe Ratio, say, for ten years of data, what is generally accepted as the risk-free rate?

(Last Updated On: March 8, 2012)

When calculating the Sharpe Ratio, say, for ten years of data, what is generally accepted as the risk-free rate? 90-day T-Bills? 1, 2 year Notes? The T-Bond yield for the comparable term at inception?

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Yes, definitely, short maturity sovereign debt. Oh, er, wait a minute… may have to rewrite those textbooks. Could be gold. Or oil maybe. Good question!

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I think i’ts the 1 year Note since the Sharpe Ratio is calculated on the annual (or risk adjusted) annual return.

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According to CFA book, you should use 10-year T-bond YTM(yield-to-maturity).
I got this in the page 41 of CFA L2 notes(book 3), it explains this in CFA LOS 35b (Equity Risk Premium), the contents as bellow:
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Risk Free rate, should correspond to the time horizon for the investment(e.g.,T-bills for shorter-term and T-bonds for longer-ter horizons.)

and, if you estmate the emerging market data, then
Risk Free rate=YTM of 10-year T-bond (US)+ the inflation difference between US and emerging martet target country.

hope this can be helpful for you:)

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I agree you should use the long term rates… or average of long term rates over the test period.

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en, yes, average of long term rates is a good idea too, sounds like the pure expectation theory:)

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Most people and professionals use shorter term maturities when calculating the Sharpe ratio, i.e. 30-90 day bills. I’m no CFA but risk premium and SR are very different. If you go to the papers on the SR it is the “one period riskless asset” return thus if you are measuring monthly returns (your one period) you should use 1 month TBills. This has been generalized as to the cost of one period financing to create the differential return. Look at Shapre’s JPM paper Fall 1994.

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yes, that corroborates what I’ve found after much digging on the web, but it’s amazing how many different definitions one finds for a measurement so routinely requested and advertised without further clarification.

In any case, as much as it’s asked for, I personally don’t find the Sharpe Ratio very meaningful for systematic trading models, which I think should be evaluated against the returns and standard deviation of the vehicle class traded, not the short term riskless rate.

The Sharpe Ratio seems more appropriate for a comprehensive portfolio approach, say a broadly diversified asset allocation model, where the question is, “how well does this do across all risk assets versus the riskless rate.”

Of course correctly reminds us, the riskless rate isn’t, after inflation.

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• I think thst point is that there is always risk, with or without inflation.

The risk-free rate started life as a mathematical toy. For reasons known only to God and Daniel Kahneman it entered practice. I don’t think we should be surprised that there is confusion about how to implement it.

I agree that the Sharpe ratio is not a good measure of trading models. But I think the proper measuring stick is the distribution of what happens when a strategy with the same constraints and zero skill is used. That is possible to get, but there is not a closed-form solution so you won’t see it much in textbooks.

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This is of course a technical question, but the underlying issue is profound. If I buy a T-bill, I am promised the return of another bill that says it is ‘legal tender for all debts’, or in the UK a note that says it will ‘pay the bearer on demand the sum of one pound”. Such statements are what makes the Buddha smile at the sound of one hand clapping. An equity on the other hand is a legal share in a real enterprise with real assets. Now there’s something to meditate upon.

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Yes always risk, with or without inflation and with or without laws and regulation (think MF Global segregated accounts!). The longer the maturities one uses the more this impacts the calculations, i.e. using 10Yr Govies one will see a lot of volatility in these risk free assets.

I fully agree SR is not a good measure especially for active strategies which specifically are targeting for upside volatility while trying to minimizing downside volatility. As we know many alternatives have been proposed – Omega, MAR, Sterling, LPM etc (BTW have enjoyed reading your papers) taking off on your thought I have used bootstrap type of testing with various types of scrambling/randomizing to create the zero skill alternative.

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Thanks for clarifying how the RF should be, I do agree with you that measuring monthly returns should use 1 month T-bill, your explanation make me more clear.

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Well, there’s nothing more sure than that posing a clear and distinct Cartesian question about the generally accepted calculation of the Sharpe Ratio shall provoke a cloud of puerile and nebulous, off-topic chat.

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I agree with those who have commented of the Sharpe Ratio being meaningless.

The SR assumes normal distribution of returns and it also assumes that the investments you are considering must have the same correlation to the portfolio you add it to.
www.shorecapmgmt.com

An investor has to parse the upside volatility from the downside volatility to determine the source of volatility and the skewness and co-skewness of the investment and portfolio. The SR does not take this into consideration.

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Great question.

SR is not as useless as you may think, if used in the wrong way then yes.

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Excellent topic. Thats what makes Linkedin a great place to be.

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know this is an old topic, but for those who are still reading, I suggest using the forward rates curve for more accurate calculations. using only the 10 year T – bills adds serious bias to the calculation.

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“For reasons known only to God and Daniel Kahneman”

Surely Monty Hall (and now Deal or No Deal) offer insight into Kahneman’s thinking.
I’ll take the cash, you keep door number 3 is what drives behavioral utility research.
In practice, I use the 3 month tbill.

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