Sharpe Ratio Calculator

What this Sharpe ratio calculator does

Two funds both returned 12 percent last year. One of them got there in a fairly straight line and the other spent the year lurching about. They are not the same investment, and comparing them on return alone tells you nothing about that difference.

The Sharpe ratio is the standard way of putting the two on the same footing. It asks how much return you got above the risk free rate, per unit of volatility you had to sit through to get it.

Give this calculator your portfolio return, the risk free rate, and your portfolio's standard deviation, all as percentages, and it returns the ratio.

It expects those figures to be already annualised. Feed it monthly numbers and you will get a monthly Sharpe ratio, which is a much smaller number and not comparable to anything anybody quotes. The conversion is below and it is the single most common mistake with this metric.

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How to use it

1. Expected portfolio return. Your annual return as a percentage. Use the realised figure if you are measuring past performance, or your expectation if you are modelling forward.
2. Risk free rate. The return available with no risk, conventionally a short dated government bill in your own currency. Match the maturity to your measurement period.
3. Portfolio standard deviation. The annualised volatility of your returns, as a percentage.

Press Calculate. Press Reset to clear it.

Two things the fields will not currently accept. The portfolio return must be positive, so a portfolio that actually lost money over the period cannot be entered. And the risk free rate must be above zero, which rules out the near zero and negative policy rates that were reality across Japan and much of Europe for years. Both are on our list. In the meantime, if either applies to you, the arithmetic is one subtraction and one division and the formula is below.

The formula, and the two versions of it

What this calculator computes:

Sharpe ratio = (portfolio return − risk free rate) ÷ portfolio standard deviation

The numerator is your excess return, the reward for taking risk rather than sitting in bills. The denominator is the volatility you endured. The ratio is reward per unit of that volatility, which is why Sharpe originally called it the reward to variability ratio.

There is a subtlety worth knowing, because it separates people who use the metric from people who understand it.

Sharpe's original 1966 formulation is the one above, using the standard deviation of the portfolio's returns. His 1994 revision defines it on the differential return instead: take the return of your portfolio minus the risk free rate in each period, then divide the mean of that series by the standard deviation of that same series.

The two agree exactly when the risk free rate is constant across your measurement period. They diverge when it moves, which over any multi year period it does. In practice the difference is usually small, most published Sharpe ratios use the simpler version, and this calculator does too. Now you know which one you are looking at, which is more than most calculators will tell you.

A worked example

A portfolio returning 12 percent a year, with a risk free rate of 4 percent, and annualised volatility of 15 percent.

(12 − 4) ÷ 15 = 0.53

So each unit of volatility bought you roughly half a unit of excess return.

Now change one thing. Same 12 percent return, same 4 percent risk free rate, but volatility of 8 percent instead of 15:

(12 − 4) ÷ 8 = 1.00

Identical return, nearly double the Sharpe ratio, purely because the ride was smoother. That is the entire point of the measure. It refuses to reward you for a return you achieved by taking more risk.

And one more. A portfolio returning 3 percent when bills pay 5 percent:

(3 − 5) ÷ 10 = −0.20

Negative, and correctly so. You took risk and were paid less than you would have been for taking none. A negative Sharpe ratio is meaningful information rather than an error, though it is worth noting that once it goes negative the ordering stops behaving sensibly, because more volatility makes a negative ratio look better.

Annualising, and the square root that everyone forgets

Almost every published Sharpe ratio is annual. If your data is monthly, weekly or daily, you have to convert, and the conversion is not what most people guess.

Returns scale with time. Volatility scales with the square root of time. So a Sharpe ratio built from period data becomes:

Annualised Sharpe = period Sharpe × √(periods per year)

Take a strategy with a mean monthly excess return of 0.9 percent and a monthly standard deviation of 4.2 percent. Its monthly Sharpe ratio is 0.21. Annualised properly, that is 0.21 × 3.464 = 0.74.

Multiply by 12 instead, as people do, and you get 2.57. That would be a world class number and it is wrong by a factor of nearly three and a half.

The error always runs the same way, making things look better, which is why it survives. If you ever see a strategy advertising a Sharpe ratio well above 3, checking how it was annualised is a reasonable first question.

Worth adding that the square root rule itself assumes returns are independent from period to period. Where they are not, and for many strategies they are not, the adjustment is only approximate. Andrew Lo's work on the statistics of Sharpe ratios sets out the corrections properly.

Reading the number

There is a set of conventional bands that get quoted everywhere. They are useful and they are rules of thumb rather than anything derived.

Two things to hold alongside that table.

First, the ratio only means anything in comparison. A Sharpe of 0.6 tells you little on its own and quite a lot next to an index fund's 0.5 over the same period, measured the same way. Always compare against a benchmark and against the same time window.

Second, broad equity markets over long periods have historically produced Sharpe ratios well under 1. So a strategy claiming 2 or 3 sustained over many years is claiming to have substantially beaten the market on a risk adjusted basis, which is a large claim and deserves the scepticism it attracts.

What it measures, and what it quietly assumes

The Sharpe ratio treats standard deviation as the definition of risk. That is a specific choice with specific consequences, and it is where most of the criticism lands.

Upside volatility is punished exactly like downside. A fund that occasionally jumps 20 percent is penalised the same as one that occasionally falls 20 percent. Most investors do not feel those two events the same way. This is the reason the Sortino ratio exists, which uses downside deviation only.

It assumes returns are roughly normally distributed. Where returns are skewed or have fat tails, standard deviation stops describing the risk well. Strategies that make small steady gains and then lose enormously all at once are exactly the case where this breaks, and the Sharpe ratio flatters them right up until the moment it does not.

It says nothing about drawdown. Two portfolios with identical Sharpe ratios can have very different worst moments, and the worst moment is often what actually determines whether an investor stays invested.

It is backward looking when built from history. A ratio calculated over the past five years describes those five years. It is not a forecast, and volatility regimes change.

None of that makes it a bad measure. It is a genuinely good one, which is why it has survived sixty years. It is one number describing one dimension of risk, and it should be read alongside maximum drawdown and the shape of the return distribution rather than instead of them.

Why a high Sharpe ratio is not always good news

Because the ratio is so widely used to allocate money, there is real incentive to make it look good, and several ways to do that without improving the underlying investment.

Lengthening the measurement period. Monthly data produces a lower measured volatility than daily data for the same strategy, because short term wobbles get averaged away inside each month. Reporting monthly instead of daily raises the Sharpe ratio without changing anything real.

Illiquid or infrequently priced holdings. Assets that are marked to model rather than to market show artificially smooth returns, which means artificially low standard deviation and an artificially high Sharpe ratio. This is a well known feature of some private and property funds.

Selling insurance-like exposure. Strategies that collect small premiums regularly and pay out rarely but heavily produce beautiful Sharpe ratios for years. The distribution is precisely the one standard deviation describes badly.

Choosing the window. Any performance statistic can be improved by selecting a flattering start date.

The practical defence is to ask three questions of any Sharpe ratio you are shown: over what period, at what data frequency, and against what benchmark. If those are not stated, the number is not really telling you anything.

Questions people ask

What is a good Sharpe ratio?

Above 1 is conventionally acceptable, 2 is very good, 3 is excellent and rare. But it only means anything compared against a benchmark over the same period, measured the same way.

My data is monthly. What do I enter?

Annualise first. Multiply your monthly Sharpe ratio by the square root of 12, which is 3.464. Multiplying by 12 is the common error and inflates the result by nearly three and a half times.

Can the Sharpe ratio be negative?

Yes, when your return is below the risk free rate. This calculator will produce one if you enter a risk free rate above your portfolio return. It will not currently accept a negative portfolio return.

What should I use as the risk free rate?

A short dated government bill in the same currency as your returns, over the same period. For annual figures a one year or three month treasury yield is conventional.

How is this different from the Sortino ratio?

Sortino uses downside deviation only, so it does not penalise upside volatility. If your returns are skewed, Sortino often tells you more.

Which version of the formula does this use?

The original 1966 form, dividing excess return by the portfolio's standard deviation. Sharpe's 1994 revision uses the standard deviation of the excess return series instead. They match when the risk free rate is constant.

Where do I get my portfolio standard deviation?

From your returns series. Take the standard deviation of your periodic returns, then annualise it by multiplying by the square root of the number of periods in a year.

References

A note on sourcing. The measure originates with William Sharpe, who introduced it as the reward to variability ratio in 1966 and revised the definition in 1994. The statistical treatment of annualisation, including the conditions under which the square root of time rule holds, is set out in Lo's 2002 paper.

1. Sharpe, W. F., Mutual Fund Performance, The Journal of Business, Vol. 39, No. 1, January 1966, pp. 119 to 138.
2. Sharpe, W. F., The Sharpe Ratio, The Journal of Portfolio Management, Vol. 21, No. 1, Fall 1994, pp. 49 to 58.
3. Lo, A. W., The Statistics of Sharpe Ratios, Financial Analysts Journal, Vol. 58, No. 4, 2002, pp. 36 to 52.
4. Markowitz, H., Portfolio Selection, The Journal of Finance, Vol. 7, No. 1, March 1952, pp. 77 to 91.