Sharpe Ratio Range of Possible Values

Which Values Can Sharpe Ratio Reach?

Sharpe ratio can theoretically reach any value.

It can be any number from negative infinite to positive infinite.

It is very obvious when you look at the Sharpe ratio formula:

Sharpe ratio formula

Sharpe ratio is portfolio excess return divided by standard deviation (or volatility) of portfolio returns. To understand the range of possible values of Sharpe ratio you need to understand the possible value ranges of its numerator (excess return) and denominator (volatility).

Excess Return Value Range

Excess return is the (expected or realized) return on the portfolio (or investment, fund, or trading strategy) less the risk-free return (typically treasury yield or money market interest rate). It can reach any value.

Volatility Value Range

Volatility, or standard deviation of the investment’s returns, can theoretically reach any positive value or it can be zero (it is zero when the returns are the same all the time). Volatility can not be negative.

Sharpe Ratio Value Range

From the ranges of possible values of excess return (numerator) and volatility (denominator), you can see that Sharpe ratio can theoretically reach any value.

Most of the time when people calculate and use Sharpe ratio, it is positive (otherwise there is not much sense in spending time to calculate it). Sharpe ratio is positive when excess return is positive, which is when the investment return is greater than the risk-free rate.

Sharpe ratio can also be zero. This is when the investment’s excess return is zero, which is when the return on the portfolio is exactly equal to the risk-free rate.

Sharpe ratio can also be negative. Because the denominator (volatility) can never be negative, Sharpe ratio is negative when the numerator (excess return) is negative, which is when the return on the investment is smaller than the risk-free rate. See more detailed explanation of negative Sharpe ratio interpretation.

On both the positive and negative side, Sharpe ratio can theoretically be infinitely small (close to zero) and it can also be infinitely large (close to positive infinite or negative infinite). Excess return is usually not an extreme number (in the millions or greater), therefore it mainly depends on the standard deviation (volatility). When volatility is high, Sharpe ratio is smaller in absolute terms (for the same excess return). Conversely, when volatility is small, Sharpe ratio is a greater positive or negative number.

An extreme case would be when the volatility would equal zero. Mathematically you would not be able to calculate Sharpe ratio (dividing by zero). You could say that the ratio is close to infinite (positive or negative). However, there is no sense in calculating and interpreting Sharpe ratio when volatility is zero, because in that case the investment itself becomes risk-free (as investing theory understands it).


Related pages


theta call optionkurtosis skewshort etf s&pmedian calculator excelwhat is the formula for dividend yieldweighted price index formulawhat is the formula for variance in excelnotepad settingsoptions puts and calls for dummieshistorical volatility formulabull call debit spreadstandard deviation calculator exceloption expiration calendarproshares fundsinterpretation of skewness and kurtosishow to calculate averages in excelderiving square rootsmacro hedge fund definitionexcel formula variancecalculating mean in exceldelta gamma theta vega rhoall etf listbear call spread examplelist of inverse etfstheta financeatr formuladefine vixexcel formula for average percentagehow to trade the vixdefault font notepadimplied volatility black scholesfinding waccsqrt rulesrsi share pricepayoff diagram for optionshow to calculate annualized volatilityinterpretation of sharpe ratiosharpe ratio calculatorblack scholes model derivationcalculating exponents in excelinterpretation of sharpe ratiovertical call spread calculatordelta formulasstatistical skewnesshow to calculate bep in excelvariance sigma squaredstatistics calculator standard deviationassumptions of black scholesbsm modelyahoo finance historical exchange ratesmean variance standard deviation calculatorhow to figure out standard deviation on excelstock straddlehow to solve kurtosisgeometric average return calculatorvariance formula in excelblack schole calculatorblack scholes delta calculatorskewness moments and kurtosisatr technical analysisetfs that track the vixskewness and kurtosis formulavix option pricingcalculate annualized return excelnotepad coloreuro stoxx 50 optionsrsi overbought and oversold conditionmacd trading strategystraddle deltalong straddle option strategykurtosis definitionvega greek symbol