Interpreting the Sharpe Ratio

by Wayne A. Thorp, CFA

The relationship between risk and return is an essential concept in finance, which argues that riskier investments should compensate investors with higher returns and safer investments should not experience exorbitant price fluctuations.

When comparing the performance of two securities, funds or portfolios, investors must consider risk-adjusted returns to see if they are being adequately compensated for the risk they are assuming. The goal is to achieve the largest return per unit of risk.

William Sharpe devised the Sharpe ratio in 1966 to measure this risk/return relationship, and it has been one of the most-used investment ratios ever since. Here, we discuss how to calculate and interpret the Sharpe ratio.

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Wayne A. Thorp, CFA is a vice president and senior financial analyst at AAII and editor of Computerized Investing. Follow him on Twitter at @AAII_CI.


Discussion

Doug from New York posted 10 months ago:

Given that a Sharpe Ratio can be driven toward INFINITY by reducing the StdDev(Rx) toward zero, one really has to watch for earnings smoothing when using the Sharpe Ratio!

As an outrageous sort of example, suppose that a company had annual returns of 4%,5%,9%,4%. By simply deciding to give management a "special bonus" (call it the Sharpe Ratio Maximization bonus :-)) equivalent to the difference of these annual returns from some attainable return like 3% (and why shouldn't management receive more when returns are higher?), we can reduce the net return to 3%,3%,3%, and 3%.

Add back in a *little* variability (to avoid StdDev(Rx)=0), say by having higher expenses in some years, and we can make the Sharpe Ratio as high as we like, at the mere cost of a somewhat lower average return.


Mac from Massachusetts posted 10 months ago:

Could you offer more specifics on how to re-create the T-bill risk-free rate shown in Table-1? My attempt with info I downloaded from www.treasury.gov/resource-center/data-chart-center/... led me to calcs that were way off. Thanks.


Mac from Massachusetts posted 10 months ago:

Could you offer more specifics on how to re-create the T-bill risk-free rate shown in Table-1? My attempt with info I downloaded from www.treasury.gov/resource-center/data-chart-center/... led me to calcs that were way off. Thanks.


Gareth Degolier from Minnesota posted 4 months ago:

First of all, thanks for an informative article on the Sharpe Ratio.

Secondly, you say that "translated into risk, high volatility means returns are inconsistent. Strong upside performance of a highly volatile stock can turn severely negative in an instant; thus it is still a risky investment."

I know that it is conventional wisdom, but I don't buy that volatility equates to risk. There are other kinds of risk that should be emphasized more than volatility for either traders or investors. With a highly volatile stock, the reverse of the above statement is also true. Strong downside performance of a highly volatile stock can turn significantly positive in an instant; thus creating a lower entry point and potentially higher returns assuming, strong fundamentals.


Justin Morrill from Colorado posted 4 months ago:

Thanks for the Sharpe ratio explanation.

While it's admittedly simple to calculate the Sharpe ratio in comparing several equities, I have come to use Beta as a proxy for standard deviation when screening a universe of stocks for possible investment. I believe that beta is a reasonable proxy since it is a measure of the volatility of an individual stock versus the volatility of the entire market. I find that this method is easier since beta of individual equities is widely published, and requires no calculation. I calculate the risk-adjusted-return by dividing the expected percentage return (equity price growth plus dividend over the same period) divided by beta. With the Treasury Bill rate near zero for the last several years, I currently gnore the risk-free expected return in this analysis. Just as with the Sharpe ratio, the higher the calculated value of this alternate ratio, the better the potential risk-adjusted-return.

Any comments on this approach?


Tony from Maryland posted 4 months ago:

Something to think about:

"If investors rely solely on quantitative risk measures such as the the ones discussed here, real risks can escape detection until the damage has been done." - Arijit Dutta, Associate Director of Mutual Fund Analysis with Morningstar

"Thus, standard deviation, the most frequently used risk measure, is likely to understate the true downside of a portfolio." - Arijit Dutta, Associate Director of Mutual Fund Analysis with Morningstar

"With 20% declines occurring, on average, every decade or so, you'd think that the standard risk models that investors use to make their asset-allocation decisions would assign a significant probability that these events will occur. Think again." - Paul Kaplan, Ph.D., CFA and V.P. of Morningstar's Quantitative Research

"I think the simple message is that there's much more risk than there appears to be and that the standard deviation doesn't capture all the risk." - Roger Ibbotson, Founder of Ibbotson Assoc.

IMO, there are tree factors to consider when evaluating risk;

1. Predicting the probability of decline with a certain time frame

2. Predicting the length of the decline

3. Predicting the severity of the decline

Is their anyone who has been able to predict the answers to these questions to an acceptable degree of certainty?

At the end of the day, risk management calculations can only tell us about the past, and nothing of the future.





Doug from New York posted 3 months ago:

Justin Morrill wrote:
[
I calculate the risk-adjusted-return by dividing the expected percentage return (equity price growth plus dividend over the same period) divided by beta.
]

So, this is basically the "Treynor Ratio".

Using a similar technique to the one I mentioned above, for the Sharpe Ratio, a company can drive beta toward zero (just keep the net earnings REALLY STABLE and the beta ought to decrease). If they can keep their expected percentage return ABOVE zero, they can drive your ratio toward infinity.

(Basically, I think ratios like this allow the denominator to be way too important, especially if it can be manipulated toward zero.)


Chris Smith from Iowa posted 2 months ago:

I agree with Gareth that volatility does not necessarily equate with risk, especially if no one is holding a gun to your head forcing you to close out your position at the most inopportune time.


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