The Sharpe ratio is a measure of a portfolio’s performance in relation to the risk of the portfolio’s investments.

### The Sharpe Ratio

The Sharpe ratio was created by now Nobel Prize winning economist William Sharpe. He originally called it the “reward-to-volatility ratio” in his 1966 paper. The Sharpe ratio helps measure the performance of a portfolio manager based on the risks he or she is taking.

A portfolio manager may obtain higher returns than their peers, but they may be taking excess risk in order to obtain those returns. Evaluating a manager based on their Sharpe ratio determines whether additional risk is worth the added returns.

### Sharpe Ratio Formula

The Sharpe ratio is calculated by:

Where Rp is the return of the portfolio

Rf is the risk free rate of return during the period (Usually, the return of treasury bonds or it may be a benchmark)

And Sigmap is the standard deviation of the portfolio during the period.

Think of the numerator (Rp – Rf) as the effective return rate or excess return rate of the portfolio, as it is the “surplus” return an investor would have received by investing outside of the risk free asset.

The denominator, sigma, is dependent on the variability of the portfolio’s returns. Although it may not always be the case, in the Sharpe Ratio “risk” is measured by the volatility in the portfolio’s performance.

A higher Sharpe ratio means that the portfolio’s returned higher performance “per unit of risk”. A negative Sharpe ratio means that investors would have been better off choosing the risk free asset.

### The Sharpe Ratio in Practice

The Sharpe ratio is primarily used to evaluate portfolio managers of mutual funds.

Mutual Fund Sharpe Ratios are published at many different sources, so comparing mutual fund performance is easy.

Let’s compare 2 different mutual funds. A Large cap actively managed mutual fund by Vanguard, and a passively managed large cap value mutual fund also by Vanguard.

The actively managed fund is the Vanguard Windsor Fund (Ticker VWNDX)

The passively managed fund is the Vanguard Value Index Fund (Ticker VVIAX)

VWNDX has an expense ratio of 0.37% (which is actually very low for an actively managed fund) and VVIAX has an expense ratio of 0.09%.

As an investor, I want to know if the additional fees for the active manager has been worth it. One way to make that comparison is to measure the Sharpe Ratios of the two funds, which will tell us how the returns of the two funds compared to the risks of the two funds.

The Sharpe Ratio of nearly any mutual fund is posted on Yahoo Finance, (and many other sites as well). Here is a side by side comparison of the two funds we are comparing:

Notice that there are 3 specific Sharpe Ratios published for each fund. Over a 3 year period, over a 5 year period and over a 10 year period.  Here are the performance charts for each of those periods:

3 Year:

5 year:

10 Year:

Notice that the actively managed fund has higher returns over the past 3 and 5 years, so it must be the better investment choice, right? Not necessarily.

Notice in the first image that VWNDX has a lower Sharpe Ratio for all 3 periods (1.01 vs 1.06 for 3 years, 1.24 vs 1.34 for 5 years and 0.42 to 0.47 for 10 years). So although VWNDX has outperformed VVIAX over the past 3 and 5 years (though not 10 years), it has taken on additional risk in terms of portfolio volatility to obtain that performance.

So an investor who has a high level of concern about portfolio volatility would be more inclined to pick the passively managed fund VVIAX because it has returned higher performance “per unit risk” compared to VWNDX.

Conclusion

Notice that this is just one measurement of a mutual fund’s performance. It should hardly be used as a sole determinate of which fund you should invest in. Investors who may be willing to take on additional risk may find the increased volatility of VWNDX to be worth the chance for additional returns.

The Sharpe Ratio is calculated based on the historical volatility (standard deviation) of a portfolio’s performance. But there is no guarantee that the portfolio or fund manager will perform or behave the same way in the future.