What Is Sharpe Ratio? Definition of Sharpe Ratio

To put it simply (and perhaps a bit too simply), the Sharpe Ratio measures the added returns investors get for taking on added risk. For a portfolio, security, asset class or fund, the Sharpe Ratio calculates returns over the ‘risk-free’ rate, compared to the underlying volatility.

The Sharpe Ratio formula is:

Where:

Rx = Expected portfolio return

Rf = Risk free rate of return

StdDev Rx = Standard deviation of portfolio return/volatility

The risk-free rate often used is the 90-day Treasury bill (though some calculations use the 1- or 2-year Treasury). The standard deviation calculates the dispersion of returns over that period (often on a monthly basis when measuring Sharpe Ratio over a multi-year period). Dispersion is the range of returns: a volatile portfolio (think buying call and put options on growth stocks)  in theory should have a greater range than a more conservative strategy (owning steady, profitable, blue-chip companies).

The Sharpe Ratio can be calculated looking backward (ex post) — or looking forward (ex ante). Ex post calculations are quite straightforward, as the data is readily available from many public sources. 

Ex ante estimates — and they are estimates — usually are based on financial modeling, using historical data. An investor might use the historical standard deviation of a portfolio’s returns and assume that standard deviation will persist going forward. Combined with an estimate of the risk-free rate, she can model the portfolio returns desired — or check that the desired returns are achievable at an acceptable level of risk.

By comparing returns to volatility, the core question Sharpe Ratio aims to answer is: lucky or good? Higher volatility creates both higher upside and higher downside. A high-volatility portfolio can create huge returns when everything is going well — but risks blowing up when trouble arises. The Sharpe Ratio can be used to help identify these problematic portfolios, asset classes, or securities.

Conversely, a lower-volatility strategy may have posted weaker returns against the risk-free rate over a time period. But it’s also less likely to have benefited simply from volatility working in its favor. 

Examples may be instructive. Let’s start with Hedge Fund A. The fund has returned 18% a year, while the risk-free rate is 2%. The standard deviation for the portfolio is 20.

Hedge Fund A thus has a Sharpe Ratio of 0.8: excess returns of 16%, divided by the standard deviation of 20.

On an absolute basis, Hedge Fund A has outperformed Hedge Fund B, which generated returns of just 12%. But Hedge Fund B has a portfolio showing far less volatility; its standard deviation is just 10. 

Hedge Fund B thus has a Sharpe Ratio of 1.2 — higher than that of Hedge Fund A, despite lower returns. The higher Sharpe Ratio suggests that Hedge Fund B offered better returns for its investors than did Hedge Fund A relative to the risks each fund took.

Put another way, it certainly looks like Hedge Fund A was lucky, while Hedge Fund B might well have had the better investment process.

Can a Sharpe Ratio be higher than 1? As our example shows, yes it can — and, ideally, it should be. 

Again, the Sharpe Ratio calculates how much incremental reward investors receive for taking incremental risk. A Sharpe Ratio below 1.0 generally suggests that the added rewards are less than the added risks. 

What does a Sharpe Ratio of 1.0 mean? It means, essentially, the incremental risk matches incremental reward. 

So in our example, Hedge Fund A has outperformed Hedge Fund B on an absolute basis. But a portfolio allocator looking at the Sharpe Ratios for the two funds — which adjust for volatility — might well see Hedge Fund A as the lower-quality option, both looking backwards and forwards.

The higher the Sharpe Ratio, the better. Beating the risk-free rate by 10 percentage points with a standard deviation of, say, 2.5 — a low-volatility result — suggests a Sharpe Ratio of 4 — an impressive performance.

Can you have a negative Sharpe Ratio? Absolutely — but probably only on an ex post basis. A Sharpe Ratio can be negative if returns are less than the risk-free rate, which obviously is possible; funds, securities, and asset classes can decline, even over multi-year periods. 

But our volatility measure has to be a positive number (a standard deviation can’t be negative), so returns below the risk-free rate are the only way to generate a negative Sharpe Ratio. 

An ex ante Sharpe Ratio thus can’t be negative. Obviously, no one would build an investment strategy with the purpose of generating returns lower than a short-term Treasury, generally considered one of the safest investments in the entire world.

Now, it’s worth noting that measuring Sharpe Ratios in such an absolute way — where a number above 1.0 is ‘good’ and a figure below 1.0 is ‘bad’ — can drive some errors. A single asset class, fund, or investment can have a low Sharpe Ratio — yet still increase the Sharpe Ratio of an overall portfolio. The cause of this is correlation.

Different investment strategies can have different standard deviations; some are higher, some are lower. Again, higher standard deviations generally lead to lower Sharpe Ratios.

But if a portfolio adds a high-volatility strategy that is negatively correlated, that added volatility can decrease the total volatility of the portfolio. An example might be call options on the price of gold. Gold often rises in times of economic or political turbulence — times which often lead to downturns and higher volatility in equity portfolios.

Call options on gold, on their own, likely offer a low Sharpe ratio; the risk-adjusted returns are not necessarily market-beating. But those call options are likely to outperform, and often with lower volatility, precisely when volatility spikes in the rest of the portfolio.

And so the strategy could decrease a portfolio’s overall standard deviation — improving its Sharpe Ratio and, at least in theory, its risk-adjusted returns going forward.

The value and importance of the Sharpe Ratio has led to variations. One is known as the “information ratio.”

The information ratio aims to answer the same question as the Sharpe Ratio: lucky or good? It, too, measures returns against volatility.

The core difference, however, is that the Sharpe Ratio uses the risk-free rate as its benchmark. The information ratio uses an index — usually (though not always) the S&P 500. 

The goal is the same: understanding the incremental benefits a strategy provides relative to the added risk. In the case of the information ratio, however, the risk is measured by the deviation from another higher-risk asset (like the S&P), instead of the lowest-risk asset in short-term U.S. Treasuries.

The Sortino Ratio too provides a slight modification to the Sharpe Ratio, but in a different way. Unlike the Sharpe Ratio, the Sortino Ratio focuses solely on the downside volatility of the portfolio. 

It does this by using the standard deviation of excess returns (the denominator of the Sharpe Ratio) only to the downside, instead of in both directions.

The theory here is that it’s downside risk that matters most to investors. Volatility to the upside can perhaps be nerve-wracking, but it doesn’t blow up portfolios. Nor does it provide such a fundamental headwind to driving long-term returns.

As with the information ratio, the Sortino Ratio is only a minor tweak. The goal of all three metrics is the same: to provide investors with a better understanding of returns relative to risk, not just on an absolute basis. 

None of the three ratios is perfect on this score; in investing, no fundamental metric ever is. But as with every metric, there’s value, when used correctly and in context.