Measuring Investment Risk with the Sharpe Ratio

You’ve probably heard investing professionals talk about risk-adjusted returns. This is a way of measuring the performance of an investment that factors in risk—specifically, the extra risk required to get higher returns. The Sharpe ratio is a way to measure the risk-adjusted returns of your investments.

What Is the Sharpe Ratio?

Investments can be evaluated solely in terms of their projected returns. However, you get a deeper understanding of an investment when you grasp how much risk you’ve taken on with a single stock or your whole portfolio to get those returns. This is what’s meant by risk-adjusted returns.

The Sharpe ratio—also known as the modified Sharpe ratio or the Sharpe index—is a way to measure the performance of an investment by taking risk into account. It can be used to evaluate a single security or an entire investment portfolio. In either case, the higher the ratio, the better the investment in terms of risk-adjusted returns.

By comparing the return on an investment to the extra risk associated with it above and beyond a risk-free asset—typically, a U.S. Treasury security—the Sharpe ratio gives investors a clear picture of whether higher returns are adequately compensating them for taking on additional risk.

How Does the Sharpe Ratio Work?

Investors typically have two conflicting goals. First, they always want to get the highest possible returns from their investments. Second, they aim to minimize risk, which is just another way of saying they want the lowest possible chances of losing money.

The Sharpe Ratio works by giving investors a score that tells them their risk-adjusted returns. It can be used to evaluate past performance or expected future performance, but in either case this key financial ratio helps the investor understand whether returns are due to smart decisions or just taking on too much risk. If it’s the latter, then investors might lose more than they’re comfortable with when market conditions change.

The Sharpe Ratio is calculated by determining an asset or a portfolio’s “excess return” for a given period of time. This amount is divided by the portfolio’s standard deviation, which is a measure of its volatility.

The Sharpe Ratio Formula

To calculate the Sharpe Ratio, use this formula:

Sharpe Ratio = (Rp – Rf) / Standard deviation

  • Rp is the expected return (or actual return for historical calculations) on the asset or the portfolio being measured.
  • Rf is the risk-free rate, which is often a U.S. Treasury bill of short maturity. However, some analysts suggest that the Treasury used should be of similar duration to the investment(s).
  • Standard deviation is a measure of risk based on volatility. The lower the standard deviation, the less risk and the higher the Sharpe ratio, all else being equal. Conversely, the higher the standard deviation, the more risk and the lower the Sharpe ratio.
  • The market risk premium is represented by the (Rp – Rf) part of the formula. This is the excess return above the risk-free rate.

The ratio should give you a clear view of the relationship between risk and return, illustrating how much excess return is received for the additional risk. The higher the ratio, the greater the investment return relative to the risk taken on with an asset or a portfolio.

A Sharpe Ratio Example

Consider two portfolios: Portfolio A is expected to return 14% over the next 12 months, while Portfolio B is expected to deliver a return of 11% over the same period. Without considering risk, Portfolio A is clearly the superior choice based on returns alone.

But what about risk? Here’s where the Sharp ratio provides you with a more holistic view of your investments. In this example, Portfolio A has a standard deviation of 8% (more risk) and Portfolio B has a standard deviation of 4% (less risk). The risk-free rate is 3%, the yield on a medium-term U.S. Treasury security.

Now, let’s calculate the Sharpe Ratio for each.

  • Portfolio A: (14 – 3) / 8 = Sharpe ratio of 1.38
  • Portfolio B: (11 – 3) / 4 = Sharpe ratio of 2

Given the greater amount of volatility that’s baked into Portfolio A, its Sharpe ratio is lower than Portfolio B’s ratio. This tells us that with a Sharpe ratio of 2, Portfolio B provides a superior return on a risk-adjusted basis.

Generally speaking, a Sharpe ratio between 1 and 2 is considered good. A ratio between 2 and 3 is very good, and any result higher than 3 is excellent.

The Limitations of the Sharpe Ratio

It’s important to note that the Sharpe ratio assumes that an investment’s average returns are normally distributed on a curve. In a normal distribution, most of the returns are grouped symmetrically around the mean and fewer returns are found in the tails of the curve.

Unfortunately, normal distributions don’t represent the real world of financial markets very well. Over the short term, investment returns don’t follow a normal distribution. Market volatility can be higher or lower, while the distribution of returns on a curve cluster around the tails. This can render standard deviation less effective as a measure of risk.

When the standard deviation fails to accurately represent the risk assumed, the result can be a Sharpe ratio that is higher or lower than it should be.

Then there’s leverage, or debt an investor takes on to increase the potential return from an investment. The use of leverage increases the downside risks in an investment. If the standard deviation rises too significantly, the Sharpe ratio will decline dramatically and the size of any loss will be significantly magnified, potentially triggering a margin call for the investor.

The Bottom Line

The Sharpe ratio is widely used among investors to evaluate investment performance. Part of its popularity is based on the ease of calculating and interpreting the ratio.

Many mutual funds, for example, publish the portfolio’s Sharpe Ratio as part of quarterly and annual performance updates distributed to clients.

Even if the details of calculating expected returns and standard deviation are disagreeably complex, any investor can understand that the higher the Sharpe Ratio, the more attractive the return is relative to the risk taken, thus the more attractive the investment.


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