# What Is the Sharpe Ratio?

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Definition

The Sharpe ratio, named after its creator, William F. Sharpe, is a way to look at how the risks of an investment compare to its potential rewards.

### Key Takeaways

• The Sharpe ratio is a rate that compares an investment's returns to its risk.
• Finding the Sharpe ratio involves subtracting the risk-free rate of return from the expected rate of return and then dividing that result by the standard deviation, otherwise known as the asset's "volatility."
• The Sharpe ratio is named after the creator, William F. Sharpe, who first introduced it in the mid-1960s.

## Definition and Example of the Sharpe Ratio

The Sharpe ratio measures the reward-to-variability rate of an investment by dividing the average risk-adjusted return by volatility. People can compare investments and assess the amount of risk that each one has per percentage point of return. This helps people better control their risk exposure. The higher the rate, the more returns the investment offers relative to the risks involved.

For example, suppose one investment manager has a portfolio return of 10%, while the second investment manager has a return of 14%. It would appear that the second investment manager has the better return. However, the Sharpe ratio for the first manager could be 1.8, and for the second manager it could be 0.7. The second manager is taking on more risk to generate the added return, which means there's also a higher risk of losses. Investors should consider their risk tolerance and the risk-adjusted return to determine whether an investment is worth the risk.

### Note

The Sharpe ratio was introduced by Stanford economist William F. Sharpe in 1966.

## How Does the Sharpe Ratio Work?

The Sharpe ratio uses the risk-free rate of return, which is typically a Treasury security since U.S. Treasuries are backed by the U.S. government. For example, if a particular Treasury had a yield of 4%, and it's used as the risk-free rate of return in the calculation, the investment would need to earn more than the risk-free rate of 4% to compensate for the risk associated with the investment. How much an investment's price fluctuates is called "volatility." Together, the risk-free rate of return and volatility can help determine whether an investment is worth the risk.

### Formula for the Sharpe Ratio

To find the Sharpe ratio for an investment, subtract the risk-free rate of return (like a Treasury bond return) from the expected rate of return of the investment. Then, divide that figure by the standard deviation of that investment's annual rate of return, which is a way to measure volatility.

To better see how the Sharpe ratio works, it might help to review volatility measurements and risk-adjusted returns.

The most common way to measure risk is by using the beta coefficient. It measures a stock or fund’s volatility against a benchmark like the S&P 500 index. If a stock has a beta of 1.1, you can expect it to be 10% more volatile than the S&P 500 index. A 30% increase in the S&P 500, for instance, should result in a 33% increase in the stock or fund with the 1.1 beta. In other words, when 30% is multiplied by 1.1, you get 33%.

Beta coefficients can be used to find an investment’s alpha. The alpha is a risk-adjusted return that accounts for risk. Alpha is found by subtracting an equity’s expected return based on its beta coefficient and the risk-free rate by its total return. A stock with a 1.1 beta coefficient that increases 40% when the S&P 500 goes up by 30% would bring an alpha of 5%. This assumes a risk-free rate of 2% (40% – 33% – 2% = 5%), which is a 5% risk-adjusted return.

It’s vital to note that investments with a higher beta must create a higher total return to see a positive alpha. For instance, a stock with a beta of 1.1 would need to see 10% greater returns than the S&P 500 index plus the risk-free rate to create a neutral alpha. As a result, safer stocks can bring higher risk-adjusted returns even if they produce lower total returns since they entail less risk of loss over the long run.

### Note

The problem with beta coefficients is that they are relative rather than absolute. By finding the rate of return per unit of volatility, you have a better sense of how the risk compares to the reward.

### Analyzing Risk

When you invest, you should always look at risk-adjusted returns when choosing where to invest your money. Not taking a clear look at risk can prove costly over the long run. While beta and alpha are good ways to do so, you may want to try using the Sharpe ratio instead, given its use of absolute rather than relative measures of risk. These metrics can be much more helpful when choosing investments.

## Limits of the Sharpe Ratio

It's vital to only compare very similar investments with the Sharpe ratio. Otherwise, it won't be as helpful. The Sharpe ratio is helpful when looking at mutual funds or exchange traded funds (ETFs) that track the same underlying index. However, it doesn't work nearly as well for comparing stocks, particularly if there are major contrasts between the companies being compared.

While the Sharpe ratio makes for a fairer comparison between similar investments, you should keep in mind that those with a higher Sharpe ratio can be more volatile than those with a lower rate. The higher Sharpe ratio simply shows that the investment's risk-to-reward profile is more optimal or proportional than another. However, there could still be big risks.

It's also vital to note that a Sharpe ratio isn't viewed on any kind of scale, which means it's only helpful when comparing options.