# What Is the Sharpe Ratio?

## How to Calculate the Sharpe Ratio

The Sharpe ratio—named after its creator, William F. Sharpe—is an analysis ratio that provides insight into how the risks of an investment compare to its potential rewards.

Learn how to calculate the Sharpe ratio, and how you can use it to compare investment products.

## What Is the Sharpe Ratio?

The Sharpe ratio measures the reward-to-variability ratio of an investment by dividing the average risk-adjusted return by volatility.﻿﻿ Investors can directly compare multiple investments and evaluate the amount of risk that each investment took on per percentage point of return. This ratio helps investors better control their risk exposure. The higher the ratio, the more returns the investment offers, relative to the risks involved.﻿﻿

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

## How Do You Calculate the Sharpe Ratio?

To calculate the Sharpe ratio for an investment, you first 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 measurement of volatility.

## How Does the Sharpe Ratio Work?

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

The most common way to measure risk is using the beta coefficient, which measures a stock or fund’s volatility relative to a benchmark like the S&P 500 index. If a stock has a beta of 1.1, investors can expect it to be 10% more volatile than the S&P 500 index. A 30% increase in the S&P 500, for example, should result in a 33% increase in the stock or fund with the 1.1 beta—30% multiplied by 1.1 gives you 33%.

Beta coefficients can be used to calculate an investment’s alpha, which is a risk-adjusted return that accounts for risk. Alpha is calculated 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 increases 30% would generate an alpha of 5% assuming a risk-free rate of 2% (40% – 33% – 2% = 5%)—a 5% risk-adjusted return.

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

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

Investors should always look at risk-adjusted returns when evaluating various opportunities, since ignoring risk can prove costly over the long run. While beta and alpha are good ways to do so, investors may want to consider using the Sharpe ratio instead, given its use of absolute rather than relative measures of risk. These metrics can be much more helpful when comparing investments.

## Limitations of the Sharpe Ratio

It's important to only compare very similar investment products with the Sharpe ratio, otherwise, it won't be as meaningful. The Sharpe ratio is great for comparing mutual funds or exchange-traded funds that track the same underlying index. It doesn't work nearly as well for comparing individual stocks, especially if there are major differences between the companies being compared.

While the Sharpe ratio makes for a fairer comparison between similar investment products, investors should keep in mind that investments with a higher Sharpe ratio can be more volatile than those with a lower ratio. The higher Sharpe ratio simply indicates that the investment’s risk-to-reward profile is more optimal or proportional than another. There could still be significant risks or volatility involved.

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

### Key Takeaways

• The Sharpe ratio is an analysis ratio that compares an investment's returns to its risk.
• Calculating the Sharpe ratio involves subtracting the risk-free rate of return from the expected rate of return, 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 the ratio in the mid-'60s.

### Article Sources

1. Stanford University. "The Sharpe Ratio." Accessed Sept. 25, 2020.

2. Corporate Finance Institute. "Sharpe Ratio." Accessed Sept. 25, 2020.