# What is the Sharpe Ratio?

The Sharpe ratio is a tool to help investors understand the amount of risk they are taking versus the reward of their investment.

## 🤔 Understanding Sharpe ratio

The Sharpe ratio was developed by Nobel Laureate William F. Sharpe to give investors an idea of how much risk they are taking to achieve a return on their investment. It measures the performance of an investment after subtracting the risk-free rate of return and dividing by the standard deviation of the excess returns. The risk-free rate is the rate of return on a relatively safe investment, such as a U.S. government bond. The standard deviation is a risk indicator that measures price fluctuations from the average price. The Sharpe ratio is a useful tool for investors when you want to compare risk-adjusted returns of similar portfolios or assets. A portfolio with a higher Sharpe ratio should have a comparatively better performance after adjusting for risk.

Let’s say you want to invest in a stock that gives you a fair return on your investment with a moderate amount of risk. You’ve narrowed it down to two stocks that delivered the same 10% annual returns over the last five years. However, Stock A has a higher average standard deviation (volatility or price fluctuations) than Stock B during this period. By comparing risk-adjusted returns using the Sharpe ratio, you can see that Stock B delivers the same 10% annual return, but with lower risk.

## Takeaway

The Sharpe ratio is like online reviews for skydiving companies...

You want the fun (return on investment) that comes with skydiving, but you want to have that fun with the least amount of risk possible. It’s the same with investing — If you can achieve the same returns while taking less risk, why wouldn’t you?

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## How do you calculate the Sharpe ratio?

The formula for the Sharpe ratio is:

In the numerator, you are trying to calculate the excess return of the portfolio. The excess return is the return that is above and beyond the risk-free rate. By subtracting the risk-free rate, you can single out the portfolio gains linked to the risk you are taking.

Generally, investors use the U.S. Government Treasury Bill for the risk-free rate. The Treasury Bill is usually considered one of the safest investments you can make, backed by the full faith of the U.S. Government. The term could vary based on the period you are using to calculate your returns.

The standard deviation is a measure of volatility or risk. It measures how much an asset’s price fluctuates in relation to its mean (average) price.

One thing to remember is that the numbers used are annualized –– numbers collected over specific periods that are scaled to represent an annual figure. It can lead to errors if you don’t take this into account. Let’s look at a couple of examples for calculating monthly and daily returns.

First, we will calculate the Sharpe ratio using monthly returns. Let’s assume a mutual fund has an average monthly expected return of 10%, a standard deviation of 8%, and we use a risk-free rate of return of 5%. The calculation would be 10% (monthly return) - 5% (risk-free rate) / 8% (standard deviation) = 0.63 (monthly Sharpe ratio). To find the annualized number, you need to multiply the monthly ratio by the square root of 12. So the annual Sharpe ratio would be 0.63 (monthly Sharpe ratio) x square root of 12 = 2.16.

Next, we can annualize daily returns to calculate the Sharpe ratio. Let’s assume a mutual fund has average daily portfolio returns of 0.25%, a standard deviation of 0.87%, and the risk-free rate is 0.16%. You calculate the daily Sharpe ratio as .25% (daily portfolio returns) - .16% (risk-free rate) / .87% (daily standard deviation) = 0.10. To get the annualized Sharpe ratio, you multiple the daily ratio by the square root of 252 (there are 252 trading days in the US market). So you end up with 0.10 (daily Sharpe ratio) x square root of 252 = 1.81.

How to calculate the Sharpe ratio in Excel

Let’s look at how to calculate the Sharpe ratio using 10 years of returns in Excel. We will assume that the Treasury Bill (risk-free rate) stays the same for the entire 10 years. Once you know the annual returns and the risk-free rate, you can calculate the excess returns.

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Next, you need to calculate the average of the annual returns. Excel has a built-in “average” formula (=AVERAGE) that you can use.

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Once you know the average of the returns, you’ll need to find the standard deviation of the excess returns. There is a standard deviation formula that you can use (=STDEV).

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Since the risk-free rate is assumed to be 2% throughout the 10 year period, there’s no need to calculate the average, as it will be 2%. If it changed during the period, you would also calculate the average.

Finally, you take the average returns - risk-free rate / standard deviation of excess returns to get the Sharpe ratio.

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## What is a good Sharpe ratio?

The Sharpe ratio is a useful tool for comparing the risk-adjusted returns of two different investments as well as determining how adding an asset to your portfolio may also affect risk-adjusted returns. The higher the Sharpe ratio, the better your risk-adjusted returns.

In general, a ratio below 1.0 is not good, meaning the amount of risk you are taking to achieve your returns may be excessive.

A result of 1 – 1.99 is considered acceptable, 2.0 – 2.99 great, and 3.0 + is generally an excellent ratio.

Let’s compare a couple of fictional investments to get a better idea of how this works in practice. Imagine Stock A has an average annual return of 19% over the last 10 years. Stock B has returned 12% and Stock C 10%. At first glance, Stock A has a better return in the previous 10 years. However, this doesn’t take into account the amount of risk (volatility) you are taking to achieve those returns.

Let’s assume Stock A has a standard deviation on excess returns of 17%, Stock B’s is 8%, and Stock C’s is 4%. We can also imagine the risk-free rate is 4%.

Using these figures, we can calculate each stock’s Sharpe ratio to compare their risk-adjusted return.

Stock A | Stock B | Stock C | |
---|---|---|---|

Sharpe Ratio | 0.88 | 1.0 | 1.50 |

Even though Stock A has a higher return overall, it has the lowest Sharpe ratio. That means the amount of risk you need to take to achieve those returns is more than the risk for Stock B or Stock C.

Remember that a ratio below 1.0 is considered not good, and anything between 1.0 – 1.99 is acceptable. The higher the ratio, the better the risk-adjusted returns of the investment.

When comparing multiple investments, the Sharpe ratio is an excellent tool to help you understand the risk you are taking to achieve a rate of return.

## How is the Sharpe ratio different from the Sortino ratio?

Both the Sharpe ratio and the Sortino ratio help an investor understand risk-adjusted returns, but they have slightly different approaches. The critical difference is how they address standard deviation and volatility.

The Sharpe ratio uses total volatility. That means it takes the standard deviation of all excess returns –– both positive and negative returns. In a way, upside volatility (increasing price movements), even though it is good, can skew the results downward, giving a lower Sharpe ratio.

The Sortino ratio uses only negative volatility. That means it uses the standard deviation of negative excess returns (also referred to as downside deviation).

Upside volatility is useful for investors. We all like it when the price rises. The Sortino ratio removes upside volatility as a “risk” and only uses the downside deviation to take this into account. In this way, the asset you are analyzing isn’t punished for positive volatility.

Many investors prefer to use the Sharpe ratio for portfolios that have low volatility –– the assets don’t have large price fluctuations. If the portfolio has a lot of volatility, investors tend to prefer the Sortino ratio, since it isolates the downside deviation.

## What are the limitations of the Sharpe ratio?

One limitation is that the Sharpe ratio looks at total volatility, both positive and negative. In a way, this can penalize and asset that has significant amounts of positive volatility (positive price swings). Because it doesn’t distinguish between positive or negative fluctuations, the ratio can be lower, even with sizeable positive price swings.

Another limitation is that the ratio can be manipulated to show better risk-adjusted returns. This can be done in several ways. First, you could measure a longer time period. In general, annualizing the standard deviation of daily returns is higher than weekly, and weekly returns are typically higher than monthly.

Another way to manipulate the result is to choose a period that gives you the best potential risk-adjusted returns. For example, choosing a period with low volatility (standard deviation). Or, someone may try and smooth the returns by cutting out the best and worst monthly returns each year. That removes the outliers and reduces volatility.

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