The Sharpe ratio, named after its creator, was developed by Nobel laureate William F. Sharpe. It is used to measure the risk-adjusted return of a financial portfolio. Simply put, you can use it to help understand the return of an investment portfolio in relation to its risk.

Sharpe wanted to cancel out the risk component of an investment in order to make comparisons of different portfolio returns more relative. To do this, he created the Sharpe ratio. Which shows how well an investment performs in comparison to a risk-free rate of return. Such as, U.S. treasury bills, notes, or bonds.

Without taking on risk, you won’t be seeing higher returns. The Sharpe ratio helps you see an investment is getting a high enough return to justify the increased risk.

## Sharpe Ratio – a better way to look at risk vs reward

A portfolio with a higher Sharpe ratio is considered better in relation to its peers. The higher the ratio, the greater the investment return relative to the risk taken on. Thus making it the better investment. The ratio can be used to evaluate a single stock investment. As well as an entire portfolio.

The Sharpe ratio has become the most widely used method for calculating the risk-adjusted return.

It helps you to maximize returns while reducing volatility.

### Formula

It’s a simple calculation. Thus making it a widely referenced measure of risk and return in the finance world.

You calculate the Sharpe ratio by subtracting the risk-free rate from the return of the portfolio and dividing the result by the standard deviation of the portfolio’s excess return. It sounds complicated but in practice, it’s not.

- Take the expected return or actual return on the investment
- Subtract the risk-free rate from that number
- Divide the difference by the standard deviation of the investment

- R(p) = return on the portfolio
- R(f) = risk-free rate
- σ(p) = standard deviation of the portfolio’s excess return

**For example:**

Assume that you expect your portfolio to return 11% next year. Also assume the risk-free rate is 3% and your portfolio has a standard deviation of .07.

You would calculate the Sharpe ratio as follows:

**Sharpe ratio = (.11 – .03) / .07 = 1.14**

If you are comparing this portfolio to another with the same 11% expected return. And the other portfolio has a Sharpe ratio of 1.5, it would be the better investment. Due to the fact that you would be taking less risk for the same reward.

### Understanding Sharpe Ratio

This measurement is particularly important when comparing two or more investment opportunities. This is because it levels out the volatility in the market and flattens out the returns as if the risk was eliminated. This lets you compare the investments as to whether you are getting more or less return for each unit of risk.

You want to maximize returns while reducing the associated risk. As volatility increases, you expect to see a meaningful increase in the return to justify the increase in risk. If returns don’t increase enough, you will find a different place for your money.

A higher Sharpe ratio is always better than a lower one. This shows the portfolio is not taking on too much risk to get higher returns.

Sharpe Ratio Grading Thresholds:

- less than one = bad
- 1 – 1.99 = acceptable
- 2 – 2.99 = very good
- greater than 3 = exceptional

Risk-free portfolios have no volatility and therefore no earnings in excess of the risk-free rate. Thus the Sharpe ratio would be zero for these portfolios.

In comparison, you might see a ratio of 1,2, or 3 in portfolios with more risk. With 3 being considered a very good investment.

Basically the ratio shows you the level of compensation you will get for the additional risk you are taking on.

The Sharpe ratio can unmask whether a portfolio’s returns are due to smart investment decisions or a result of too much risk. When you look at a portfolio and see a really high return, it’s exciting. But it is only a good investment if the higher return does not exist because of an excess amount of additional risk.

### Using the Sharpe Ratio

The Sharpe ratio can be used to evaluate both the past performance and the future/ expected performance of a portfolio. The difference comes from using the realized returns from a prior period vs. the expected returns over a future period.

### You might use this equation to see how comfortable you are with a particular investment. For example, given your risk profile, you might feel the return on an investment isn’t high enough for the level of volatility. In this case, you would deem it a bad investment and look elsewhere for a higher Sharpe ratio.

### Examples of Use

You can use the Sharpe ratio in many ways. Comparing risk to reward between two investment options is the most common.

Ways to use the Sharpe ratio:

- Portfolio allocation
- Comparing risk-reward between investment options
- Investment manager performance comparison

You can look at an example of each below.

### Portfolio allocation

You are considering adding another fund to your portfolio. Your portfolio currently has a return of 15%. The current risk-free rate is 3% and the volatility of your portfolio’s return is 12%. This gives the portfolio a Sharpe ratio of 1.

Sharpe ratio (current portfolio) = (.15 – .03) / .12 = 1

Adding the investment will increase your expected return to 18%. But it will also increase the volatility to 14%. With the risk-free rate expected to stay at 3%, you would calculate the Sharpe ratio to compare the two options.

Sharpe ratio (with added fund) = (.18 – .03) / .14 = 1.07

As you can see, the ratio goes from 1 up to 1.07 by adding the new investment to your portfolio. You would therefore add the investment as it increased the performance on a risk-adjusted basis. If the ratio had gone down, you would not want to add it.

### Comparing risk-reward between investments

In this example you want to compare two funds in order to decide which one to put your money in. The fund with more risk will most likely have the higher return. But you need to know if the higher return is simply due to excess risk, or if the return is worth it in relation to risk.

- Fund #1
- Portfolio return: 10%
- Risk-free rate: 3%
- Standard deviation: 6

- Fund #2
- Portfolio return: 18%
- Risk-free rate: 3%
- Standard deviation: 20

- Sharpe Ratios
- Investment #1 = (.10 – .03) / .06 =
**1.17** - Investment #2 = (.18 – .03) / .20 =
**0.75**

- Investment #1 = (.10 – .03) / .06 =

Although fund #2 has a higher return, it has a lower ratio at .75. This is telling you that the return is due to taking on too much risk. Adjusted for risk, an investment in fund #1 would be a better choice.

### Investment manager performance comparison

You can also use the Sharpe ratio to compare the performance of different investment managers.

**For example:**

Investment manager 1 generates a 14% return and investment manager 2 generates a 12% return. On the surface it appears investment manager 1 is a better performer. You can compare them using the Sharpe ratio to see.

- Investment manager 1
- Portfolio return: 14%
- Risk-free rate: 3%
- Standard deviation: 10

- Investment manager 2
- Portfolio return: 12%
- Risk-free rate: 3%
- Standard deviation: 6

- Sharpe ratios
- Investment manager 1 = (.14 – .03) / .10 =
**1.1** - Investment manager 2 = (.12 – .03) / .06 =
**1.5**

- Investment manager 1 = (.14 – .03) / .10 =

So on the surface manager 1 was performing better. However adjusting for risk you would see that manager 2 is actually better at managing your money.

## Limitations of using the Sharpe ratio

- It’s a relative measure of risk-adjusted return. If considered in isolation, it doesn’t provide much information about the fund’s performance.
- Considers standard deviation as a proxy for risk. Standard deviation doesn’t accurately measure the downside risk. As it assumes that price movements both up and down are equally risky.
- Manipulation by portfolio managers seeking to boost their risk-adjusted returns.
- Lengthening the measurement level- this will result in a lower estimate of volatility.
- Choosing a period for the analysis with the best potential Sharpe ratio, rather than a neutral look-back period.

- Assumes that returns are normally distributed.
- Returns in the financial markets are skewed from the average because of a large number of surprising drops and spikes in prices.

## What’s one without the other…

The Sharpe ratio is a valuable and often used tool that shows the risk-adjusted performance of an investment. A high ratio is better than a lower one when you are comparing portfolios. It also shows how well an investment performs in relation to a risk-free investment.

When considering investment choices, you should always evaluate risk and reward together. The Sharpe ratio will help you to find the best investment choice by putting risk and reward into perspective.