There are many different ways to compare investment returns to different types of risk. But why would you even want to compare returns to levels of risk?

Well, that’s because it helps you determine whether the return you received was worth the risk you took.

Sometimes investments that have the potential to make a lot of money also have a higher chance of losing it. This potential for loss is called risk. When you compare your investment returns to the level of risk you take, it helps you see if the amount of money you made was worth the chance you took of losing it. This can help you make better decisions about where to invest so you can try to make the most money possible without taking on too much risk.

## What Is a Risk-Adjusted Return?

Risk-adjusted return measures the return on an investment relative to its risk level. The idea is that the return should be as high as possible for a given level of risk. The higher the risk-adjusted return, the better it is for the investor. For example, if there are two investments with the same return, but one has a lower risk compared to the other. Which would you pick?

Obviously the one with the lower risk. That’s the whole concept of risk-adjusted return.

But risk can be measured in different ways. That’s where different types of risk-adjusted returns come in. Let’s explore the top 4 most popular ones below.

## 1. Sharpe Ratio

The Sharpe ratio compares the return to the volatility or standard deviation of an investment. Multiple investments’ Sharpe ratios should be compared to one another before deciding which asset/security to buy. The highest Sharpe ratio investments should be picked because those indicate more attractive risk-adjusted returns.

The formula is:

Sharpe Ratio = (Expected or Actual Return – Risk-Free Rate) / Standard Deviation

For example, let’s say you’re trying to decide which tech company stock to buy. They both have good opportunities for growth and you can’t make up your mind.

- Company ABC is expected to return 15% over one year.
- Company DEF is expected to return 12% over one year.

You may say I will go with Company ABC because it’s expected to generate more return over the year. But what if it’s riskier? Let’s say the standard deviations are:

- Company ABC 10% standard deviation.
- Company DEF 5% standard deviation.

Which would you pick now?

It’s hard to say just by looking at these numbers. You need to calculate the Sharpe ratio to help you with this decision. You should also know the risk-free rate, usually measured by the t-bill rate so that you know what excess return you can get by investing in one of these companies instead of investing risk-free. Let’s say the risk-free rate is 4%.

Then the Sharpe ratios are:

- Company ABC Sharpe ratio = (15% – 4%) / 10% = 1.1
- Company DEF Sharpe ratio = (12% – 4%) / 5% = 1.6

This means that despite the lower return, Company DEF is a better bet for the given level of risk.

Here’s a good video that explains the Sharpe ratio really well:

## 2. Treynor Ratio

Treynor ratio is another measure of risk-adjusted return that compares the return on investment to the volatility of the overall market, as measured by beta. Similar to the Sharpe ratio, a higher Treynor ratio indicates a more attractive risk-adjusted return.

Treynor Ratio = (Expected Return – Risk-Free Rate) / Beta

Let’s take the same example from above and calculate the Treynor ratio instead. For that, we would need to know the systematic risk as measured by Beta for Company ABC and Company DEF. Let’s say it’s:

- Company ABC Beta is 1.2
- Company DEF Beta is 0.9

The Treynor ratios for these two investments are:

- Company ABC Treynor ratio = (15% – 4%) / 1.2 = 9.17%
- Company DEF Treynor ratio = (12% – 4%) / 0.9 = 8.89%

In this case, despite the higher systematic risk (as measured by Beta) of Company ABC, the risk-adjusted return is higher. Therefore, Company ABC is a better investment when using the Treynor ratio for comparison.

Here’s a good video that explains how to calculate the Treynor ratio:

## 3. Jenson’s Alpha

Jenson’s alpha is a metric that measures the risk-adjusted return of an investment or portfolio by comparing its actual return to the return that would be expected given its level of risk. A positive alpha indicates that the investment has outperformed its expected return, while a negative alpha indicates underperformance.

The formula is:

Jenson’s Alpha = Actual Return – Expected Return

Again, from our example above, let’s say a year passed and Company ABC returned 15%, while Company DEF returned 13%. In this case, it may seem like Company ABC is a better-performed investment, but that’s not the case when considering Jenson’s Alpha. Let’s calculate it for both of these investments:

- Company ABC Jenson’s Alpha = 15% – 15% = 0%
- Company DEF Jenson’s Alpha = 13% – 12% = 1%

As you can see, Company ABC has no excess return above its level of risk, while Company DEF has outperformed expectations by 1%. This means Company DEF has done really well compared with the level of risk.

Here’s a video that exands on Jensen’s Alpha further by explaining how to calculate the expected return using the Capital Asset Pricing Model (CAPM):

It’s a bit complex if it’s the first time you’re hearing about CAPM, but don’t worry, we’ll explain that in the Elemetary section:

## 4. Sortino Ratio

The Sortino ratio is similar to the Sharpe ratio, but it focuses specifically on downside risk rather than overall risk. It divides the excess return of investment above the minimum acceptable return (MAR) or risk-free rate by its standard deviation of negative returns. A higher Sortino ratio indicates a more attractive risk-adjusted return.

The formula is:

- Sortino Ratio = (Expected or Actual Return – Risk-Free Rate) / Standard Deviation of Downside Returns

As you can see the formula is nearly identical to the Sharpe ratio, except for the denominator. So let’s focus on that. What is the standard deviation of downside returns?

Downside deviation, also known as the standard deviation of downside returns, is a measure of the dispersion of returns that fall below a certain threshold, called the “target return.” Most often the target rate is the risk-free rate. Downside deviation is used to quantify the risk of an investment, specifically the risk of experiencing losses or underperforming the target return.

To calculate downside deviation, you would first need to calculate the difference between each individual return and the target return (called the “downside deviation score”), and then take the standard deviation of those scores.

Here is an example of how to calculate downside deviation for a set of returns. We’ll use the same risk-free rate of 4% from before.

Let’s say the returns for this new investment were:

- Year 1: 12%
- Year 2: 2%
- Year 3: 3%
- Year 4: 15%
- Year 5: -5%

**Step 1: Calculate the downside deviation scores for each return**

- Year 1: 12% – 4% = 8%
- Year 2: 2% – 4% = -2%
- Year 3: 3% – 4% = -1%
- Year 4: 15% – 4% = 11%
- Year 5: -5% – 4% = -9%

**Step 2: Remove all positive values because we’re calculating only the downside deviation. Square those remaining negative amounts.**

Only these three deviations are included: -2%, -1%, -9%

- -2% ^ 2 = 4%
- -1% ^ 2 = 1%
- -9% ^ 2 = 81%

**Step 3: Divide the sum of the deviations by the total number of periods.**

- ( 4% + 1% + 81% ) / 5 = 17.2%

**Step 4: Get the square root of the number from step 3.**

- Square root of 17.2% = 4.15%

Therefore, the standard deviation of downside returns is 4.15%.

Going back to calculating the Sortino ratio. In this case, it’ll be:

The average return from the 5 years will be used return in the formula (even though past performance does not equal future performance, as we all know) because we used historical data to calculate the downside deviation.

- Average return = ( 12% + 2 + 3 + 15% – 5% ) / 5 = 5.4%
- Sortino ratio = (5.4% – 4%) / 4.15% = 0.34

Here’s a video that explains and gives a good example of the difference between the Sharpe and Sortino ratio:

## Final Thoughts

In conclusion, risk-adjusted return is important to consider when evaluating investments. It helps investors understand whether the return they received was worth the risk they took. There are several ways to calculate the risk-adjusted return, including the Sharpe ratio, Treynor ratio, Jensen’s alpha, and Sortino ratio.

By understanding and using these measures, investors can make more informed decisions about their investments and seek out opportunities that offer a good balance between return and risk. It’s important to remember that all investments come with some level of risk, and it’s up to the investor to decide how much risk they are willing to take on in pursuit of a higher return.