# What Is a Risk Adjusted Return? Definition, Formula, and More

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3672 Risk adjusted return is something that many investors choose to overlook. Unfortunately, making this same mistake can have a negative impact on your investment strategy and investment performance. Your overall asset management and average return may be affected due to the market risk associated with the investment. Our article is going to teach you about a risk adjusted return and the various ways it is calculated.

## What Is a Risk Adjusted Return?

Risk adjusted return is often one of the most misunderstood basics of investing. Often looked over by beginner investors, these calculations can really help put your overall market portfolio risk in perspective.

By its simplest definition, a risk adjusted return is basically a measurement of the amount of return your given investment has made compared to the various risks that were associated with it. The resulting figure is generally displayed as a numerical value or a rating.

Common examples of risk measurement include alpha, beta, R-squared, Sharpe ratio, and standard deviation. The way you calculate risk adjusted return will be further discussed below.

## How Is Risk Adjusted Return Calculated?

As mentioned in the definition section above, there are primarily five different ways to calculate a risk adjusted return. We will teach you how to calculate your risk adjusted return using each of these formulas in the below sections.

### Alpha Calculations

The first way that you can use to calculate risk adjusted return is alpha. It’s important to note that Alpha is also known as the Jensen Index. Alpha is used in the world of finance to help gauge an investment’s performance. Mainly used to calculate the active return of an investment, the performance of an investment is measured against the performance of a wider benchmark that relates to it.

The resulting comparison is most often displayed as a number like -3 or 5. With these examples, this would mean that investment did three percent worse than a given benchmark or five percent better.

To calculate Alpha, the formula is as follows:

Alpha = r – Rf – beta * (Rm-Rf )

R: The investment’s return.
Rf: The risk-free rate of return.
Beta: The systemic risk associated with a portfolio.
Rm: The market return.

### Beta Calculations

The second way to calculate risk adjusted return is beta. Beta is a measurement of the volatility associated with a particular investment. Otherwise known as the Beta Coefficient, this figure is used in the Capital Asset Pricing Model.

The way that Beta is calculated is through the use of regression analysis. Regression analysis seeks to find a relation between a given factor and a specific force or item that directly impacts a stock or investment. Since these types of calculations are often extremely complex, it helps to use a program like Excel to calculate them.

To do this for a specific stock, simply create three columns in Excel. The first column will have the individual dates that you want to use for the given stock. The second column will contain the closing price for the stock that you are interested in for each day. As for the third column, enter the closing value for the index that you plan on using.

Once this is done, you’re ready to create two new columns to calculate the daily change in the stock and index’s value represented as a percentage.

The formulate for this is as follows:  Daily percent change=(Today’s price-yesterday’s price) / Yesterday’s price x 100

Once this is done, you are ready to calculate the Beta. The calculation for the Beta is as follows:

Beta= Covariance (Stock’s percent daily change, Index’s percent daily change) / VAR (Index’s percent daily change)

### R-Squared

R-squared is a measurement that reflects the amount of movement for a given stock, mutual fund or investment that can be explained by a similar movement in an appropriate index. In layman’s terms, it basically shows the amount of movement that can be explained by movement from other similar investments in similar business sectors.

R-squared values are mostly reported as percentages. When reading them, an investment with an R-squared value of 70 percent or less is often viewed as not behaving in line with the appropriate index. The closer value is to 100 percent, the more in line the investment is behaving when compared to the given index.

To start calculating R-squared, you start with an equation called the line of best fit. A line of best-fit equation seeks to predict a Y value for a given X value. Once you have this, you take the stock’s predicted Y value and subtract the actual Y value. You will do this for each of the figures that you are using and add them up to get the sums of errors squared.

The next step is to take the predicted Y value and subtract the average actual value. Sum up all of these differences like you did in the previous step. Further, take the first sum of errors you found and divide it by the second sum of errors. Lastly, subtract the end result from one and you are left with your R-squared calculation.

### Standard Deviation

Standard deviation seeks to measure the dispersion of an investment from its mean. The formula can be a bit complicated to look at and will often scare off all but the most die-hard math aficionados.

However, you can easily calculate it yourself by following a few simple steps. The first step is to calculate the mean price for the number of days that you are observing the stock. Next, subtract the actual stock’s closing price from the mean to find your deviation.

Now, take the deviation figure and square it. Sum all of your squared deviations together and divide this number by the number of days that you charted the stock. Square the final number and that leaves you with the standard deviation for the period that you initially selected for the stock.

### Sharpe Ratio

The Sharpe Ratio is the most popular way to calculate the risk-adjusted return. In short, the Sharpe Ratio is the average amount of return that is earned beyond the risk-free earnings rate. This figure is then compared to the overall volatility of the fund or stock. To calculate the Sharpe ratio yourself, follow this formula:

Sharpe Ratio=(Your mean portfolio return – Your risk-free return rate) / The standard deviation of portfolio returns

As you can see, this uses the standard deviation figure we discussed previously. Simply follow the instructions in that step and plug that value into your formula to find the Sharpe Ratio.

## Summing Up

While it is super easy to get lost when calculating these figures yourself, you can rest easy knowing that most standard investment platforms offer tools that will automatically calculate these figures for you. The important thing to remember is that you understand why risk-return is such an important element to factor into your investment decisions.  