How to Calculate Excess Returns, Basics Explained

How to Calculate Excess Returns, Basics Explained - Calculator
Bill Cascade   NEW 18/08/2019 00:00:00 Guides

When trading, you’ll come across the term excess returns. This is the most common of market references. This concept is an essential way of gauging the performance of the trading market. Thus, excess returns play a crucial part when it comes to investing. It’s a good idea to study beforehand how to calculate this before beginning trading. That way, you can perform better on the markets when investing.

This article looks at the basics of excess returns, offering a simple process of how to get to grips with it. It also shows how you can put in place such calculations into your own trading activities. Thus, you can improve your own trading performance.

What Do We Mean by Excess Returns?

To understand what it can do for your trading, you’ll need to understand what excess returns are.

All traders want to see a positive excess return on their investments! This is simply because that excess amount means more money gained for themselves. 

Thus, excess returns are the returns that traders receive which are above and beyond of commission.

When excess returns are visible in investments, traders can actively gauge their performance. This allows them to pit such investments here against other alternative means.

How Do I Calculate an Excess Return?

When it comes to the calculation used for excess returns, the most basic way to arrive at a figure is:

The return rate achieved from an investment
Minus (-)
The total return percentage obtained from the benchmark investment rate

As an example of this calculation, let’s say that the benchmark rate was 2.0%. Then, the portfolio in question received a return of 8.5%. 

The excess return would thus have a calculation of:

8.5% – 2.0% = 6.5% difference.

How Are Comparisons Used in Excess Returns?

Comparisons are another way of analyzing and calculating excess returns. These are in addition to that most basic of calculations mentioned above. 

Some investors like to compare their excess returns against closely comparable benchmarks. This will tend to offer similar risk and comparable return features.

Such excess returns comparison as this can be positive, or negative.

Excess Returns - Positive Excess Returns

Positive Excess Returns: Occurs when an investment outperforms its comparison. 

Negative Excess Returns: Occurs when an investment underperforms.

It’s important to note in undertaking such comparisons, not everything’s considered. This means that a simple benchmark comparison won’t consider all potential trading costs. These can include those items such as costs of investing or management fees when investing.

How Can Risk-Less Rates Enhance Return Rates?

Like low-risk investments, risk-less rates are sometimes used by investors. This is especially so when seeking a good level of excess returns. This is because they can offer a way of preserving capital for specific goals.

A good example here is that of US Treasuries. These tend to be seen by many traders as risk-less security and one in its most basic form.

Other examples of low risk and risk-less investments exist widely. These include municipal bonds, money market accounts, and certificates of deposits.

Using the Term Alpha in Excess Returns

When looking to calculate excessive returns, Alpha is widespread among the trading industry.

In its simplest forms, Alpha is a comparable calculation. It helps the investor when they want to carefully determine the excess return.

This means taking just a benchmark that offers comparable risk. That is, alongside one with return characteristics for an investment. 

Alpha has a commonly calculated method in investment fund management. That is – the excess returns a fund manager achieves over that of funds from a stated benchmark.

Using the Term Beta in Excess Returns

Beta is a market metric which can help you as an investor to understand excess returns. Most importantly, it can help determine whether the excess return achieved is actually worthwhile. 
Beta is an essential metric. This is because the excess return is usually closely associated with risk. Yet, there is an investment theory which states its importance better. That is – the more risk an investor is willing to take, the greater their opportunity for higher returns. 

So, Beta can be a useful tool to use as analysis to determine investments with less potential for loss.

Before we look at calculating Beta, there are three result types possible here:

A Beta of One

Indicates an investment likely to experience similar levels of return from systematic market moves as those market indexes. 

A Beta Above One

Indicates an investment with higher return volatility. Thus, one with a higher potential for gains or losses.

A Beta Below One

Indicates an investment with less return volatility. So, one with less movement from those systematic market effects. It also highlights the lesser potential for gain but also the smaller potential for a loss here. 

How to Calculate Beta in Excess Returns

The calculation for Beta is an easy one to remember: 

​​​Beta = Co-variance / Variance


Co-variance refers to the measure of stocks return, relative to that of the market.

Variance refers to the measure of how the market moves relative to its mean.

The beta calculation claims to aid investors significantly. This is particularly so when offering a clearer understanding of excess return levels. 

Other Common Calculations Applied When Dealing with Excess Returns

Excess Returns - Other Common Calculations

There are two other calculations you may come across when calculating excess returns. These include that of Jensen’s Alpha and Sharpe Ratio.

Jensen’s Alpha

This is a more in-depth analysis of Alpha. Alpha itself is a metric that’s employed when it comes to evaluating a manager’s performance. Thus, Jensen’s Alpha refers to a method of providing necessary transparency. This is about the determining of a manager’s excess returns. It’s also about how much of it was related to those risks beyond the funds’ benchmark. 

The result of a favorable Jensen’s Alpha calculation means investors have been overcompensated for risk by the fund manager.

Whereas, a negative Jensen’s Alpha result, thus, means the opposite.

Calculating Jensen’s Ratio:

Jensen’s Ratio is calculated using the formula

R(i) – (R(f) + B(R(m) – R(f)))


Broken down, this means:

R(i) is the portfolios or investments realized return

R(m) is the appropriate market index realized return

R(f) is the current period’s risk-free rate of return

B is the portfolio or investment beta. This is concerning the chosen market index.

Sharpe Ratio

Similarly, the Sharpe Ratio is another metric. This can also help investors understand excess returns concerning risk.

Investors usually use Shape Ratio for investments to compare equal returns. This means they can further locate where excess returns are being sensibly achieved. 
Thus, a higher Sharpe Ratio figure for an investment suggests the higher an investor is compensated, as per unit of risk.

Calculating the Sharpe Ratio:
The Sharpe ratio is calculated using the following formula

(R(p) – R(f))) / Portfolio Standard Deviation


Broken down, this is further explained by:

R(p) refers to Portfolio Return

R(F) Refers to Riskless Rate

Some Final Thoughts on Calculating Excess Returns

When summing up, the calculations used to determine excess returns aren’t just about arriving at a final number on the calculator!

When fully understood and correctly utilized, such metrics have great potential. Calculations can thus further enhance your trading abilities. They can also help you make better financial decisions. This is especially so when it comes to potential investments and portfolios. 

So, by making great use of such calculations, you can determine where the potential risks are. You can also make sure you minimize such risk, managing it as carefully as you can whenever you trade. 



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