Excess ReturnsIs your investment overperforming or underperforming?

Investing in financial instruments such as stocks often comes with risks.

And oftentimes, the higher the risk, the higher the rewards.

Or in this case, the higher the returns since we’re talking about investments after all.

This is why investors still invest in volatile and high risk stocks even if they carry very high risks, even myself.

If I were to invest in one of those investment options, I would like the highest return possible for my investment.

And yes, even if it comes with a higher risk.

If an investor wants higher returns, s/he should not just invest in risk-free investments.

S/he should invest in investment options that have the potential to earn higher returns.

One of the ways to assess an investment’s (stock or fund) performance is through the calculation of excess returns.

In the simplest terms, they are an investment’s returns that are above and beyond a specified benchmark.

As an investor, the higher the excess returns are, the better it is for you.

Is that really the case though? Do high excess returns always indicate that the fund or stock is performing well?

We’ll try to answer these questions as we go along with this article.

But first, we need to define the term “excess returns”.

We also need to learn how to calculate it.

So, let’s get to it!

Excess Returns: Defined

Excess returns refer to an investment’s returns that are above and beyond a specified benchmark.

It is one of the metrics that gauge whether an investment (e.g. stocks, funds) is over performing or underperforming.

The benchmark to which the investment’s return will be compared can vary.

The basic ones include the riskless or risk-free rate, as well as the rate of returns of investments that carry the same level of risk as the investment being analyzed.

We can also refer to excess returns as “alpha”.

Though we refer to them as “excess”, excess returns can still be either positive or negative.

Positive excess returns indicate that the investment is performing better than the benchmark.

On the other hand, negative excess returns indicate that the investment is performing worse than the benchmark.

Negative excess returns also mean that the investment earned less than what was expected of it.

Note that choosing the benchmark to which the investment’s rate of return will be compared is an important step.

Choosing an irrelevant benchmark will most likely result in a faulty evaluation of the investment’s performance.

Due to how having excess returns means deviating from the benchmark, some also refer to them as the abnormal rate of return.

This is also due to how excess returns depict a part of the investment’s returns that the benchmark or the market rate of return cannot justify.

Understanding Excess Returns

Excess returns can be a powerful tool for an investor.

It helps gauge whether an investment is performing better or worse than its investment alternatives.

An investor would want his/her investment to perform better.

The higher the excess returns, the better the investment’s performance is when compared to its investment alternative.

However, just having positive excess returns is already a win for the investor.

Having positive excess returns already means that the investor is receiving more money than what s/he would earn by investing in another investment alternative.

But of course, choosing a benchmark to which the investment’s rate of return will be compared must be addressed first.

One option is to compare the investment’s rate of return with that of a risk-free investment such as treasury bills.

Another option is to compare the investment’s rate of return with that of another investment that has similar risk and return behavior.

Going with this option results in an excess return measure we refer to as alpha.

Do note that just purely comparing an investment’s returns with a benchmark may result in an excess return measure that ignores all potential trading costs.

For example, one of the benchmarks that analysts commonly use is the S&P 500.

While it is a great benchmark, it typically does not take into consideration the cost of investing in all 500 stocks in the Index.

It also does not consider the management fees for investing in a fund with such stocks.

Calculating Excess Returns

We can identify an investment’s excess return by subtracting the benchmark rate of return from the investment’s actual rate of return.

For example, let’s assume that the investor wants to make a risk-free investment as the benchmark.

Let’s say that a US treasury bill currently has a rate of return of 3.0%.

The investment being analyzed had an actual rate of return of 15.0%.

This results in an excess return of 12.0%.

Seems pretty simple right? Well, that is the simple calculation after all.

If we were to compute excess returns using the Capital Asset Pricing Model (CAPM), things will get a little more complicated.

First, let’s take a look at the CAPM formula:

R_a​= R_rf​+ (β × (R_m​−R_rf​))

Where:

R_a – The expected return on an investment (e.g. security, stocks, funds)

R_rf  – The risk-free rate

R_m – Expected return on the market

(R_m​−R_rf) – Equity market premium

β – Beta of the investment

 

The beta refers to an investment’s sensitivity to market changes.

A beta of exactly means that the investment will experience the same level of volatility as that of a market index.

Having a beta of more than one means that the investment’s rate of returns will experience a higher level of volatility than that of a market index.

This favors the investment if there’s a positive change in the market conditions.

However, if there’s a negative change, the investment will be affected greatly.

Conversely, a beta of less than one means that the investment won’t be as sensitive to changes in the market condition.

Using the CAPM formula, we can make a variation that considers an investment’s excess return:

Excess Return = R_i – R_a

-or-

Excess Return = R_i –( R_rf​+ (β × (R_m​−R_rf​)))

Where:

R_i – The actual or total return of the investment

R_a – The expected return on an investment (e.g. security, stocks, funds) which we can derive by using the CAPM formula

We can also refer to the excess return measure that results from this formula as the Jensen’s Alpha.

This metric not only gauges an investment’s performance but also evaluates a fund manager’s performance. 

Excess Returns: Example

To better understand the calculation of excess returns, let’s have an example.

Let’s assume that you are a stock analyst.

You were given the following information:

• The stock you’re analyzing recently has a total rate of return of 17.9%; this is this stock’s R_i 
• This particular stock is currently traded on the New York Stock Exchange (NYSE) which is domiciled in the US
• This particular stock has a beta of 1.3
• A US 10-year treasury bill currently has a rate of 3.8%; this is the R_rf
• The historical average yearly return for stocks in the US market is 7.7%; this is the R_m

With the above information, let’s calculate the stock’s excess returns:

Excess Return = R_i –( R_rf​+ (β × (R_m​−R_rf​)))

= 17.9% – ( 3.8% + (1.3 x (7.7%-3.8%)))

= 17.9% – (3.8% + (1.3 x 3.9%))

= 17.9% – (3.8% + 5.07%)

= 17.9% – 8.87%

= 9.03%

As per computation, the stock has a positive excess return of 9.03%.

This means that the stock is performing better than its investment alternatives.