Expected Rate of ReturnDefined with Formula and Examples

Written By:
Lisa Borga

The expected rate of return or simply expected return is the amount that an investor can expect to make on their investment based on its historical rates of return.

The expected rate of return is a crucial guide to what an investor can expect a given investment or portfolio of investments to return.

However, it is equally important to keep in mind that there are no guarantees that the expected return will be an accurate representation of what will actually occur.

An investor can find the expected rate of return by taking all of the potential outcomes and multiplying them by the chances that they will occur, and then adding them together to find the total expected rate of return.

For a portfolio of multiple investments, the expected return will be the weighted average of the expected rate of return for each investment.

How to Calculate Expected Rate of Return

The calculation for the expected rate of return is a key part of effective business operation.

In fact, it is a crucial component of certain investment theories such as Modern Portfolio Theory, which aims to help investors maximize their return for a certain level of risk.

For an example of the expected rate of return in action, let’s assume that a given investment possesses a 70% chance of returning a profit of 25% and that this same investment may hold a 30% chance of losing 15%.

In this case, the expected rate of return would be (70% * 25% + 30% * -15% = 13%).

The expected rate of return can tell you whether or not an investment has a track record of positive or negative results.

This is calculated by finding the expected value of a given investment using its potential return under every different possible result, and this is represented by the formula:

Expected Rate of Return = (P1 * R1) + (P2 * R2) +…

Pi: The Probability of a Given Return

Ri:  The Rate of a Given Return

You can easily find the expected return of an entire portfolio by this same principle.

In this case, you will simply find the weighted average of returns in the portfolio.

Here is the formula:

Expected Return of a Portfolio = (w1 * r1) + (w2 * r2) + …

Wi = weight of each investment in the portfolio

Ri = rate of return of each investment in the portfolio

These calculations will provide a weighted average of the historical results of an investment which can provide a reasonable idea of what an investment may be expected to return.

However, it is also important to keep in mind that this calculation cannot guarantee that the result will be realized in the future.

For our example, we found an expected return of 13%, but this is not a guarantee that this result will actually come to be in the future.

It is important to remember that investments are always subject to risks, both systematic, which refers to risks present in an entire market or segment, or unsystematic, which refers to a narrower risk limited to a particular industry or even company.

How Is Expected Rate of Return Different than Standard Deviation?

The expected rate of return is only one of the multiple ways to statistically analyze an investment portfolio, with another popular option being standard deviation.

With the expected rate of return, we are attempting to judge what amount of return we can expect from an investment or, essentially, the average return.

Standard deviation instead attempts to calculate the amount that returns fall from the average amount, which can serve as an excellent measure of the risk of an investment.

The Limitations of Using the Expected Rate of Return

As you have seen, the expected rate of return is simply an estimated projection of the future based on historical precedent.

As such, it would be foolish to base an investment decision off of expected return alone.

Instead, investors should consider several factors when choosing between options for investment, not least of which should be the standard deviation.

For example, consider two investment portfolios, both offering three assets.

We could choose either of these portfolios, and to help consider which of them to choose, we have the previous six years of performance for both.

These are:

• Portfolio 1: 10%, 9%, -2%, 14%, 12%, and 11%
• Portfolio 2: 15%, 14%, -7%, 11%, 10%, and 11%

When the expected rate of return is calculated, both of these portfolios have returns of precisely 9%.

When the standard deviation is calculated, however, it is plain to see that portfolio 1 is less risky of an investment than portfolio two.

Portfolio 1 offers a standard deviation of 5.16%, and portfolio 2 offers 7.37%.

Unlike the expected rate of return, standard deviation measures an investment’s risk by calculating its past volatility.

Like the expected rate of return, this is only a prediction using historical data; however, it can give investors an idea of the likelihood of achieving a given return rather than simply what the average return is.

It is wise to consider both of these metrics before making an investment decision.

Pros and Cons of the Expected Rate or Return

Pros of Using the Expected Rate of Return

• Shows how an asset has previously performed
• Takes the weight of different possibilities into account

Cons of Using the Expected Rate of Return

• Fails to account on the risk of an investment
• Primarily based on historical performance

Examples of the Expected Rate of Return

As we have seen, we can use the expected rate of return to calculate anything from a single asset to an entire portfolio with numerous different investments.

To start, let’s consider an example with only two assets.

Example #1

Let’s assume that an investor is attempting to choose between two securities with equal risk.

Security A offers a 25% chance of a -5% return, a 50% chance of a 10% return, and a 20% chance of a 25% return. Security B offers a 40% chance of a -2% return, a 40% chance of a 12% return, and a 20% chance of an 18% return.

To find which of these offers a better expected return, all we have to do is take the probabilities by the rate of return and add them like so:

Expected Return for Security A = (25% * -5%) + (50% * 10%) + (20% * 25%) = 8.75%

Expected Return for Security B= (40% * -2%) + (40% * 12%) + (20% * 18%) = 7.6%

Now it is plain to see that Security A would be the better investment decision assuming all other factors are equally based upon the expected rate of return.

Example #2

Once we know the expected rate of return for all of the investments within a portfolio, all we must do is to find the weighted average of all the investments within the portfolio, and this will be its expected return.

As an example, let’s assume an investor is looking over their stock portfolio and is curious what the expected rate of return would be.

Their portfolio includes:

• Garden Supplies Incorporated: Investment of $650,000 with an expected return of 10%
• Seed and Bulbs Incorporated: Investment of $200,000 with an expected return of 20%
• Sod n’ Turf Incorporated: Investment of $150,000 with an expected return of 8%

We can calculate the weight of each investment by finding what percentage of the $1 million whole they each are, which in respective order is 65%, 20%, and 15%.

Now we can find the expected rate of return for the entire portfolio like so:

(65% * 10%) + (20% * 20%) + (15% * 8%) = 11.7%

Now we know that the expected rate of return for this portfolio is 11.7%.

How Is the Expected Rate of Return Used in Finance?

Businesses and private investors alike use calculations of the expected rate of return regularly both as a part of business operation and to manage investment portfolios.

This calculation is used in investment models such as modern portfolio theory and is used to find whether a given investment has historically possessed an average of positive or negative net outcomes.

What Are Historical Returns?

Historical returns are simply the past returns from a particular security or from an entire index, for example, NASDAQ.

This data is frequently used by investment analysts in order to make predictions for what future returns may be or for how an investment may fare in a given economic situation.