Expected Return Formula

Asset Management Tutorial

Expected Return refers to the expected rate of return on an investment and is often calculated by applying the weights of all the Investments in the portfolio with their respective returns and then doing the sum total of results.

Table of Contents

What is Expected Return Formula?
Examples
Calculator

What is Expected Return Formula?

The formula of expected return for an Investment with various probable returns can be calculated as a weighted average of all possible returns which is represented as below,

Expected return = (p₁ * r₁) + (p₂ * r₂) + ………… + (p_n * r_n)

p_i = Probability of each return
r_i = Rate of return with different probability.

Also, the expected return formula of a portfolio is a simple extension from a single investment to a portfolio which can be calculated as the weighted average of returns of each investment in the portfolio and it is represented as below,

Expected return = (w₁ * r₁) + (w₂ * r₂) + ………… + (w_n * r_n)

w_i = Weight of each investment in the portfolio
r_i = Rate of return of each investment in the portfolio

Explanation of the Expected Return Formula

How to Calculate Expected Return of an Investment?

The formula for expected return for an investment with different probable returns can be calculated by using the following steps:

Step 1: Firstly, the value of an investment at the start of the period has to be determined.

Step 2: Next, the value of the investment at the end of the period has to be assessed. However, there can be several probable values of the asset and as such the asset price or value has to be assessed along with the probability of the same.

Step 3: Now, the return at each probability has to be calculated based on the asset value at the beginning and at the end of the period.

Step 4: Finally, the expected return of an investment with different probable returns is calculated as the sum product of each probable return and corresponding probability as given below –

Expected return = (p₁ * r₁) + (p₂ * r₂) + ………… + (p_n * r_n)

How to Calculate Expected Return of a Portfolio?

On the other hand, the expected return formula for a portfolio can be calculated by using the following steps:

Step 1: Firstly, the return from each investment of the portfolio is determined which is denoted by r.

Step 2: Next, the weight of each investment in the portfolio is determined which is denoted by w.

Step 3: Finally, the calculation of expected return equation of the portfolio is calculated by the sum product of the weight of each investment in the portfolio and the corresponding return from each investment as given below,

Expected return = (w₁ * r₁) + (w₂ * r₂) + ………… + (w_n * r_n)

Examples of Expected Return Formula (with Excel Template)

Let’s see some simple to an advanced example of expected return equation to understand it better.

You can download this Expected Return Formula Excel Template here – Expected Return Formula Excel Template

Expected Return Formula – Example #1

Let us take an example of an investor who is considering two securities of equal risk to include one of them in his portfolio. The probable returns of both the securities (security A and B) are as follows:

In below-given template is the data for the calculation of Expected Return Equation.

For the calculation of expected return formula first, we will need to calculate the probability and return for each scenario.

So, the calculation for Security A will be-

So, the calculation for Scenario Worst (p1)of Security A will be-

So, the calculation for Scenario Moderate(p2) of Security A will be-

So, the calculation for Scenario Best(p3) of Security A will be-

Therefore, calculation of Expected Return Formula of Security A is :

Expected return of Security (A) = 0.25 * (-5%) + 0.50 * 10% + 0.25 * 20%

So, Expected Return For Security A will be:

i.e Expected Return for Security A is 8.75%.

So, Expected Return For Security B will be:

i.e Expected Return for Security B is 8.90%.

Similarly, we can do the calculation of Security B for Expected Return Equation as mentioned above:

Considering that both securities are equally risky, Security B should be preferred because of a higher expected return.

Expected Return Formula – Example #2

Let us take an example of a portfolio which is composed of three securities: Security A, Security B, and Security C. The asset value of the three securities is $3 million, $4 million and $3 million respectively. The rate of return of the three securities is 8.5%, 5.0%, and 6.5%.

Given, Total portfolio = $3 million + $4 million + $3 million = $10 million

r_A = 8.5%
r_B = 5.0%
r_C = 6.5%

In below-given table is the data for the calculation of Expected Return Equation.

For the calculation of portfolio’s expected return formula first, we will need to calculate the weight of each asset.

So, the Weight of each investment will be-

Therefore ,the calculation of weight of each asset is w_A = $3 million / $10 million = 0.3

w_B = $4 million / $10 million = 0.4
w_C = $3 million / $10 million = 0.3

So, the calculation of expected return formula for fortfolio is:

Expected return = 0.3 * 8.5% + 0.4 * 5.0% + 0.3 * 6.5%

So, Expected Return of the Portfolio= 6.5%.