Expected Return Formula

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,

• 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,

• 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.

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%.

Expected Return Formula Calculator

You can use the following Expected Return Formula calculator –

 

Relevance and Use of Expected Return Formula

• It is important to understand the concept of portfolio’s expected return equation as it is used by investors to anticipate the profit or loss on an investment. Based on expected return formula an investor can decide whether to invest in an asset based on the given probable returns.
• Further, an investor can also decide on the weight of an asset in a portfolio and do the required tweaking.
• Also, an investor can use the expected return formula for ranking the asset and eventually make the investment as per the ranking and include them in the portfolio. In short, higher the expected return, better is the asset.

Recommended Articles

This has been a guide to Expected Return Formula. Here we discuss how to calculate Expected Return of a Portfolio Investment using practical examples and downloadable excel template. You can learn more about financial analysis from the following articles –

• What is Portfolio Investment?
• Portfolio Return Formula
• Rate of Return Formula
• Return on Investment Formula (ROI)