Expected Return Formula

What is the Expected Return Formula?

Expected Return formula 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.

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) + ………… + (pn * rn)

Also, the expected return 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) + ………… + (wn * rn)
  • wi = weight of each investment in the portfolio
  • ri = rate of return of each investment in the portfolio
Expected-Return-Formula

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Source: Expected Return Formula (wallstreetmojo.com)

How to Calculate Expected Return of an Investment?

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

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

  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.

  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.

  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) + ………… + (pn * rn)

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) + ………… + (wn * rn)

Examples

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

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

Example 1

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

  • So, the calculation for Security A will be-
Example 1.1png

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

Example 1.2png

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

Expected Return formula example 1.3png

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

Example 1.4png

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

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

Expected Return formula example 1.5png

So, the Expected Return For Security A will be:

Expected Return formula example 1.6png

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

  • So, the Expected Return For Security B will be:
Expected Return formula example 1.7png

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

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

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

Example #2

Let us take an example of a portfolio that 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

  • rA = 8.5%
  • rB = 5.0%
  • rC = 6.5%

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

Security ASecurity BSecurity C
Asset Value$3$4$3
Total Portfolio$10$10$10
Rate of Return of each Asset (r)8.5%5.0%6.5%

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

So, the Weight of each investment will be-

Expected Return formula example 1.8png

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

  • wB = $4 million / $10 million = 0.4
  • wC = $3 million / $10 million = 0.3
Expected Return formula example 2 .2png

So, the calculation of expected return for fortfolio is:

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

Expected Return formula example 2 .2png

So, Expected Return of the Portfolio= 6.5%.

Expected Return Calculator

You can use the following Expected Return calculator –

p1
r1
p2
r2
p3
r3
Expected Return Formula =
 

Expected Return Formula = p1r1 + p2r2 + p3r3
0 * 0 + 0 * 0 + 0 * 0 = 0

Relevance and Use

  • It is important to understand the concept of a portfolio’s expected to return as it is used by investors to anticipate the profit or loss on an investment. Based on the 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, the higher the expected return, the better is the asset.

Recommended Articles

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

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