WallStreetMojo

WallStreetMojo

WallStreetMojo

MENUMENU
  • Blog
  • Free Video Tutorials
  • Courses
  • All In One Bundle
  • Login
Home » Financial Modeling Tutorials » Excel Modeling » Expected Value Formula

Expected Value Formula

By Abhilash RamachandranAbhilash Ramachandran | Reviewed By Dheeraj VaidyaDheeraj Vaidya, CFA, FRM

Formula to Calculate Expected Value

Expected value formula is used in order to calculate the average long-run value of the random variables available and according to the formula the probability of all the random values is multiplied by the respective probable random value and all the resultants are added together to derive the expected value.

Mathematically, the expected value equation is represented as below,

Expected value = p1 * a1 + p2 * a2 + ………… + pn * an = = Σin Pi * ai

Expected Value Formula

where

  • pi = Probability of random value
  • ai = Probable random value

Expected Value Calculation (Step by Step)

The calculation of the expected value of a series of random values, we can derive by using the following steps:

  • Step 1: Firstly, determine the different probable values. For instance, different probable asset returns can be a good example of such random values. The probable values are denoted by ai.
  • Step 2: Next, determine the probability of each of the values mentioned above, denoted by pi. Each probability can be any number in the range of 0 to 1 such that the total of the probabilities is equal to one, i.e., 0 ≤ p1, p2,…., pn ≤ 1 and p1 + p2 +….+ pn = 1.
  • Step 3: Finally, we calculate the expected value of all different probable values, as the sum product of each probable value and corresponding probability as below,

Expected value = p1 * a1 + p2 * a2 + ………… + pn * an

Examples

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

Example #1

Let us take an example of Ben, who has invested in two securities within his investment portfolio. The probable rate of return of both the securities (security P and Q) are as given below. Based on the given information, help Ben to decide which security is expected to give him higher returns.

We will use the following data for the calculation of the expected value.

expected value formula example 1.1

In this case, the expected value is the expected return of each security.

Expected Return of Security P

The expected return of security P can be calculated as,

Popular Course in this category
Sale
All in One Financial Analyst Bundle (250+ Courses, 40+ Projects)
4.9 (1,067 ratings)
250+ Courses | 40+ Projects | 1000+ Hours | Full Lifetime Access | Certificate of Completion
View Course

expected value formula example 1.2

  • Expected return (P) = p1 (P) * a1 (P) + p2 (P) * a2 (P) + p3 (P) * a3 (P)
  • = 0.25 * (-5%) + 0.50 * 10% + 0.25 * 20%

Therefore, the calculation of Expected return is as follows,

expected value formula example 1.3

  • Expected return = 8.75%

Expected Return of Security Q

The expected return of security Q can be calculated as,

expected value formula example 1.4

  • Expected return (Q) = p1 (Q) * a1 (Q) + p2 (Q) * a2 (Q) + p3 (Q) * a3 (Q)
  • = 0.35 * (-2%) + 0.35 * 12% + 0.30 * 18%

Therefore, the calculation of Expected return is as follows,

expected value formula example 1.5

  • Expected Return= 8.90%

Therefore, for Ben security Q is expected to give higher returns than that of security P.

Example #2

Let us take another example where John is to assess the feasibility of two upcoming development projects (Project X and Y) and choose the most favorable one. According to estimates, Project X is expected to achieve a value of $3.5 million with a probability of 0.3 and achieve a value of $1.0 million with a probability of 0.7. On the other hand, Project Y is expected to achieve a value of $2.5 million, with a probability of 0.4 and achieve a value of $1.5 million, with a probability of 0.6. Determine for John which project is expected to have a higher value on completion.

We will use the following data for the calculation of the expected value.

example 2.1 data

Expected Value of Project X

The calculation of the expected value of Project X can be done as follows,

example 2.2 Project X

  • Expected Value (X) = 0.3 * $3,500,000 + 0.7 * $1,000,000

Calculation of Expected Value of Project X will be –

example 2.3 Project X

  • Expected Value (X) = $1,750,000

Expected Value of Project Y

The calculation of the expected value of Project Y can be done as follows,

example 2.4 Project Y

  • Expected Value (Y)= 0.4 * $2,500,000 + 0.6 * $1,500,000

Calculation of Expected Value of Project Y will be –

example 2.5 Project Y

  • Expected Value = $1,900,000

Therefore, on completion Project Y is expected to have a higher value than that of Project X.

Relevance and Use

An analyst needs to understand the concept of expected value as it is used by most investors to anticipate the long-run return of different financial assets. The expected value is commonly used to indicate the anticipated value of an investment in the future. Based on the probabilities of possible scenarios, the analyst can figure out the expected value of the probable values. Although the concept of expected value is often used in various multivariate models and scenario analysis, it is predominantly used in the calculation of expected return.

Recommended Articles

This article has been a guide to the Expected Value Formula. Here we learn how to calculate the expected value along with examples and a downloadable excel template. You can know more about financial analysis from the following articles –

  • Value Formula in Excel
  • Binomial Distribution Formula
  • Median Formula
  • Formula of Present Value
0 Shares
Share
Tweet
Share
All in One Financial Analyst Bundle (250+ Courses, 40+ Projects)
  • 250+ Courses
  • 40+ Projects
  • 1000+ Hours
  • Full Lifetime Access
  • Certificate of Completion
LEARN MORE >>
Primary Sidebar
Footer
COMPANY
About
Reviews
Contact
Privacy
Terms of Service
RESOURCES
Blog
Free Courses
Free Tutorials
Investment Banking Tutorials
Financial Modeling Tutorials
Excel Tutorials
Accounting Tutorials
Financial Statement Analysis
COURSES
All Courses
Financial Analyst All in One Course
Investment Banking Course
Financial Modeling Course
Private Equity Course
Venture Capital Course
Excel All in One Course

Copyright © 2021. CFA Institute Does Not Endorse, Promote, Or Warrant The Accuracy Or Quality Of WallStreetMojo. CFA® And Chartered Financial Analyst® Are Registered Trademarks Owned By CFA Institute.
Return to top

WallStreetMojo

Free Investment Banking Course

IB Excel Templates, Accounting, Valuation, Financial Modeling, Video Tutorials

* Please provide your correct email id. Login details for this Free course will be emailed to you

Book Your One Instructor : One Learner Free Class
WallStreetMojo

Free Investment Banking Course

IB Excel Templates, Accounting, Valuation, Financial Modeling, Video Tutorials

* Please provide your correct email id. Login details for this Free course will be emailed to you

Let’s Get Started
Please select the batch
Saturday - Sunday 9 am IST to 5 pm IST
Saturday - Sunday 9 am IST to 5 pm IST

This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy

Login

Forgot Password?

WallStreetMojo

Download Expected Value Formula Excel Template

Special Offer - All in One Financial Analyst Bundle (250+ Courses, 40+ Projects) View More