Expected Value Formula

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,

You are free to use this image on your website, templates etc, Please provide us with an attribution linkHow to Provide Attribution?Article Link to be Hyperlinked
For eg:
Source: Expected Value Formula (wallstreetmojo.com)

where

• p_i = Probability of random value
• a_i = Probable random value

Expected Value Calculation (Step by Step)

Examples

Example #1

Let us take an example of Ben, who has invested in two securities within his investment portfolioInvestment PortfolioPortfolio investments are investments made in a group of assets (equity, debt, mutual funds, derivatives or even bitcoins) instead of a single asset with the objective of earning returns that are proportional to the investor's risk profile.read more. 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.

In this case, the expected value is the expected returnExpected ReturnThe Expected Return formula is determined by applying all the Investments portfolio weights with their respective returns and doing the total of results. Expected return = (p1 * r1) + (p2 * r2) + ………… + (pn * rn), where, pi = Probability of each return and ri = Rate of return with probability. read more of each security.

Expected Return of Security P

The expected return of security P can be calculated as,

• 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 return = 8.75%

Expected Return of Security Q

The expected return of security Q can be calculated as,

• 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 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.

Expected Value of Project X

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

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

Calculation of Expected Value of Project X will be –

• 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,

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

Calculation of Expected Value of Project Y will be –

• 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 assetsFinancial AssetsFinancial assets are investment assets whose value derives from a contractual claim on what they represent. These are liquid assets because the economic resources or ownership can be converted into a valuable asset such as cash.read more. 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