Expected Value Formula How To Calculate Step By Step

Formula to Calculate Expected Value

Mathematically, the expected value equation represents as below,

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where

pi = Probability of random valueai = Probable random value

Expected Value Calculation (Step by Step)

Examples

Example #1

Let us take the 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 expects to give him higher returns.

Firstly, determine the different probable values. For instance, other probable asset returns can be a good example of random values. Therefore, the probable values are denoted by ai. 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. 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

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

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

One can calculate the expected return of security P 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 the expected return is as follows,

Expected return = 8.75%

Expected Return of Security Q

One can calculate the expected return of security Q 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%
Expected Return= 8.90%

Therefore, for Ben, security Q is expected to give higher returns than 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 expects to achieve a value of $3.5 million with a probability of 0.3. In addition, a value of $1.0 million with a probability of 0.7. On the other hand, Project Y expects to achieve a value of $2.5 million, with a probability of 0.4. In addition, achieved a value of $1.5 million, with a probability of 0.6. Determine for John which project expects to have a higher value on completion.

Expected Value of Project X

The calculation of the expected value of Project X can be 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 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 Project X.

Relevance and Use

An analyst needs to understand the concept of expected value as most investors use it 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 an investment’s anticipated future value. 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 calculating expected return.

Formula to Calculate Expected Value#

Expected Value Calculation (Step by Step)#

Examples#

Example #1#

Example #2#

Relevance and Use#

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