Financial Modeling Tutorials

- Excel Modeling
- Financial Functions in Excel
- Sensitivity Analysis in Excel
- Sensitivity Analysis
- Capital Budgeting Techniques
- Time Value of Money
- Future Value Formula
- Present Value Factor
- Perpetuity Formula
- Present Value vs Future Value
- Annuity vs Pension
- Present Value of an Annuity
- Doubling Time Formula
- Annuity Formula
- Present Value of an Annuity Formula
- Future Value of Annuity Due Formula
- Maturity Value
- Annuity vs Perpetuity
- Annuity vs Lump Sum
- Deferred Annuity Formula
- Internal Rate of Return (IRR)
- IRR Examples (Internal Rate of Return)
- NPV vs XNPV
- NPV vs IRR
- NPV Formula
- NPV Profile
- NPV Examples
- Advantages and Disadvantages of NPV
- Mutually Exclusive Projects
- PV vs NPV
- IRR vs ROI
- Break Even Point
- Break Even Analysis
- Breakeven Analysis Examples
- Break Even Chart
- Benefit Cost Ratio
- Payback Period & Discounted Payback Period
- Payback period Formula
- Discounted Payback Period Formula
- Payback Period Advantages and Disadvantages
- Profitability Index
- Feasibility Study Examples
- Cash Burn Rate
- Interest Formula
- Simple Interest
- Simple Interest vs Compound Interest
- Simple Interest Formula
- CAGR Formula (Compounded Annual Growth Rate)
- Growth Rate Formula
- Effective Interest Rate
- Loan Amortization Schedule
- Mortgage Formula
- Loan Principal Amount
- Interest Rate Formula
- Rate of Return Formula
- Effective Annual Rate
- Effective Annual Rate Formula (EAR)
- Compounding
- Compounding Formula
- Compound Interest
- Compound Interest Examples
- Daily Compound Interest
- Monthly Compound Interest Formula
- Discount Rate vs Interest Rate
- Discounting Formula
- Rule of 72
- Geometric Mean Return
- Geometric Mean vs Arithmetic Mean
- Real Rate of Return Formula
- Continuous compounding Formula
- Weighted average Formula
- Average Formula
- EWMA (Exponentially Weighted Moving Average)
- Average Rate of Return Formula
- Mean Formula
- Mean Examples
- Population Mean Formula
- Weighted Mean Formula
- Harmonic Mean Formula
- Median Formula in Statistics
- Range Formula
- Outlier Formula
- Decile Formula
- Midrange Formula
- Quartile Deviation
- Expected Value Formula
- Exponential Growth Formula
- Margin of Error Formula
- Decrease Percentage Formula
- Relative Change
- Percent Error Formula
- Holding Period Return Formula
- Cost Benefit Analysis
- Cost Benefit Analysis Examples
- Cost Volume Profit Analysis
- Opportunity Cost Formula
- Opportunity Cost Examples
- APR vs APY
- Mortgage APR vs Interest Rate
- Normal Distribution Formula
- Standard Normal Distribution Formula
- Normalization Formula
- Bell Curve
- T Distribution Formula
- Regression Formula
- Regression Analysis Formula
- Multiple Regression Formula
- Correlation Coefficient Formula
- Correlation Formula
- Correlation Examples
- Coefficient of Determination
- Population Variance Formula
- Covariance Formula
- Coefficient of Variation Formula
- Sample Standard Deviation Formula
- Relative Standard Deviation Formula
- Standard Deviation Formula
- Standard Deviation Examples
- Effect Size
- Sample Size Formula
- Volatility Formula
- Binomial Distribution Formula
- Multicollinearity
- Hypergeometric Distribution
- Exponential Distribution
- Central Limit Theorem
- Poisson Distribution
- Central Tendency
- Hypothesis Testing
- Gini Coefficient
- Quartile Formula
- P Value Formula
- Skewness Formula
- R Squared Formula
- Adjusted R Squared
- Regression vs ANOVA
- Z Test Formula
- Z Score Formula
- Z Test vs T Test
- F-Test Formula
- Quantitative Research
- Histogram Examples

Related Courses

**Formula of Expected Value (Table of Contents)**

## What is the Expected Value Formula?

The term “expected value” refers to the long run average value of all possible values. In the financial parlance, it can also represent the anticipated value for a given investment at any point in time. The formula for expected value with various probable values can be computed on the basis of the probability-weighted average of all the possible values. Mathematically, the expected value equation is represented as below,

**Expected value formula = p**

_{1}* a_{1}+ p_{2}* a_{2}+ ………… + p_{n}* a_{n}or

**Expected value formula= Σ**

_{i}^{n }P_{i}* a_{i}where

- p
_{i}= Probability of random value - a
_{i}= Probable random value

### Explanation of the Expected Value Formula

The formula for the calculation of the expected value of a series of random values can be derived 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 a_{i}.

**Step 2:** Next, determine the probability of each of the above-mentioned values and they are denoted by p_{i}. Each probability can be any number in the range of 0 to 1 such that the sum total of the probabilities is equal to one, i.e. 0 ≤ p_{1}, p_{2},…., p_{n} ≤ 1 and p_{1} + p_{2} +….+ p_{n} = 1.

**Step 3:** Finally, the equation for the expected value of all different probable values is calculated as the sum product of each probable value and corresponding probability as shown below,

**Expected value = p _{1} * a_{1} + p_{2} * a_{2} + ………… + p_{n} * a_{n}**

### Examples of Expected Value Formula (with Excel Template)

Let’s see some simple to advanced examples of expected value equation to understand it better.

4.9 (1,067 ratings)

#### 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 equation.

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,

- Expected return (P) = p
_{1}(P) * a_{1}(P) + p_{2}(P) * a_{2}(P) + p_{3}(P) * a_{3 }(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) = p
_{1}(Q) * a_{1}(Q) + p_{2}(Q) * a_{2}(Q) + p_{3}(Q) * a_{3 }(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 equation.

**Expected Value of Project X **

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

- Expected Value Formula (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 expected value of Project Y can be done as follows,

- Expected Value Formula (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

It is important to understand for an analyst to understand the concept of expected value formula 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. On the basis of 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 the case of various multivariate models and scenario analysis, it is predominantly used in the calculation of expected return.

### Recommended Articles

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

- 15 Common Techniques for Financial Analysis
- 4 Most Common Tools of Financial Analysis
- Value Formula in Excel
- Examples of Standard Normal Distribution (with Excel Template)
- Excel MEDIAN Formula
- Formula of Binomial Distribution
- Lognormal Distribution Excel
- Median Formula
- Formula for Exponential Growth

- 250+ Courses
- 40+ Projects
- 1000+ Hours
- Full Lifetime Access
- Certificate of Completion