# Expected Return Calculator

This Expected Return Calculator is a valuable tool to assess the potential performance of an investment. Based on the probability distribution of asset returns, the calculator provides three key pieces of information: expected return, variance, and standard deviation.

How to use the calculator: Enter the probability, return on Stock A, and return on Stock B, for each state. Ensure that the sum of probabilities equals 100%. Press "Calculate" to obtain expected return, variance, and standard deviation.

Expected Return Calculator
State #ProbabilityReturn on
Stock A
Return on
Stock B
1%%%
2%%%
3%%%

Expected Return:  0%0%
Variance:
Standard Deviation:  0%0%

## Expected Return: Formula, Calculation, Example

Expected rate of return represents the mean of the probability distribution of future returns on a stock. The table below provides the probability distribution for returns on stocks A and B.

State #ProbabilityReturn on
Stock A
Return on
Stock B
115%−5%5%
250%10%15%
335%20%35%

In this probability distribution, there are three possible states of the economy: a recession (State #1), a normal economy (State #2), or a boom (State #3). Each of these states is assigned a probability, indicating the likelihood of it occurring. It is important to note that the sum of these probabilities must equal 100%, as something must happen. Additionally, the last two columns in the table present the expected returns for stocks A and B in each of the three states. To calculate the expected return for a given probability distribution of returns, we can use the following equation:

E(r) = r̄ = p1r1 + p2r2 + ... + pnrn

E(r) = r̄ =
n
p i * ri
i = 1

Where:

E(r)  is the expected return on the stock ,

r̄  is the mean return ,

∑  is the summation symbol ,

pi  is the probability of state i ,

ri  is the return on the stock in state i ,

n  is the number of states.

Consider the probability distribution for returns on stocks A and B, provided in the table above.

Expected Return on Stock A: E(rA) = .15(−.05) + .50(.10) + .35(.20) = .1125 = 11.25%

So the expected return on Stock A is 11.25%.

Expected Return on Stock B: E(rB) = .15(.05) + .50(.15) + .35(.35) = .205 = 20.5%

The expected return on Stock B is 20.5%.

Stock B offers higher expected return than Stock A, but also has higher risk.

Risk reflects the deviation of actual return from expected return. One way to measure risk is by calculating variance and standard deviation of return distribution.

Given an asset's expected return, its variance can be calculated by using the following equation:

Var(r) = σ2 = p1(r1 − r̄)2 + p2(r2 − r̄)2 + ... + pn(rn − r̄)2

Var(r) = σ2 =
n
p i * (ri − r̄)2
i = 1

The standard deviation is calculated as the positive square root of the variance.

SD(r) = σ = √σ2

So, the variance and standard deviation of Stock A are:

Var(rA) = .15(−.05 − .1125)2 + .50(.10 − .1125)2 + .35(.20 − .1125)2 = .00672

SD(rA) = √(.00672) = .0819 = 8.2%

The variance and standard deviation of Stock B are as follows:

Var(rB) = .15(.05 − .205)2 + .50(.15 − .205)2 + .35(.35 − .205)2 = .01248

SD(rB) = √(.01248) = .1117 = 11.17%

Stock B offers higher expected return than Stock A, but it is also riskier as its variance and standard deviation are greater.

You may also be interested in our CAPM Calculator or Expected Value Calculator