Expected Return Formula

Expected Return Formula (Table of Contents)

• Expected Return Formula
• Examples of Expected Return Formula (With Excel Template)
• Expected Return Formula Calculator

Expected Return Formula

Expected Return can be defined as the probable return for a portfolio held by investors based on past returns or it can also be defined as an expected value of the portfolio based on probability distribution of probable returns.

Here’s the Expected Return Formula –

Where

• R_i – Return Expectation of each scenario
• P_i – Probability of the return in that scenario
• i – Possible Scenarios extending from 1 to n

Examples of Expected Return Formula (With Excel Template)

Let’s take an example to understand the calculation of the Expected Return formula in a better manner.

Expected Return Formula – Example #1

Let’s take an example of a portfolio of stocks and bonds where stocks have a 50% weight and bonds have a weight of 50%. The expected return of stocks is 15% and the expected return for bonds is 7%.

Expected Return is calculated using formula given below

Expected Return for Portfolio = Weight of Stock * Expected Return for Stock + Weight of Bond * Expected Return for Bond

• Expected Return for Portfolio = 50% * 15% + 50% * 7%
• Expected Return for Portfolio = 7.5% + 3.5%
• Expected Return for Portfolio = 11%

Expected Return Formula – Example #2

Let’s take an example of portfolio which has stock Reliance, Tata Steel, Eicher Motors and ITC.

Expected Return is calculated using formula given below

Expected Return for Portfolio = ∑ Weight of Each Stock * Expected Return for Each Stock

• Expected Return for Portfolio = 25% * 10% + 25%* 8% + 25% * 12% + 25% * 16%
• Expected Return for Portfolio = 2.5% + 2% + 3% + 4%
• Expected Return for Portfolio = 11.5%

Expected Return Formula – Example #3

Let’s take an example of portfolio of HUL, HDFC and 10 year government bond.

Expected Return is calculated using the formula given below

Expected Return for Portfolio = ∑ Weight of Each Component * Expected Return for Each Component

• Expected Return for Portfolio = 40% * 15% + 40% * 18% + 20% * 7%
• Expected Return for Portfolio = 6% + 7.2% + 1.40%
• Expected Return for Portfolio = 14.60%

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

Explanation of Expected Return Formula

Expected Return can be defined as the probable return for a portfolio held by investors based on past returns or it can also be defined as an expected value of the portfolio based on probability distribution of probable returns. The expected return can be looked in the short term as a random variable which can take different values based on some distinct probabilities. This random variable has values within a certain range and can only take values within that particular range. Hence the expected return calculation is based on historical data and hence may not be reliable in forecasting future returns. It can be looked at as a measure of various probabilities and the likelihood of getting a positive return on one’s investment and the value of that return.

The purpose of this is to give an investor an idea of for a different level of risk what are the various scenarios with different probabilities that will yield a return possible greater than the risk free return. As we all know, the risk free return would be the 10 year Treasury bond yield of United States Government.

Relevance and Uses of Expected Return Formula

As mentioned above the Expected Return calculation is based on historical data and hence it has a limitation of forecasting future possible returns. Investors have to keep in mind various other factors and not invest based on the expected return calculated. Taking an example: –

Portfolio A – 10%, 12%, -9%, 2%, 25%

Portfolio B – 9%, 7%, 6%, 6%, 12%

If we consider both the above portfolios, both have an expected return of 8% but Portfolio A exhibits lot of risk due to lot of variance in returns. Hence investors must take into account this risk which is calculated by measures such as Standard Deviation and Variance.

• Variance – It can be defined as a variation of a set of data points around their mean value. It is calculated by the probability-weighted average of squared deviations from the mean. It is a measure of risk that needs to be taken into account by investors.

First one has to calculate the mean of all returns. Then each return’s deviation is found out from the main value and squared to ensure all positive results. And once they are squared, they are multiplied with respective probability values to find out the variance.

Portfolio variance can be calculated from the following formula: – If there are two portfolios A and B

Portfolio Variance = w_A² * σ_A² + w_B² * σ_B² + 2 * w_A * w_B * Cov (A, B)

Where Cov (A, B) – is covariance of portfolios A and B

• Standard Deviation – It is another measure that denotes the deviation from its mean. Standard deviation is calculated by taking a square root of variance and denoted by σ.

Expected Return Formula Calculator

You can use the following Expected Return Calculator.

Conclusion

Expected Return can be defined as the probable return for a portfolio held by investors based on past returns. As it only utilizes past returns hence it is a limitation and value of expected return should not be a sole factor under consideration by investors in deciding whether to invest in a portfolio or not. There are other measures that need to be looked at such as the portfolio’s variance and standard deviation.

Recommended Articles

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