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# Expected Return

Step-by-Step Guide to Understanding Expected Return in Corporate Finance

Last Updated March 5, 2024

## How to Calculate Expected Return

By measuring the expected return on a probability-weighted basis, investors can estimate the return from an investment or portfolio of securities.

In corporate finance, the expected return of a portfolio signifies the anticipated yield that could potentially be generated over a pre-defined time frame.

Understanding the expected risk-adjusted return on a portfolio contributes to more informed investment decisions, where the risk-return profile of the investment can be structured to more closely align with the investor’s risk appetite and target yield.

The expected return is a critical component to constructing a portfolio that can generate the target return while mitigating risk to a manageable level.

The expected return is calculated by multiplying the probability of each possible return scenario by its corresponding value and then adding up the products.

The expected return metric – often denoted as “E(R)” – considers the potential return on an individual security or portfolio and the likelihood of each outcome.

However, the implied return is not merely a simple average but rather a range of potential outcomes, which facilitates a more comprehensive assessment of the risk-reward profile of the investment portfolio.

The incorporation of probability weights in analyzing potential returns improves the depth of the decision-making process for investors, especially with regard to understanding the potential upside and downside of an investment portfolio, akin to performing scenario analysis.

## Expected Return Formula

The formula to calculate the expected return on an individual security, or “cost of equity”, is determined using the capital asset pricing model (CAPM), which adds the product of beta (β) and the equity risk premium (ERP) to the risk-free rate (rf).

Expected Return, E(R) = Risk-Free Rate (rf) + Beta (β) × Equity Risk Premium (ERP)

Where:

• Risk-Free Rate (rf) → The risk-free rate is the yield on the debt issuances by the government, e.g. the 10-year Treasury note for U.S.-based public companies.
• Beta (β) → Beta is the measure of systematic risk, i.e. the volatility of a security to the broader market, which represents non-diversifiable risk.
• Equity Risk Premium (ERP) → The equity risk premium, or “market risk premium” is the extra, incremental return expected from investors for investing in the stock market rather than risk-free securities.

The risk-free rate and beta are readily observable via Bloomberg and related online sources, and the equity risk premium (ERP) is computed as the difference between the expected market return and the risk-free rate.

Equity Risk Premium (ERP) = Market Return (rm)  Risk-Free Rate (rf)

Further, the formula to calculate the expected return on a portfolio requires weighting each potential outcome by its probability and then adding together these weighted returns.

Portfolio Expected Return E(R) = Σ r(i) × p(i)

Where:

• Σ → Summation Notation
• p(i) → Probability of Outcome
• r(i) → Return in Outcome

## Expected Return Calculator

We’ll now move to a modeling exercise, which you can access by filling out the form below.

#### Excel Template

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## Portfolio Expected Return Calculation Example

Suppose we’re tasked with estimated the expected return on a portfolio of equity securities under three different scenarios (“Recession”, “Normal”, and “Boom”).

The probability weight and the expected rate of return in each scenario is as follows.

State of Economy Probability Weight (%) Portfolio Return (%)
Recession
• 5.0%
• (5.0%)
Normal
• 80.0%
• 10.0%
Boom
• 15.0%
• 16.0%

Since the expected return equals the sum of the product of the return in each potential outcome, we can use the “SUMPRODUCT” function in Excel to calculate the expected return.

=SUMPRODUCT(F5:F7,I5:I7)

The first array is the probability weight (i.e. the likelihood of occurrence), whereas the second array is the expected return in the coinciding scenario.

The implied expected return on the portfolio comes out to be 10.2%, which reflects the probability-weighted return expected by the investor.

• Expected Return, E(R) = 10.2%

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