Calculating Expected Rate Of Return

The Expected Rate of Return (E(R)) is the average return an investor anticipates receiving on an investment, considering all possible returns and the probability of each return occurring. It’s essentially a probability-weighted average of all potential outcomes

There are two primary ways to calculate the expected rate of return, depending on whether you are analyzing a single investment with multiple scenarios or an entire investment portfolio.

A: SINGLE STOCK – Calculating Expected Return for a Single Investment (Scenario Analysis)

This method is used when you identify different potential economic or company-specific scenarios and estimate the probability and return for each.

The formula for the expected rate of return for a single investment based on different scenarios is:

Where:

= Expected Rate of Return

= Return in scenario

= Probability of scenario occurring

= Summation sign (meaning you add up the results of all scenarios)

Example Calculation

Imagine a stock investment with three potential scenarios:

Scenario	Return (Ri​)	Probability (Pi​)	Weighted Return (Ri​×Pi​)
Boom (Strong Economy)	25% (0.25)	20% (0.20)
Normal (Stable Economy)	10% (0.10)	60% (0.60)
Recession (Weak Economy)	-5% (-0.05)	20% (0.20)
Total		100% (1.00)	0.100

The probabilities must always sum up to (or ).

Expected Rate of Return: or 10.0%.

The expected return on this stock is .

B: PORTFOLIO – Calculating Expected Return for a Portfolio

For a portfolio containing multiple assets (like stocks and bonds), the expected return is the weighted average of the expected returns of all the individual assets.

The formula for the expected rate of return of a portfolio is:

Where:

= Expected Rate of Return of the Portfolio

= Weight of asset in the portfolio (the percentage of the total portfolio value invested in asset )

= Expected Rate of Return of asset (which may be calculated using the scenario analysis method above or based on historical data)

= Summation sign

Example Calculation

Consider a portfolio with a total value of , split among three assets with the following characteristics:

Asset	Value Invested	Weight (wi​)	Expected Return (E(Ri​))	Weighted Return (wi​×E(Ri​))
Stock A			(0.12)
Bond B			(0.05)
Stock C			(0.15)
Total

The portfolio weights must always sum up to .

Expected Portfolio Return: or 10.5%.

The expected return on the entire portfolio is .

Alternative Method: Using the Capital Asset Pricing Model (CAPM)

The CAPM is a widely used financial model that calculates the theoretically required or expected rate of return for an individual security based on its risk, relative to the overall market.

Where:

= Expected Return of security

= Risk-Free Rate (e.g., the return on a long-term government bond)

= Beta of security (a measure of the security’s volatility relative to the market)

= Expected Market Return (e.g., the expected return of a broad market index like the S&P 500)

= Market Risk Premium (the extra return expected for taking on market risk)

Real Business Example: Calculating Required Return for Apple Inc. (AAPL)

An analyst wants to estimate the required return for Apple’s stock using the CAPM, based on the following assumptions:

Risk-Free Rate ():

Apple’s Beta (): (meaning it’s more volatile than the market)

Expected Market Return ():

The steps for the calculation are:

First, calculate the Market Risk Premium ():

Next, calculate the Risk Premium for AAPL ():

Finally, add the Risk-Free Rate to the Risk Premium for AAPL to find the Expected Return ():

The Expected Rate of Return for Apple Inc. (AAPL) is .