Calculating Expected Rate Of Return — Super Business Manager

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:

$E(R) = \sum_{i=1}^{n} (R_i \times P_i)$

Where:

$E(R)$ = Expected Rate of Return

$R_i$ = Return in scenario $i$

$P_i$ = Probability of scenario $i$ occurring

$\sum$ = 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)	$0.25 \times 0.20 = 0.050$
Normal (Stable Economy)	10% (0.10)	60% (0.60)	$0.10 \times 0.60 = 0.060$
Recession (Weak Economy)	-5% (-0.05)	20% (0.20)	$-0.05 \times 0.20 = -0.010$
Total		100% (1.00)	0.100

The probabilities must always sum up to $1.00$ (or $100\%$ ).

Expected Rate of Return: $E(R) = 0.050 + 0.060 + (-0.010) = 0.100$ or 10.0%.

The expected return on this stock is $10.0\%$ .

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:

$E(R_p) = \sum_{i=1}^{n} (w_i \times E(R_i))$

Where:

$E(R_p)$ = Expected Rate of Return of the Portfolio

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

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

$\sum$ = Summation sign

Example Calculation

Consider a portfolio with a total value of $$100,000$ , split among three assets with the following characteristics:

Asset	Value Invested	Weight (wi)	Expected Return (E(Ri))	Weighted Return (wi×E(Ri))
Stock A	$$50,000$	$0.50$	$12\%$ (0.12)	$0.50 \times 0.12 = 0.060$
Bond B	$$30,000$	$0.30$	$5\%$ (0.05)	$0.30 \times 0.05 = 0.015$
Stock C	$$20,000$	$0.20$	$15\%$ (0.15)	$0.20 \times 0.15 = 0.030$
Total	$$100,000$	$1.00$		$0.105$

The portfolio weights must always sum up to $1.00$ .

Expected Portfolio Return: $E(R_p) = 0.060 + 0.015 + 0.030 = 0.105$ or 10.5%.

The expected return on the entire portfolio is $10.5\%$ .

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.

$E(R_i) = R_f + \beta_i \times (E(R_m) - R_f)$