What Is Expected Return? Formula and Examples

Search Fintrev

Search our guides, reviews and glossary.

Expected return is the probability-weighted average of the returns an investment could produce: the average result if the same bet could be repeated many times under the same conditions. It is an estimate, not a forecast of any single year and not a guarantee. An investment with a 7% expected return may lose money next year and gain 20% the year after.

The Expected Return Formula

The general formula for expected return is:

E(R) = Σ (Rᵢ × Pᵢ)

where Rᵢ is the return in outcome i, Pᵢ is the probability of that outcome, and the probabilities add up to 100%.

Hypothetical example: two outcomes. An investment has a 50% chance of gaining 20% and a 50% chance of losing 10%.

E(R) = (0.50 × 20%) + (0.50 × −10%) = 10% − 5% = 5%

The 5% never occurs in any single outcome; it is the average across many repetitions.

Hypothetical example: three scenarios. An analyst models a stock for the coming year:

• Strong economy (30% probability): +25%
• Normal economy (50% probability): +10%
• Recession (20% probability): −15%

E(R) = (0.30 × 25%) + (0.50 × 10%) + (0.20 × −15%) = 7.5% + 5% − 3% = 9.5%

The result is only as good as the probabilities and returns assigned to each scenario. Changing the recession probability to 30% (and the normal case to 40%) drops the expected return to 6.5%.

How to Calculate Expected Return From Historical Returns

Without explicit scenarios, a common shortcut treats each past period as an equally likely outcome, so expected return becomes the simple (arithmetic) mean of historical returns. For example, annual returns of 12%, 2%, 25%, −9% and 10% sum to 40%, giving 40% ÷ 5 = 8%. Using this as the expected return assumes the future will resemble the sample period, which is the method’s main weakness.

Expected Return Using CAPM

The capital asset pricing model gives a widely used model-based expected return for a stock or portfolio:

E(Rₐ) = R_f + β × (E(Rₘ) − R_f)

• E(Rₐ) = expected return on the asset
• R_f = risk-free rate of return
• β = the asset’s beta, its sensitivity to market moves
• E(Rₘ) = expected market return

The term E(Rₘ) − R_f is the market risk premium. CAPM says an investment earns the risk-free rate plus a premium proportional to how much market (systematic) risk it carries.

Hypothetical example: with a risk-free rate of 4%, an expected market return of 9% and a beta of 1.2:

E(Rₐ) = 4% + 1.2 × (9% − 4%) = 4% + 6% = 10%

A stock with a beta of 0.8 under the same assumptions would have an expected return of 8%. Because CAPM produces the return investors should demand for a given level of market risk, its output is often called the required return. When a stock’s own forecast return exceeds its CAPM figure, the difference is a form of alpha.

Expected Return of a Portfolio

A portfolio’s expected return is the weighted average of each holding’s expected return, with weights based on each holding’s share of total portfolio value.

Hypothetical example: a $1,000,000 portfolio holds:

• Fund A: $500,000, expected return 15% (weight 50%)
• Fund B: $200,000, expected return 6% (weight 20%)
• Fund C: $300,000, expected return 9% (weight 30%)

E(Rₚ) = (0.50 × 15%) + (0.20 × 6%) + (0.30 × 9%) = 7.5% + 1.2% + 2.7% = 11.4%

Weights are the main lever. Shifting $100,000 from Fund A to Fund B lowers the portfolio’s expected return to 10.5%. Unlike portfolio risk, the expected return does not depend on how the holdings move relative to one another; correlation affects only the portfolio’s volatility.

Expected Return for Bonds

For debt, the promised return and the expected return differ. A bond’s yield to maturity assumes every coupon and the principal are paid in full. Expected return accounts for the chance that they are not.

Hypothetical example: a bond held for one year returns 6% if the issuer pays and −50% if it defaults, with a 2% default probability.

E(R) = (0.98 × 6%) + (0.02 × −50%) = 5.88% − 1.0% = 4.88%

The gap between 6% and 4.88% is the cost of default risk. The higher the default probability or the lower the recovery, the further expected return falls below the quoted yield.

How Expected Return Is Used

• Comparing investments. It shows whether an opportunity has a positive or negative average outcome and ranks alternatives on the same basis.
• Portfolio construction. Modern portfolio theory (MPT) combines expected returns with volatilities and correlations to find portfolios offering the highest expected return for a given level of risk.
• Pricing and valuation. Required returns from models like CAPM serve as discount rates, and expected values sit at the core of option-pricing frameworks such as Black-Scholes.
• Planning. The assumed rate of return in retirement and savings projections is an expected return.

Expected Return vs. Standard Deviation

Expected return measures the center of the possible outcomes. Standard deviation measures how widely actual returns spread around that center, which makes it a common proxy for risk.

Consider two hypothetical investments with five years of returns:

• Investment A: 12%, 2%, 25%, −9%, 10%
• Investment B: 7%, 6%, 9%, 12%, 6%

Both average 8%. Investment A’s standard deviation is about 11.26%, while Investment B’s is about 2.28% (population standard deviation), roughly five times less volatile. An investor relying on expected return alone would treat them as equivalent. Measures such as the Sharpe ratio combine both figures by dividing excess return by volatility.

Other Distinctions Readers Confuse

Expected return vs. compounded return. An arithmetic expected return overstates what a volatile investment compounds to over time. The +20% / −10% investment above has a 5% expected return, but a gain of 20% followed by a loss of 10% leaves $100 at $108 after two years, a compound rate of about 3.9% per year. The compound figure is what CAGR measures, and the gap widens as volatility rises.

Expected return vs. ROI. Return on investment measures the gain or loss already realized. Expected return looks forward and is probability-weighted.

Expected return vs. required return. Required return is the minimum an investor demands for bearing a given risk. If an asset’s expected return is below its required return, it is unattractive at its current price.

Limitations of Expected Return

• Inputs are estimates. Probabilities, scenario returns and historical sample periods are judgments; small changes can move the result substantially, and past averages can miss regime changes.
• Risk can still prevent it. Systematic risk (market-wide factors such as recessions or rate changes) and unsystematic risk (problems specific to a company or industry) can keep an investment from coming close to its expected return. Diversification reduces unsystematic risk but not systematic risk.
• It ignores dispersion and timing. Identical expected returns can hide very different risk, and over a short holding period the realized return can differ sharply from the expected figure.

FAQs

The Bottom Line

Expected return matters to anyone comparing investments, building a portfolio or setting the assumed rate in a retirement or savings projection. The result is only as reliable as the probabilities and returns fed into it, and it reveals nothing about dispersion or timing. Reading it alongside standard deviation or the Sharpe ratio gives a fuller picture, and a volatile investment will compound at a lower rate than its arithmetic expected return.