Expected Return Calculator

Expected return is the expected value (probability-weighted average) of an investment’s future return. The formula is E(R) = p1×R1 + p2×R2 + ... + pn×Rn, where pi is the probability of scenario i and Ri is scenario i’s return. Example: bear (20% probability, −10% return), base (50%, 8%), and bull (30%, 20%) scenarios give E(R) = 0.2×(−10%) + 0.5×(8%) + 0.3×(20%) = 8%. This 8% is the average of the distribution of possibilities, not a promise.

Expected return looks forward: the mathematical expectation based on scenarios, the CAPM model, or portfolio weights. Realized return looks backward: the return that actually happened, usually computed as CAGR (compound annual growth rate) from historical data. Expected return can miss realized return because the realization is just one of many possibilities. To compute historical returns that already happened, use the annualized rate of return calculator.

The CAPM model computes an asset’s expected return with E(Ri) = Rf + βi × (E(Rm) − Rf). Rf is the risk-free rate, βi is the asset’s beta (market sensitivity), and E(Rm) is the market’s expected return. The difference E(Rm) − Rf is called the market risk premium. Example: Rf = 4%, β = 1.2, E(Rm) = 10% → market risk premium = 6% and E(Ri) = 4% + 1.2 × 6% = 11.2%. An asset with β = 1 moves with the market; β > 1 is more market-sensitive; β = 0 means its expected return equals the risk-free rate.

Negative beta means the asset’s return tends to move opposite the market: when the market rises, this asset tends to fall, and vice versa. Example: β = −0.5, Rf = 3%, E(Rm) = 9% → E(Ri) = 3% + (−0.5) × 6% = 0%. This is a statistical property of the historical data used to estimate beta, not a forecast of future direction.

No. Expected return is the average of a distribution of possibilities, while the actual outcome can be above or below it. In the bear/base/bull example above, the actual result could be −10% (bear scenario) even though the expected return is 8%. Expected return describes the center of the distribution, not a guaranteed outcome. Always treat this figure as an educational estimate, not investment advice.

The math is the same expected value (sum of probability × outcome), but the domains differ. Expected return is used for investment returns in percent (stocks, portfolios), while EMV is used for decision analysis with monetary payoffs (e.g. choosing projects or business decisions under uncertainty, including EVPI). For business decision analysis, use the EMV calculator.

A portfolio’s expected return is the weighted average of each asset’s expected return: E(Rp) = w1×E(R1) + w2×E(R2) + ... + wn×E(Rn), where wi is asset i’s weight in percent and total weight must be 100%. Example: 60% asset A with 10% expected return and 40% asset B with 4% expected return → E(Rp) = 0.6×10% + 0.4×4% = 7.6%. This calculator accepts up to 10 assets.

The risk (standard deviation) of a 2-asset portfolio is computed with σp² = w1²σ1² + w2²σ2² + 2×w1×w2×ρ12×σ1×σ2, where ρ12 is the correlation between the two assets (−1 to 1). Correlation below 1 gives a diversification effect: portfolio risk is smaller than the weighted average of each asset’s risk. Example: 50/50 weights, σ1 = 20%, σ2 = 10%, ρ = 0.3 → σp ≈ 12.45%. For 3 or more assets the computation needs the full correlation/covariance matrix between asset pairs, so this calculator limits risk computation to 2-asset portfolios.

The CAPM tab in this calculator computes an asset/investment’s expected return from the investor’s perspective. If you are computing a company’s cost of equity for WACC (weighted average cost of capital) or capital structure analysis, use the cost of capital calculator, which is designed for that corporate finance context.