Expected Return

An expected return answers one question: if I buy at today's price, what do I anticipate earning? For a share, the inputs are the current price, the dividends the investor expects and the price the investor expects at the end of the horizon. For a bond, they are the price, the promised payments and an assessment of the chance that those payments are not made. Because the price is part of the calculation, a lower price for the same expected cash flows means a higher expected return.

When the future is described as a set of scenarios, the expected return is the probability-weighted average of the scenario returns. It is a mean, not a promise: in any single period the realized return will almost always differ from it, and the dispersion of outcomes around it is what standard deviation measures.

Three terms are easy to conflate. The required return is set by risk: it is the minimum an investor demands for holding an asset with that risk, and models such as the CAPM estimate it. The expected return is set by price and the investor's forecast. The discount rate is a role in a calculation: in valuation, the required return is the rate used to discount future cash flows to an estimate of value.

The link between them is the market price. If the price equals intrinsic value, expected and required return coincide. If the asset is undervalued, expected return exceeds required return, because the investor also anticipates the price moving toward value; the extra return materializes only if that convergence actually happens within the horizon.

Mean-variance analysis describes every asset by its expected return, its standard deviation and its correlations with other assets. A portfolio's expected return is simply its holdings' expected returns averaged with value weights, so diversification leaves it unchanged, whereas portfolio risk falls as less correlated assets are combined. That asymmetry is what makes diversification valuable.

Under the equilibrium assumption of the capital asset pricing model, an asset's expected return is the risk-free rate plus its beta times the market risk premium: E(Rᵢ) = r_f + βᵢ[E(Rₘ) − r_f]. When the security market line is used to judge mispricing, it gives the required return: an asset whose own forecast return plots above the line looks undervalued, and one below it looks overvalued.

Candidates should compute expected returns from probability distributions, combine them into portfolio expected returns, and estimate them for equities by rearranging a dividend discount model to solve for the return implied by today's price. They should also be able to explain, in a mispricing question, why an expected return differs from a required return.

In practice, expected returns are the hardest input in portfolio construction to estimate. Historical averages are noisy, and small changes in assumed expected returns can swing an optimized allocation dramatically. That is why institutions publish ranges and scenarios rather than single figures, and why many allocators blend historical data with forward-looking measures such as current yields and valuations.