Probabilities must sum to 100%. Return can be negative.
E(R) = Sum(Pi x Ri)
Where Pi is the probability of scenario i and Ri is the return in scenario i.
Expected return is a probability-weighted average of all possible returns an investment could generate. It is a fundamental concept in modern portfolio theory and helps investors estimate the average outcome of an investment given different market scenarios and their respective likelihoods. By assigning probabilities to various outcomes, investors can make more informed decisions about where to allocate their capital.
The calculation involves multiplying each possible return by its probability of occurring, then summing all these products. For example, if there is a 50% chance of earning 10% and a 50% chance of losing 5%, the expected return is (0.50 x 10%) + (0.50 x -5%) = 2.5%. This single number provides a useful summary of the investment's potential, though actual results will vary.
Expected return is most useful when comparing multiple investment opportunities. By calculating the expected return of different assets or portfolios, investors can identify which options offer the best risk-adjusted returns. It serves as a baseline for decision-making but should always be considered alongside risk metrics such as standard deviation, beta, and the Sharpe ratio to get a complete picture of an investment's profile.
Keep in mind that expected return is a forward-looking estimate based on assumptions about probabilities and outcomes. The accuracy of the result depends entirely on the quality of those inputs. Historical data, analyst forecasts, and economic models can help inform scenario probabilities, but markets are inherently uncertain and actual returns may differ significantly from expectations.
Expected return does not guarantee actual results -- it is a theoretical average. It does not capture the full distribution of outcomes, tail risks, or black swan events. Additionally, accurately estimating probabilities for future market scenarios is extremely challenging. Investors should use expected return as one tool among many in their analysis, combining it with risk measures and diversification strategies to build robust portfolios.