# What is an Expected Return?

D. Poupon

An expected return is the value that investors expect an asset to earn or lose on average over a given time period. More precisely, it is the sum of all possible financial outcomes of an asset that are weighted by the probability of the outcome’s occurrence. Easily calculated using a tree diagram, if an asset has a 70 percent chance of earning 6 percent and a 30 percent chance of earning 9 percent in a year, then the expected return of the asset is calculated as 6.9 percent. The interest, dividends, and capital gains and losses of assets affect their expected returns. Also referred to as the mean return, it is an investor’s best predictor of future market behavior. Expected return is the sum of all possible financial outcomes of an asset that are weighted by the probability of the outcome’s occurrence.

#### Actual Versus Expected Returns

In contrast to an expected return, an actual return is the reported amount that an asset gained or lost over a given period. A total return is an asset’s actual return over an investment horizon, including reinvestment rates. It is very unlikely that an asset’s actual return will be exactly the same as the expected return, so an asset is considered "on stream" if its actual and expected returns are sufficiently close. If an asset has significantly underperformed or outperformed the predicted return, then it is called an abnormal return, which might occur because of mergers, interest rate changes, or lawsuits, all of which affect the particular asset instead of the market as a whole.

#### Prediction Methods

In order to detect and exploit abnormal returns, investors rely on a variety of methods to accurately predict the expected return of an asset. Besides the tree diagram calculation mentioned earlier, another simple method is to take the historical mean of past annual returns. The historical mean is not a bad estimate if a company has a long history, has accurate historical data, and has made few changes in its structure, policies and strategies. On the other hand, the calculation does not take into consideration volatility, which is a measure of the price variation of investment options from year to year, and therefore is a rather primitive estimate.

#### Risk-free Assets

Some economists have noticed that risk-free assets, such as bonds, have unexplained, lower, long-term total returns than more volatile assets such as stocks. As a result, risk-free assets can negatively affect the calculation of an expected return. The economists Edward C. Prescott and Rajnish Mehra called this phenomenon "the equity premium puzzle," which economists have struggled to understand. Equity premium is the excess return that is left over when risk-free assets’ returns are subtracted from the expected market return. Modern economic models such as the Capital Asset Pricing Model (CAPM) attempt to solve the equity premium puzzle by estimating the expected return of risk-free assets differently from risky assets. The model takes into consideration the volatility of risky assets and their sensitivity to changes in the market.

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