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Expected Return

The future is uncertain. Investors do not know with certainty whether the economy will be growing rapidly or be in recession. As such, they do not know what rate of return their investments will yield. Therefore, they base their decisions on their expectations concerning the future.

The expected rate of return on a stock represents the mean of a probabilty distribution of possible future returns on the stock. The table below provides a probability distribution for the returns on stocks A and B.

State Probability Return on
Stock A
Return on
Stock B
1 20% 5% 50%
2 30% 10% 30%
3 30% 15% 10%
3 20% 20% -10%

In this probability distribution, there are four possible states of the world one period into the future. For example, state 1 may correspond to a recession. A probability is assigned to each state. The probability reflects how likely it is that the state will ocurr. The sum of the probabilities must equal 100%, indicating that something must happen. The last two columns present the returns or outcomes for stocks A and B that will occur in the four states.

Given a probability distribution of returns, the expected return can be calculated using the following equation:


  • E[R] = the expected return on the stock,
  • N = the number of states,
  • pi = the probability of state i, and
  • Ri = the return on the stock in state i.
Expected Return on Stocks A and B

Stock A

Stock B

So we see that Stock B offers a higher expected return than Stock A. However, that is only part of the story; we haven't yet considered risk.

Example Problems
Find the Expected Return on a stock given the following
probability distribution of returns for the stock.
State Probability Return
1 % %
2 % %
3 % %
4 % %
Expected Return: %


© 2002 - 2010 by Mark A. Lane, Ph.D.