2 Expected Return The future is uncertain. Investors do not know with certainty whether the economy will be growing rapidly or be in recession.Investors 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 probability distribution of possible future returns on the stock.
3 Expected ReturnThe table below provides a probability distribution for the returns on stocks A and BState Probability Return On Return OnStock A Stock B% % %% % %% % %% % %The state represents the state of the economy one period in the future i.e. state 1 could represent a recession and state 2 a growth economy.The probability reflects how likely it is that the state will occur. The sum of the probabilities must equal 100%.The last two columns present the returns or outcomes for stocks A and B that will occur in each of the four states.
4 Expected ReturnGiven a probability distribution of returns, the expected return can be calculated using the following equation:NE[R] = S (piRi)i=1Where:E[R] = the expected return on the stockN = the number of statespi = the probability of state iRi = the return on the stock in state i.
5 Expected ReturnIn this example, the expected return for stock A would be calculated as follows:E[R]A = .2(5%) + .3(10%) + .3(15%) + .2(20%) = 12.5%Now you try calculating the expected return for stock B!
6 Expected Return Did you get 20%? If so, you are correct. If not, here is how to get the correct answer:E[R]B = .2(50%) + .3(30%) + .3(10%) + .2(-10%) = 20%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 considered risk.
7 Measures of RiskRisk reflects the chance that the actual return on an investment may be different than the expected return.One way to measure risk is to calculate the variance and standard deviation of the distribution of returns.We will once again use a probability distribution in our calculations.The distribution used earlier is provided again for ease of use.
8 Measures of Risk E[R]A = 12.5% E[R]B = 20% Probability Distribution: State Probability Return On Return OnStock A Stock B% % %% % %% % %% % %E[R]A = 12.5%E[R]B = 20%
9 Measures of RiskGiven an asset's expected return, its variance can be calculated using the following equation:NVar(R) = s2 = S pi(Ri – E[R])2i=1Where:N = the number of statespi = the probability of state iRi = the return on the stock in state iE[R] = the expected return on the stock
10 Measures of RiskThe standard deviation is calculated as the positive square root of the variance:SD(R) = s = s2 = (s2)1/2 = (s2)0.5
11 Measures of RiskThe variance and standard deviation for stock A is calculated as follows:s2A = .2( )2 + .3( )2 + .3( )2 + .2( )2 =sA = ( )0.5 = = 5.12%Now you try the variance and standard deviation for stock B!If you got .042 and 20.49% you are correct.
12 Measures of RiskIf you didn’t get the correct answer, here is how to get it:s2B = .2( )2 + .3( )2 + .3( )2 + .2( )2 = .042sB = (.042)0.5 = = 20.49%Although Stock B offers a higher expected return than Stock A, it also is riskier since its variance and standard deviation are greater than Stock A's.This, however, is still only part of the picture because most investors choose to hold securities as part of a diversified portfolio.
13 Portfolio Risk and Return Most investors do not hold stocks in isolation.Instead, they choose to hold a portfolio of several stocks.When this is the case, a portion of an individual stock's risk can be eliminated, i.e., diversified away.From our previous calculations, we know that:the expected return on Stock A is 12.5%the expected return on Stock B is 20%the variance on Stock A isthe variance on Stock B isthe standard deviation on Stock A is 5.12%the standard deviation on Stock B is 20.49%
14 Portfolio Risk and Return The Expected Return on a Portfolio is computed as the weighted average of the expected returns on the stocks which comprise the portfolio.The weights reflect th