Portfolio Expected Returns The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio E(Rp)=∑w,E(R,) i=l You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities 10
10 Portfolio Expected Returns n The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio n You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities m j E RP wjE Rj 1 ( ) ( )
Example:Expected Portfolio Returns Consider the portfolio weights computed previously.If the individual stocks have the following expected returns,what is the expected return for the portfolio? DCLK:19.65% a KO: 8.96% INTC: 9.67% o KEI: 8.13% ■E(Rp)=.133(19.65)+.2(8.96)+.267(9.67) +.4(8.13)=10.24% 11
11 Example: Expected Portfolio Returns n Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio? q DCLK: 19.65% q KO: 8.96% q INTC: 9.67% q KEI: 8.13% n E(RP) = .133(19.65) + .2(8.96) + .267(9.67) + .4(8.13) = 10.24%
Portfolio Variance Compute the portfolio return for each state: Rp=WR1+W2R2+.…+WmRm Compute the expected portfolio return using the same formula as for an individual asset Compute the portfolio variance and standard deviation using the same formulas as for an individual asset 12
12 Portfolio Variance n Compute the portfolio return for each state: RP = w1R1 + w2R2 + … + wmRm n Compute the expected portfolio return using the same formula as for an individual asset n Compute the portfolio variance and standard deviation using the same formulas as for an individual asset
Example:Portfolio Variance Consider the following information Invest 50%of your money in Asset A State Probability A B Portfolio a Boom .4 30% -5% 12.5% o Bust .6 -10% 25% 7.5% What is the expected return and standard deviation for each asset? What is the expected return and standard deviation for the portfolio? 13
13 Example: Portfolio Variance n Consider the following information q Invest 50% of your money in Asset A q State Probability A B q Boom .4 30% -5% q Bust .6 -10% 25% n What is the expected return and standard deviation for each asset? n What is the expected return and standard deviation for the portfolio? Portfolio 12.5% 7.5%
Another Example Consider the following information State Probability X Z Boom .25 15% 10% o Normal .60 10% 9% a Recession .15 5% 10% What is the expected return and standard deviation for a portfolio with an investment of $6,000 in asset X and $4,000 in asset Z? 14
14 Another Example n Consider the following information q State Probability X Z q Boom .25 15% 10% q Normal .60 10% 9% q Recession .15 5% 10% n What is the expected return and standard deviation for a portfolio with an investment of $6,000 in asset X and $4,000 in asset Z?