Remember in calculating these values, you can work out the expected return on a portfolio by find ing the portfolio returns in each state and continuing as if the portfolio was just another security(weight each return by the probability of the state and add up) An easier method for the expected return is to multiply each security's expected return by its portfolio weight and add up. The standard deviation is a little more difficult. One method is to find the portfolio returns in each state and continue as if you were finding the standard deviation for a security. If you tried to adapt the quick method for the portfolio expected return here you would get the wrong answer e. You can check that expected return here is 29. 42% and standard deviation is 21.966% f. Expected return now is 19.46% and standard deviation is 10.983%. Note this portfolio is 50% invested in the risk-free security A and 50% invested in the risky' portfolio created part(e).(If you have trouble seeing this, consider an investment of f 1000 and work out how much you would invest in securities B and C in parts(e)and(f). You will find the amounts invested in B and C are in the proportions 3: 7 in each case. ) Because of this he expected return on the portfolio here equals half the return on the risk-free security plus half the expected return on the portfolio from part(e). However, this is now also true of the standard deviation The risk-free security has a zero standard deviation and the portfolio standard deviation is half the standard deviation in the portfolio in part(e). This result holds because security a has no risk. Therefore, there can be no risk diversification effect. Because the return on security a does not vary at all it cannot offset any of the variation in portfolio(e),'s return. If you invest 50% in the risk-free and 50% in portfolio (e)you get 50% of portfolio(e),'s risk g. The covariance between B and C is =03x(5%-185%)0%-34.1%)+03×(40%-185%(27%-341%) +04×(20 0%-185%65%-341%) 0.021315 and the correlation coefficient 0.026766 0.45 0,0. 1747%×27.31% Question 3 Assume that asset 1 is at&t stock and asset 2 is microsoft stock a. The weight of investment in AT&T(asset 1)of the minimum variance portfolio is calculated using G2二P1201 G1+02-2P12O1 ◎徐信忠 MBA公司财务学© 徐信忠 MBA 公司财务学 3 Remember in calculating these values, you can work out the expected return on a portfolio by finding the portfolio returns in each state and continuing as if the portfolio was just another security (weight each return by the probability of the state and add up). An easier method for the expected return is to multiply each security's expected return by its portfolio weight and add up. The standard deviation is a little more difficult. One method is to find the portfolio returns in each state and continue as if you were finding the standard deviation for a security. If you tried to adapt the quick method for the portfolio expected return here you would get the wrong answer. e. You can check that expected return here is 29.42% and standard deviation is 21.966%. f. Expected return now is 19.46% and standard deviation is 10.983%. Note this portfolio is 50% invested in the risk-free security A and 50% invested in the `risky' portfolio created in part (e). (If you have trouble seeing this, consider an investment of £ 1000 and work out how much you would invest in securities B and C in parts (e) and (f). You will find the amounts invested in B and C are in the proportions 3:7 in each case.) Because of this, the expected return on the portfolio here equals half the return on the risk-free security plus half the expected return on the portfolio from part (e). However, this is now also true of the standard deviation. The risk-free security has a zero standard deviation and the portfolio standard deviation is half the standard deviation in the portfolio in part (e). This result holds because security A has no risk. Therefore, there can be no risk diversification effect. Because the return on security A does not vary at all it cannot offset any of the variation in portfolio (e)'s return. If you invest 50% in the risk-free and 50% in portfolio (e) you get 50% of portfolio (e)'s risk. g. The covariance between B and C is: ( ) ( )( ) ( )( ) ( )( ) 0.021315 0.4 20% 18.5% 65% 34.1% 0.3 5% 18.5% 0% 34.1% 0.3 40% 18.5% 27% 34.1% cov , 1 2 = +  − − =  − − − +  − − r r and the correlation coefficient is ( ) 0.45 17.47% 27.31% cov , 0.026766 1 2 1 2 12 =  − = =    r r Question 3 Assume that asset 1 is AT&T stock and asset 2 is Microsoft stock. a. The weight of investment in AT&T (asset 1) of the minimum variance portfolio is calculated using: 12 1 2 2 2 2 1 12 1 2 2 2 min   2       + − − w =