5. The expected returns and standard deviation of returns for two securities are

Question

5. The expected returns and standard deviation of returns for two securities are as follows: Security Z Security Y Expected Return 15% 35% Standard Deviation 20% 40% The correlation between the returns is + .25. (a) Calculate the expected return and standard deviation for the following portfolios: i. all in Z ii. .75 in Z and .25 in Y iii. .5 in Z and .5 in Y iv. .25 in Z and .75 in Y v. all in Y (b) Draw the investment opportunity set. (c) Which portfolios might be held by an investor who likes high mean and low standard deviation?

Explanation / Answer

a>All in Z , expected return Xz=15% and SDz=20% 0.75 Z and 0.25 Y, Expected return=0.75*15+0.25*35 20 or 0.2 Variance=(0.75^2)*(0.20^2)+(0.25^2)*(0.4^2)+2*0.75*0.25*0.20*0.40*0.25 0.04 SD=Square Root of (0.04) 0.2 0.5 in Z and 0.5 in Y , Expected Return=0.5*15+0.5*35 25 or 0.25 Variance=(0.5^2)*(0.2^2)+(0.5^2)*(0.4^2)+2*0.5*0.5*0.2*0.4*0.25 0.06 SD=Square Root(0.06) 0.24 0.25 in Z and 0.75 in Y , Expected Return=0.25*15+0.75*35 30 or 0.3 Variance=(0.25^2)*(0.2^2)+(0.75^2)*(0.4^2)+2*0.25*0.75*0.2*0.4*0.25 0.1 SD=Square Root(0.1) 0.32 All in Y , expected return Xy=35% and SDy=40% b> The investment opportunity set are (0.15/0.20) , (0.2/0.2),(0.25,0.24),(0.3,0.32),(0.35,0.4) c>Third option (50% Z and 50% Y) has high return of 25% and low SD of 24%.

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