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 t he 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=15% and SD=20% 0.75 in Z and 0.25 in Y=0.75*15+0.25*35 20 Variance(ZY)=(0.75^2)*(0.2^2)+(0.25^2)*(0.4^2)+2*(0.75*0.25*0.2*0.4*0.25) 0.04 SD=Square Root(0.02) 0.2 0.5 in Z and 0.5 in Y=0.5*15+0.5*35 25 Variance(ZY)=(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=0.25*15+0.75*35 30 Variance(ZY)=(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=35% , SD=40% b>Invest Opportunity sets are (X,SD)[ (0.15,0.2),(0.2,0.2),(0.25,0.24),(0.30,0.32),(0.35,0.4) c>(0.2,0.2) is the right choice i.e. 75% in Z and 25% in Y

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