Question

13-E1. There are two possible investments you are considering. Throughout this question we measure return on investment in units of percent per annum. Shares in Solid Pty. Ltd. have returns whose mean has been assessed as 5.5 with a standard deviation of 2.1. On the other hand, you could invest in Avago Co., whose shares enjoy an expected long-term return of 12.5 but with a larger standard deviation of 7.5. The correlation between the returns of the two investments is 0.098.

1. What does the positive correlation imply in the words?
2. Calculate the mean and standard deviation of the return on a portfolio that has 50% of your money invested in each company.
3. Calculate the mean and standard deviation of the return on a portfolio that has 95% of your money invested in Solid. Pty. Ltd. Do you notice anything about this portfolio compared to a 100% investment in Solid Pty. Ltd?

Answer 1

(a) positive correlation imply if there is increase in  return on solid Pty. Ltd there will be increase in return in Avago Co and vice versa

(b) mean=9 and standard deviation=3.99 of the return of  portfolio

let S=solid Pty Ltd , A=Avago Co. and P=portfolio

P=0.5S+0.5A

mean(P)=0,5*mean(S)+0.5*mean(A)=0.5*5.5+0.5*12.5=9

var(P)=var(0.5S+0.5A)=0.5*0.5var(S)+0.5*0.5var(A)+2*0.5*0.5*cov(S and A)=

=0.25*2.1*2.1+0.25*7.5*7.5+2*0.5*0.5*0.098*2.1*7.5=15.94

and standard deviation of P = sqrt(15.94)=3.99

(c)

P=0.95S+0.05A

mean=0.95*5.5+0.05*12.5=5.85

var(P)=var(0.95S+0.05A)=0.95*0.95var(S)+0.05*0.05var(A)+2*0.95*0.05*cov(S and A)=

=0.95*0.95*2.1*2.1+0.05*0.05*7.5*7.5+2*0.95*0.05*0.098*2.1*7.5=4,27

Standard deviation=sqrt(4,27)=2.07

there is more return as compared to 100 invest in solid Pty ltd