Question

Stocks X and Y have the following probability distributions of expected future returns:

Probability	Stock X	Stock Y
0.15	-5%	-8%
0.35	7%	10%
0.30	15%	18%
0.20	10%	25%
Expected return
Standard deviation	6.42%
Correlation between Stock X and Stock Y	0.8996

i. Calculate the expected return for each stock.

ii. Calculate the standard deviation of returns for Stock Y.

iii. You have $2,000. You decide to put $500 of your money in Stock X and the rest in Stock Y. Calculate the expected return of your portfolio.

iv. Calculate the standard deviation of your portfolio based on the weight of Stocks X and Y stated in part (iii).

Please Show workings.

Answer 1

1.
Expected returns=Sum(probability*returns)

X=0.15*(-5%)+0.35*7%+0.30*15%+0.20*10%=8.2000%

Y=0.15*(-8%)+0.35*10%+0.30*18%+0.20*25%=12.7000%

2.
Standard deviation=Sqrt(Sum(probability*(returns-expected returns)^2))

=sqrt(0.15*(-8%-12.7%)^2+0.35*(10%-12.7%)^2+0.30*(18%-12.7%)^2+0.20*(25%-12.7%)^2)
=10.2718%

3.
Expected return=w1*r1+w2*r2=(500/2000)*8.2%+(1500/2000)*12.7%=11.5750%

4.
Standard deviation=sqrt((w1*s1)^2+(w2*s2)^2+2*w1*s1*w2*s2*correlation)=sqrt((500/2000*6.42%)^2+(1500/2000*10.2718%)^2+2*(500/2000)*(1500/2000)*6.42%*10.2718%*0.8996)=9.1745%

where
w1 is weight of asset 1
w2 is weight of asset2
r1 is return os asset 1
r2 is return of asset 2
s1 is standard deviation of asset 1
s2 is standard deviation of asset 2
correlation is correlation between asset 1 and asset 2