Question

Stock A and B have the following returns:

	Stock A	Stock B
1	0.11	0.07
2	0.04	0.02
3	0.15	0.05
4	-0.04	0.03
5	0.08	-0.03

a. What are the expected returns of the two​ stocks?

b. What are the standard deviations of the returns of the two​ stocks?

c. If their correlation is 0.43, what is the expected return and standard deviation of a portfolio of 77% Stock A and 23% Stock B?

Answer 1

a. Expected Return of Stock A =(0.11+0.04+0.15-0.04+0.08)/5 =6.80%
Expected Return of Stock B =(0.07+0.02+0.05-0.03-0.03)/5 =2.80%

Standard Deviation of Stock A =((0.11-6.80%)^2+(0.04-6.80%)^2+(0.15-6.80%)^2+(-0.04-6.80%)^2+(0.08-6.80%)^2)/(5-1))^0.5=7.26%
Standard Deviation of Stock B =((0.07-2.80%)^2+(0.022.80%)^2+(0.052.80%)^2-(0.032.80%)^2+(-0.032.80%)^2)/(5-1))^0.5=3.77%

c. Standard Deviation =((Weight of Stock A*Standard Deviation of A)^2+(Weight of Stock A*Standard Deviation of B)^2+2*Weight of Stock A* Standard Deviation of A*Weight of B * Standard Deviation of B*correlation)^0.5 =
((77%*7.26%)^2+(23%*3.77%)^2+2*77%*23%*7.26%*3.77%*0.43)^0.5 =6.01%