Question

Stocks A and B have the following​ returns:  ​(Click on the following icon

  

in order to copy its contents into a​ spreadsheet.)

	Stock A	Stock B
1	0.09	0.07
2	0.06	0.02
3	0.13	0.04
4	−0.05	0.02
5	0.08	−0.01

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

0.47​,

what is the expected return and standard deviation of a portfolio of

55​%

stock A and

45​%

stock​ B?

Answer 1

a. Expected Returns of the Stock A =(0.09+0.06+0.13-0.05+0.08)/5 =6.20%
Expected Returns of the Stock B =(0.07+0.02+0.04+0.02-0.01)/5 =2.80%

b. Standard Deviation of Stock A
=(((0.09-6.20%)^2+(0.06-6.20%)^2+(0.13-6.20%)^2+(-0.05-6.20%)^2+(0.08-6.20%)^2)/(5-1))^0.5 =6.760178% or 6.76%

Standard Deviation of Stock B
=(((0.07-2.80%)^2+(0.02-2.80%)^2+(0.04-2.80%)^2+(0.02-2.80%)^2+(-0.01-2.80%)^2)/(5-1))^0.5 =2.949576% or 2.95%

c. Expected return =Weight of Stock A*Return of Stock A+Weight of Stock B*Return of Stock B =55%*6.20%+45%*2.80%
=4.67%
Standard Deviation of Portfolio =((Weight of Stock A*Standard Deviation of Stock A)^2+(Weight of Stock B*Standard Deviation of Stock B)^2+2*Weight of Stock A*Standard Deviation of Stock A*Weight of Stock B*Standard Deviation of Stock B*Correlation)^0.5 =((55%*6.760178%)^2+(45%*2.949576%)^2+2*55%*45%*6.760178%*2.949576%*0.47)^0.5 =4.50%
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