Question

   Stock A   Stock B
1   0.09   0.07
2   0.06   0.03
3   0.13   0.04
4   -0.03   0.02
5   0.08   -0.04

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 62​% stock A and 38​% stock​ B?

Answer 1

Answer:

A) Expected return =$\sum_{I=1}^{5} Xi/5$

Xi=rate of return for period I

So For Stock A expected return r1 =(0.09+0.06+0.13-0.03+0.08)/5=0.066

So For Stock B expected return r2=(0.07+0.03+0.04+0.02-0.04)/5=0.024

B)

Standard Deviation = $\sqrt{\sum_{I=1}^{5} (Xi-X)^2/5}$

Standard deviation for stock A SD1=0.0594

Standard deviation for stock B SD2=0.0403

C)

Correlation q=0.43

Weightage of stock A w1=62%

Weightage of stock B w2=38%

Portfolio expected return = w1*r1+w2*r2=62%*0.066+38%*0.024=0.05004=5.004%

Standard deviation of portfolio= $\sqrt{w1^2*SD1^2+w2^2*SD2^2+2*w1*w2*SD1*SD2*q}$

Standard deviation of portfolio=$\sqrt{0.62^2*0.0594^2+0.38^2*0.0403^2+2*0.62*0.38*0.0594*0.0403*0.43}$

Standard deviation of portfolio==4.56%