Question

Suppose the expected returns and standards deviations of two stocks were

stock A: E (R) =9%, STANDARD DEVIATION = 36%

STOCK B: E (R) = 15%, STANDARD DEVIATION = 62%

A. calculate the expected return of a portfolio that is composed of 35% of stock A and 65% of stock B.

b. calculate the standard deviation of this portfolio when the correlation coefficient between the returns is 0.5

c. calculate the standard deviation of this portfolio (same weights in each stock) when the correlation coefficient is now -0.5

d. how does changes in the correlation between the returns on A and B affect the standard deviation of the portfolio

refer table below and answer the questions that follow

Economic state Probability of economic state return on stock j return on stock k

Beer 0.25 -0.02 0.034

normal 0.60 0.138 0.062

bull 0.15 0.218 0.092

a. calculate the expected return of each stock

b. if the portfolio was created with from 30% of stock j and 70% of stock k what is the expected return of the portfolio

c. calculate the standard deviation of each stock

d. calculate the covariance between the two stocks

e, calculate the correlation coefficient between the two stocks

f, what is the portfolio standard deviation

Answer 1

A
a.Expected Return of Portfolio =Weight of Portfolio A*Expected Return of A+Weight of Portfolio B*Expected Return of B
=35%*9%+65%*15% =12.9%

b. Standard Deviation = ((Weight of A * Standard Deviation of A)² + (Weight of B * standard Deviation of B)² + 2* Weight of A * Standard Deviation of A * weight of B * standard Deviation of B * correlation)^0.5
=((35%*36%)^2+(65%*62%)^2+2*35%*65%*36%*62%*0.5)^0.5 =47.86%

c. Standard Deviation = ((Weight of A * Standard Deviation of A)² + (Weight of B * standard Deviation of B)² + 2* Weight of A * Standard Deviation of A * weight of B * standard Deviation of B * correlation)^0.5
=((35%*36%)^2+(65%*62%)^2-2*35%*65%*36%*62%*0.5)^0.5 =35.71%

d. Lower the correlation rate lower is the standard deviation and higher the correlation higher is the standard deviation.


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