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Homework answers / question archive / Compute the expected return and the beta () of the following portfolio: Security Number of shares Price per share Asset B Expected in portfolio coefficient on security 100 $20 1
Compute the expected return and the beta () of the following portfolio: Security Number of shares Price per share Asset B Expected in portfolio coefficient on security 100 $20 1.0 5% 200 10 1.2 10% A B 1 11. In problem 10 above, assume that the standard deviation of security A's return is 2% and that the standard deviation of security B's return is 7%. The correlation coefficient between A and B is -0.5. a) (5 pts) What is the standard deviation of the expected return on the portfolio, given the portfolio's asset allocation in problem 10? b) (5 pts) What would happen to the required return of the portfolio as each asset's beta coefficient increases? Explain.
a
Value of stock A = number of shares *price per share
=100*20 = 2000
Value of stock B = number of shares *price per share
=200*10 = 2000
total portfolio value = 2000+2000=4000
weight of A in total portfolio (wA) = value of stock A/total portfolio value
=2000/4000 = 0.50
weight of B in total portfolio (wB) = value of stock A/total portfolio value
=2000/4000 = 0.50
standard deviation of A ( σA)=2%
standard deviation of B( σB)=7%
correlation between A and B (rAB)=-0.5
Standard deviation formula (σp) =√ ( (wA * σA ) ^2 + (wB * σB ) ^2 + (2 * wA* wB*σA *σB* rAB )
√((0.5*2%)^2 + (0.5*7%) ^2+ (2*0.5*0.5*2%*7%*-0.5))
=0.03122498999 or 3.12%
Standard deviation of portfolio is 3.12%
b
If each stock's coefficient beta increases, then required return of each stock will increases. When each stock required return increases, required return of portfolio will also increase.
So portfolio requried return will increase, if beta of both stocks increases