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

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