financial risk management question

Q1:
a. You manage a risky portfolio with an expected rate of return of 18% and a standard deviation
of 28%. The T-bill rate is 8%.
Your client chooses to invest 70% of a portfolio in your fund and 30% in T-bill money market
fund. What is the expected value and standard deviation of the rate of return on his portfolio?
Solution:
Expected return = .3 * 8% + .7 * 18% = 15% per year.
Standard deviation = .7 * 28% = 19.6% per year
The correlation between risk-free assets and portfolio is zero!
b. Estimate the risk and return of a portfolio with 60% of wealth in share A and 40% in share B,
given the following:

E(Ri) SD(Ri)
Share A 0.20 0.60
Share B 0.15 0.50
COVAB 0.20


Solution:
E(Rp )= w1 E(r1 ) w2 E(r2 )
E(Rp) = 0.6(0.2) + (0.4)(0.15) = 18%
n n n
 =  w  +  wi w j Cov( ri , rj ), j  i
2
p
2
i i
2

i =1 i =1 j =1
Var(p) = (0.6) (0.6)2 + (0.4)2(0.5)2 + 2(0.6)(0.4)(0.2)
2


= 0.2656
SD(p) = 51.53%


Q2: The expected return on the market is 15%, the risk-free rate is 5%, what the is required
return of stock A with beta 1.2? using CAPM model
Solution:
𝐸(𝑅𝐴 ) = 5% + 1.2 ∗ (15% − 5%) = 17%