Suppose 3 risky assets whose random rates of return are governed by r1 = 8 + 2f1 + 3f2 r2 = 5 + f1 + 2f2 r3 = 26 + 6f1 +

[answerhappygod]

Suppose 3 risky assets whose random rates of return are governed
by
r1 = 8 + 2f1 +
3f2
r2 = 5 + f1 +
2f2
r3 = 26 + 6f1 + 10f2
where f1 and f2 are risk factors observing
E[f1]=E[f2]=0
a) We want to form a riskfree portfolio of these 3 risky assets,
whose weightings are w1, w2, w3.
Explain why the solution of the following 3 equations gives the
required riskfree portfolio.
w1 + w2 + w3 =
1
2w1 + w2 +
6w3 = 0
3w1 + 2w2 + 10w3 =
0
B)
The solution of the above system of equations is solved to
be w1= w2 =2/3
and w3 = -1/3.
Suppose the expected rates of return of the 3 assets are given
by
μ1= λ0+ 2λ1 +
3λ2
μ2 = λ0 + λ1 +
3λ2
μ3 = λ0 +
6λ1 + 10λ2
Under no arbitrage assumption, solve
for λ0, λ1 and λ2.
Give the financial interpretation of the factor risk
premiums: λ1 and λ2.
C) If the risk-free rate is 1%, identify whether there is
any arbitrage opportunities.
If yes, what is the arbitrage strategy?
If no, explain why.