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

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Suppose 3 Risky Assets Whose Random Rates Of Return Are Governed By R 8 2f 3f R 5 F 2f R3 26 6f 1 (41.15 KiB) Viewed 31 times

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 [2 marks] 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 μη= λο+ 2λη + 32 με = λο + λη + 32 μ3 = λο + 6λι + 1012 Under no arbitrage assumption, solve for A0, A₁ and A₂. Give the financial interpretation of the factor risk premiums: ₁ and ₂. [4 marks] 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. [2 marks] d) If the above assets do not follow the model perfectly, i.e., there are non zero residual risks. Can you construct an arbitrage portfolio? If yes, how? If no, why? [2 marks]