2. In a market in which the Arbitrage Pricing Theory (APT) model holds, the expected return is given by E[R;] = 20 + ßi,1λ₁ + ßi,2λ2+, ..., +ßi,nλn a) Assume that risk-free rate in this economy is 0.02. Consider a two-factor model, n = 2 and two well diversified portfolios P₁ and P2 with the following features: P1 P2 Expected returns: E(R₁) 0.18 0.05 Sensitivity to factor 1: ẞi,1 0.2 0.1 Sensitivity to factor 2: ẞi,2 0.7 0.3 Find the risk premiums for each factor. = b) Assume there is another well diversified security P3 in this economy with factor sensitivities, ẞ3,1 = 0.2, and ẞ3,2 = 0.7. The expected return of this security is E(R3) = 0.25. State whether the APT is satisfied. If yes, explain why, if not propose an arbitrage strategy.
2. In a market in which the Arbitrage Pricing Theory (APT) model holds, the expected return is given by E[R;] = 20 + ßi,1λ₁ + ßi,2λ2+, ..., +ßi,nλn a) Assume that risk-free rate in this economy is 0.02. Consider a two-factor model, n = 2 and two well diversified portfolios P₁ and P2 with the following features: P1 P2 Expected returns: E(R₁) 0.18 0.05 Sensitivity to factor 1: ẞi,1 0.2 0.1 Sensitivity to factor 2: ẞi,2 0.7 0.3 Find the risk premiums for each factor. = b) Assume there is another well diversified security P3 in this economy with factor sensitivities, ẞ3,1 = 0.2, and ẞ3,2 = 0.7. The expected return of this security is E(R3) = 0.25. State whether the APT is satisfied. If yes, explain why, if not propose an arbitrage strategy.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![2. In a market in which the Arbitrage Pricing Theory (APT) model holds, the expected
return is given by
E[R;] = 20 + ßi,1λ₁ + ßi,2λ2+, ..., +ßi,nλn
a) Assume that risk-free rate in this economy is 0.02. Consider a two-factor model, n = 2
and two well diversified portfolios P₁ and P2 with the following features:
P1
P2
Expected returns: E(R₁)
0.18
0.05
Sensitivity to factor 1: ẞi,1
0.2
0.1
Sensitivity to factor 2: ẞi,2
0.7
0.3
Find the risk premiums for each factor.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08f364a7-58c9-40cd-a04d-83636aa816ab%2Faa662865-5a6f-42e5-97b7-33a810c330bb%2Fcj54h2_processed.png&w=3840&q=75)
Transcribed Image Text:2. In a market in which the Arbitrage Pricing Theory (APT) model holds, the expected
return is given by
E[R;] = 20 + ßi,1λ₁ + ßi,2λ2+, ..., +ßi,nλn
a) Assume that risk-free rate in this economy is 0.02. Consider a two-factor model, n = 2
and two well diversified portfolios P₁ and P2 with the following features:
P1
P2
Expected returns: E(R₁)
0.18
0.05
Sensitivity to factor 1: ẞi,1
0.2
0.1
Sensitivity to factor 2: ẞi,2
0.7
0.3
Find the risk premiums for each factor.
Transcribed Image Text:=
b) Assume there is another well diversified security P3 in this economy with factor
sensitivities, ẞ3,1 = 0.2, and ẞ3,2 = 0.7. The expected return of this security is E(R3) =
0.25. State whether the APT is satisfied. If yes, explain why, if not propose an arbitrage
strategy.
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