Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

6. Using the factor portfolios of Example 7.8(see below), find the fair rate of return on a security with 1=.2 and 2=1.4. EXAMPLE 7.8 Multifactor

image text in transcribed

6. Using the factor portfolios of Example 7.8(see below), find the fair rate of return on a security with 1=.2 and 2=1.4. EXAMPLE 7.8 Multifactor SML Suppose the two factor portfolios, here called portfolios 1 and 2, have expected returns E(r1)=10% and E(r2)=12%. Suppose further that the risk-free rate is 4%. The risk premium on the first factor portfolio is therefore 6%, while that on the second factor portfolio is 8%. Now consider an arbitrary well-diversified portfolio (P), with beta on the first factor, P1=.5, and on the second factor, P2=.75. Like the multifactor CAPM, the multifactor APT states that the portfolio risk premium must equal the sum of the risk premiums required as compensation for each source of systematic risk. The risk premium attributable to risk factor 1 is the portfolio's exposure to factor 1,P1, times the risk premium earned on the first factor portfolio, E(r1) - rf. Therefore, the portion of portfolio P s risk premium that is compensation for its exposure to the first risk factor is P1[E(r1)rf]=.5(10%4%)=3%, while the risk premium attributable to risk factor 2 is P2[E(r2)rf]=.75(12%4%)=6%. The total risk premium on the portfolio, therefore, should be 3+6=9%, and the total return on the portfolio should be 13%. 6. Using the factor portfolios of Example 7.8(see below), find the fair rate of return on a security with 1=.2 and 2=1.4. EXAMPLE 7.8 Multifactor SML Suppose the two factor portfolios, here called portfolios 1 and 2, have expected returns E(r1)=10% and E(r2)=12%. Suppose further that the risk-free rate is 4%. The risk premium on the first factor portfolio is therefore 6%, while that on the second factor portfolio is 8%. Now consider an arbitrary well-diversified portfolio (P), with beta on the first factor, P1=.5, and on the second factor, P2=.75. Like the multifactor CAPM, the multifactor APT states that the portfolio risk premium must equal the sum of the risk premiums required as compensation for each source of systematic risk. The risk premium attributable to risk factor 1 is the portfolio's exposure to factor 1,P1, times the risk premium earned on the first factor portfolio, E(r1) - rf. Therefore, the portion of portfolio P s risk premium that is compensation for its exposure to the first risk factor is P1[E(r1)rf]=.5(10%4%)=3%, while the risk premium attributable to risk factor 2 is P2[E(r2)rf]=.75(12%4%)=6%. The total risk premium on the portfolio, therefore, should be 3+6=9%, and the total return on the portfolio should be 13%

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Multinational Finance

Authors: Kirt C. Butler

4th Edition

1405181184, 978-1405181181

More Books

Students also viewed these Finance questions

Question

What are blogs? How are they used? Who is using them?

Answered: 1 week ago