Ross5eChap12sm - Chapter 12 An Alternative View of Risk and...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 12: An Alternative View of Risk and Return: The Arbitrage Pricing Theory 1. Since we have the expected return of the stock, the revised expected return can be determined using the innovation, or surprise, in the risk factors. So, the revised expected return is: R = 11% + 1.2(4.2% – 3%) – 0.8(4.6% – 4.5%) R = 12.36% 2. a. If m is the systematic risk portion of return, then: m = β GNP ΔGNP + β Inflation ΔInflation + β r ΔInterest rates m = .000586($5,436 – 5,396) – 1.40(3.80% – 3.10%) – .67(10.30% – 9.50%) m = 0.83% b. The unsystematic return is the return that occurs because of a firm specific factor such as the bad news about the company. So, the unsystematic return of the stock is –2.6 percent. The total return is the expected return, plus the two components of unexpected return: the systematic risk portion of return and the unsystematic portion. So, the total return of the stock is: ε + + = m R R R = 9.50% + 0.83% – 2.6% R = 7.73% 3. a. If m is the systematic risk portion of return, then: m = β GNP ΔGNP + β r ΔInterest rates m = 2.04(4.8% – 3.5%) – 1.90(7.80% – 7.10%) m = 1.32% b. The unsystematic is the return that occurs because of a firm specific factor such as the increase in market share. If ε is the unsystematic risk portion of the return, then: ε = 0.36(27% – 23%) ε = 1.44% c. The total return is the expected return, plus the two components of unexpected return: the systematic risk portion of return and the unsystematic portion. So, the total return of the stock is: ε + + = m R R R = 10.50% + 1.32% + 1.44% R = 13.26% 4. The beta for a particular risk factor in a portfolio is the weighted average of the betas of the assets. This is true whether the betas are from a single factor model or a multi–factor model. So, the betas of the portfolio are: F 1 = .20(1.20) + .20(0.80) + .60(0.95) Answers to End–of–Chapter Problems B–175
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
F 1 = 0.97 F 2 = .20(0.90) + .20(1.40) + .60(–0.05) F 2 = 0.43 F 3 = .20(0.20) + .20(–0.30) + .60(1.50) F 3 = 0.88 So, the expression for the return of the portfolio is: R i = 5% + 0.97 F 1 + 0.43 F 2 + 0.88 F 3 Which means the return of the portfolio is: R i = 5% + 0.97(5.50%) + 0.43(4.20%) + 0.88(4.90%) R i = 16.45% 5. We can express the multifactor model for each portfolio as: E(R P ) = R F + β 1 F 1 + β 2 F 2 where F 1 and F 2 are the respective risk premiums for each factor. Expressing the return equation for each portfolio, we get: 18% = 6% + 0.75F 1 + 1.2F 2 14% = 6% + 1.60 F 1 – 0.2 F 2 We can solve the system of two equations with two unknowns. Multiplying each equation by the respective F 2 factor for the other equation, we get: 3.6% = 1.2% + .15 F 1 + 0.24 F 2 16.8% = 7.2% + 1.92 F 1 – 0.24 F 2 Summing the equations and solving F1 fr gives us: 20.40% = 8.40% + 2.07 F 1 F 1 = 5.80% And now, using the equation for portfolio A, we can solve for F 2 , which is: 18% = 6% + 0.75(5.80%) + 1.2F 2 F 2 = 6.38% 6. a. The market model is specified by: ε β + - + = ) ( M M R R R R so applying that to each Stock: Stock A: Answers to End–of–Chapter Problems B–176
Image of page 2
A M M A A A R R R R ε β + - + = ) ( R A = 10.5% + 1.2(R M – 14.2%) + ε A Stock B: B M M B B B R R R R ε β + - + = ) ( R B = 13.0% + 0.98(R M – 14.2%) + ε B Stock C: C M M C C C R R R R ε β + - + = ) ( R C = 15.7% + 1.37(R M – 14.2%) + ε C b. Since we don't have the actual market return or unsystematic risk, we will get aformula with those values as unknowns: R P = .30R A + .45R B + .30R C R P = .30[10.5% + 1.2(R M – 14.2%) + ε A ] + .45[13.0% + 0.98(R M – 14.2%) + ε B ] + .25[15.7% + 1.37(R M – 14.2%) + ε C R P = .30(10.5%) + .45(13%) + .25(15.7%) + [.30(1.2) + .45(.98) + .25(1.37)] (R M – 14.2%)+ .30 ε A + .45 ε
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern