Royal Melbourne Institute of Technology

BAFI 1045

Topic 4

Use the following information for the next question(s):

1. 1. 1. 1. Capital markets are perfectly competitive
         2. Quadratic utility function
         3. Investors prefer more wealth to less wealth with certainty
         4. Normally distributed security returns
         5. Representative as a K factor model
         6. A market portfolio that is mean-variance efficient
1. Refer to Exhibit 9-1. In the list above which are assumptions of the Arbitrage Pricing model?
2. Refer to exhibit 9-1. Which are not assumptions of the Arbitrage Pricing model?

3. To date, the results of empirical tests of the Arbitrage Pricing Model have been
4. Unlike the capital asset pricing model, the arbitrage pricing theory requires only the following assumption(s):

5. Consider the following two factor APT model E(R)= X0+X1b1+X2b2

6. In the APT model the idea of riskless arbitrage is to assemble a portfolio that
7. In one of their empirical tests of the APT, Roll and Ross examined the relationship between a security’s returns and its own standard deviation. A finding of a statistically significant relationship would indicate that
8. Cho, Elton and Gruber tested the APT by examining the number of factors in the return generating process and found that

9. Dhrymes, Friend, and Gultekin, in their study of the APT found that

10. Assume that you are embarking on a test of the small-firm effect using APT. You form 10 size- based portfolios. The following finding would suggest there is evidence supporting APT

11. The equation for the single-index market model is

12. The excess return form of the single-index market model is

13. Consider the following list of risk factors:

1. Monthly growth in industrial production
2. Return on high book to market value portfolio minus return on low book to market value portfolio
3. Change in inflation
4. Excess return on stock market portfolio
5. Return on small cap portfolio minus return on big cap portfolio
6. Unanticipated change in bond credit spread

Which of the following factors would you use to develop a macroeconomic-based risk factor model?

14. Consider the following list of risk factors:

7. Monthly growth in industrial production

8. Return on high book to market value portfolio minus return on low book to market value portfolio
9. Change in inflation
10. Excess return on stock market portfolio
11. Return on small cap portfolio minus return on big cap portfolio
12. Unanticipated change in bond credit spread

Which of the following factors would you use to develop a microeconomic-based risk factor model?

15.   In a macro-economic based risk factor model, the following factor would be one of many appropriate factors.

16. In a multifactor model, confidence risk represents

17. In a multifactor model, time horizon risk represents

18. In a micro-economic( or characteristic) based risk factor model the following factor would be one of many appropriate factors:

19. A Study by Chen, Roll and Ross in 1986 examined all of the following factors in applying the Arbitrage Pricing Model (APT) except the

20. Which of the following is not a step required for a multifactor risk model to estimate expected return for an individual stock position?

21. A 1994 study by Burmeister, Roll, and Ross defined all of the following risk factors except
22. Under the following conditions, what are the expected returns for stocks X and Y?

X0=0.04, k1=0.035, k2= 0.045

Bx,1= 1,2 bx,2=0.75 by,1=0.65                                                                       by,2=1.45 Rx=0.04+(1.2)(0.035)+(0.75)(0.045)=11.58%

Ry=0.04+(0.65)(0.035)+(1.45)(0.045)= 12.8%

23. Under the following conditions, what are the expected returns for stocks Y and Z ?

X0=0.05 k1=0.06       k2=0.05

By,1=0.75 by,2=1.35 bz,1=1.5 bz,2=0.85

24. Under the following conditions, what are the expected returns for stocks A and B?

X0=0.035 k1=0.05 k2=0.06

ba,1 =1     ba,2=1.40 bb,1=1.70 bb,2=0.65

25. Under the following conditions, what are the expected returns for stocks X and Y?

X0=0.05 k1=0.03 k2=0.04

bx,1=0.90 bx,2=1.60 by,1=1.50 by,2=0.85

26. Under the following conditions, what are the expected returns for stocks A and C?

X0=0.07 k1=0.04 k2=0.03

ba,1=0.95 ba,2=1.10 bc,1=1.10 bc,2=2.35

27. Consider a two-factor APT model where the first factor is changes in the 30-year T-bond rate, and the second factor is the percent growth in GNP. Based on historical estimates you determine that the risk premium for the interest rate factor is 0.02, and the risk premium on the GNP factor is

0.03. For a particular asset, the response coefficient for the interest rate factor is -1.2, and the response coefficient for the GNP factor is 0.80. The rate of return on the zero-beta asset is 0.03. Calculate the expected return for the asset.

Use the following information for the next problems

Consider the three stocks, stock X, stock Y and Stock Z, that have the following factor loadings ( or factor betas)

THe zero-beta return (X0)=3% and the risk premia are X1=10% and X2=8% Assume that all three stocks are currently priced at $50

28. Refer to Exhibit 9-2. The expected returns for stock X, Y and Z are E(Rx)=0.03+(-.55)(.1)+(1.2)(.08)=.071=7.1%

29. Refer to Exhibit 9-2, the expected prices one year from now for stocks X, Y, Z are E( price stock X)= 50(1+0.071)=$53.55

30. Refer to Exhibit 9-2. If you know that the actual prices one year from now are stock X$55, stock Y 52, and stock Z $57, then

31. Refer to Exhibit 9-2. Assume that you wish to create a portfolio with no net wealth invested. The portfolio that achieves this has 50% in stock X, -100% in stock Y, and 50% in stock Z. The weighted exposure to risk factor 1 for stocks X, Y, and Z are

32. Refer to Exhibit 9-2. Assume that you wish to create a portfolio with no net wealth invested. The portfolio that achieves this has 50% in stock X, -100% in stock Y, and 50% in stock Z. The weighted exposure to risk factor 2 for stocks X, Y, and Z are

33. Refer to Exhibit 9-2. Assume that you wish to create a portfolio with no net wealth invested. The portfolio that achieves this has 50% in stock X, -100% in stock Y, and 50% in stock Z. The net arbitrage profit is

34. Refer to Exhibit 9-2. The new prices now for stocks X, Y, and Z that will not allow for arbitrage profits are

35. The table below provides factor risk sensitivities and factor risk premia for a three model for a particular asset where factor 1 is MP the growth rate in U.S industrial production, factor 2 is UI the difference between actual and expected inflation, and factor 3 is UPR the unanticipated change in bond credit spread.

Calculate the expected excess return for the asset.

Exhibit 9-3

USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)

Stock A, B, and C have two risk factors with the following beta coefficient. The zero-beta return (X0)

=0.25 and the risk premium for the two factors are (X1) = .12 and (X0) = .10.

36. Refer to Exhibit 9-3. Calculate the expected returns for stocks A, B, C.