P1.T1. Foundations of Risk Bionic Turtle FRM Practice Questions Zvi Bodie, Alex Kane, and Alan J. Marcus, Investments, 10th Edition By David Harper, CFA FRM CIPM www.bionicturtle.com
Bodie, Chapter 10: Arbitrage Pricing Theory and Multifactor Models of Risk and Return Summary from Bodie s Chapter 10... 3 This document contains three types of questions: The core, updated practice question sets: T1.704-705 and T1.400-402. As usual, this syntax indicates 100% original questions written and maintained by Bionic Turtle. The four hundred series (T1.400 402) questions were written/published in 2014, while the T1.704 and T1.705 were written/published in 2017. Every year we updated the base number. In this way, you know how old questions are. For example, question TX.517 was published in 2015, question TX.625 was published in 2016. End of Chapter Questions & Answers: these are the textbook s own end of chapter questions (and answers). We did not write these. We include them for those who want additional practice. The Appendix contains our own (Bionic Turtle s) practice questions. They were written for this topic (Arbitrage Pricing Theory) but they were written against a previous (or old) assigned reading. In most cases, they do remain relevant. But of course, these are not necessary for you. They are also provided in case they are helpful to those who want to spend additional time on the topic. 2
Summary from Bodie s Chapter 10 1. Multifactor models seek to improve the explanatory power of single-factor models by explicitly accounting for the various systematic components of security risk. These models use indicators intended to capture a wide range of macroeconomic risk factors. 2. Once we allow for multiple risk factors, we conclude that the security market line also ought to be multidimensional, with exposure to each risk factor contributing to the total risk premium of the security. 3. A (risk-free) arbitrage opportunity arises when two or more security prices enable investors to construct a zero-net-investment portfolio that will yield a sure profit. The presence of arbitrage opportunities will generate a large volume of trades that puts pressure on security prices. This pressure will continue until prices reach levels that preclude such arbitrage. 4. When securities are priced so that there are no risk-free arbitrage opportunities, we say that they satisfy the no-arbitrage condition. Price relationships that satisfy the noarbitrage condition are important because we expect them to hold in real-world markets. 5. Portfolios are called well-diversified if they include a large number of securities and the investment proportion in each is sufficiently small. The proportion of a security in a welldiversified portfolio is small enough so that for all practical purposes a reasonable change in that security s rate of return will have a negligible effect on the portfolio s rate of return. 6. In a single-factor security market, all well-diversified portfolios have to satisfy the expected return beta relationship of the CAPM to satisfy the no-arbitrage condition. If all well-diversified portfolios satisfy the expected return beta relationship, then individual securities also must satisfy this relationship, at least approximately. 7. The APT does not require the restrictive assumptions of the CAPM and its (unobservable) market portfolio. The price of this generality is that the APT does not guarantee this relationship for all securities at all times. 8. A multifactor APT generalizes the single-factor model to accommodate several sources of systematic risk. The multidimensional security market line predicts that exposure to each risk factor contributes to the security s total risk premium by an amount equal to the factor beta times the risk premium of the factor portfolio that tracks that source of risk. 9. A multifactor extension of the single-factor CAPM, the ICAPM, is a model of the risk return trade-off that predicts the same multidimensional security market line as the APT. The ICAPM suggests that priced risk factors will be those sources of risk that lead to significant hedging demand by a substantial fraction of investors. 3
Bodie, Chapter 10: Arbitrage Pricing Theory and Multifactor Models of Risk and Return P1.T1.704. Bodie's multifactor models P1.T1.705. Fama-French three factor model (Bodie's multifactor models continued) P1.T1.400 Arbitrage pricing theory (APT) introduction P1.T1.401. Arbitrage pricing theory (APT) for well-diversified portfolios P1.T1.402. ABT and Fama-French three-factor model P1.T1.704. Bodie's multifactor models Learning objectives: Describe the inputs, including factor betas, to a multifactor model. Calculate the expected return of an asset using a single-factor and a multifactor model. 704.1. Suppose that three factors have been identified for the U.S. economy: Expected inflation rate (IR) is +2.00% Expected 10-year Treasury yield (T-NOTE) is 2.40% Expected growth in productivity (PROD) is +3.00% A stock with an expected return of 9.0% has the following betas with respect to these factors: β(ir) = +1.50, β(t-note) = -1.20 and β(prod) = 0.70. In turns out that that economy's actual factor performance is the given by the following set of results: Actual inflation rate (IR) is + 2.60% Actual 10-year Treasury yield (T-NOTE) is 3.00% Actual growth in productivity (PROD) +2.00% What is the revised estimate of the stock's expected rate of return (note: this is a variation on Bodie's Problem 10.1)? a) 8.480% b) 9.000% c) 9.250% d) 10.375% 4
704.2. Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 1.0%, and all stocks have independent firm-specific components with a standard deviation of 25%. The following are well-diversified portfolios; e.g., Portfolio (A) has a beta sensitivity to factor the first factor, β(f1), of 1.20 and an expected return of 13.0%: Which is the correct return-beta relationship in this economy? a) E[R(P)] = 1.0% - β(f1)*6.0% - β(f2)*4.0% b) E[R(P)] = 1.0% - β(f1)*5.0% + β(f2)*2.0% c) E[R(P)] = 1.0% + β(f1)*9.0% + β(f2)*3.0% d) E[R(P)] = 1.0% + β(f1)*12.0% + β(f2)*8.0% 704.3. Your colleague Richard has designed the first draft of an explicit multifactor model for your review. You immediately make the following four observations about his model. According to Bodie, which of the following observations probably should raise a red flag; i.e., which observation by itself is the MOST LIKELY to indicate that Peter may have developed an inferior multifactor model? a) One of the model's factor risk premium is negative b) The model contains Fama-French type size and value factors which are obviously firmspecific but not macroeconomic c) Few, if any, investors seek to hedge the model's systematic risk factors or realistically even care about the associated uncertainties d) The model contains fewer than ten systematic factors in attempting to explain excess returns in a complex economy and these factors are correlated with major sources of uncertainty 5
Answers 704.1. A. 8.480%. Revised estimate = 9.0% + [1.5 * (2.6% - 2.0%)] + [-1.20 * (3.0% - 2.4%)] [0.70 * (2.0% - 3.0%)] = 8.480% 704.2. D. E[R(P)] = 1.0% + β(f1)*12.0% + β(f2)*8.0%. We need to solve for two equations with two unknowns: 0.13 = 0.01 + 1.20*RP(1) - 0.30*RP(2) 0.05 = 0.01 + 0.60*RP(1) - 0.40*RP(2) One way is to double the second equation and subtract it from the first in order to eliminate RP(1): 0.13 = 0.01 + 1.20*RP(1) - 0.30*RP(2) - 2*[0.05 = 0.01 + 0.60*RP(1) - 0.40*RP(2)] = 0.03 = -0.01 + 0.5*RP(2) --> RP(2) = 0.04/0.5 = 0.08. 704.3. C. This is the only red flag in the list: few, if any, investors seek to hedge the model's risk factors or realistically care about the associated uncertainties Bodie says that good factors should correlate with major sources of uncertainty and, ideally, should related to investment and consumption opportunities in the economy. Further, they should be invest-able and at least some fraction of investors should want to hedge them as sources of risk. In regard to (A), (B) and (D), none are problematic observations. In regard to (A), unlike the single-factor CAPM, a multifactor CAPM or APT can contain negative risk premiums In regard to (B), Bodie explains that while the Fama-French factors "are not themselves obvious candidates for relevant risk factors, the argument is that these variables may proxy for yet-unknown more-fundamental variables. " In regard to (D), Bodie says that in order to be USEFUL a good mutlifactor model should contains a "reasonably limited number of explanatory variables" Discuss here in forum: https://www.bionicturtle.com/forum/threads/p1-t1-704-bodiesmultifactor-models.10108/ 6