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P1.T1.400: Arbitrage pricing theory (APT) introduction

Nicole Seaman

Director of FRM Operations
Staff member
P1.T1.400 Arbitrage pricing theory (APT) introduction

AIMs: Describe the inputs, including factor betas, to a multi-factor model. Calculate the expected return of an asset using a single-factor and a multi-factor model


400.1. Sally Smith, FRM, is considering a switch in the theoretical basis of her risk model from a simple single-factor capital asset pricing model (CAPM) to a multi-factor arbitrage pricing theory (APT) model. To her manager, she claims the following differences between the two models. Each of her statements below is correct EXCEPT which is not?

a. Compared to only one specific factor (i.e., market index) in the simple CAPM, the APT model will be able to recognize multiple systematic risk factors
b. While the CAPM requires a mean-variance efficient market portfolio and assumes normally distributed returns, APT requires neither of these assumptions
c. Although APT does not require several of the restrictive assumptions of the CAPM, it is largely silent on where to look for priced sources of risk
d. In contrast to the simple CAPM, the APT cannot include the market index as a common factor, nor can it be extended over multiple periods

400.2. Peter Parker, FRM, is identifying risk factors for the construction of his multifactor APT model. His colleague Barbara gives him the following four pieces of advice. Each of the following is a good or reasonable statement about a multifactor APT model EXCEPT which is not?

a. He should restrict himself to a limited number of systematic factors with considerable ability to explain security returns
b. He should choose factors that are likely to be important as major sources of uncertainty; i.e., factors that concern investors sufficiently that they will demand meaningful risk premiums to bear exposure to those sources of risk
c. He should exclude factors that produce negative factor risk premiums as they lack narrative credibility
d. He model will retain a firm-specific (non-systemic) component, like CAPM, with zero expected value

400.3. Suppose three factors have been identified for the U.S. economy: the growth rate of industrial production (IP), the inflation rate (IR), and the excess return of 30-year Treasury bonds over T-bills (TB). IP is expected to be 4.0%, IR is expected to be 3.0%, and TB is expected to be 2.0%. A stock that is expected to provide a rate of return of 9.0% has a beta of 0.8 on IP, a beta of 0.6 on IR, and a beta of 0.5 on TB. If industrial production (IP) actually grows by 5.0%, the inflation rate (IR) turns out to be 2.0%, and the excess long-term Treasury bond (TB) is realized as 2.0%, what is the revised estimate of the expected rate of return on the stock?

a. 8.80%
b. 9.20%
c. 10.30%
d. 11.50%

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