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# P1.T1.402. ABT and Fama-French three-factor model

#### David Harper CFA FRM

##### David Harper CFA FRM
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P1.T1.402. ABT and Fama-French three-factor model

AIMs: Describe the Arbitrage Pricing Theory (APT) and the Fama-French three-factor model, and explain the underlying assumptions of each. Explain how to construct a portfolio to hedge exposure to multiple factors.

Questions:

402.1. Assume security returns are generated by the single-index model: where R(i) is the excess return for security(i) and R(M) is the market's excess return. The risk free-rate is 1.0% and the volatility of the market index is 20.0%. Suppose that there are three securities, (A), (B) and (C), characterized by the following data: Compound question: Is there an arbitrage opportunity, and which security has the highest volatility?

a. No, there is no arbitrage opportunity because all three portfolios plot on the security market line (SML); and all have the same volatility.
b. No, there is no arbitrage opportunity because all three portfolios plot on the SML; and Security A has the highest volatility
c. No, there is no arbitrage opportunity because all three portfolios plot on the SML; and Security C has the highest volatility
d. Yes, there is an arbitrage; and Security B has the highest volatility

402.2. Recall that a factor portfolio is a well-diversified portfolio constructed to have a beta of 1.0 on one of the factors in a multi-factor arbitrage pricing theory (APT) model, and a beta of zero on any other factor. Assume that exactly two (2) systematic factors affect stock returns and there exists the following two factor portfolios:
• The first factor portfolio, with exposure only to factor F(1), has an expected return of 9.0%.
• The second factor portfolio, with exposure only to factor F(2), has an expected return of 11.0%.
The risk-free rate is 2.0%. Consider a well-diversified portfolio (A) with beta on the first factor, B(A,1), equal to 0.40 and beta on the second factor, B(A,2) equal to 0.80. What is the expected return on portfolio (A)?

a. 9.50%
b. 10.25%
c. 12.00%
d. 14.75%

402.3. Here is the Fama-French (FF) three-factor model: According to Bodie, Kane, Marcus, each of the following is true about the FF three-factor model EXCEPT which is false?

a. Unlike the CAPM, this FF model does NOT capture any systematic risk(s) originating from macroeconomic factors
b. While Small Minus Big (SMB) and High Minus Low (HML) are not themselves candidates for relevant risk factors, the argument is that these variables are proxies for fundamental variables
c. None of the three factors can be directly and clearly identified as hedging a significant source of uncertainty
d. It is an important question whether the FF reflects an APT or multi-index CAPM approximation model, but the debate is unsettled