Chapter 6 - The Arbitrage Pricing Theory and Multifactor Models of Risk and Return
Unit 12: Fundamentals of Economics, Microeconomics, Macroeconomics and types of Economics
Chapter 6 - The Arbitrage Pricing Theory and Multifactor Models of Risk and Return
1. What is the primary difference between the Arbitrage Pricing Theory (APT) and the Capital Asset Pricing Model (CAPM)?
A. CAPM accounts for multiple risk factors, whereas APT considers only one factor
B. APT is a single-factor model, while CAPM is a multi-factor model
C. APT considers multiple risk factors, while CAPM relies on a single index
D. CAPM accounts for idiosyncratic risk, whereas APT does not
CAPM assumes that a financial asset’s risk is determined by its exposure to a single index, such as the S&P 500. In contrast, APT allows for multiple risk factors, such as macroeconomic variables and financial indices.
2. According to Arbitrage Pricing Theory (APT), what happens if an arbitrage opportunity exists in the market?
A. It will persist indefinitely
B. It will increase due to market inefficiency
C. It has no impact on asset pricing
D. It will quickly disappear due to market participants' trading actions
APT assumes that arbitrage opportunities do not persist because traders will exploit them, causing prices to adjust until the arbitrage opportunity is eliminated.
3. In the APT model equation, what does the term \( e_i \) represent?
A. Systematic risk
B. Idiosyncratic (company-specific) risk
C. Market risk
D. Risk premium
In the APT model, \( e_i \) represents the random error term accounting for company-specific risk, also known as idiosyncratic risk, which is independent of systematic risk factors.
4. Which of the following is NOT considered a potential risk factor in the APT model?
A. Interest rate metrics
B. GDP growth rate
C. A company’s management team
D. Commodity price indices
APT focuses on systematic risk factors like macroeconomic variables and financial indices. A company’s management team is an internal factor and is considered idiosyncratic risk, not a systematic risk factor.
5. Which of the following statements about the Arbitrage Pricing Theory (APT) is correct?
A. It assumes that arbitrage opportunities do not persist in efficient markets
B. It is a single-factor model like CAPM
C. It does not allow for multiple risk factors
D. It is only applicable to stock markets
APT assumes that arbitrage opportunities do not last because traders will act to exploit them, leading to price adjustments. Unlike CAPM, APT is a multi-factor model that can be applied to various asset classes.
6. Which of the following is NOT an assumption of the Arbitrage Pricing Theory (APT)?
A. Market participants seek to maximize their profits
B. Markets are frictionless
C. Arbitrage opportunities do not persist
D. APT specifies the exact factors to include in the model
APT does not specify the exact factors to use in the model, giving analysts flexibility. The other three options are core assumptions of APT.
7. Which of the following is a challenge associated with using APT for asset pricing?
A. It does not account for systematic risk
B. It only applies to stock markets
C. The risk factors and their sensitivities need periodic updates
D. APT strictly defines which risk factors to use
APT requires continuous updating of macroeconomic factors and their sensitivities (betas) to maintain accuracy, making it more complex to implement compared to CAPM.
8. Which of the following is one of the macroeconomic factors proposed by Chen, Roll, and Ross for use in the APT model?
A. Company management efficiency
B. The spread between short-term and long-term interest rates
C. A firm’s profit margin
D. The number of outstanding shares of a company
The spread between short-term and long-term interest rates (yield curve) is one of the four macroeconomic factors suggested by Chen, Roll, and Ross for APT analysis.
9. Why does APT suggest that arbitrage opportunities should not exist for long?
A. Profit-maximizing investors will quickly exploit them
B. APT assumes that all stocks are perfectly priced
C. Governments intervene to correct arbitrage
D. Arbitrage does not exist in financial markets
APT assumes that arbitrage opportunities disappear quickly because traders will take advantage of mispricing, leading to rapid price adjustments.
10. What is the main reason an investor might prefer APT over CAPM?
A. APT is simpler to use than CAPM
B. APT only considers a single factor, reducing complexity
C. APT guarantees more accurate predictions than CAPM
D. APT accounts for multiple risk factors, making it more flexible
Unlike CAPM, which uses only one factor (market index), APT incorporates multiple risk factors, making it more flexible for asset pricing in dynamic markets.
11. In a multifactor model, what does the term \( \beta_k F_k \) represent?
A. The error term in the model
B. The expected return of the stock
C. The contribution of a specific factor to the stock’s return
D. The risk-free rate
In a multifactor model, each \( \beta_k F_k \) term represents the contribution of a specific risk factor (e.g., interest rate changes, GDP growth) to the stock’s return.
12. What does the error term (\( e_i \)) in a multifactor model represent?
A. The systematic risk of a stock
B. The firm-specific return unexplained by the model
C. The average expected return of the market
D. The sensitivity of a stock to macroeconomic factors
The error term (\( e_i \)) represents firm-specific return that is not captured by the model, arising from random events, irrational market behavior, or excluded variables.
13. In a multifactor model, what does a factor’s beta (\( \beta \)) represent?
A. The market-wide risk premium
B. The expected return of the stock
C. The idiosyncratic risk of the stock
D. The sensitivity of a stock’s return to a particular risk factor
The beta (\( \beta \)) in a multifactor model measures how sensitive a stock’s return is to a specific risk factor, such as GDP growth or inflation.
14. If the actual GDP growth rate is 2.2%, while the expected rate is 3.2%, and the GDP beta (\( \beta_{GDP} \)) is 2.0, what is the expected impact on the stock’s return?
A. -2%
B. -1%
C. 2%
D. No impact
The GDP deviation is -1% (2.2% - 3.2%). With a GDP beta of 2.0, the expected impact on the stock’s return is \( 2.0 \times (-1\%) = -2\% \).
15. Why is the expected value of the error term (\( e_i \)) in a multifactor model assumed to be zero?
A. It represents systematic risk, which is always zero
B. It is derived from known market factors
C. Firm-specific events are random and their expected impact cancels out over time
D. The error term is directly influenced by macroeconomic conditions
Since firm-specific events are unpredictable and occur randomly, their expected impact averages out to zero in the long run.
16. In a single-factor model, the expected return of an asset is primarily influenced by:
A. Multiple macroeconomic factors
B. Company-specific risk
C. A single systematic risk factor
D. Investor sentiment
A single-factor model captures the impact of one systematic risk factor on an asset's expected return. Other risks are considered residual.
17. In the given example, HealthCare Inc.'s expected return is 10%, and the factor beta for GDP surprises is 2.0. If the GDP surprise is -0.60%, what is the expected return based on the single-factor model?
A. 10.2%
B. 9.4%
C. 8.5%
D. 8.8%
Using the formula: RHCI = E(RHCI) + βGDP*FGDP*, we get RHCI = 0.10 + 2.0(-0.006) = 8.8%.
18. What is the key limitation of a single-factor model in predicting asset returns?
A. It accounts for too many risk factors
B. It does not capture all systematic risk influences
C. It is difficult to compute
D. It ignores expected returns
A single-factor model does not capture all systematic influences, leading to deviations from actual returns.
19. In the multifactor model for HealthCare Inc., what additional factor was included to improve return prediction?
A. Interest rate changes
B. Inflation rate
C. Unemployment rate
D. Consumer sentiment
The multifactor model included consumer sentiment as an additional factor to better capture systematic influences on returns.
20. If the consumer sentiment growth rate was expected to be 1.0% but the actual rate was 0.75%, what was the consumer sentiment surprise factor?
A. -0.50%
B. 0.25%
C. -0.25%
D. 1.25%
The consumer sentiment surprise factor is calculated as 0.75% - 1.0% = -0.25%.
21. What is the primary objective of Arbitrage Pricing Theory (APT)?
A. To replace CAPM as the dominant asset pricing model
B. To eliminate systematic risk from portfolios
C. To explain asset returns using multiple factors
D. To create arbitrage opportunities in financial markets
APT is a multifactor model that explains asset returns based on multiple factors rather than a single market risk factor, making it an alternative to CAPM.
22. What is the main condition for a portfolio to be considered well-diversified?
A. It contains only stocks from the same sector
B. It includes assets with low correlation to reduce idiosyncratic risk
C. It holds a large number of stocks with high beta values
D. It minimizes both systematic and unsystematic risks completely
A well-diversified portfolio mixes financial assets with different correlations to eliminate idiosyncratic risk while retaining systematic risk.
23. What happens when assets in a portfolio have high correlations?
A. Diversification benefits decrease
B. Systematic risk is eliminated
C. Portfolio beta becomes zero
D. Idiosyncratic risk increases
High correlations between assets reduce diversification benefits because assets move together, limiting risk reduction.
24. Why are multifactor models preferred in asset return analysis?
A. They consider only systematic risk
B. They assume all assets have equal risk exposure
C. They eliminate the need for diversification
D. They capture multiple sources of risk affecting asset returns
Multifactor models account for various risk factors beyond market risk, providing a more comprehensive analysis of asset returns.
25. According to APT, what is the relationship between expected returns and factor betas in a well-diversified portfolio?
A. Expected returns are unrelated to factor betas
B. Expected returns are only influenced by market beta
C. Expected returns are proportional to factor betas
D. Factor betas do not affect expected returns
APT states that expected returns on a well-diversified portfolio depend on multiple factor betas, which measure exposure to different risk factors.
26. When can the APT relationship fail for an individual security?
A. When arbitrage opportunities exist in the market
B. When the security has no exposure to systematic risk
C. When the security is included in a poorly diversified portfolio
D. When the effect of the violation is too small to allow arbitrage
If APT is violated for a single security, the effect is usually too small to create arbitrage opportunities, meaning the model can still hold for the overall portfolio.
27. Under what condition must the APT relationship hold for a well-diversified portfolio?
A. Only when all securities strictly follow APT
B. When it holds for nearly all securities in the portfolio
C. Only if the portfolio consists of risk-free assets
D. When arbitrage opportunities are frequently available
APT must hold for nearly all securities in a well-diversified portfolio; otherwise, arbitrage opportunities would emerge, violating market equilibrium.
28. What is the primary advantage of using multifactor models for hedging?
A. They eliminate all market risks
B. They allow targeted exposure management
C. They guarantee arbitrage profits
D. They eliminate transaction costs
Multifactor models help investors build portfolios that retain specific exposures while mitigating others, allowing more precise risk management.
29. How can an investor hedge exposure to GDP surprise risk in the given example?
A. Taking a long position in Portfolio 2
B. Taking a long position in Portfolio 3
C. Taking a long position in Portfolio 1 and a short position in Portfolio 2
D. Shorting Portfolio 1 and Portfolio 3
A long position in Portfolio 1 and a short position in Portfolio 2 results in a zero beta for GDP surprise risk.
30. If an investor wants to neutralize consumer sentiment exposure while retaining GDP surprise, which strategy should they use?
A. Long Portfolio 2 and short Portfolio 3
B. Long Portfolio 1 and short Portfolio 2
C. Long Portfolio 3 and short Portfolio 1
D. Long Portfolio 1 and short Portfolio 3
A long position in Portfolio 1 and a short position in Portfolio 3 neutralizes consumer sentiment exposure while retaining GDP surprise exposure.
31. What is the role of derivatives in constructing a hedged portfolio?
A. They can be used to hedge specific factor exposures
B. They eliminate all market risk
C. They always guarantee a positive return
D. They reduce transaction costs to zero
Derivatives can be structured to hedge against specific factor exposures, allowing for precise risk management.
32. What potential risk is associated with the hedging strategy discussed?
A. Complete elimination of risk
B. Unlimited arbitrage profits
C. Model risk due to changing factor sensitivities
D. No impact on market conditions
Model risk arises if factor sensitivities change, leading to incorrect hedging results.
33. Why might an investor frequently rebalance a hedged portfolio?
A. To increase trading costs
B. To adjust for changing factor sensitivities
C. To eliminate all systematic risk
D. To take on additional risk
Frequent rebalancing ensures the hedge remains effective as market conditions and factor sensitivities change.
34. What is the primary limitation of the Arbitrage Pricing Theory (APT)?
A. It only considers market risk
B. It assumes a risk-free rate of zero
C. It does not specify which factors to include in the model
D. It cannot be applied to diversified portfolios
A major weakness of APT is that it does not provide guidance on which specific factors should be included in a multifactor model.
35. What are the three factors included in the Fama-French Three-Factor Model?
A. Market risk, volatility, and liquidity
B. Interest rates, inflation, and credit risk
C. GDP growth, earnings growth, and firm size
D. Market risk premium, small minus big (SMB), high minus low (HML)
The Fama-French Three-Factor Model includes the market risk premium, the size factor (SMB), and the value factor (HML).
36. What does the "small minus big" (SMB) factor in the Fama-French model represent?
A. The difference in returns between growth and value stocks
B. The difference in returns between small and large firms
C. The risk premium for market fluctuations
D. The effect of interest rates on stock returns
SMB represents the difference in returns between small-cap and large-cap stocks, adjusting for the size effect in asset pricing.
37. What does the "high minus low" (HML) factor in the Fama-French model measure?
A. The difference in volatility between high-risk and low-risk stocks
B. The return differential between high-growth and low-growth firms
C. The difference in returns between high and low book-to-market ratio stocks
D. The effect of dividend yields on stock prices
HML captures the value effect, where stocks with high book-to-market ratios tend to generate higher returns than those with low book-to-market ratios.
38. How does the Fama-French model improve upon the Capital Asset Pricing Model (CAPM)?
A. It eliminates the need for a risk-free rate
B. It accounts for company-specific (idiosyncratic) risk
C. It replaces beta with alternative factors
D. It incorporates size and value factors along with market risk
The Fama-French model extends CAPM by adding size and value factors (SMB and HML) to better explain asset returns.
39. What does the SMB factor represent in the Fama-French three-factor model?
A. A measure of market beta
B. A factor for momentum investing
C. A hedge strategy that is long small firms and short big firms
D. A factor measuring volatility
SMB (Small Minus Big) is a factor in the Fama-French model that accounts for the historical excess returns of small-cap stocks over large-cap stocks, acting as a hedge strategy.
40. What is the purpose of the HML factor in the Fama-French three-factor model?
A. It measures exposure to momentum
B. It predicts market volatility
C. It represents an alternative to the market beta
D. It is a hedge strategy that is long high book-to-market firms and short low book-to-market firms
HML (High Minus Low) captures the tendency of stocks with high book-to-market ratios to outperform those with low book-to-market ratios, forming part of the Fama-French model.
41. What key assumption underlies the Fama-French three-factor model?
A. Market returns alone explain stock returns
B. Small-cap stocks and value stocks provide higher expected returns due to their higher inherent risk
C. Stocks with low beta provide better returns
D. The model assumes market efficiency is absolute
The Fama-French model assumes that small-cap and high book-to-market stocks have higher expected returns because they are riskier investments.
42. What additional factor did Mark Carhart introduce in 1997 to expand the Fama-French model?
A. Momentum
B. Liquidity
C. Volatility
D. Market beta squared
Mark Carhart extended the Fama-French model by adding a momentum factor, which captures the tendency of stocks that have performed well in the past to continue performing well.
43. What additional factors were introduced in the 2015 extension of the Fama-French model?
A. Liquidity and Volatility
B. Interest Rate Sensitivity and Credit Risk
C. Robust Minus Weak (RMW) and Conservative Minus Aggressive (CMA)
D. Dividend Yield and Earnings Growth
In 2015, Fama and French expanded their model by adding RMW, which accounts for operating profitability, and CMA, which adjusts for the firm's investment behavior.
44. Using the Fama-French three-factor model, what is the expected return of a stock with βM = 0.85, βSMB = 1.65, and βHML = -0.25, given RF = 2.75%, RPM = 8.5%, SMB factor = 2.5%, and HML factor = 1.75%?
45. What is the key difference between the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT)?
A. CAPM considers multiple macroeconomic factors, while APT focuses only on market risk
B. APT assumes a single-factor approach, whereas CAPM is a multifactor model
C. APT allows for multiple factors, while CAPM considers only market risk
D. CAPM and APT use the same assumptions regarding risk pricing
The CAPM only accounts for broad market risk, whereas the APT allows analysts to incorporate multiple macroeconomic factors that may influence expected returns.
46. What is a key advantage of Arbitrage Pricing Theory (APT) compared to CAPM?
A. It relies on a single-factor model
B. It offers flexibility in choosing macroeconomic factors
C. It assumes all investors have the same expectations
D. It is easier to implement than CAPM
APT provides more flexibility than CAPM because analysts can choose multiple relevant macroeconomic factors, rather than being limited to market risk.
47. In a multifactor model, what does each beta coefficient represent?
A. The stock’s exposure to firm-specific risk
B. The expected return on the stock
C. The correlation between different stocks in a portfolio
D. The stock’s sensitivity to a specific factor
In a multifactor model, each beta coefficient measures the sensitivity of a stock’s return to a particular factor.
48. Why do multifactor models improve forecasting ability compared to single-factor models?
A. They focus exclusively on company-specific risk
B. They eliminate all systematic risk
C. They account for multiple sources of systematic risk
D. They assume that stock returns are independent of macroeconomic factors
A single-factor model may not capture all systematic risks, whereas a multifactor model allows analysts to incorporate multiple risk sources, leading to better forecasts.
49. How does diversification help in Arbitrage Pricing Theory (APT)?
A. It eliminates all systematic risk
B. It reduces the impact of firm-specific risk
C. It increases correlation between assets
D. It ensures that all factors contribute equally to risk
A well-diversified portfolio reduces firm-specific risk, making systematic risk exposures more predictable and better suited for multifactor analysis.
50. How can multifactor models be used for hedging?
A. By targeting specific factor exposures for elimination
B. By increasing a portfolio’s exposure to systematic risk
C. By relying only on a single-factor approach
D. By ignoring firm-specific risks
Multifactor models allow investors to hedge by targeting specific factor exposures for elimination, reducing unwanted risks in a portfolio.
51. What are the three factors in the Fama-French model?
A. Market risk, inflation risk, and interest rate risk
B. Stock beta, bond yield, and liquidity risk
C. Equity premium, dividend yield, and company revenue
D. Equity risk premium, size (SMB), and value (HML)
The Fama-French three-factor model includes the equity risk premium, size factor (SMB), and value factor (HML) to better explain stock returns.
