Lecture 4: Asset Pricing III (3/4/5 - factor models) Flashcards
APT focuses on ? risk factors.
But Reilly & Brown (2015) focused on ? risk factors, i.e. different ? of t’ sample of assets: “?-based approach.”
=> 3/ 4/ 5 - factor models.
APT focuses on macroeconomic risk factors.
But Reilly & Brown (2015) focused on microeconomic risk factors, i.e. different characteristics of t’ sample of assets: “characteristics-based approach.”
=> 3/ 4/ 5 - factor models.
Fama & French (1993) 3-factor model:
(𝑅_(𝑖,𝑡) − 𝑅𝐹𝑅_𝑡)=𝛼_𝑖 + 𝑏_𝑖1 (𝑅_𝑀𝑡− 𝑅𝐹𝑅_𝑡 ) + 𝑏_𝑖2 *𝑆𝑀𝐵_𝑡 +𝑏_𝑖3 *𝐻𝑀𝐿_𝑡 +𝑒_𝑖𝑡
Where:
𝑅_𝑀𝑡 − 𝑅𝐹𝑅_𝑡 = return on stock market portfolio
𝑆𝑀𝐵_𝑡 (small minus big) = return to a portfolio of small cap stocks minus the returns to a portfolio of large cap stocks
𝐻𝑀𝐿_𝑡 (high minus low) = return on a portfolio of stocks with a high B/M ratio to one with a low B/M.
RFR: risk-free rate
Coefficient 𝑏_𝑖1 represents the beta in the standard CAPM, if we left aside the two other risk factors.
Fama & French (1993) 3-factor model:
(𝑅_(𝑖,𝑡) − 𝑅𝐹𝑅_𝑡)=𝛼_𝑖 + 𝑏_𝑖1 (𝑅_𝑀𝑡− 𝑅𝐹𝑅_𝑡 ) + 𝑏_𝑖2 *𝑆𝑀𝐵_𝑡 +𝑏_𝑖3 *𝐻𝑀𝐿_𝑡 +𝑒_𝑖𝑡
Where:
𝑅_𝑀𝑡 − 𝑅𝐹𝑅_𝑡 = return on stock market portfolio
𝑆𝑀𝐵_𝑡 (small minus big) = return to a portfolio of small cap stocks minus the returns to a portfolio of large cap stocks
𝐻𝑀𝐿_𝑡 (high minus low) = return on a portfolio of stocks with a high B/M ratio to one with a low B/M.
RFR: risk-free rate
Coefficient 𝑏_𝑖1 represents the beta in the standard CAPM, if we left aside the two other risk factors.
Fama & French (1993) 3-factor model:
- ”? effect” : small firms generated ? returns than did larger ones because they were ?.
=> 𝑆𝑀𝐵_𝑡: proxy for the size factor.
Fama & French (1993) 3-factor model:
- “size effect” : small firms generated higher returns than did larger ones because they were riskier.
=> 𝑆𝑀𝐵_𝑡: proxy for the size factor.
F&F 3-factor model:
HML is included to distinguish between ‘growth’ stocks (characterised by ? B/M ratios) and ‘value’ stocks (characterised by ? B/M ratios).
F&F 3-factor model:
HML is included to distinguish between ‘growth’ stocks (characterised by low B/M ratios) and ‘value’ stocks (characterised by high B/M ratios).
Fama and French took a broad sample of stock during the period July 1963 to December 1991 and divided them into five portfolios on an annual basis according to their ?/? ratios.
Key takeaways:
- Significant differences between the ?values between low and high P/E portfolios in the single factor model in comparison with the multifactor model.
In the single factor model the ? portfolio accounts for some of the risk that the additional factors, SMB and HML, explain in the multifactor model.
- Low P/E stocks ? correlated with the low cap premium which is not the case with high P/E stocks.
- Low P/E stocks have ? B/M ratios whereas high P/E stocks have ? B/Ms.
Fama and French took a broad sample of stock during the period July 1963 to December 1991 and divided them into five portfolios on an annual basis according to their P/E ratios.
Key takeaways:
- Significant differences between the beta values between low and high P/E portfolios in the single factor model in comparison with the multifactor model.
In the single factor model the market portfolio accounts for some of the risk that the additional factors, SMB and HML, explain in the multifactor model.
- Low P/E stocks positively correlated with the low cap premium which is not the case with high P/E stocks.
- Low P/E stocks have high B/M ratios whereas high P/E stocks have low B/Ms.
Carhart (1997) 4-factor model:
(𝑅_(𝑖,𝑡) − 𝑅𝐹𝑅_𝑡) = ??
𝑀𝑂𝑀 = “?” = average return of set of stocks with best return in the previous year minus those with the worst returns.
Finds the ? statistically significant and improves the explanatory power by as much as 15%.
Carhart (1997) 4-factor model:
(𝑅_(𝑖,𝑡) − 𝑅𝐹𝑅𝑡)=𝛼_𝑖 + 𝑏_𝑖1 (𝑅_𝑀𝑡− 𝑅𝐹𝑅𝑡 ) + 𝑏_𝑖2 *𝑆𝑀𝐵𝑡 +𝑏_𝑖3 *𝐻𝑀𝐿𝑡 + b_i4 * MOMt + 𝑒_𝑖𝑡
𝑀𝑂𝑀 = “Momentum” = average return of set of stocks with best return in the previous year minus those with the worst returns.
Finds the beta statistically significant and improves the explanatory power by as much as 15%
Fama & French 5-factor model:
(𝑅_(𝑖,𝑡) − 𝑅𝐹𝑅𝑡) = ….?
Where:
𝑅𝑀𝑊 = “is the difference between the returns on diversified portfolios of stocks with ? and ? ?”
𝐶𝑀𝐴 = “is the difference between the returns on diversified portfolios of low and high investment stocks, which we call ? and ?”.
The empirical results indicate that the 𝐻𝑀𝐿 factor ceases to be statistically significant when the 𝑅𝑀𝑊 and 𝐶𝑀𝐴 are included.
Five factor model explains returns better than does the thee factor model.
Fama & French 5-factor model:
(𝑅_(𝑖,𝑡) − 𝑅𝐹𝑅𝑡)=𝛼_𝑖 + 𝑏_𝑖1 (𝑅_𝑀𝑡− 𝑅𝐹𝑅𝑡 ) + 𝑏_𝑖2 *𝑆𝑀𝐵𝑡 +𝑏_𝑖3 *𝐻𝑀𝐿𝑡 + + b_i4 * RMWt + b_i5 * CMAt + 𝑒_𝑖𝑡
Where:
𝑅𝑀𝑊 = “is the difference between the returns on diversified portfolios of stocks with Robust and Weak profitability”
𝐶𝑀𝐴 = “is the difference between the returns on diversified portfolios of low and high investment stocks, which we call Conservative and Aggressive”.
The empirical results indicate that the 𝐻𝑀𝐿 factor ceases to be statistically significant when the 𝑅𝑀𝑊 and 𝐶𝑀𝐴 are included.
Five factor model explains returns better than does the thee factor model.
F&F 5-factor model - Critique:
Musarurwa (2019) argues that “The five-factor model’s main setback is its failure to capture the ??? on ? stocks”
F&F 5-factor model - Critique:
Musarurwa (2019) argues that “The five-factor model’s main setback is its failure to capture the low average returns on small stocks”
F&F 5-factor model - Critique:
Blitz et al 2018 criticised bec:
- still maintain t’ ? relation bet market beta & return.
- ignore ? effect
- ? concerns & questions of ?? of t’ 2 new risk factors.
- still not settle t’ main asset pricing debates.
F&F 5-factor model - Critique:
Blitz et al 2018 criticised bec:
- still maintain t’ CAPM relation bet market beta & return.
- ignore momentum effect
- robustness concerns & questions of economic rationale of t’ 2 new risk factors.
- still not settle t’ main asset pricing debates.
F&F 5-factor model - Critique:
Arnott et al (2020) :
- misspecification of the ? variable can account for its poor performance
- ? investing has underperformed ?investing since 2007.
F&F 5-factor model - Critique:
Arnott et al (2020) :
- misspecification of the 𝐻𝑀𝐿 variable can account for its poor performance
- value investing has underperformed growth investing since 2007.
