Factor Models - Fama-French three factor model
12 important questions on Factor Models - Fama-French three factor model
Company characteristics used in the research:
- Book-to-market (BE/ME): book value of the company (accounting value) divided by the market value (stock market)
- Size (ME): stock market capitalization (number of outstanding stocks times the stock price)
- Assets (A): total assets (accounting value)
- Earnings(E): earnings per share of the company
What are the methods of the Fama-French three factor model?
- Sorting: Sort stocks in buckets based on company characteristics in previous period and check return in this period. No need to assume linear relation
- FMB: For each month run a cross-sectional regression with the returns of this preiod as dependent variable and company characteristics in previous period as explanatory variables -> Fama-McBeth method
Why use sorting (Method 1)?
- We know that properly estimating beta is hard:
- Solutions here:
- portfolio betas (post-ranking) instead of individual stock betas
- Adjusted market model (extra B term + market premium)
- Additional issue here: strong relation between beta and size making it difficult to seperate effects
- Solution:
- Double-sorting
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How does Method 1 (double-sorting) work?
- Sort stock into deciles
- Take 2-5 years of data prior to size sorting date to estimate beta per stock -> "pre-ranking betas"
- Within each size decile, sort stocks into beta deciles -> 100 size-beta portfolios
- Calculate return of portfolio over next year
- Redo steps 1 to 4 each year
- For each of the 100 size-beta portfolios, estimate a portfolio beta over the full sample preiod -> "post-ranking beta"
What are the Fama-French (1992) sorted results on post ranking beta and size?
- There is a relation between size and return
- There is no relation between beta and return
What are the further results on in the three factor model sorted on BtM and size?
- Negative Relation between size and return
- Larger size (ME) -> smaller average returns
- Positive Relation between BtM and return
- Larger BtM -> larger average returns
How does the second method (Fama-McBeth regressions) work?
- For each month, different forms of the following cross-sectional regression are estimated
- Take the average of the estimated gamma's (over the months)
What are the result of the Fama-McBeth regressions?
- Beta: Nothing!
- Size: Significant!
- Size: Significant!
- B-t-M: Significant!
- A/ME, BE/ME: Significant!
- E/P: Significant!
- ME + B/M: Robust
- ME:B/M: Robust
- ME:E/P: Not robust
- ME, B/M and E/P: Not robust
- ME, B/M, and E/P: Not robust
What is the conclusion of Fama-French (1992) three factor model?
- Apparently, beta is NOT a complete measure of risk
- Size and B/M are relevant
- In a follow-up paper, Fama and French (1993) propose two additional factors or factor mimicking portfolios:
- Small Minus Big - SMB
- High Minus Low - HML
What is the costruction of the SMB factor mimicking portfolio?
- Sort all stocks on their market capitalization (ME or size) and split across the median
- Go long in the bottom half, go short in the top half
What is the construction of the HML factor mimicking portfolio?
- Sort all stocks on their book-to-market value (BE/ME) and split in three parts (30/40/30)
- Go long in the top 30%, go short in the bottom 30%
What is the conclusion of the Fama & French
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