Multifactor models - APT Flashcards
Multifactor models
A financial model where multiple factors are used to estimate the expected returns.
Multifactor models example
APT
ICAPM
What does APT stand for?
Arbitrage Pricing Theory
Who developed APT
Ross(1976)
How is the APT different from CAPM?
It doesn’t assume investor behaviour.
It has multiple factors rather than just risk (one beta)
Key assumptions of APT?
All investors believe that returns are driven by a linear K-factor statistical model
What is K?
K is the number of factors in the model
What does the factor model s=do to unanticipated stock return
It splits it into:
A part due to K common factors
A residual term (idiosyncratic risk)
What does this splitting of unanticipated stock returns show?
That most of the return surprise can be explained by broad economic forces, with the rest being random
What does ATP imply about pricing and arbitrage?
If no arbitrage opportunity exists, expected returns must be a linear function of K factor betas.
Based on Law of One Price (LOP)
What is the Law of One Price (LOP)?
The LOP states that any two assets with identical payoffs must sell for the same price
Consequences of not having the LOP?
Investors could make instantaneous profit by shirt selling the more expensive asset and buying the cheaper asset.
What happens in the APT model if the residual term (idiosyncratic risk)
equals 0?
There is no random component in the assets return and it can be entirely explained by the K factors
What does it imply in practical terms if the residual term (idiosyncratic risk)
equals 0?
The return on asset i can be perfectly replicated by a portfolio of the K factor portfolios
What is the APT equation equivalent to in CAPM?
SML but it is extended to include multiple factors
Why is APT a multifactor model?
Because it assumes systematic risk is multi-dimensional, meaning asset returns are influenced by several different risk factors
How does APT relate to CAPM?
CAPM is a special case of APT with only one factor—the market. APT generalizes CAPM by allowing multiple sources of systematic risk
What makes APT a more general model than CAPM?
It doesn’t rely on strong assumptions about investor behaviour and allows for multiple sources of systematic risk
Limitations of APT?
- It doesn’t identify what the K common factors are
- Doesn’t specify how many factors are important
- Tells us nothing about the size or signs of the size or signs of risk factor premiums
What is the key implication of APT regarding the mean-variance frontier?
A combination of the K factor portfolios will like on the ex ante mean-variance frontier
What is the relationship between expected returns and betas in APT?
There is a linear relationship
What does APT suggest about the role of stock characteristics in explaining returns?
After controlling for the K-factor betas, stock characteristics should not affect expected returns — only systematic risk matters
How to identify the common K factors
Three different approaches have been applied (Ferson(2003))
What are the three approaches to identify common K -factors
- Statistical
2.Macroeconomic factors
3.Portfolio factors
Statistical approach
Using statistical tools to identify a small set of factors that best explain the covariance of asset returns
What is the goal of the statistical approach in factor identification?
Data reduction exercise
Simplifying as many asset return variables into a few key underlying factors.
What are two common statistical techniques used to identify factors?
Factor analysis (Roll and Ross, 1980)
Principle components analysis (PCA) (Connor and Korajczyk, 1986, 1988)
Weakness of the statistical technique?
Often lacks economic meaning.
Huang, Li and Zhoue (2019) propose a reduced rank approach
Macroeconomic factors
Using economic factors that may impact future cash flows or discount rates.
Who are the key contributors to the macroeconomics factor model?
Chen, Roll and Ross(1986).
What did Chen, Roll and Ross (1986) propose?
Using macro variables like inflation, industrial production, and interest rate changes.
What is the advantage of using microeconomics factors in APT?
Stronger theoretical motivation making it more interpretable
Weaknesses of the macroeconomic factors?
Often subject to large measurement error.
Reducing reliability
Portfolio-based factors
Using stock characteristics known to be related to cross-sectional returns to form empirical factors
What role does the market index play in empirical factor models?
All models include the stock market index and a baseline factor.
What does the stock market factor typically represent?
Overall market risk.
How are the empirical factors typically constructed?
As long-short portfolios
Long short portfolio factor
Factor = return on one group of stocks - return on another group of stocks.
What is the size factor(SMB)?
Small minus Big (SMB) = return on small-cap stocks minus return on large cap stocks
What is the value factor (HML)?
High minus Low (HML)= return on value stocks(high book-to-market) - return on growth stocks (low B/M)
Who introduced SMB and HML?
Fama and French (1993)
How did Asness and Frazzini(2013) improve HML?
Propose a more timely version using up-to-date valuations
What is the momentum factor (WML)?
Winners Minus Losers (WML) = return on past winners minus return on past losers.
Who introduced momentum factor (WML)?
Carhart (1997)
What do Pastor and Stambaugh propose as a factor?
An aggregate liquidity factor.
What would an aggregate liquidity factor measure?
How sensitive a stock’s return is to market-wide liquidity conditions.
What new factors did Fama and French (2015) add in their five-factor model?
- RMW (Robust minus Weak) = profitability
- CMA (conservative minus Aggressive) = investment.
This model is an extension of their three-factor model
Stambaugh and Yuan (2017) 4 factor model.
Additional factors are
size and two mispricing factors.
The mispricing factors are formed from 11 efficient market anomalies
How are the mispricing factors formed?
The mispricing factors are formed from 11 efficient market anomalies
