Multifactor models - APT

Question 1

Multifactor models

Answer 1

A financial model where multiple factors are used to estimate the expected returns.

Question 2

Multifactor models example

Answer 2

APT
ICAPM

Question 3

What does APT stand for?

Answer 3

Arbitrage Pricing Theory

Question 4

Who developed APT

Answer 4

Ross(1976)

Question 5

How is the APT different from CAPM?

Answer 5

It doesn’t assume investor behaviour.
It has multiple factors rather than just risk (one beta)

Question 6

Key assumptions of APT?

Answer 6

All investors believe that returns are driven by a linear K-factor statistical model

Question 7

What is K?

Answer 7

K is the number of factors in the model

Question 8

What does the factor model s=do to unanticipated stock return

Answer 8

It splits it into:
A part due to K common factors
A residual term (idiosyncratic risk)

Question 9

What does this splitting of unanticipated stock returns show?

Answer 9

That most of the return surprise can be explained by broad economic forces, with the rest being random

Question 10

What does ATP imply about pricing and arbitrage?

Answer 10

If no arbitrage opportunity exists, expected returns must be a linear function of K factor betas.
Based on Law of One Price (LOP)

Question 11

What is the Law of One Price (LOP)?

Answer 11

The LOP states that any two assets with identical payoffs must sell for the same price

Question 12

Consequences of not having the LOP?

Answer 12

Investors could make instantaneous profit by shirt selling the more expensive asset and buying the cheaper asset.

Question 13

What happens in the APT model if the residual term (idiosyncratic risk)
equals 0?

Answer 13

There is no random component in the assets return and it can be entirely explained by the K factors

Question 14

What does it imply in practical terms if the residual term (idiosyncratic risk)
equals 0?

Answer 14

The return on asset i can be perfectly replicated by a portfolio of the K factor portfolios

Question 15

What is the APT equation equivalent to in CAPM?

Answer 15

SML but it is extended to include multiple factors

Question 16

Why is APT a multifactor model?

Answer 16

Because it assumes systematic risk is multi-dimensional, meaning asset returns are influenced by several different risk factors

Question 17

How does APT relate to CAPM?

Answer 17

CAPM is a special case of APT with only one factor—the market. APT generalizes CAPM by allowing multiple sources of systematic risk

Question 18

What makes APT a more general model than CAPM?

Answer 18

It doesn’t rely on strong assumptions about investor behaviour and allows for multiple sources of systematic risk

Question 19

Limitations of APT?

Answer 19

1. It doesn’t identify what the K common factors are
2. Doesn’t specify how many factors are important
3. Tells us nothing about the size or signs of the size or signs of risk factor premiums

Question 20

What is the key implication of APT regarding the mean-variance frontier?

Answer 20

A combination of the K factor portfolios will like on the ex ante mean-variance frontier

Question 21

What is the relationship between expected returns and betas in APT?

Answer 21

There is a linear relationship

Question 22

What does APT suggest about the role of stock characteristics in explaining returns?

Answer 22

After controlling for the K-factor betas, stock characteristics should not affect expected returns — only systematic risk matters

Question 23

How to identify the common K factors

Answer 23

Three different approaches have been applied (Ferson(2003))

Question 24

What are the three approaches to identify common K -factors

Answer 24

1. Statistical
   2.Macroeconomic factors
   3.Portfolio factors

Question 25

Statistical approach

Answer 25

Using statistical tools to identify a small set of factors that best explain the covariance of asset returns

Question 26

What is the goal of the statistical approach in factor identification?

Answer 26

Data reduction exercise Simplifying as many asset return variables into a few key underlying factors.

Question 27

What are two common statistical techniques used to identify factors?

Answer 27

Factor analysis (Roll and Ross, 1980) Principle components analysis (PCA) (Connor and Korajczyk, 1986, 1988)

Question 28

Weakness of the statistical technique?

Answer 28

Often lacks economic meaning. Huang, Li and Zhoue (2019) propose a reduced rank approach

Question 29

Macroeconomic factors

Answer 29

Using economic factors that may impact future cash flows or discount rates.

Question 30

Who are the key contributors to the macroeconomics factor model?

Answer 30

Chen, Roll and Ross(1986).

Question 31

What did Chen, Roll and Ross (1986) propose?

Answer 31

Using macro variables like inflation, industrial production, and interest rate changes.

Question 32

What is the advantage of using microeconomics factors in APT?

Answer 32

Stronger theoretical motivation making it more interpretable

Question 33

Weaknesses of the macroeconomic factors?

Answer 33

Often subject to large measurement error. Reducing reliability

Question 34

Portfolio-based factors

Answer 34

Using stock characteristics known to be related to cross-sectional returns to form empirical factors

Question 35

What role does the market index play in empirical factor models?

Answer 35

All models include the stock market index and a baseline factor.

Question 36

What does the stock market factor typically represent?

Answer 36

Overall market risk.

Question 37

How are the empirical factors typically constructed?

Answer 37

As long-short portfolios

Question 38

Long short portfolio factor

Answer 38

Factor = return on one group of stocks - return on another group of stocks.

Question 39

What is the size factor(SMB)?

Answer 39

Small minus Big (SMB) = return on small-cap stocks minus return on large cap stocks

Question 40

What is the value factor (HML)?

Answer 40

High minus Low (HML)= return on value stocks(high book-to-market) - return on growth stocks (low B/M)

Question 41

Who introduced SMB and HML?

Answer 41

Fama and French (1993)

Question 42

How did Asness and Frazzini(2013) improve HML?

Answer 42

Propose a more timely version using up-to-date valuations

Question 43

What is the momentum factor (WML)?

Answer 43

Winners Minus Losers (WML) = return on past winners minus return on past losers.

Question 44

Who introduced momentum factor (WML)?

Answer 44

Carhart (1997)

Question 45

What do Pastor and Stambaugh propose as a factor?

Answer 45

An aggregate liquidity factor.

Question 46

What would an aggregate liquidity factor measure?

Answer 46

How sensitive a stock's return is to market-wide liquidity conditions.

Question 47

What new factors did Fama and French (2015) add in their five-factor model?

Answer 47

1. RMW (Robust minus Weak) = profitability 2. CMA (conservative minus Aggressive) = investment. This model is an extension of their three-factor model

Question 48

Stambaugh and Yuan (2017) 4 factor model.

Answer 48

Additional factors are size and two mispricing factors. The mispricing factors are formed from 11 efficient market anomalies

Question 49

How are the mispricing factors formed?

Answer 49

The mispricing factors are formed from 11 efficient market anomalies