1. Arbitrage Pricing Theory and Multifactor Models of Risk and Return
Chapter 10

4. https://variety.com/2018/legit/reviews/pretty-woman-musical-review-1202739203/

5. Single Factor Model Returns on a security come from two sources
Common macro-economic factor
Firm specific events
Possible common macro-economic factors
Gross Domestic Product Growth
Interest Rates

6. Single Factor Model Equation
Ri = E(ri) + Betai (F) + ei
Ri = Return for security i
Betai = Factor sensitivity or factor loading or factor beta
F = Surprise in macro-economic factor
(F could be positive, negative or zero)
ei = Firm specific events

7. Multifactor Models
Use more than one factor in addition to market return
Examples include gross domestic product, expected inflation, interest rates etc.
Estimate a beta or factor loading for each factor using multiple regression.

8. Multifactor Model Equation
Ri = Excess return for security i βGDP = Factor sensitivity for GDP βIR = Factor sensitivity for Interest Rate ei = Firm specific events

9. Interpretation The expected return on a security is the sum of:
The risk-free rate
The sensitivity to GDP times the risk premium for bearing GDP risk
The sensitivity to interest rate risk times the risk premium for bearing interest rate risk

10. Multifactor SML Models
E(r) = rf + BGDPRPGDP + BIRRPIR
BGDP = Factor sensitivity for GDP
RPGDP = Risk premium for GDP
BIR = Factor sensitivity for Interest Rate
RPIR = Risk premium for GDP

11. Arbitrage Pricing Theory
The discussion of multifactor models gives way to the idea that portfolios of stocks that “load” the same way on a given factor model (i.e., have the same betas) should have the same expected return. This leads to the idea of the APT.
Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit.
Since no investment is required, an investor can create large positions to secure large levels of profit.
In efficient markets, profitable arbitrage opportunities should quickly disappear.

12. It’s the word of the day!
Word of the day

14. Arbitrage Pricing Theory
Example

20. APT & Well-Diversified Portfolios
RP = E (RP) + bPF + eP
F = some factor
For a well-diversified portfolio:
eP approaches zero
Similar to CAPM

21. APT and CAPM Compared
APT applies to well diversified portfolios and not necessarily to individual stocks.
With APT it is possible for some individual stocks to be mispriced - not lie on the SML.
APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio.
APT can be extended to multifactor models.
Requires formation of factor portfolios
What factors?
Factors that are important to performance of the general economy
Fama French Three Factor Model

22. Portfolios and Individual Security
E(r)%
Portfolio
Individual Security

23. Disequilibrium Example
E(r)% 10 A D 7 6 C
Risk Free 4
Beta for F .5
1.0

24. Disequilibrium Example
Short Portfolio C
Use funds to construct an equivalent risk, higher return Portfolio D.
D is comprised of A & Risk-Free Asset
Arbitrage profit of 1%

25. Let’s arbitrage with an example!

31. Examples of the Multifactor Approach
Work of Chen, Roll, and Ross
Chose a set of factors based on the ability of the factors to paint a broad picture of the macro-economy (page 425).
% change in IP, %change in expected inflation, % change in unanticipated inflation, returns of corporate bonds over government bonds, returns of government bonds over t-bills.

32. Examples of the Multifactor Approach
Fama-French Three-Factor Model
The factors chosen are variables that on past evidence seem to predict average returns well and may capture the risk premiums
Where:
SMB = Small Minus Big, i.e., the return of a portfolio of small stocks in excess of the return on a portfolio of large stocks
HML = High Minus Low, i.e., the return of a portfolio of stocks with a high book to-market ratio in excess of the return on a portfolio of stocks with a low book-to-market ratio

33. Examples of firms that use APT