Week 8 - APT and French Fama Three Factor Model

Question 1

What the sources of a return on a stock?

Answer 1

Common macro-economic factor (Gross Domestic Product Growth, Interest Rates) and firm specific events

Question 2

When using the Single Factor model, how do we calculate the excess return on Security i?

Answer 2

Ri = E(Ri) + βiF + εi

Where:
- F = Surprises in Macro-Econ Factor
F = g to power of GDP - E (g to power of GDP
- εi = Firm Specific Event

Question 3

How do you calculate the excess return in the multifactor model?

Answer 3

Ri = E(Ri) + βi,gdp GDP + βi,ir IR + εi

Where:

• > βi,GDP: Factor sensitivity for GDP
• > βi,IR: Factor sensitivity for Interest Rate

Question 4

What does the APT Theory predict?

Answer 4

Predicts a security market line linking expected

returns to risk, SML.

Question 5

What are the 3 assumptions of the APT Theory?

Answer 5

(1) Securities described with a Factor Model
(2) There are enough securities to diversify away idiosyncratic risk
(3) Arbitrage will disappear quickly

Question 6

When does an Arbitrage Opportunity arise?

Answer 6

• > Arises when a zero investment portfolio has a sure profit
• > No investment is required so investors can create large positions to obtain large profits

Question 7

In efficient markets what happens to Arbitrage Opportunity?

Answer 7

In efficient markets, profitable arbitrage opportunities will quickly disappear -> Since every investor would want to get free money

Question 8

What is the key difference between CAPM and the APT?

Answer 8

CAPM -> large number of investors are mean-variance optimizers is critical

APT -> implication of a no-arbitrage condition is that a few investors who identify an arbitrage opportunity will mobilize large dollar amounts and quickly restore equilibrium

Question 9

In a well diversified portfolio, what happens to εp (Portfolio Specific Event) according to APT?

Answer 9

εp:

1. Approaches zero as the number of securities in the portfolio increases
2. And their associated weights decrease.

Therefore any value of εp virtually zero
-> More stocks, lower εp and in turn excess return similar to E(r)

Question 10

What does Arbitrage involve?

Answer 10

Forming a riskless costless portfolio that earns a positive return.

SEE EXAMPLE IN NOTES

Question 11

When is a stock overpriced and underpriced in the APT model?

Answer 11

Excess Demand -> Underpriced
Excess Supply -> Overpriced

This causes arbitrage

Question 12

Using the APT model, what is the expected return of a well diversified portfolio?

Answer 12

E(Rp) = αp + βpE(Rm)

Where M is mkt factor

Question 13

What does the expected return formula of a well diversified portfolio imply?

Answer 13

Securities with same beta, should have same excess return and lie on SML

Question 14

What happens when Beta is different?

Answer 14

SEE GRAPH IN NOTES

Question 15

What does the Arbitrage activity pin for risk premium of any 0 beta well diversified portfolio to?

Answer 15

arbitrage activity will quickly pin the risk premium of
any zero-beta well diversified portfolio to zero. This implies
αp = 0 which means: E(Rp) = βpE(RM )

With APT it is possible for some individual stocks to be
mispriced- not lie on the SML, although APT must hold for most stocks.

Question 16

What are the differences between APT and CAPM?

Answer 16

APT:

• > Equilibrium means no arbitrage opportunities.
• > APT equilibrium is quickly restored upon arbitrage.
• > Assumes a diversified portfolio, but residual risk is still a factor.
• > Does not assume investors are mean-variance optimizers.
• > Reveals arbitrage opportunities

CAPM:

• > Model is based on an inherently unobservable “market” portfolio.
• > Rests on mean-variance efficiency.
• > The actions of many small investors restore CAPM equilibrium.
• > CAPM describes equilibrium for all assets.

Question 17

How do you calculate the Excess Return in a multifactor model?

Answer 17

-> Use more than one systematic factor:

Ri = E(Ri) + βi1F1 + βi2F2 + εi

Question 18

What do you need to construct the Multifactor model?

Answer 18

Requires formation of factor portfolios

Question 19

What are factor portfolios?

Answer 19

Tracks a particular source of macroeconomic risk, but are uncorrelated with other sources of risk

-> Each factor portfolio has β = 1 for one of the factors and 0 for all other factors

Question 20

What does the multifactor model generate?

Answer 20

2-factor equivalent of
the SML:
E(ri) = rf + βi1(E(r1) − rf ) + βi2(E(r2) − rf )

Same interpretation as single factor model

Question 21

How do you implement factor portfolios?

Answer 21

• > Putting the factors into the model

- > Construct a factor mimicking portfolio -> THIS IS WHAT FRENCH FAMA DOES

Question 22

What does the French Fama 3 Factor Model consider?

Answer 22

• > that value and small-cap stocks outperform markets on a regular basis.
• > Whereas big cap and growth stocks see lower alphas and lower return given Beta

Question 23

How does the French Fama Model add on to CAPM?

Answer 23

adding size risk and value risk factors to the market risk factor in CAPM.

Question 24

What are the 3 Systematic Risk Factors the French Fama Model considers?

Answer 24

1. firm size
2. book-to-market ratio (B/M)
3. the market index.

Question 25

Why does the French Fama Model state that a stock’s Beta is not an adequate measurement of systematic risk?

Answer 25

• > Only way positive-alpha strategies can persist in a market is if some barrier to entry restricts competition.
• > However, the existence of these trading strategies has been widely known for more than 15 years.
• > Another possibility is that the market portfolio is not efficient, and therefore, a stock’s beta with the market is not an adequate measure of its systematic risk.

Question 26

What is the first factor mimicking portfolio in the French Fama Model?

Answer 26

Self-financing (or zero-net investment size-factor) portfolio

->long position in the market portfolio and short position in the risk-free security.
-> This is used because even when the model
fails (positive alpha), portfolios with higher average returns do tend to have higher betas.

Question 27

What is the second factor mimicking portfolio in the French Fama Model?

Answer 27

Market Capitalization Strategy(small-minus-big (SMB)
portfolio): place firms into one of two portfolios based on their market value of equity:

• > Firms with market values below the median of NYSE firms form an equally weighted portfolio, S (small)
• > Firms with market values above the median of NYSE firms form an equally weighted portfolio, B (big)

Question 28

What is the third factor mimicking portfolio in the French Fama Model?

Answer 28

Book-to-Market Ratio Strategy (high-minus-low (HML)
portfolio):

• > Firms with book-to-market ratios less than the 30th percentile of NYSE firms form an equally weighted portfolio, L (low)
• > Firms with book-to-market ratios in the middle 40th, medium, and greater than the 70th percentile of NYSE firms form an equally weighted portfolio, H (high)

Question 29

What are the returns on the Big and Small Portfolios?

Answer 29

RS = 1/3(RS/L +RS/M +RS/H );

RB =1/3 (RB/L +RB/M +RB/H )

Question 30

What are the returns on the High and Low Portfolios?

Answer 30

RH = 1/2(RS/H + RB/H )
RL = 1/2(RS/L + RB/L)

Question 31

Therefore, what are the overall return on the SMB portfolio and the HML portfolio?

Answer 31

R smb = RS − RB (Long small, Short Big)

R hml = RH − RL (Long high B/M, Short low B/M)

Question 32

Why do we long small and short the high portfolio in the 3 Fama Model

Answer 32

Since small stocks give higher alphas -> Outperform the mkt

Question 33

Why do we long high B/M and short the low B/M portfolio in the 3 Fama Model

Answer 33

Higher Book to market ratios been undervalued stocks -> Higher alpha -> Generally higher returns

Question 34

How do we calculate the French Fama Model therefore?

Answer 34

E(ri) = rf + βMkt(E(ri) − rf )+ si E(rSMB ) + hi E(rHML)

s = small 
h = high