Section 2a Multi-Factor models

Question 1

Does alpha or beta capture all compensation for risk in CAPM?

Answer 1

Beta, alpha is assumed to be zero.

Question 2

What does a positive or negative alpha imply=

Answer 2

A arbitrage opportunity

Question 3

How do you test for CAPM for individual stocks?

Answer 3

First stage:
Run regression of monthly return of stock i on market excess return
rit −rft = αi + βi (rmt −rft ) + uit
estimate beta for each stock

Second stage:
Use estimate of beta and see if average of relized return is solely determined by the systematic risk:
mean(ri - rf) = α + γβi + λVar(ui)
We gotta get alpha=0, γ ≈ mean(rm −rf ), λ = 0

Question 4

What are some potential explanations of failure

Answer 4

1. Is S&P500 a good proxy for what we call market portfolio in derivation of CAPM?
2. Maybe average realized returns are poor estimates for expected returns?
3. May investors borrow freely at the risk-free rate=
   - Betas as RHS variable in the second-stage regression are noisy estimates out of first-stage regressions

Question 5

Size Portfolios

Answer 5

Sort stocks based on size: market value, then construct 10 portfolios, obtain beta for each size-portfolios (time-series regressions), plot excess return verssus beta (in cross section)
A pattern of positive alpha for small stocks is identified- known as size effect

Question 6

Book-to-Market Portfolios

Answer 6

Sort stocks based on book-to-market, then construct 10 portfolios, obtain beta for each portfolio (time-series regressions), plot excess return versus beta (in cross section)
A pattern of positive alpha for value stocks is identified.

Question 7

Labor Income Risk

Answer 7

We care not only about financial wealth but other nontradable and valuable assets as well.
Different individuals have different exposure to the labor market.
Since we cannot trade human capital as company’s stock in the market, so it is no counted as the market portfolio.

Question 8

The Fama-French Three-Factor Model (FF3)

Answer 8

A risk factor can be measured by the return on a self-financing portfolio.
Fama & French- double sort portfolios, based on market value and book-to-market ratio each year.
3 Risk factors: Market excess return, SMB, and HML

Question 9

Momentum

Answer 9

Buy stocks with high past returns, short (selling) stocks with low past returns.
Rank stocks based on the past 6-12 month realized returns, earn a positive alpha in the next 3-12 months.
Timing is a crucial factor since there is a large risk that you would earn a negative return if you follow this strategy with a delay “long-term Reversal”.
It is all about excess return not explained by beta of the market or common risk factors like FF3.

Question 10

Smart Beta (Factor investing)

Answer 10

Investors may not care about various factors equally, some may not care about a specific risk factor at all.
Investors may tilt their portfolio towards factors they don’t care about/are not naturally exposed to.

Question 11

Characteristic-based method

Answer 11

A model for future realized return.