Week 4 - Empirical evidence of the CAPM & Multifactor models

Question 1

Describe the empirical evidence on the two-pass cross-sectional tests of the CAPM.
Within the framework of these tests, comment on the results of Fama and French
(1992), who find that size and Book-to-Market are significant in explaining the cross-
section of stock returns in the US.

Answer 1

1. Excess stock returns and beta have a LINEAR POSITIVE RELATIONSHIP
   - consistent with CAPM
2. The relationship between excess returns and beta has a NON-ZERO INTERCEPT
   - CAPM predicts a zero intercept
3. SLOPE of the estimated SML is TOO FLAT
   - the estimated slope coefficient on beta is
   smaller than the market risk premium
   - CAPM predicts that it should be
   the market risk premium {R_m mean}
4. Other variables, besides beta, seem to matter in explaining excess returns, like size
   and book-to-market.
   - Fama and French (1992) find that the market capitalization of a stock and its book-to-market are SIGNIFICANT and dominate beta in CROSS-SECTIONAL REGRESSIONS {2nd pass of the 2-pass test} of excess stock returns.
   - CAPM predicts that only BETA should matter.

[include 2nd pass equation]
- CAPM implies that gamma_2 = 0
- It is not clear whether size and book-to-market represent RISK (e.g. risk related to small
firms or to distressed firms), or whether they are a manifestation of BEHAVIOURAL BIASES.

Question 2

How to comment if the Excel multifactor model R^2 is higher than the one obtained from the CAPM?

Answer 2

We can EXPLAIN a LARGER proportion of Disney’s RETURN VARIATION with a multifactor model.

Question 3

How to comment if the Excel SENSITIVITY to SMB is now significant?

Answer 3

The data suggest that the returns of
Disney CO-VARY with the RETURNS of LARGE FIRMS.

Question 4

CAPM (preference-based) vs Arbitrage Pricing Theory (arbitrage-based)

Answer 4

CAPM
- Investors care about their portfolio’s mean and variance;
– They dislike assets that increase variance;
– Hence, they demand higher expected return to invest in them;
– CAPM explains why MARKET FACTOR is relevant.

APT
- Based on constructing arbitrage-type strategies;
– Factors are taken as given, and are motivated by data;
– APT does not explain where the factors come from;

Question 5

3+2 main differences between the APT and the CAPM

[lecture slides + 2019 paper]

Answer 5

APT, like CAPM, also stipulates a relationship between expected return
and risk, but it uses different assumptions and techniques.
1. The APT assumes:
APT, like CAPM, also stipulates a relationship between expected return
» 𝑟𝑗 -𝑟𝑓 = 𝛼𝑗 + 𝛽1𝑗 𝐹 1𝑡 +… + 𝛽𝐾t 𝐹𝐾t + 𝜀𝑗t
i) Residuals 𝜀𝑗 are UNCORRELATED across assets. This is not an assumption of the CAPM.
ii) Returns are possibly NON-NORMAL (which CAPM usually assumes).
iii) Investors might care about MORE THAN just MEAN AND VARIANCE (In CAPM investors care only
about mean and variance)
2. The CAPM is PREFERENCE-BASED: If investors care about their portfolio’s mean and variance, they
dislike assets that increase the variance. Hence, they demand a higher expected return for investing in them. CAPM explains why market factor is relevant.
* The APT is ARBITRAGE-BASED: If expected return was not related to factor betas, then we would be
able to find arbitrage opportunities. APT does not tell us where the factors come from.