Tests of CAPM and Factor Models Flashcards
Why is linear regression a good estimator of the CAPM?
The Beta coefficient is measured as Covariance between Y and X over the Variance of X.
How can the variance of an asset’s excess returns be decomposed?
It can be decomposed into a systematic part (Beta squared times market variance) and the asset specific variance, which is news.
What should be the true value of alpha in the CAPM regression? Why is that?
The true value of alpha should be zero. The moel doesn’t have an alpha term.
What does Blume’s 1975 paper say about Beta estimation of portfolios with larger vs smaller number of securities?
Correlation coefficient for portfolios containing a larger number of securities are more correlated to past betas than those with few.
Discuss Blume’s 1971 paper on Beta estimation in and out of sample.
Out of sample Betas tend to be closer to 1 then in sample Beta.
Empirically, what do Black, Jense and Scholes 1972 have to say about excess returns and Beta?
That High beta stocks have lower excess returns than CAPM implies, while low beta have higher excess returns than CAPM implies.
How do Fama and MacBeth verify if the CAPM predictions hold? What are the results?
First estimate beta’s using OLS. Then regress excess returns on Beta, Beta square and idiosyncratic risk. The results are mixed, depend on time period.
What is a multi-factor model and why is it used?
Multifactor models incorporate potential sources of risks, which inccur a premium, other than market exposure. It is used because there is evidence that such risks are present.
Describe the Chen, Roll and Ross Multifactor model.
Model similar to FF Three factor models, but using macroeconomic variables.
1. growth in industrial production
2. unexpected component of inflation
3. quality risk premium
4. term premium
5. broad stock market returns
All are factors which might affect expected dividends and discount rates.
What are the three factors of the Fama-French Three-Factor Model.
Factors:
1. Excess returns
2. Payoff on portfolio which is long Small-Cap and short Big Cap (SMB)
3. Payoff on portfolio long High book-to-market stocks and short low boot-to-market stocks. (HML)
How do Fama and French construct their three factors portfolios.
They attempt to remove the effect of the other factors in any portfolio focus on any one factor. For example, the HML porfolio is Long a portfolio subset of HS and HB and short LS and LB.
HS: High Value - Small Cap.
HB: High Value - Big Cap.
LS: Low Value - Small Cap.
LB: Low Value - Big Cap.
Why would the R squared of a regression on a diversified portfolio be higher than that of a regression on one security?
Because the idiosynchratic variance on a diversified portfolio goes to zero.
What are two key assumptions of factor models?
- The residual returns are uncorrelated across securities.
- Covariance of X, i.e. return, with residual returns are zero.
Discuss one way of removing estimation in error in a market portfolio optimization problem?
Instead of using historical returns, use a market model return. That is, use returns from a CAPM, imposing an alpha parameter of zero.
