Asset Pricing: Home Assignment 1
Submitted by: Marc Ercolao, Lennart Janssen, Florian Preis,
Dominik Rappe, and Ludwig Skogman
Question 1
In this section, we regress the excess returns of the S&P 500 on the market risk premium of
the S&P 500 between January 1964 and January 1993. The mean returns of the 25 FF
portfolios, as well as their betas and alphas, are presented in Tables 1 to 3. All the variables in
the following regressions are retrieved from Kenneth R. French’s database using value
weighted monthly average returns. The regressions are executed in STATA.
Table 1. Mean Excess Returns
Low 2 3 4 High
Small 0.29% 0.74% 0.76% 0.96% 1.09%
2 0.40% 0.67% 0.90% 0.96% 1.07%
3 0.44% 0.74% 0.68% 0.89% 1.01%
4 0.46% 0.38% 0.64% 0.79% 0.91%
Big 0.33% 0.34% 0.35% 0.50% 0.61%
Table 2. CAPM Betas
Low 2 3 4 High
Small 1.427 1.253 1.160 1.075 1.108
2 1.436 1.233 1.113 1.041 1.125
3 1.362 1.167 1.035 0.979 1.076
4 1.230 1.136 1.045 0.972 1.091
Big 1.005 0.987 0.868 0.853 0.869
Table 3. Alphas
Low 2 3 4 High
Small -0.300 0.218 0.272 0.516 0.624
2 -0.196 0.153 0.432 0.530 0.603
3 -0.128 0.253 0.250 0.477 0.559
4 -0.057 -0.089 0.207 0.383 0.456
Big -0.092 -0.067 -0.016 0.147 0.248
Question 2
As presented in Table 1, the mean excess returns tend to grow larger in the north-east
direction. More specifically, as firms’ market capitalization decreases and book-to-market
ratio increases, their mean excess return grows. This is consistent with the small-firm effect
and the book-to-market ratio anomalies that are left unexplained while applying the CAPM.
Question 3
As presented in Figure 1, the mean excess returns of the 25 FF portfolios tend to grow larger
as firm size decreases and the book-to-market ratio increases. However, for all observed
portfolios, this relationship is not systematic. For instance, within the range of low book-to-
market portfolios, there is no clear trend of increasing excess returns, given a decreasing firm
size.
Figure 1. Mean Excess Returns Figure 2. Betas
The model, however, exhibits a more compelling, positive relationship between betas of the
25 FF portfolios, given a decreasing firm size and an increasing book-to-market ratio (as
shown in Figure 2). If we imagine the anomaly as a ratio between the excess return and the
given beta for a certain portfolio, it becomes clear that the portfolios within the lowest
valuation quintile exhibits the lowest trade-off between mean excess return and beta.
Therefore, the puzzle lies in the fact that CAPM overestimates betas for firms within the first
and second quintile of the book-to-market ratio.
Question 4
The alpha intercepts capture the anomalies that the CAPM model fails to explain when
regressing the excess return of the portfolios on the market risk premium. If the p-value of an
alpha indicates significance, we fail to reject the null hypothesis and therefore, we have to
question the reliability of CAPM.
Overall, the alphas tend to be significant at higher book-to-market values wher...
