The document presents an analysis of the "January effect" hypothesis which claims that stock returns are higher in January. The analysis tests this hypothesis in multiple ways: (1) Within the CAPM framework, it is not possible to test for a January premium. (2) Regressions of returns for various companies show no significant difference in January intercepts or slopes. (3) Allowing the January intercept to differ in a CAPM regression also shows no significant differences. Based on these results, the analysis concludes that returns and risk premiums are not significantly different in January compared to other months.

1. Exercise 8:
“Is January
Different?”
Group – 6
Alice Nušlová, Rocio Cataño
Lov Loothra & Nikhil Garg

2. Agenda
 BriefIntroduction
 Our solution for
Exercise 8
(Parts A - E, sans D)
 Conclusion (Part F)
 References

3. Introduction
 There is evidence that stock returns in the
month of January are relatively higher
 This is curious because even if we consider
investors selling losing stocks in December,
the expectation of higher January returns
should shift supply-demand curves and
equilibrate returns
 We will try to empirically and statistically
test this hypothesis in our presentation

4. Part A
 Assumption: “January Premium”, jm affects
market return and risk free return
 Market risk premium is then given by:
MRP = r'm – r'f = (rm + jm) – (rf + jm)
MRP ≡ rm – rf
 MRPis thus not affected by the January
Premium

5. Part A
 Testing the “January is different” hypothesis
within the CAPM framework:
rj – rf = αj + ßj (rm – rf) + εj
 Not possible as the independent variable of
the regression (rm – rf) would be unchanged
 Also not reasonable to assume that “January
is different” only for risky assets because, if so,
the returns of all stocks (including the risk-free
returns) should differ (not just risky assets)

6. Part B
 If r'm = rm + jm and the risk-free assets return
is unaffected:
MRP = r'm – rf = rm + jm – rf
 Further,if the CAPM model were true and
the α and ß parameters were constant:
r'p = rf + α + ß (r'm – rf)
=> r'p = rf + α + ß (rm – rf) + ß jm

7. Part B
 Since, rf + α + ß (rm – rf) = rp, our equation
becomes:
r'p ≡ rp + ß jm
 Re-writing the CAPM eq. using the right-hand
sides of the above expression:
r'p – rf = α + ß (r'm – rf ) + ε
=> rp + ß jm – rf = α + ß (rm + jm – rf) + ε
=> rp + ß jm – rf = α + ß (rm – rf ) + ß jm + ε

8. Part B
 Considering ß jm to be unobservable, we
subtract it from both the sides to get:
rp – rf = α + ß (rm – rf) + ε
 We observe that the equation has reduced to
the original CAPM equation sans the January
premium
 We conclude that we cannot estimate the
“January premium” within the CAPM
framework under these assumptions as well

9. Part C
 For
this part, we chose the following three
industries and their corresponding
companies:
 Computers (IBM and DATGEN)
 Foods (GERBER and GENMIL)
 Banks (CONTIL and CITCRP)
 For each of these companies we ran the
following regression:
rp = α + ß (DUMJ)

10. Part C
Intercept Slope (DUMJ)
Industry Company
LSE SE p-val LSE SE t-stat p-val
IBM 0.00817273 0.005633 0.1495 0.017327 0.019512 0.888016 0.3763
Computers
DATGEN 0.00405455 0.012163 0.7395 0.041146 0.042133 0.976555 0.3308
GERBER 0.0157636 0.008398 0.063 0.007636 0.029093 0.262482 0.7934
Foods
GENMIL 0.0170909 0.006225 0.007 -0.00609 0.021566 -0.28244 0.7781
CONTIL -0.0064818 0.014327 0.6518 0.064582 0.04963 1.30127 0.1957
Banks
CITCRP 0.0118455 0.007753 0.1292 0.000155 0.026857 0.005754 0.9954
Summary of Regression Analysis

11. Part C
 We test for the following hypothesis:
H0: ß = 0
Ha: ß ≠ 0
 Using a 95% confidence interval, we cannot
reject H0 for any of the chosen companies
because:
 For all observations, p-value is larger than 0.05
 Equivalently, t--statistic is less than 1.98
 We thus conclude that January is not different
for all the chosen companies

12. Part E
 For this part, we ran the following regression
for all the companies we’d chosen in part c:
rp – rf = α + ß1(DUMJ) + ß2(rm – rf) + ε
 By doing this, we have restricted the slope
coefficients to be the same for all months but
have allowed the intercept term for January
to be different from the common intercept for
the other months

13. Part E
Intercept DUMJ Market Risk Premium
Industry Company
LSE p-val LSE t-stat p-val LSE p-val
IBM -0.001173 0.8093 0.008424 0.501443 0.617 0.454218 0.0000
Computers
DATGEN -0.0084713 0.4102 0.02148 0.605076 0.5463 1.02418 0.0000
GERBER 0.00545394 0.462 -0.00453 -0.17696 0.8598 0.626992 0.0000
Foods
GENMIL 0.00875192 0.148 -0.01159 -0.5566 0.5789 0.273791 0.0015
CONTIL -0.0172848 0.207 0.050747 1.07557 0.2843 0.715408 0.0003
Banks
CITCRP 0.00129034 0.8415 -0.01284 -0.57597 0.5657 0.670978 0.0000
Summary of Regression Analysis

14. Part E
 We will now test for the null hypothesis that
“January is different”:
H0: ß1 = 0
Ha: ß1 ≠ 0
 Using a 5% significance level and checking the p-
values of the DUMJ variable, we observe that we
cannot reject H0 (for each observation p-value is
larger than 0.05 and t-statistic is smaller than 1.98)
 We conclude that the intercept in the CAPM
regression is the same for January and the
remaining 11 months of the year

15. Part E
 We now test the null hypothesis that “January is
better” which corresponds to a one-sided test for
the DUMJ variable:
H0: ß1 = 0
Ha: ß1 > 0
 We compare the t--statistic of the ß1 parameter for
each of the observations with 1.658 and observe
that it is less than 1.658 in all the cases
 We therefore conclude that the “January is
better” hypothesis is false for all our chosen
companies

16. Part F
 In Part A, “January premium” affected the returns
of both the risk-free and the risky assets & in Part B,
we assumed that the premium affected only the
risky assets returns. But we concluded in both
cases that if a “January premium” does exist, it
cannot be tested for within the CAPM framework.
 In Part C, we used 6 companies from 3 different
industries and investigated them by introducing a
dummy variable for January (DUMJ) and running
the regression: rp = α + ß (DUMJ), but we were not
able to reject the null hypothesis and can
conclude that “January is different” at 5%
significance level for every company.

17. Part F
 In part E we allowed for a difference only in the
intercept term within the CAPM framework and
ran the regression: rp – rf = α + ß1(DUMJ) + ß2(rm – rf) +
ε. We concluded that at a 95% confidence
interval, the intercept does not change
significantly in January for all the chosen
companies.
 Hence, based on the results in each part of the
given exercise we are in a position to conclude
that the returns and the risk-premiums are not
significantly different in January as compared to
the other months of the year, i.e., January is not
different.

18. References
 [1] Berndt, "The Practice of Econometrics;
Chapter 2 – The Capital Asset Pricing
Model: An Application of Bivariate
Regression Analysis”
 [2] Prof. Dr. Bernhard Schipp, Course
Script: “Financial Markets and Financial
Institutions (Essentials of Quantitative
Finance)”

19. Thank you!