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# Testing for the 'January Effect' under the CAPM framework

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In this project, we used the Capital Assets Pricing Model (CAPM) to test for the ‘January effect’ - a calendar‐related market anomaly in the financial market where financial security prices increase …

In this project, we used the Capital Assets Pricing Model (CAPM) to test for the ‘January effect’ - a calendar‐related market anomaly in the financial market where financial security prices increase in the month of January.

Please refer to "Chapter 2 – The Capital Asset Pricing Model: An Application of Bivariate Regression Analysis" of the book "The Practice of Econometrics" by Ernst R. Bernd for the test data, background and problem statement.

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• 1. Exercise 8: “Is January Different?” Group – 6Alice 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 = rm – rf = (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 rm = rm + jm and the risk-free assets return is unaffected: MRP = rm – rf = rm + jm – rf Further,if the CAPM model were true and the α and ß parameters were constant: rp = rf + α + ß (rm – rf) => rp = rf + α + ß (rm – rf) + ß jm
• 7. Part B Since, rf + α + ß (rm – rf) = rp, our equation becomes: rp ≡ rp + ß jm Re-writing the CAPM eq. using the right-hand sides of the above expression: rp – rf = α + ß (rm – 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 0.3763Computers 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 0.7934Foods 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 0.1957Banks 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 0.0000Computers 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 0.0000Foods 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 0.0003Banks 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!