If the market is efficient, what value would you expect for alphas? Are they supposed to be close to any number? Do alphas from your analysis support the notion that financial markets are efficient? Or, are they against market efficiency?

DISCUSSION ESSAY

Your Report
In your report, you answer the following questions. You must review the course slides before starting the project. Do not copy reports that are publicly available from financial websites. You must rely on your own test results to answer the questions.

Limit all your answers to four pages (single space). Use the first two pages for your answers (pages 1–2) and use the next two pages for two regression tables. On page 3, include the table based on Q1–Q8 and the other table on page 4 to answer Q9 after expanding the data. The third and fourth pages need to be landscape so that you can include all nine regressions in one table. Also, attach the proof of regression work you obtain from a statistical program such as STATA results. That is, your completed project will have a four–page report along with the detailed regression results that I can review.

1. Make one table with nine columns for nine individual regressions following the format below. Report all coefficients and corresponding t–statistics in parentheses. Note that the numbers in parentheses do not mean negative values. They are t–statistic values you obtain from the regression tests. Use ***, **, * signs to indicate statistical significance at the 1%, 5%, and 10% levels, respectively. If the estimated coefficients are not significant at the l0% level, do not use the asterisk signs. Use p–values to know the levels of statistical significance. For example, if a p–value is less than 0.01 (i.e., 1% level), give *** to the number. In this way, we can easily find which relationships are strong. At the bottom, report the number of observations and R2. Use four and two decimals for coefficients and t–statistics, respectively.

Example) AESGX BSCFX FLPSX FMAGX GSIFX UNWPX VTSMX VWINX Your Pick
Alpha 0.2814 0.2014 0.0586 4.9839 –0.1315 0.1962 –0.0019 0.2602** 0.3330***(0.81) (0.84) (0.32) (1.30) (–0.61) (0.25) (–0.06) (2.02) (1.67)MmR–F mR 0.7715*** 0.9551*** 0.9491*** –0.9436 0.8053*** 0.6078*** 1.0002*** 0.2727*** 1.0739*** (8.14) (14.73) (18.98) (–0.91) (13.84) (2.82) (124.18) (7.81) (8.92)
SMB 0.8386*** 0.5044*** 0.4669*** 0.3069 –0.0057 0.6556** –0.0064 –0.0771* 0.3887
(6.86) (6.03) (7.24) (0.23) (–0.08) (2.36) (–0.62) (–1.71) (0.20)
HML –0.1404 0.0482 –0.1461* 1.4635 –0.1085 –0.1383 –0.0210 –0.0524 4.2353*
(–0.90) (0.45) (–1.78) (0.86) (–1.14) (–0.39) (–1.60) (–0.91) (1.72)
RMW –0.1952 0.1417 0.4205*** –1.4794 –0.0943 0.4114 0.0172 0.1467** –1.9932
(–1.20) (1.27) (4.90) (–0.83) (–0.94) (1.11) (1.25) (2.45) (–0.77)
CMA 0.1333 –0.3487** 0.3429*** –1.4151 0.0930 –0.1510 0.0350* 0.2403*** –4.0104
(0.63) (–2.42) (3.08) (–0.61) (0.72) (–0.32) (1.97) (3.09) (–1.20)
UMD –0.0523 0.0506 –0.1672*** –0.6164 –0.1037** 0.0051 –0.0301*** –0.1174*** –0.2826
(–0.77) (1.09) (–4.67) (–0.83) (–2.49) (0.03) (–5.25) (–4.69) (–0.26)
N of obs. 237 237 237 237 237 237 237 237 237
R2 0.531 0.667 0.733 0.011 0.623 0.077 0.991 0.351 0.016

This table reports the estimated coefficients of six factors. The monthly data on the four factors are collected from Prof. French’s website, http://mba.tuck.dartmouth.edu/pages/faculty/ken.frenc /data_library.html. t–statistics are reported in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.

2. Which alphas are positive and negative? Based on the p–values, are they significantly different from zero?

3. Is the alpha of VTSMX close to zero? If then, why is it supposed to be around zero?  (Hint: Look at the full name of the fund).

4. Now, provide general interpretations. Give your detailed answers for the estimated alphas (intercepts) from all nine regressions. Learn how to read regression results. To comment on the findings, you must have a good understanding of estimated coefficients, p–values, and t–statistics. There are various sources of information on the internet and the textbook. Concentrate on the alphas and do not interpret betas. Your interpretations should include the numbers reported in the table. That is, try to anticipate how much returns you can make using these funds. Also, tell the boss how confident you are with your estimations.

5. You need to find one specific fund and add it to your analysis. Which fund do you include in this report? Briefly introduce the fund and explain why you selected it.

6. Based on the alphas, which fund do you recommend for future investment? And, why do you choose it?

7. Based on the alphas, which fund is worst in your analysis? And, why?

8. If the market is efficient, what value would you expect for alphas? Are they supposed to be close to any number? Do alphas from your analysis support the notion that financial markets are efficient? Or, are they against market efficiency?

9. Are your answers for the best and worst funds changed if you extend the data to any available period for each fund? For instance, the monthly returns of FMAGX are available from the early 1980s. Use the same ending month. Make another table for this change.

Hint: The “if” code for the first–month restriction can be removed to include the earlier information. (e.g., reg dep ind if year_month>=200111 & year_month<=202112).