This problem set contains two parts. Part 1 tests your ability to set up and execute a time-series regression analysis in Excel. Part 2 requires you to modify the cross-sectional analysis of mutual funds returns in Lesson 2 and consider the differences.

**Part 1:** Recall the weak form of the efficient markets hypothesis. It states that there is no useful information in past prices or returns that would allow us to forecast future returns. You will test this hypothesis with a time series of daily returns for Apple.

Suppose you could forecast future stock prices by examining patterns in past prices or returns. This would be a great way to make money, and there is a field of study, technical analysis, where practitioners try to identify recurring patterns in stock prices and returns. However, there is a considerable body of evidence suggesting there is no useful memory in past prices. Let's do a quick experiment. The spreadsheet attached to this assignment contains two years of daily stock returns for Apple. The experiment is simple. Is today's return explained by the returns generated over each of the previous five trading days?

The regression approach can be modeled like this:

R_{t} = a + b_{1}(R_{t-1}) + b_{2}(R_{t-2}) + b_{3}(R_{t-3}) + b_{4}(R_{t-4}) + b_{5}(R_{t-5}) + e

The spreadsheet contains 502 daily returns. These are your Rt, or dependent variables. You will need to create five additional columns with the lagged returns. The lagged returns are just those occurring 1, 2, 3, 4, and 5 days prior to a particular value of Rt. Note that this means you must discard the first 5 observations. It's not until the 5th day of your sample that you can compute a complete set of independent variables.

- What are the null and alternative hypotheses associated with this test?
- Run the regression described above. Discuss your results. Do they support the weak form of the efficient markets hypothesis? Why or why not?
- Attach a copy of the Excel output for your regression analysis.

**Part 2:** Recall the analysis of our sample of small cap growth oriented mutual funds in Lesson 2. The data behind this analysis is linked to a slide within the lesson. In the analysis presented in Lesson 2, we ran two regressions. The first employed logtna (the log of total net assets under management, column E) and a number of control variables to explain returns on our sample of funds. The second regression added [logtna – avg.logtna]^{2}, denoted on the spreadsheet as size_sq (column F).

- Rerun the first regression using the raw (unlogged) values of total net assets (column D on the spreadsheet instead of column E). Use the control variables in columns G through J as well. (Note: You may want to rearrange the columns before running the new regression.)
- Before rerunning the second regression, recreate the values for the quadratic term, size_sq (column F) using raw (unlogged) values of total net assets. In other words, create a variable: [tna - avg.tna]
^{2}.Now rerun the second regression. - Discuss your results for both of the new regressions focusing on the expected signs and significance of the independent variables. Also discuss any differences between these results and the original regressions that used the logged values of total net assets.

Subject | Mathematics |

Due By (Pacific Time) | 04/04/2015 12:00 am |

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