 # Regression

| July 16, 2015

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:

Rt = a + b1(Rt-1) + b2(Rt-2) + b3(Rt-3) + b4(Rt-4) + b5(Rt-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.

1. What are the null and alternative hypotheses associated with this test?
2. Run the regression described above. Discuss your results. Do they support the weak form of the efficient markets hypothesis? Why or why not?
3. Attach a copy of the Excel output for your regression analysis. Get a 5 % discount on an order above \$ 150
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