Assignment on Ponzironi. (Individual)

Write up the discussion question carefully. The other questions can be answered in as minimal a fashion as you can. You don't have to clean up graphs and output for any of the questions but the discussion question.

1. This problem will have you reanalyze Dent's data. I will walk you through a series of precise questions. You should have a handout which has the Business Week article on Dent (on line link). The data can be downloaded from the class web page.
   1. Generate a plot that matches the business week plot as well as possible. (i.e. use as close to the same years as he uses.) Use the VW (which is included in the dataset) instead of the DOW. You will need to multiply the VW returns together to generate the VW series itself. Then take the log of the VW you just created. Now generate a plots of the whole time series. Does his model seem to do well in the first part of the century? Can you think of a reason why things might have been different then?

   2. To check his claim that population predicts the DOW, run a regression of the ln(DOW) on age45. (Actually, you have the market value weighted and not the DOW. It is hard to come by silly indices like the DOW for long time series.) What is the R-sqrd? Impressive or not?

   3. Get both your time series plot and your regression up on screen at the same time. Now use a brush to brush the points on the time series graph and watch what is happening on the regression graph. Does it appear random? To see this as a static graph, plot the residuals vs. time. Do they appear as a shot-gun pattern?

   4. Create a column of last years residuals. (This is called lagging a variable. You can do it in JMP by using a subscript of row-1.) Plot last years residuals (X) vs. this years residuals (Y). If they were independent you would not see any pattern at all. Describe what you see.

   5. To fix this problem with the residuals, compute the difference of the log(VW). (This generates a log return.) Now compute the difference of the age45 variable. Notice that if age45 predicts log(VW) then difference of age45 should predict difference of log(VW). (This means you have to compute age45_t-age45_t-1.) Run this regression. Check if the residuals have the problems discussed above. Finally we now have a model where we can believe the p-values. Does age45 seem significant?

2. (Bonferroni concepts.) In this problem we will try to predict the VW returns by looking at population. From the last problem we see that differences are statistically much better to analyze than the raw index itself. So we need to generate a table that has differences in the log(VW) and differences in each of the age variables. In about 30 minutes you could do this in JMP by creating 80 new columns like dif(Age0,1), dif(Age1,1), etc. Or you can do it much more "efficiently" by dumping it into a spread sheet, and doing it all at one time. (Estimate time 45 minutes, but some have done it in less than 5 minutes.)
   1. First let's see if age 45 is the best age when trying to predict the VW returns. Run a stepwise regression of the VW returns on dif(age0), up to dif(age80). Have it do one step and it will add a single variable. Did dif(age45) do the best? What is the p-value for this variable? Is it significant?

   2. Now let stepwise regression run to completion. What is the best R-squared you can find? You might as well use both the dif(age) variables, and the age variables themselves.

   3. Possible it isn't just he population itself that matters, but interactions between different ages. So generate a model that has all of the ages in it and all of the products between different ages in it. (One way, to do this is to highlight all the ages and then use the macro button for "response surface".) Change the p-value to enter to a small value and also change the p-value to leave. Now run the model. How high an R-squared do you get? Your final model should look pretty impressive in terms of t-statistics. Is this the case? But, are your p-values impressive from a Bonferroni perspective? (Use .05/number of variables to check the Bonferroni level of significance.)

   4. Save your predictions of your best fitting model to a column. Now use a formula to invest in the market whenever your prediction is for the market to outperform cash that year and invest in cash otherwise. (Assume cash grows at 3% per year.) Compute your average returns of using this policy. These returns are Ponzironi!

3. (Discussion) Discuss your analysis of Dent. Pretend you were writing an article to be put up on Business Weeks' web page. Communicate your point with punch, and have any geeky stuff in an appendix. You will probably want to have a graph or two to communicate your main point in the body of your story. Make the graph self-contained. Ideally someone should be able to cut out your graph and use it in class to communicate much of the point of your story. You may want to put other graphs and discussions in an appendix. Aim for less than 2 pages of text. The editor might decide to use only the first few paragraphs of your story, so make sure you put your key points early!

4. For each of the following situations estimate an appropiate n to use for a Bonferonni correction. (You should read the Dawkins paper to get an idea of how to think about these.) Provide the number and a sentence describing your justification.

   1. You are looking at the returns over the past year for the 3000 stocks trades on the NYSE. You find one that appears to be a winner.

   2. You download 100 economic variables to use to predict the SP500's returns. You compute all the interaction terms: (I.e. X1 * X3, X17 * X99, X12 * x12). One of these seems to predict the SP500 returns.

   3. You are wondering what IBM's has excess returns. You look at their return over the past month, over the past 2 months, over the past quarter, the 1/2 year, the past year, the past 2 years, the past 5 years, the past 10 years, the past 20 years, and the past 50 years. In each case you test if IBM has excess returns. You appear to find a time period which has excess returns.

   4. A friend suggests that you look at stock XYZ (which is traded on the NYSE). She says that it has excess returns over the past 5 years.

   5. You are reading a on-line investment advisory which suggests that you should use the GNP/capita times the 5 year Eurodollar futures price to generate a leading indicator for the DOW. Looking at the track record, it seems to predict well.