BA 411 Homework Assignment #4: Forecasting the stock market



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Homework Assignment #4: Choose either option 1 or option 2 below (due Tuesday, April 25)

Option 1: Steelware, Inc.

"Steelware, Inc., is a midwestern firm engaged in the warehousing and machining of rod and bar stock. The company primarily handles four types of rod and bar stock: stainless steel, cold drawn steel, brass, and aluminum. The machining operations consist primarily of close tolerance grinding and finishing services on these four kinds of stock. The grinding and finishing operations are sold on an hourly basis and are the company's most profitable operation.

The major difficulty encountered in selling these services is with the quotation procedure. Steelware must provide its customers with binding quotations on all its orders, yet orders vary with respect to the type of material, the number of bars, the diameter, and the required tolerance. At the time the data of this application were collected, every quotation was submitted to the foreman of the grinding department for an estimate of the number of grinding shop hours that the order would require. The

foreman's estimates were based on his experience, current shop conditions, and other subjective considerations. The procedure was time-consuming, costly, and inaccurate. Many potential orders were lost because of the delay in response to a request for a quotation.

...It was decided to explore the possibility of statistical forecasting. In the exploratory student for which data are given here, attention was focussed on grinding orders for stainless steel. One hundred of the most recent orders completed by the company in the late autumn ... were used as a sample."

(From Conversational Statistics with IDA by Harry Roberts and Robert Ling, Scientific Press, 1982. Used with permission.)

The data file contains information about a sequence of orders for grinding stainless steel stock. The variables are all time series--i.e., the observations are arranged in the same order in which the jobs were performed.

The variables are:

HOURS in grinding shop required by the order

Number of BARS in the order

DIAMETER (in inches) of rod or bar prior to grinding

Required TOLERANCE (max. allowable spread in 1000's of an inch)

The data are in a tab-delimited text file called STEEL.TXT (available on the web at duke.edu/~rnau/steel.txt).

Your task: Use the data to derive a model for generating quotations of the hours required to complete an order, given the number of bars and the diameter and tolerance--i.e., develop a model for forecasting the number of HOURS that a job will require, which can be used as the basis for a binding price quotation for the job.

How to proceed: You may wish to consider nonlinear transformations of the variables, and/or you may wish to consider using nonlinear regression, either in the Advanced Regression procedure in Statgraphics or in Excel's Solver. A scatterplot matrix may be revealing. (For more information on nonlinear regression, see the note on nonlinear regression that begins on page 163 in your coursepack. It’s also available on the course web site at .) Some things to think about: What kind of price quotation model will make sense to the customer? To management? What is the relevant measure of error that should be minimized? How accurate (or inaccurate) is your model in practical terms? What can be learned from these data that might be of use to management? Do you have any recommendations for changes in operating procedures or the collection and analysis of further data?

What to hand in: Your executive summary should be written in the form of a report to management, presenting your final forecasting model and justifying it in commonsense terms, together with any other recommendations you wish to make. You should also include a thorough description of the data analysis you performed, commenting on the important features of the data and comparisons among alternative forecasting models that were tested. Naturally, you should hold out some data for purposes of validation. If transformations of variables were used, be sure to include “before and after” pictures and an explanation of the rationale for the transformations.

Option 2: Forecasting international stock market returns

Stock market indices, when viewed in isolation, tend to appear as geometric random walks, but this does not necessarily mean that they are completely unpredictable. The objective of this assignment is to explore the extent to which the behavior of a country’s stock market index can be predicted one month in advance using fundamental variables and risk factors such as dividend yields, short- and long-term interest rates, inflation, industrial production, etc. The data set for this assignment has been provided by Professor Campbell Harvey, who is widely known for his research on predictable returns in international asset markets. (Some of the data is confidential--please do not use it outside the School. Also, please don’t ask Prof. Harvey for advice on this assignment. He has generously provided the data but otherwise offers his services only through his own courses. There is a great deal of background information available on his web page at .)

The data files include Morgan Stanley Capital International equity data for 24 different countries—Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, Malaysia, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, United Kingdom, and United States—plus World and EAFE. For each country, the indices represent value-weighted portfolios of the largest and most actively traded stocks--typically about 75% of the total market. Note: The EAFE column is the "Europe-Australia-Far East" index, and the "AC WLD" column is the "All Countries--World" index. The latter index contains more emerging markets than the MCSI "World" index in the first column, but unfortunately it contains data for only the last few years for some variables.

The stock market data are contained in an Excel workbook called MSCIJ97.XLS, available in the course web directory (i.e. at ). Each sheet in the workbook contains a different type of variable, and different columns on the sheet contain data for different countries. The sheet names and their contents as follows:

UNHEDGED: market total index (price+accumulated dividends) referenced to US$

LOCAL: market total index in local currency

HEDGED: market index w/ currency hedge (from Dec. ‘87 only)

YLD: average dividend yield

PE: price to earnings ratio

PBV: price to book value ratio

PCE: price to cash ratio

A second Excel workbook, called FACTORS.XLS, also available in the course web directory, contains data on interest rates, industrial production, and other factors that might be relevant to equity returns, arranged in a similar fashion. All of these variables are expressed as monthly percentages (rates, returns, or changes as the case may be). The sheet names and their contents are as follows:

SHORT: short-term interest rates

LONG: long-term interest rates

INDPROD: industrial production (already in units of percentage change!)

M1: money supply

INFLATION: inflation

OTHER: gold, silver, and art

USBENCH: U.S. benchmarks (annual data only)

All the time series begin in December 1969, and all are monthly except for the U.S. Benchmark series. The MSCIJ97 file contains data through December 1996, while most of the series in the FACTORS file extend until June or July 1997, with some variation. You are welcome to use additional variables obtained from Datadisk or Datastream, but that is not required for purposes of the assignment. The FACTORS file does not provide industrial production, interest rates, etc., for all countries, but data from the U.S. and other large economies may still be relevant to the prediction of stock returns in other countries.

Your task: Find the best multiple regression model for predicting the total market return in any one country of your choice. (You may use either the “local” or the “unhedged” return.) As independent variables, you may use any other variables lagged by at least one month. In other words, your model must be an “honest” forecasting model that can be used to forecast at least one month in advance (e.g., as the basis for a trading strategy). Identify and fit your model using only the first 277 observations (up to December 1992) and hold out the last 48 observations for validation. Compare the in-sample and out-of-sample performance of your model against the appropriate naive model for returns. The theory of finance suggests that variables such as dividend yields, expectations about inflation and industrial production, ratios of stock prices to cash and/or book value, and spreads between short- and long-term interest rates are likely to affect stock prices. The question here is whether such variables have predictive value one month or more in advance--and whether their predictive value is persistent enough over time to hold up in out-of-sample testing.

How to proceed:

(i) Choose a country to analyze, and build a Statgraphics data file containing the necessary variables. The easiest way to do this is to open both spreadsheet files and then copy and paste the desired columns of data to the Statgraphics data spreadsheet. (I suggest using Paste rather than Paste-Link, so that Excel doesn’t need to stay running.) You should copy the data only, not the column titles from the Excel worksheet--i.e., copy the cells in each column beginning with the data entry in the row corresponding to December 1969. It is CRITICAL that the different columns of data should be correctly aligned in time. If the first data entry in each column on the Statgraphics spreadsheet corresponds to December 1969, you should have no trouble. It doesn’t matter if some columns contain more data--i.e., more recent values--than others, as long as they all begin in the same month. Be sure to use the right-mouse-button “Modify Column” command to assign a descriptive name to each column as soon as the data is pasted in (if not before) so that you don’t get them mixed up. I suggest that you use generic names that do NOT specify the country (e.g., use UNHEDGED, LOCAL, PE, etc.). Then assign the FILE a name that identifies the country. Later, if you want to re-run your analysis and your model on a different country’s data, you will just have to open a different data file containing variables with the same names.

(ii) The date code on the Excel spreadsheets (6912 = December 1969) will not work as an index variable for selecting or plotting against in Statgraphics, so you should next use the “Generate Data” option on the Statgraphics spreadsheet to create a time index variable. To do this, highlight an unused column, hit the right mouse button, and choose “Generate Data” from the menu. COUNT(1,325,1) as the expression. This will fill the column with a series of index numbers. Now use the “Modify Column” command to assign the name INDEX to the new column.

VERY IMPORTANT: On every procedure that you use from this point onward--until you have selected your final model and are ready for out-of-sample testing--you should type INDEX ................
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