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# In the accompanying data file, you are given monthly returns of four stocks: JCPenney, Amoco, GM and JPMorgan for 240 months during the 20 year period from 1975 to 1994.

INSTRUCTIONS TO CANDIDATES

Question 1:

Portfolio Optimization:

In the accompanying data file, you are given monthly returns of four stocks: JCPenney, Amoco, GM and JPMorgan for 240 months during the 20 year period from 1975 to 1994. We are interested in developing optimal portfolios (in Markowitz' sense) using only the last 14 years (1981-1994) of data. In so doing, you will go through the following steps and present your results in a report.

(a) Using JMP IN or EXCEL analyze each of the four stock returns and estimate the mean, variance and standard deviation of the monthly returns. In so doing, identify the stocks with the maximum expected return and minimum variance (or standard deviation).

(b) Using JMP IN or EXCEL estimate the correlation between each pair of stocks and identify whether any of the stocks are negatively correlated.

(c) Using the results from parts (a) and (b), develop a spreadsheet model where you obtain the covariance for each pair of stocks (as we did in class).

(d) Now assume that a particular investor will allocate his/her monthly funds equally between these four stocks. Obtain the monthly portfolio mean and variance (or standard deviation) for this investor.

(e) Consider another investor who allocates funds equally between Amoco and JPMorgan (that is, nothing is invested in JCPenney and GM). Compare this portfolio's mean and variance (or standard deviation) with that portfolio in part (d). That is, discuss which one has a higher average return and which one has a higher standard deviation (or variance).

(f) Using EXCEL solver find the minimum variance portfolio that guarantees at least an average (mean) monthly return of 0.0125. How are the funds allocated in this portfolio ? Compare the average return and standard deviation of this portfolio with that of the investor in part (d).

(g) Find the minimum variance portfolios (separately) with at least an average return of 0.013, an average return of 0.0135, and an average return of 0.014. Compare the means and standard deviations of these portfolios as well as their optimal allocations (including the one in part (f)). What do you observe as you are increasing the minimum average return requirement in the portfolio?

Question 2 (Pronto Pizza):

After receiving your report, Tony Scapelli decided to delay the 29-minute guarantee program until after collecting additional data based on your recommendations. Tony also decided to hire two additional drivers for Friday and -Saturday deliveries. Over a period of five weeks, Tony monitored deliveries and collected data on the same variables as in his first data collection. To avoid the sampling bias of the earlier data, Tony sampled every 10th pizza delivery order. He carefully measured the time required to prepare the order and the amount of time it had to wait for a driver to become available. Instead of going on the delivery to measure the travel time, Tony phoned ahead to the waiting customer and offered a discount coupon if the customer would call back with the exact time the Pizza arrived. In this way, Tony hoped to avoid the potential for response bias with the delivery person. At the end of the five-week period, Tony had collected data on 324 deliveries.

Assignment: Once again, Tony is relying on you to provide an analysis of the new data that he has collected and to recommend whether or not be should offer the 29-minute guarantee on Pronto Pizza deliveries. He is committed to going with the 29-minute delivery guarantee unless the data strongly indicate that the percentage of free pizzas given away due to late deliveries exceeds the 5% break-even point.

Thoroughly analyze the new data collected by Tony contained in the file ProntoRevisited. Write a statistical consulting report detailing your analysis and your recommendation on the 29-minute guarantee. Be sure to discuss any other innovative things that Tony might do in order to improve his pizza delivery process and compete with his new rival.

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