Statistics 103
  Probability and Statistical Inference
 

Instructions for lab 6

Lab Objective

The purpose of the lab is to examine how common statistical methods are used in investments, as well as to review the method we have learned so far.

Lab Procedures

Investors look at the historical performance of stocks when deciding where to put their money.  This is not completely reliable.  Every stock or mutual fund advertisement includes a disclaimer like, "Results may not be the same as past performance."  Nonetheless, one can get some information from the past.  In this lab, we'll use some of the graphical tools we've learned in class so far to examine the performance of several stocks.

Open the data set stocks.jmp by clicking on the link.    The data contain the stock prices at the end of each week from 1986 - 2000 for General Motors (they make cars), Pfizer (they make drugs), and Intel (they make computer chips).  The data also contain the prices for the Standard and Poor's 100, which is an average of the stocks of 100 large companies.  GM, Pfizer, and Intel are included in the S&P 100.

Questions:

1.  Just after classes ended last spring, the S&P 100 was priced at 530 per share.  If we use the historical record from 1986 - 2000 as a baseline, would you consider 530 an unusually high value (in upper 5% of prices), a high value (in upper 25% of prices), a typical price (with 25% of median), a low value (in lower 25% of prices), or an unusually low value (in lower 5% of prices).

2. Calculate the estimated probability of the price being above 530 using a normal curve.  Why is your estimate far away?  Would you recommend to your boss that she use a normal curve to calculate similar probabilities for the S&P 100 prices?

3.  Would you use a normal curve to calculate probabilities for any of the stock prices?

4.  Look at the trend of the S&P 100 prices over time.  Around what date does the trend in prices appear to increase in slope?   Tip:  Putting your cursor over a data point in the graph shows the row number of that data point.

4a)   Look at the trends of the other stocks over time.  Notice the meteoric rise of Intel over the late 1990s, when its chips became popular.  Then, it starts to drop incredibly in September 2000.  This is because the company projected revenues much less than what the market was expecting.   You don't have to turn in anything for this problem, but they're worth seeing to help with later questions on the lab.

5.   One common approach to investments is to pick a portfolio of stocks such that its components do not have strong positive correlations.  This minimizes the variability in the stock returns (as we discuss in class).  This is the basis of the Markowitz portfolio selection model, named after economist Harry Markowitz who won a Nobel Prize in economics in 1990 for this work. 

Examine the correlations among the four investments, and answer the following questions.  You can examine the correlations and scatter plots for the prices for all variables by selecting, Analyze-Multivariate Methods-Multivariate, putting all the price variables into the Y box. 
a)  In general, do these four investments' prices tend to move in the same or in opposite directions?
b)  Suppose you already own the S&P 100.  Which company's stock appears to be the most useful to buy, according to the Markowitz selection model? 

6)  The data set also contains the weekly rates of return for each stock, defined as the percentage change in the stock price going from one week to the next.  Examine the distributions of weekly percent returns for each stock, as well as the trends in the return rates over time, and answer the following questions.

a)  Do normal curves appear to describe reasonably well percentage return rates for the stocks?
b) Which of the four investments has the most volitility in return rates?
c)  Do the return rates have a clear trend over time, or are they roughly independent of time?

7)   Investment analysts commonly look at the "alpha" and "beta" for a stock.  These may sound really technical and sophisticated, but they're actually pretty simple concepts.  The alpha and beta are, respectivel, the intercept and slope of the regression line using the rates of return for the stock as the dependent variable and the rates of return of an index, like the S&P 100, as the independent variable.  Stocks with high betas are said to have high market risk, in that their prices are more closely tied to overall prices in the market.  Stocks with low betas are relatively immune to overall market risk.  As examples, energy prices tend to have low betas, whereas consumer goods tend to have high betas.

a) Which stock has the largest market risk?
b) Do you think the regression lines fit the data well?   Refer to graphical displays in your answer.