# Question

Apple, Dell, IBM, and Microsoft are well known in the computer industry. If the computer industry is doing well, then we might expect the stocks of all four to increase in value. If the industry goes down, we’d expect all four to go down as well. How strong is the association among these companies? After all, they compete in some areas. For example, Dell and IBM both sell powerful computer systems designed to power Web sites like Amazon or weather.com.

This data set has monthly returns for Apple, Dell, IBM, and Microsoft for January 1990 through September 2011 The returns are calculated as

Rt = Pt – Pt–1 / Pt–1

In this fraction, Pt is the price of the stock at the end of a month and Pt -1 denotes the price at the end of the prior month. If multiplied by 100, the return is the percentage change in the value of the stock during the month. The returns given here have been adjusted for accounting activities (such as dividend payments) that would otherwise produce misleading results. The data are from the Center for Research in Security Prices (CRSP), as are other stock returns used in this book.

Motivation

(a) Investors who buy stocks often buy several to avoid putting all their eggs into one basket. Why would someone who buys stocks care whether the returns for these stocks were related to each other?

(b) Would investors who are concerned about putting all their eggs into one basket prefer to buy stocks that are positively related, unrelated, or negatively related?

Method

(c) How can an investor use correlations to deter-mine whether these three stocks are related to each other? How many correlations are needed?

(d) Correlations can be fooled by patterns that are not linear or distorted by outliers that do not conform to the usual pattern. Before using correlations, how can the investor check the conditions needed for using a correlation?

(e) A key lurking variable anytime we look at a scatterplot of two time series is time itself. How can an investor check to see if time is a lurking factor when looking at stock returns?

Mechanics

(f) Obtain the scatterplots needed to see whether there are patterns that relate the returns of these stocks. Does it matter which stock return goes on the x-axis and which goes on the y-axis? Do you find that the returns are associated? Is the association linear?

(g) Obtain the correlation matrix that has all of the correlations among these four stocks.

(h) Look at timeplots of the returns on each stock. Why are these important when looking at time series?

Message

(i) Summarize your analysis of the association among these returns for an investor who is thinking of buying these stocks. Be sure to talk about stocks, not correlations.

This data set has monthly returns for Apple, Dell, IBM, and Microsoft for January 1990 through September 2011 The returns are calculated as

Rt = Pt – Pt–1 / Pt–1

In this fraction, Pt is the price of the stock at the end of a month and Pt -1 denotes the price at the end of the prior month. If multiplied by 100, the return is the percentage change in the value of the stock during the month. The returns given here have been adjusted for accounting activities (such as dividend payments) that would otherwise produce misleading results. The data are from the Center for Research in Security Prices (CRSP), as are other stock returns used in this book.

Motivation

(a) Investors who buy stocks often buy several to avoid putting all their eggs into one basket. Why would someone who buys stocks care whether the returns for these stocks were related to each other?

(b) Would investors who are concerned about putting all their eggs into one basket prefer to buy stocks that are positively related, unrelated, or negatively related?

Method

(c) How can an investor use correlations to deter-mine whether these three stocks are related to each other? How many correlations are needed?

(d) Correlations can be fooled by patterns that are not linear or distorted by outliers that do not conform to the usual pattern. Before using correlations, how can the investor check the conditions needed for using a correlation?

(e) A key lurking variable anytime we look at a scatterplot of two time series is time itself. How can an investor check to see if time is a lurking factor when looking at stock returns?

Mechanics

(f) Obtain the scatterplots needed to see whether there are patterns that relate the returns of these stocks. Does it matter which stock return goes on the x-axis and which goes on the y-axis? Do you find that the returns are associated? Is the association linear?

(g) Obtain the correlation matrix that has all of the correlations among these four stocks.

(h) Look at timeplots of the returns on each stock. Why are these important when looking at time series?

Message

(i) Summarize your analysis of the association among these returns for an investor who is thinking of buying these stocks. Be sure to talk about stocks, not correlations.

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