Percentage changes (or returns) on the stock market follow a normal distribution—if we don’t reach too far into the tails of the distribution. Are returns on stocks in individual companies also roughly normally distributed? This example uses monthly returns on McDonald’s stock from 1990 through the end of 2011 (264 months).
Motivation
(a) If the returns on stock in McDonald’s during this period are normally distributed, then how can the performance of this investment be summarized?
(b) Should the analysis be performed using the stock price, the returns on the stock, or the percentage changes? Does it matter?
Method
(c) Before summarizing the data with a histogram, what assumption needs to be checked?
(d) What plot should be used to check for normality if the data can be summarized with a histogram?
Mechanics
(e) If the data are summarized with a histogram, what features are lost, and are these too important to conceal?
(f) Does a normal model offer a good description of the percentage changes in the price of this stock?
(g) Using a normal model, estimate the chance that the price of the stock will increase by 10% or more in at least one month during the next 12 months.
(h) Count the historical data rather than using the normal model to estimate the probability of the price of the stock going up by 10% or more in a coming month. Does the estimate differ from that given by a normal model?
Message
(i) Describe these data using a normal model, pointing out strengths and any important weaknesses or limitations.