The table below gives a sample of artificial historical data for an energy company (Stock A) and a phone company (Stock B). Each indicated return rate is end of month to end of month and is based on adjusted closing prices. For example, RA Jan-2012 is the return rate from the last trading day in December 2011 to the last trading day in January 2012. Using the table, express your answers in percentages where appropriate.

1. a) Sketch the graph of the monthly total return rates of each stock as a function of time during 2012. Briefly discuss the movement of the stocks during two equal-length-time periods in 2012.

2. b) Estimate the expected monthly total return rate of each stock in the table. What is your answer if you use data only from Dec-2011 to Jun-2012? Compute the monthly volatility of each stock for the year 2012.

3. c) Estimate the monthly variance of each stock and determine the covariance and correlation coefficient between the monthly total return rates for the two stocks during 2012. Is the result what you expected? Briefly discuss.

Date Rmonthly Ronthly Jan-2012 2.45% 2.69% Feb-2012 3.35% 1.81% Mar-2012 3.24% 4.94% Apr-2012 2.93% 5.88% May-2012 6.13% 2.51% Jun-2012 6.19% -0.35% Jul-2012 0.78% 1.59% Aug-2012 -0.19% -3.83% Sep-2012 4.65% 5.24% Oct-2012 3.53% 4.85% Nov-2012 5.03% 2.48% Dec-2012 -1.71% 4.03%