Yahoo! Finance provides data on the stock price at https://finance.yahoo.com. Download the data on the monthly stock prices (close prices) of Visa Inc. (V) and Mastercard Incorporated (MA) from January 1, 2011 to October 1, 2021.
(a) (5pt) Draw one chart illustrating the historical monthly prices of the two stocks for the whole period (from January 1, 2011 to October 1, 2021).
(b) (15pt) Let the stock prices of Mastercard Incorporated and Visa Inc. be the X and Y values, respectively. Using the data from January 1, 2011 to January 1, 2020, conduct the co-integration procedure. In other words, find the coefficients a and b; calculate the correlation coefficient ρ and the R-square R2; and check whether they have a strong linear relationship.
(c) (20pt) Suppose that you are allowed to take short positions for at most 100 shares of any stock, and that each time you earn a profit, you deposit it into a bank account which gives you a monthly return of 0.25%. Set your own thresholds δ, γ; conduct the pairs trading for the period from February 1, 2020 to October 1, 2021; and report the total profit on October 1, 2021, resulting from your strategy.