Please submit one homework answer set for your group, along with individual versions of your code for each member of the team.  Groups are expected to work together, but all individuals are expected to maintain their own unique code base (code submissions must be different for each person in the team).  The best way to learn the material is to think about how you want to structure your code together as a team, and then actually implement it yourself!


For questions ___, load the monthly stock data and “Fama-French” factors in Python.  Use the methodology in Module3_RegressionAndCAPM_ipynb to get the data frame excessReturns.

1) Regress excess returns for CAT on an intercept and the excess return of the market (ie, test the validity of the CAPM for CAT).  Please provide the estimates and standard errors for both the intercept and the market beta.  Also report the regression R2.  (15 points)

2) What would you expect the excess return of CAT to be if the market returned the following: (15 points)

a. 1%

b. 1.5%

c. -2.5%

d. 0%

e. -5.5%

3) Run a hypothesis test for the null hypothesis that the coefficient on the intercept (‘alpha’) is zero.  Can you reject this hypothesis at a 5% confidence level (ie, you reject if the probability of getting the alpha we saw or a value more extreme on either side of zero is less than 5%).  Why or why not? (15 points)

4) Plot CAT excess returns on the y-axis versus market excess returns on the x-axis.  Add a trend line to your plot that corresponds to the fit OLS model from part 1.  Make the trend line red. (15 points)

For questions on options, use this option set-up:  Suppose we have a stock with a current price of image.png ，Consider a European call option on this stock with a strike price of K=$50, time to expiration of T = 3 months (1/4 of a year).

5) Is this option currently in the money, out of the money, or at the money? (5 points)

6) Plot the option payoff (ie, at date T = ¼) as a function of final stock price, for all final prices between $40 and $60. (15 points)

7) Suppose that the distribution of the change in the stock price between now and the option expiration image.png is normal with a mean of zero and a variance of one.  Generate 100000 normal random variables, and use these to find the expected payoff of the option given the current stock price of $49.25.  (20 points)