Arbitrage Pricing Theory (40 points) Question 2.1: (10 points) Does it single stock or an index of stoclos with an identical beta have more systematic risk Ww Question 2.2: (10 points) Show that a diversification increases the weight in each security in the portfolio o dow) the non- systematic risk does down. Hint '() () (2) Question 2.3: (10 points) Write down an equation for a multi-factor model, where the two factors are excess returns on two diversified market indexes front-r/) and (3) Question 2.4: (10 points) Assume that you are working for a large investment firm and have been tasked with modeling the expected returns on a variety of individual stocks. Your boss says that the firm has been using a single factor index model and you trying to convince her that the firm would have a better model if it used the two-factor model that you wrote in the above question. Assume that you have identified the two-factor model to be a truly better representation of expected returns. What arguments would you make to your boss, in terms of the performance of your model as measured by a and R-squared? (Hint: Mrs Boss, my model is better because it's a is higher/lower /the same, and that implies....)