Consider a 2-period portfolio optimization problem witht= 0,1,2. The utility function to be maximized is the same as in the class notes. AssumeA= 2. There are only 2 securities in each period: the 1-period risk-free rate, and a stock. Similar to the class notes, we use log returns so all the price below are really log prices and we compute return as difference in price. The one-period risk-free rate = 0 in each period.

Solve the following two scenarios independently of each other.

1. (a)Assume there are two possibilities att= 1: stock price = $1.2 or $0.8, each with 50% probability. If stock price att= 1is $1.2, mean price att= 2is $1.4; if stock price att= 1is $0.8, mean price att= 2is $1. The volatility of stock priceatt=2is100%. Thestockpriceatt=0is$1. Whatisyouroptimal allocation to the stock att= 0? What is the Markowitz allocation att= 0?
2. (b)Assume that everything else is the same as the previous part except that: If stock price att= 1is $1.2, mean price att= 2is $1.3; if stock price att= 1is $0.8, mean price att= 2is $1.1. What is your optimal allocation to the stock att= 0? What is the Markowitz allocation att= 0?