sol06 - ECON 251 Financial Theory Professor John...

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ECON 251: Financial Theory Spring 2012 Professor: John Geanakoplos Yale University TA: Bin Li Problem Set #6: Answer Key 1. A fund’s quarterly returns are independent. Its long run annual volatility is 64%. In the long run, what is its quarterly volatility? Solution : Let random variable be the quarterly return and Y be the long run annual return, then ( ) ( ) ( ) Since are independent for each i. hence, 2. Oklahoma and Miami play a series of games to determine who NBA champion is. Miami has a 70% chance of winning each game. Use the spread sheet to figure out what the odds are of Miami winning a 5, 7, 9, or 11 game series. Solution : We use backward induction to calculate the 5 game series. 1. Define V(O,M) is the probability of Miami wins finally, where O is the number of Orlando wins, and M is the number of Miami wins. 2. Thus, V(0,3) = V(1,3) = V(2,3) = 1 and V(3,2) = V(3,1) = V(3,0) = 0 3. By backward induction, when we know the value of game in (O+1, M) and (O, M+1), V(O,M) = 0.7*V(O,M+1)+0.3*V(O+1,M) 4. Hence, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) From the Excel spread sheet, we could see, the probability of Miami winning a 5, 7, 9, and 11 game series are: 83.69%, 87.40%, 90.12%, and 92.18%, respectively. 3. (Monte Hall problem): You don’t .t know which of three closed doors has a prize behind it. You pick a door. Then Monte Hall (who does know which door has the prize) opens a door without a
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