Exercise 43 You have the current wealth of 500$ and the following power utility function: Wi-7 U(W) (+1) 1-7 where y is the relative risk-aversion coefficient. (i) Show that the risk premium (Arrow-Pratts) is proportional to 7. = (ii) With y=2, find the Arrow-Pratt's risk premium of a fair game that gives 100$ cash flow if you win and -100$ if you lose. The chance of winning and losing the game is equal. (iii) In (ii), what are the certainity equivalent amounts of the fair game and the (Markowitz) risk premium ? Compare the risk premium with the answer of (ii). (iv) In (ii), the probability of winning the game is p, and the probability of losing the game is 1-p. At what probability is playing or not playing this fair game is indiffferent ? Exercise 43 You have the current wealth of 500$ and the following power utility function: Wi-7 U(W) (+1) 1-7 where y is the relative risk-aversion coefficient. (i) Show that the risk premium (Arrow-Pratts) is proportional to 7. = (ii) With y=2, find the Arrow-Pratt's risk premium of a fair game that gives 100$ cash flow if you win and -100$ if you lose. The chance of winning and losing the game is equal. (iii) In (ii), what are the certainity equivalent amounts of the fair game and the (Markowitz) risk premium ? Compare the risk premium with the answer of (ii). (iv) In (ii), the probability of winning the game is p, and the probability of losing the game is 1-p. At what probability is playing or not playing this fair game is indiffferent