Certainty Equivalent The Certainty Equivalent is the amount of wealth (Wce) you would require (with no...

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Certainty Equivalent The Certainty Equivalent is the amount of wealth (Wce) you would require (with no uncertainty) to make your utility indifferent between taking the gamble and taking the certain wealth. U(Wce) = E(U(W)) = 11.37 In(Wce) = 11.37 Wce W ce - e11.37 = e = $86,603 A risky portfolio is desirable only if it costs less or returns more than the (risk-free) certainty equivalent. You are offered the opportunity to play in the following game, which involves a coin toss. The coin will be tossed a maximum of 10 times. If the coin ever turns up Tails, the game ends immediately; otherwise the game proceeds until the coin has been tossed 10 times or turns up Tails in another round. [Note: We'll count the 10th toss as a Tail" no matter how it actually lands so the game will at most last 10 rounds.] Your payout is a function of the number of Heads that occur before the game ends. If there are two tosses before the game ends (i.e., the coin lands Heads then Tails), you receive $2. If there are four tosses (i.e., H, H, H, T), you receive $2. Thus, your payout from the game is given by the function $2", where n is the number of Heads to occur before the game ends. Your utility is given by the function Uln(W), where W is the payout you receive from the game. 1) Assume it costs $2 to play the game. What is your expected payout from the game? 2) Assume it costs $2 to play the game. What is your expected utility from the game? 3) What is the most you would be willing to pay to play this game? [Hint: Think about the Certainty Equivalent.] Certainty Equivalent The Certainty Equivalent is the amount of wealth (Wce) you would require (with no uncertainty) to make your utility indifferent between taking the gamble and taking the certain wealth. U(Wce) = E(U(W)) = 11.37 In(Wce) = 11.37 Wce W ce - e11.37 = e = $86,603 A risky portfolio is desirable only if it costs less or returns more than the (risk-free) certainty equivalent. You are offered the opportunity to play in the following game, which involves a coin toss. The coin will be tossed a maximum of 10 times. If the coin ever turns up Tails, the game ends immediately; otherwise the game proceeds until the coin has been tossed 10 times or turns up Tails in another round. [Note: We'll count the 10th toss as a Tail" no matter how it actually lands so the game will at most last 10 rounds.] Your payout is a function of the number of Heads that occur before the game ends. If there are two tosses before the game ends (i.e., the coin lands Heads then Tails), you receive $2. If there are four tosses (i.e., H, H, H, T), you receive $2. Thus, your payout from the game is given by the function $2", where n is the number of Heads to occur before the game ends. Your utility is given by the function Uln(W), where W is the payout you receive from the game. 1) Assume it costs $2 to play the game. What is your expected payout from the game? 2) Assume it costs $2 to play the game. What is your expected utility from the game? 3) What is the most you would be willing to pay to play this game? [Hint: Think about the Certainty Equivalent.]