1. Suppose there is a dice game- you toss a dice, get S1000 if the number is 5 o
ID: 364819 • Letter: 1
Question
1. Suppose there is a dice game- you toss a dice, get S1000 if the number is 5 or 6, but lose S500 if the number is , 2, 3 or 4 (1) Is this a fair game? Would a risk-averse person play this game? (2) Suppose your utility function is U(W)-In(W) and initial wealth is $1000. a. Does this utility function display risk aversion? Would you choose playing the game or not? b. What is the certainty equivalent wealth of playing the game? What is the risk premium you are willing to pay to avoid playing the game?Explanation / Answer
(1) For a Risk-averse investor, this is a fair game. Because a risk-averse investor is one who prefers lower returns with known risks rather than higher returns with unknown risks. The details given in this problem exactly replicate this situation of lower returns with known risks. So, yes a risk-averse person will play this game.
(2) Suppose my utility function is U(W) = In(W) and the initial wealth = $1000
(a) This utility function represents that the utility function of the exponential function is equal to its natural logarithm which is defined as its inverse function. With this definition, we choose to play the game as there is no risk with the initial investment made.
(b) The certainty equivalent wealth of playing the game is, the initial investment is not at risk as the exponential function is equal to the inverse function. The risk premium that I'll be willing to pay to avoid playing the game will be the difference of my investment and loss which is equal to $500 ($1000 - $500)
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