1. Suppose there is a dice game--you toss a dice, get $1000 if the number is 5 o
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Question
1. Suppose there is a dice game--you toss a dice, get $1000 if the number is 5 or 6, but lose $500 if the number is 1, 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)A risk-averse investor prefers lower returns with known risks than higher returns with unknown risks.So this is a fair game for risk-averse investor. In this game,it is quite evident that a person gets lower returns with known risks, so a risk-averse person would play this game.
2. Suppose the utility function is U(W) = ln(W) and initial wealth is $1000.
a) The utility function of the exponential function is equal to its natural logarithm, which is defined as its inverse function. As a result there is no risk involved playing this game, and thus I would choose playing the game.
b) The initial investment is not at risk as the exponential function is equal to its natural logarithm which is its inverse function.This is the certainty equivalent wealth of playing the game. The risk premium I am willing to pay to avoid playing the game is the difference between the initial wealth investment and the loss,ie. $500.
It is $1000 - $500 = $500.
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