Q.1A

Suppose my utility function for asset position x is given by u(x)=sqrt(x)/100.

I now have $20,492 and am considering the following two lotteries:

L1: With probability 0.5 I gain $10000

With probability 0.5 I lose $10000

L2: With probability 0.85 I gain $1,594

With probability 0.15 I lose $6,040

What is the risk premium of L2? Round your answer to the nearest integer.

Q.1B

My friend, Ahmad, is trying to determine which of two opportunities he should invest in (only one of them). His options are Bitcoin and S&P 500.

If he invests in Bitcoin, he believes that he has a 10% chance of making 15% profit, a 25% chance of only 8% profit, 15% of losing 10% of his investment capital (-10%), and a 50% chance of no change in his investment capital (0%).

If Ahmad invests in S&P500, he has a 70% chance for the 8% profit, a 25% chance for no change (0%), 3% chance for losing -10%, and 2% for a 15% profit.

Ahmad is indifferent between the following lotteries.

If Ahmad wants to invest in what maximizes his expected return on investment, which investment is the best? Please note: x=0.33 and y=0.99. In the box below put the expected utility for the investment he should pick. Write your answer with three decimals.