Afternoon Exam solutions

Checking the variance only for lotteries with the

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Unformatted text preview: cond order stochastically dominates A. Additional remark (for those who are confused about this question; you didn’t need to write this): In Lecture 6, when we went over first and second order stochastic dominance, we saw that second order stochastic dominance (which is defined as the lottery being preferred by any concave utility function) is the same as a mean preserving spread (slide 34). Then, on slides 40 42, we saw that some lotteries with the same mean and higher variance are preferred by some (reasonable) concave utility functions. Therefore, checking the variance is not enough to verify second order stochastic dominance. (Checking the variance only, for lotteries with the same mean, is the same as checking only for quadratic utility functions – since those are utility functions leading to the mean variance criterion).  ­ 2  ­ Part II: Quantitative Question Question 8. (28 minutes) Paul owns a house evaluated at $300,000. He also owns a total of $60,000 in other assets. Paul believes that a major earthquake, which would severely destroy the property and reduce its value to $30,000, will happen with probability 1%. Paul's total wealth is equal to the value of his house plus the total amount of other assets. Paul has a Bernoulli utility function , where W denotes his total wealth. Hints: , and . a. (4 minutes) What is the Value at Risk of Paul’s total wealth at 2% level? Paul’s wealth has the following distribution: 90,000 with probability 1% 360,000 with probability 99% Therefore, the VaR of Paul’s total wealth at 2% is 360,000. b. (4 minutes) What is the expected shortfall of Paul's total wealth at 2% level? The expected shortfall of P...
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