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AcF 215: Advanced Principles of Finance

Lent Term 2019

Problem Solving Workshop Week 12

Exercise 1

Consider the following lotteries

and three individuals: John, Oscar and Nicholas, with the following utility functions:

● UJohn(z) =log(z)

● UOscar (z) = z

● UNicholas(z) = z2

a)  Calculate the expected payoffs and variance of and y˜ . Which of or y˜ is more risky?

b) Plot the three utility functions. Which of the three individuals is: risk averse, risk neutral and risk loving?

c)  Calculate the expected utilities of gambles and y˜ for each of the three individuals. Assume that the outcome of and y˜ represent possible values of their final wealth.

d)  Calculate the utilities of expected wealth in and y˜ .  Compare them with the expected utilities of and y˜ .

e) Which of the two gambles does each of the individuals prefer?

Exercise 2

You are a contestant on Deal Or No Deal, your current wealth is _200,000 and your utility function is of the form U (z) = , where 1 + U is the relative risk aversion. Three boxes remain and you have an equal chance of ending up with each of them. They contain _250,000, _15,000 and _0.01.

How much would you accept in order to not take the gamble for the following levels of risk aversion?

a) U = 0, this is equivalent to U (z) = ln(z)

b) U = 1

c) U = 5

d) U = 10