Your bank is currently using a scoring system that maps the customer's score onto a risk budget

for his/her recommended portfolio. You have been hired with your Master in Wealth

Management in order to improve the bank's methodology. The Head of Private Banking (HPB),

who remembers his finance courses in the mid-eighties, proposes that you improve the system

by associating a risk aversion score to the client's profile according to the quadratic utility

function.

a. From this utility function, explain how you would compute the certainty equivalent of

a portfolio. Show this graphically on a risk-return framework

b. Draw a numerical example showing how someone with a risk aversion coefficient of 2

could obtain a better expected utility than the risk-free rate set to 1%/year

c. If the risk aversion of the client is indeed greater than 2, at what risk level could the

portfolio that you designed in question b. lead to the indifference with the risk-free rate?

d. What are the main two drawbacks of the utility function you are using?

e. What is the main drawback of the way you have measured risk?