Question

1. A retired person’s income comes from earnings on her savings of £200,000. The table below shows how she values different levels of income.

Income	Total Utility
5,000	12
10,000	22
15,000	30
20,000	36
25,000	40
30,000	42

1. Describe, using first and second derivatives, her attitude toward risk? Briefly explain.

2. She is currently earning 10% on her £200,000 in a risk-free investment. She has the choice of investing in a project that has a 40% probability of yielding a return of £30,000 return on her investment and a 60% probability of yielding $10,000 return on her investment. Will she be better off if she moved her £200,000 to the risky project? Explain.

2. Consider an investment with three possible cash flow outcomes:

£100 will be received with probability 0.1.

£50 will be received with probability 0.2.

£10 will be received with probability 0.7.

1. What is the expected value and standard deviation of the cash flows?

2. What would a risk-neutral person pay for the investment?

3. An individual’s utility function is u(y) = y^1/2 where y is the cash flow. What would she pay for the investment? Explain any differences with your answer to (ii).

Answer 1

From the table given above one can imply that as the wealth increases, the utility increases. Therefore the first derivative of Utility function is positive. Now, for every 5000 increase in income, increase in utility starts diminishing, this implies that second derivative of utility is negetive. This means that every additional increase in income is less valuable then it's previous increase.

Therefore taking above findings into consideration, this person seems to be Risk Averse.

b) For a risk averse investor, expected probability of positve outcome should be more than that of a negetive outcome (they should get a risk premium for risky investment) which is not the case in the following argument, therefore she will NOT be better off with this investment.