Question

Consider the utility function U(W) = W^0.5 where W = wealth

a) Perform the necessary calculations to demonstrate the order of preference of an investor with this utility function. Order them from most preferred to least preferred.

-Prospect 1: 50% chance of $1000, 50% chance of $2000

-Prospect 2: 25% chance of $500, 25% chance of $2000, 50% chance of $1000

-Prospect 3: $1000 for certain.

b) Explain the meaning of the expression certainty equivalent. (That is, Provide the definition)

c) Calculate the certainty equivalent of prospect 1.

Answer 1

A) Expected Net Present Value of Prospect 1 = 0.5 * 1000 + 0.5 * 2000 = 500 + 1000 = 1500

Expected Net Present Value of Prospect 2 = 0.25 * 500 + 0.25 * 2000 + 0.5 * 1000 = 125 + 500 + 250 = 875

Expected Net Present Value of Prospect 3 = 0.5 * 1000 = 500

Order of Preference, As (1 > 2 > 3)

1) Prospect 1

2) Prospect 2

3) Prospect 3

B) Certainty Equivalent:-

It is a sure return that someone accepts now rather than taking a chance of a higher return in the future. Higher the risk, higher the chances of high return. An investor must pay a premium to get return higher than Risk-Free rate. It shows an investor's attitude towards Risk.

C) Certainty Equivalent of Prospect 1:-

Here Expected Cash Flow = Expected Net Present Value

Risk Premium =(Rate of Return for the Prospect - Risk-Free Rate)

For Prospect 1,

Expected Cash Flow = 1500

Risk Premium = 0.12 - 0.03 = 0.09 (If we assume Rate of Return = 12% & Risk Free Rate = 3% )