Question

1. I propose to you the following gamble: I flip a fair coin, and if it is heads, I give you $5. If it is tails, you give me $6. What is the expected value of this gamble?

2. So you correctly surmised that question 1 was a bad gamble. How about the following? You have a utility function of U = X0.5, where X is your wealth. You currently have $100. I propose this fair coin flip: If it comes up heads, I give you $101, raising your wealth to $201. If it comes up tails, you give me your $100, lowering your wealth to 0. Do you take the bet? Explain, including a discussion of the fact that the EV of this bet is positive.

3. Use words to describe the concept of certainty equivalent.

4. What do you think about prospect theory? Significant improvement on expected utility? Or just some people have weird attitudes towards risk, and risky outcomes?

Answer 1

1. Expected value of the gamble = 0.5*(5) + 0.5*(-6) = -0.5

2. To check this we compare the utility from expected payoff for taking the bet and not taking the bet

(100^0.5) < (0.5(201) + 0.5(0))^0.5

10<10.025

We will take the bet because the utility of expected payoff from taking the bet is more than the utility of from not taking the bet. Also there is a net positive expected value, so we must take the bet.

3. Certainty equivalent is the amount of payoff that would make someone indifferent between the given payoff and a lottery. This means that the person would not accept the given payoff under riskier asset as the payoff in that case would be higher.

4. Prospect theory is a part of behaviorial economics that states that investors value profits and losses differently giving more importance to profits as losses give a more emotional impact.

This may depend upon the utility functions of individuals and their personal choices towards risk according to which they are risk averse , risk neutral and risk lover. Some people interested in gambling and mutiplying the wealth might be risk lovers because the returns are higher in riskier invetsment. So, it depende upon person's wealth, income choices, purpose of investment etc according to which the nature is derived for each investor.