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This is about the utility of annual income in retirement. The idea is to decide how to allocate your pension fund between safe and risky investments. Suppose that, when you retire, you will get $25,000/year in social security (in today's dollars). The questions here refer to what you get in addition to that, from your own saving. The range of possibilities is from $0 to $200,000 per year.
We shall assume that the utility of $0 is 0 and the utility of $200,000 is 100. You will use 3 methods to get your utility function for the intermediate intervals.
The first method is direct ratings. Remembering that the utility of $0 is 0 and the utility of $200,000 is 100, what is the utility of $100,000? This is a question about judgment, not calculation. The utility of $100,000 might be more than 50 or less than 50.
Now rate the utility of $50,000 and $150,000. for $50,000. for $150,000.
The next method you use is the standard gamble. What question should you ask yourself to get each of the three ratings you just did, so that the answer (without any change) would be the utility of $100,000? Select the question and answer it. (Try not to think about your earlier answers, and answer in percent without adding another percent sign.)
At what probability P would I be indifferent between $200,000 with probability P (and 0 with probability 1-P) and $100,000 for sure? At what probability P would I be indifferent between $200,000 with probability 1-P (and $0 with probability P) and $100,000 for sure? At what probability P would P times $200,000 equal $100,000?
Answer to the question you asked yourself: %
Now chose the corresponding question and provide answer for $150,000, and then just give the answer for $50,000. At what probability P would I be indifferent between $200,000 with probability P (and 0 with probability 1-P) and $150,000 for sure? At what probability P would I be indifferent between $200,000 with probability 1-P (and $0 with probability P) and $150,000 for sure? At what probability P would P times $200,000 equal $150,000?
% for $150,000. % for $50,000.
The third method you use is another way to do direct rating, namely, bisecting intervals. What salary would have a utility of 50? That is, in terms of what matters to you, the difference between this level and $0 should be the same as the difference between this level and $200,000. $,000
Now answer this question in the same way, by dividing each half in half, for utilities of 75 and 25: $,000 for 75. $,000 for 25.
If your utilities measured by gambles and those measured by bisection (third method) are different, how? Consider only the utility of $100,000 (relative to $0 and $200,000).
Gambles are more concave. Gambles are more convex (less concave). Equal.
Which of the following would explain greater concavity for gambles than for bisection? Answer yes or no for each. Declining marginal utility would lead people to overvalue the outcome that was certain. Yes No The certainty effect would lead people to overvalue the outcome that was certain. Yes No People tend to be risk seeking in the domain of losses. Yes No If people adopt the certain outcome (e.g., $100,000) as a reference point, then loss aversion would make them more risk averse. Yes No
Portfolios with the highest average returns also tend to have the highest chance of short-term losses. The table provides the average dollar return of four hypothetical investments of $100,000 and the possibility of losing some money (coming out below $100,000) over a one-year holding period. Figures are adjusted for inflation. Note that you could get more than the expected value. Which would you choose? (Note: This example is based on one used by TIAA-CREF.) Expected value after 1 year: $100,000.Chance of losing money at the end of 1 year: 0% (In other words, this has no risk.) Expected value after 1 year: $105,000.Chance of losing as much as $5,000 at the end of 1 year: 15% Expected value after 1 year: $110,000.Chance of losing as much as $10,000 at the end of 1 year: 30% Expected value after 1 year: $115,000.Chance of losing as much as $15,000 at the end of 1 year: 45% Expected value after 1 year: $120,000.Chance of losing as much as $20,000 at the end of 1 year: 60%
Why might the last question yield answers that, if taken at face value, would fail to maximize utility? (Answer yes or no to each.) Loss aversion leads to more risk aversion than would be inferred from the utility function for income at retirement. Yes No A concave utility function for income at retirement leads to excessive risk aversion. Yes No Decision utility could differ from experienced (true) utility. Yes No The value function for income at retirement is convex for losses. Yes No
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