Topics Lecture 3: Prospect Theory, Framing, and Mental Accounting Expected Utility Theory Violations of EUT Prospect Theory Framing Mental Accounting Application of Prospect Theory, Framing, and Mental Accounting: Equity Premium Puzzle Master of Arts program in Applied Finance Nattawut Jenwittayaroje, Ph.D, CFA NIDA Business School 1 2 Expected Utility Theory The key features are as follows: The value is measured by utility. Utility depends on the state of wealth. A rational individual s utility function is assumed to be a positive function of wealth. The expected utility of a prospect is probability-weighted utility (i.e., the sum of the products of utilities times their probabilities). The weight put on any outcome probability is simply equal to its probability. A rational, risk-averse individual s utility function is assumed to be a concave function of wealth. Utility x-y x x+y Wealth 3 4
Allais Paradox The Allais paradox is a choice problem designed by Maurice Allais to show an inconsistency of actual observed choices with the predictions of expected utility theory. Allais question 2: Which do you prefer? Allais Paradox (con t) Allais question 1: Which do you prefer? A. a 100% chance of getting $1,000,000, or A* a gamble where the outcomes are as follows:» a 1% chance of getting nothing» a 89% chance of getting $1,000,000» a 10% chance of getting $5,000,000. 5 or 6 B. a gamble where the outcomes are as follows:» a 89% chance of getting nothing» A 11% chance of getting $1,000,000 B* a gamble where the outcomes are as follows:» a 90% chance of getting nothing» a 10% chance of getting $5,000,000. Allais Paradox (con t) From Question 1: U(1,000,000) > 0.89U(1,000,000) +.10U(5,000,000) Rearranging we get: 0.11U(1,000,000) > 0.10U(5,000,000) From Question 2: 0.10U(5,000,000) > 0.11U(1,000,000) Such choices are clearly contradictory!! Reconsidering Allais Paradox Modified Question 1: Which do you prefer? A. a gamble where the outcomes are as follows:» a 89% chance of getting $1,000,000» a 11% chance of getting $1,000,000, or A* a gamble where the outcomes are as follows:» a 89% chance of getting $1,000,000» a 1% chance of getting nothing» a 10% chance of getting $5,000,000. 7 8
Reconsidering Allais Paradox (con t) Modified question 2: Which do you prefer? or B. a gamble where the outcomes are as follows:» a 89% chance of getting nothing» A 11% chance of getting $1,000,000 B* a gamble where the outcomes are as follows:» a 89% chance of getting nothing» a 1% chance of getting nothing» a 10% chance of getting $5,000,000. Reconsidering Allais Paradox (con t) Notice that after removing commonalities, now the choices between prospect A and A* or B and B* are exactly the same! Thus people should choose (A and B) or (A* and B*). Without such aids, many people do not seem to understand the structure of the decision and choose A and B*. 9 10 Problems with expected utility theory A number of violations of expected utility have been discovered. Expected utility theory assumes that people should have consistent choices, regardless of presentation (i.e., frame). A decision frame is defined to be a decision-maker s view of the problem and possible outcomes. A frame is affected by the presentation mode and the individual s perception of the question, and personal characteristics. People have different perspectives and come up with different decisions depending on how a problem is framed. Sometimes frames are opaque, and thus trickier to see through. For this reason, a change in frame can lead to a change in decision, as in Allais questions. 11 Problems with expected utility theory A number of violations of expected utility have been discovered. Alternative theories have been developed which seek to account for these violations. Best-known is prospect theory of Daniel Kahneman and Amos Tversky. 12
Prospect theory Prospect theory was developed by Kahneman and Tversky base on observing actual behavior. Experimental evidence says that people often behave contrary to expected utility theory. Expected utility theory is normative. What people should do While prospect theory is positive. What people actually do Risk aversion vs. risk seeking Prospect pair 1 -- choose between: A: (.5, 6,000, 0.5, 0) B: (3,000) In other words, the choice is between a sure gain of $3,000 and a 50% chance to gain 6,000. Prospect pair 2 choose between: C: (.5, -6,000, 0.5, 0) D: (-3,000) In other words, the choice is between a sure loss of $3,000 and a 50% chance to lose 6,000. 13 14 Key Aspect 1 Reference Point For Prospect pair 1, 84% of the respondents chose B, consistent with risk aversion. For Prospect pair 2, 84% of the respondents chose C, consistent with risk seeking. Expected Utility theory cannot incorporate changes in risk attitude like this. People sometimes exhibit risk aversion and sometimes exhibit risk seeking, depending on the nature of the prospect. If you are richer by $5,000 and you have to choose between A) a 50% chance to win $6,000 and a 50% chance to win nothing B) receive $3,000. If you are richer by $11,000 and you have to choose between C) a 50% chance to lose $6,000 and a 50% chance to lose nothing D) lose $3,000 15 16
Key Aspect 2 Notice that the two decisions are effectively the same. But 72% chose B) and 64% chose C) The problem shows that risk attitude is not the same across gains and losses. seem gains or losses is what people care about, rather than the level of wealth. People evaluate an outcome based on the gain or loss from a reference point (usually taken to be current wealth or status quo). Expected Utility theory people value outcomes based on the final wealth position, regardless of the person s initial wealth. Peoples valuations of prospects depend on gains and losses relative to a reference point. This reference point is usually the status quo. Loss aversion Prospect pair 3 -- choose between: A: no prospect B: (0.5, $100, -$100) A is the status quo. Most choose A. Losses loom larger than gains. In other words, the loss of $100 is more painful than a gain of $100 is pleasurable. This is called loss aversion. 17 18 Key Aspect 3 Prospect pair 4 -- choose between: A: no prospect B: (0.5, $X, -$25) What value of X would make you indifferent between A and B? The average person requires a gain of $61 to be indifferent between accepting or rejecting the gamble. People are averse to losses because losses loom larger than gains. 19 Development of prospect theory These and other results led to prospect theory as an alternative to expected utility theory. Key precepts: Value function in prospect theory replaces the utility function in expected utility theory. Value is in terms of gains or losses, relative to a reference point (usually the status quo). Risk aversion (i.e., concave) in positive domain Risk seeking (i.e., convex) in negative domain Loss aversion people dislike losses, so the value function is steeper for losses than for gains. 20
(Utility) Value $100 Losses($) $100 Gains ($) The Prospect Theory (Utility) Value Function Expected Utility (EU) vs Prospect Theory Barberis and Thaler (2003) Should financial economists be interested in alternatives to expected utility? It may be that EU theory is a good approximation to how people evaluate a risky gamble like the stock market, even if it does not explain attitudes to the kinds of gambles studied in experimental settings. However, they go on to say: On the other hand, the difficulty the EU approach has encountered in trying to explain basic facts about the stock market suggests that it may be worth taking a closer look at the experimental evidence. Indeed, recent work in behavioral finance has argued that some of the lessons we learn from violations of EU are central to understanding a number of financial phenomena. 21 22 Some more prospects Prospect pair 5 you are given $1000 then choose between: A: (.5, another $1000) B: ($500) Prospect pair 6 you are given $2000 then choose between: A: (.5, -$1000) B: (-$500) Results for 5: most prefer B. Results for 6: most prefer A. Problems are identical! People have chosen differently because of different frames. An odder example You must make two lottery choices. One draw will be in morning; other in afternoon. Prospect pair 7: A: ($2400) B: (.25, $10,000) Most people (84%) choose 7A. Prospect pair 8: A: (-$7500) B: (.75, -$10,000) Most people (87%) prefer 8B. 23 24
An odder example (con t.) Suppose now you have another prospect to decide. Prospect pair 9: A: (0.25, $2,400, -$7,600) B: (0.25, $2,500, -$7,500) (All) People choose 9B. An odder example (con t.) But combining 7A and 8B leads to: (0.25, $2400, -$7,600) 9A And combining 7B and 8A leads to: (0.25, $2500, -$7,500) 9B While 7B and 8A can be seen to be better than 7A and 8B when framed as 9B and 9A, most people do not see through the opaque framing in the original two decisions. Why? They have difficulty getting past frame. 25 26 Another example: Framing with nonmonetary outcomes Imagine that Thailand is preparing for the outbreak of an unusual disease, which is expected to kill 1,000 people. Two alternative programmes, A and B, have been proposed to combat the disease. (Survival Frame): If A is adopted, 250 people will be saved. If B is adopted, there is 25% that 1,000 will be saved, and 75% that no people will be saved. Which of the two programs do you choose? 27 Another example: Framing with nonmonetary outcomes Consider another situation Imagine that Thailand is preparing for the outbreak of an unusual disease, which is expected to kill 1,000 people. Two alternative programmes, C and D, have been proposed to combat the disease. (Mortality Frame): If C is adopted, 750 people will die. If D is adopted, there is 25% that nobody will die, and 75% that 1,000 people will die. Which of the two programs do you choose? 28
Another example: Framing with nonmonetary outcomes (Note that A = C, and B = D). Of the respondents to the first problem (Survival Frame), about 72% chose program A. People are risk averse for gains lives saved are seen as gains. The reference point here starts from full mortality. The second problem (Mortality Frame), 78% chose program D. By contrast, they are risk seeking for losses the current reference point is that nobody has yet died (or full survival), so any deaths are seen as losses. Another example: Framing with nonmonetary outcomes The results are consistent with prospect theory. In other words, we again have loss aversion and framing dependence. Therefore, in order to understand and model asset prices or trading behaviour of investors, we need to make some assumptions about investor preferences and how investors make decisions under risky situations. 29 30 Mental accounting Related to prospect theory and frames. Mental accounting is the set of cognitive operations used by individuals and households to organize, evaluate, and keep track of financial activities. Expenditure accounts (foods, housing, entertainment), Wealth account (checking account, retirement savings) Note that these accounts are mental constructs rather than actual accounts. Mental accounting is beneficial. For example, it helps people exert self-control, encouraging the use of rules such as don t dip into retirement savings, pay for luxuries out of savings. 31 Mental accounting However, often tendency to use mental accounting leads to odd and suboptimal decisions. Traditionally, economists assume that funds are fungible (substitutable). But, because of mental accounting, this may not be so. Actual decisions people make indicate that money is not always substitutable. A few highlights of mental accounting follow 32
Theater ticket problems 1. Imagine you have decided to see a play where admission is $10. As you enter theater you discover that you have lost a $10 bill. Would you still pay $10 for a ticket to the play? 2. Imagine that you have decided to see a play and paid the admission price of $10 per ticket. As you enter the theater you discover that you have lost the ticket. The seat was not marked and the ticket cannot be recovered. Would you pay $10 for another ticket? 33 Theater ticket problems cont. Nothing is really different about the problems. However, Of respondents given first question, 88% said they would buy a ticket. Of respondents given second question, 54% said they would not buy a ticket. In 1 st question, the lost $10 bill is not directly linked to the ticket, so people are willing to buy a new ticket. In 2 nd question, when the ticket is originally purchased, a ticket purchase account was set up, and would be closed after the show ended. In 2 nd question, therefore, the price of an additional ticket is posted to the still open ticket purchase account, so the price of a ticket is now seems to be $20, which many find to be too high a price. 34 Opening and closing accounts In the ticket problem, there was a natural time to close an account. That is when the show is consumed. Once an account is closed, you go back to zero. Other accounts may, however, be somewhat more subtle, for example, saving and investment accounts. Evidence that people avoid closing accounts at a loss: Selling a stock at a loss is painful: disposition effect (to be further discussed). Companies rarely have low negative earnings but often have low positive earnings: They manage earnings either pushing things to low positive Or they take a bath and move to high negative 35 Earnings Management to avoid losses Burgstahler and Dichev 1997 Earnings management to avoid earnings decreases and losses Journal of Accounting and Economics Shen and Chih 2005 Investor protection, prospect theory, and earnings management: an international comparison of the banking industry Journal of Banking and Finance 36
The equity premium puzzles Several big puzzles relate to aggregate stock market behavioral finance has partial explanations for some of these puzzles: Equity premium puzzle: stock returns are higher than they should be given risk borne by investors in stock markets Historical (realized) equity premium in U.S. Historically, a well-diversified portfolio of stocks has substantially outperformed fixed income securities. Important to look at real returns which control for inflation effects. Difference between expected equity return and fixedincome return is known as equity premium. This is return for bearing additional risk of stocks relative to bonds or bills What can explain this puzzle? Standard Expected Utility Theory vs Prospect Theory 37 38 Total nominal return indexes: 1802-1997 Total real return indexes: 1802-1997 Siegel, J.J.. From "The Future Value of an 1802 Dollar Invested in Different Asset Classes (in nominal terms)," in Stocks for the Long Run 2nd Edition (McGraw Hill, New York, New York), 1998. 1998 by McGraw-Hill, Inc. All rights reserved. Reproduced by permission. 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted 39 to a publicly available website, in whole or in part. Siegel, J.J.. From "The Future Value of an 1802 Dollar Invested in Different Asset Classes (in real terms)," in Stocks for the Long Run 2nd Edition (McGraw Hill, New York, New York), 1998. 1998 by McGraw-Hill, Inc. All rights reserved. Reproduced by permission. 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly available website, in whole or in part. 40
Average historical real returns for stocks, bonds and bills Why is the equity risk premium puzzle? Stocks are riskier and therefore should earn higher returns.. But, the equity premium seems too high Theorists have shown that realized equity premium implies an improbably large degree of risk aversion. First, In an economy with reasonable parameters, average return on stock market would be just 0.1% higher than risk-free rate, not 3.9% (or higher) observed in most studies. Siegel, J. J.. From "Average Real Returns (in %) on Stocks, Bonds and Bills," in Stocks for the Long Run, 2nd Edition, 1998 (McGraw Hill, New York, New York). 1998 by McGraw-Hill, Inc. All rights reserved. Reproduced by permission. 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly available website, in whole or in part. 41 42 Why is the equity risk premium puzzle? Second, based on a typical logarithmic utility function, the coefficient of relative risk aversion is 1.0. The coefficient of relative risk aversion needed to justify the observed equity risk premium would have to be a whopping 30 in order to explain observed returns! Third, recalling prospects and certainty equivalents, consider the following prospect: P1(0.50, $50,000, $100,000) What certainty equivalent, $x, would make someone indifferent between P1 and this $x? For someone with a coefficient of relative risk aversion of 30, $x would need to be $51,209!! 43 What can explain this equity premium puzzle? Benartzi and Thaler (1995) have linked prospect theory to equity premium puzzle. Key is to remember loss aversion (investors hate losing money) and mental accounting (consider how often investors evaluate their portfolios) Intuitively, if you evaluate your position every day, there is a very good chance that by day s end you will have lost money, so you find stocks very risky and unattractive. But if you evaluate stocks once per decade there is a much smaller chance that you will lose money, so you will find stocks not so risky. The loss aversion does not have much effect on you. Benartzi and Thaler (1995), Myopic loss aversion and the equity premium puzzle, the Quarterly Journal of Economics, page 73-92 44
What can explain this equity premium puzzle? Loss aversion Benartzi and Thaler assume a loss aversion factor of 2.5. In other words, the loss of $1 is 2.5 times more painful than a gain of $1 is pleasurable. Mental accounting Consider P(0.5, $200, $-100) as an investment where one can make $200 or lose $100. The expected gain is $50, is the risk of the investment worth the potential gain? Or should we just do nothing rather than accept the prospect? V(P) = 0.50(200) + 0.50(2.5(-100)) = -25 Reject the prospect! 45 What can explain this equity premium puzzle? Mental accounting What if the prospect is allowed to be run twice before the investor carefully notes the results? The possible outcomes for two gambles are $400 (with a probability of 25%), $100 (with a probability of 50%), and -$200 (with a probability of 25. We label it Px V(Px) = 0.25(400) + 0.50(100) + 0.25(2.5(-200)) = +25 Note that now a loss is only half as likely (25% vs 50%) to occur. While this person remains loss averse, she is now more willing to take the risk of the investment as long as she evaluate the outcomes two prospects at a time (i.e., looking at her portfolio every two periods). 46 What can explain this equity premium puzzle? QUESTION: Given prospect theory approach, what evaluation period is consistent with historically observed market risk premium? ANSWER: About a year which is logically how often a typical investor gives his portfolio a careful look. Reasons: Tax is paid annually Portfolio assessment and adjustments are often annual Benartzi and Thaler refer to these loss aversion and shorthorizon portfolio evaluation as myopic loss aversion. 47