Incentives and Behavior Prof. Dr. Heiner Schumacher KU Leuven 5. Portfolio Choice Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 1 / 22
Introduction In this lecture, we use prospect theory to explain one of the most famous problems in …nance, the “equity premium puzzle.” Loosely speaking, the equity puzzle says that if people’s risk preferences can be described by EUT, they invest too little of their wealth into stocks. Prospect theory provides a very elegant and intuitive explanation for the equity premium puzzle. This explanation has an important message for private investors. 1 We also look at some other applications of prospect theory in …nance and labor economics. 1 Benartzi, Shlomo, and Richard Thaler (1995): “Myopic Loss Aversion and the Equity Premium Puzzle,” Quarterly Journal of Economics 110(1), 73 - 92. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 2 / 22
Introduction Overview The Equity Premium Puzzle Explaining the Equity Premium Puzzle with Myopic Loss Aversion Evidence on MLA from the …eld Other Applications of Prospect Theory Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 3 / 22
The Equity Premium Puzzle In the period 1889–1978, the average annual return on the Standard and Poor 500 Index (stocks) was seven percent, while the annual return on short-term debt (bonds) was less than one percent. Mehra and Prescott (1985) found that this is inconsistent with standard economic models: the equity premium of six percent is much too high, or investors must have implausibly high risk aversion. 2 An example: investors would have to be indi¤erent between a bet equally likely to pay 50.000 EUR or 100.000 EUR and a certain payo¤ of 51.209 EUR (Mankiw and Zeldes 1991). 2 Mehra, Rajnish, and Edward C. Prescott (1985): “The Equity Premium: A Puzzle,” Journal of Monetary Economics 15(2), 145-161. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 4 / 22
The Equity Premium Puzzle In Mehra and Prescott’s (1985) model, expected utility is given by � ∞ � β t U ( c t ) E ∑ , t = 0 where β 2 [ 0 , 1 ] is the discount factor and U ( c t ) the utility from consumption in period t . They assume the utility function U ( c , α ) = c 1 � α � 1 , 1 � α where α 2 ( 0 , ∞ ) measures the degree of risk aversion. Reasonable estimates show that α � 1. Mehra and Prescott vary β 2 [ 0 , 1 ] and α 2 ( 0 , 10 ) in order to obtain the highest admissible equity premium. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 5 / 22
The Equity Premium Puzzle Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 6 / 22
Explaining the Equity Premium Puzzle with Myopic Loss Aversion Benartzi and Thaler (1995) provide an explanation for the equity premium puzzle that is based on Prospect Theory. Loss aversion: investors have preferences over returns (i.e., gains and 1 losses) rather than over the consumption pro…le the returns help provide. A short evaluation period: investors frequently evaluate their 2 portfolios and then perceive the utility from gains or losses. The shorter is the evaluation period, the less attractive are risky assets (because they are more likely to end up in the domain of losses than riskless assets). Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 7 / 22
Explaining the Equity Premium Puzzle with Myopic Loss Aversion “Suppose that the investor must choose between a risky asset that pays an expected 7 percent per year with a standard deviation of 20 percent (like stocks) and a safe asset that pays a sure 1 percent. [...] The attractiveness of the risky asset will depend on the time horizon of the investor. The longer the investor intends to hold the asset, the more attractive the risky asset will appear, so long the investment is not evaluated frequently.” Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 8 / 22
Explaining the Equity Premium Puzzle with Myopic Loss Aversion If investors are loss averse, how often would they have to evaluate their portfolios to explain the equity premium? What combination of stocks and bonds would maximize prospective utility given a certain evaluation period? Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 9 / 22
Explaining the Equity Premium Puzzle with Myopic Loss Aversion Procedure 100.000 n � month returns are drawn from a data set containing the monthly returns on stocks and bonds from 1926–1990. Returns are then ranked, from best to worst. From this one can derive a distribution function and then the prospective utility of the given asset for the speci…ed holding period. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 10 / 22
Explaining the Equity Premium Puzzle with Myopic Loss Aversion Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 11 / 22
Explaining the Equity Premium Puzzle with Myopic Loss Aversion The evaluation period for which a stock portfolio o¤ers the same prospective utility than a bond portfolio is 13 months (for real returns it is between 10 and 11 months). An evaluation period of one year seems plausible: investors …le taxes annually and receive the detailed reports from their broker/mutual fund/retirement account once a year. Results are mainly driven by loss aversion, not the speci…cation of the decision weights. What is the best portfolio for a one-year planning horizon? Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 12 / 22
Explaining the Equity Premium Puzzle with Myopic Loss Aversion Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 13 / 22
Explaining the Equity Premium Puzzle with Myopic Loss Aversion Portfolios between 30 and 55 percent all yield approx. the same prospective utility. Again, this matches the investment behavior of many investors and institutions (like pension funds). The most frequent allocation between stocks and bonds is 50-50! By how much does the equity premium fall, when the evaluation period increases? Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 14 / 22
Explaining the Equity Premium Puzzle with Myopic Loss Aversion Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 15 / 22
Evidence on MLA from the …eld An important implication of MLA is that investors invest more of their endowment in risky assets when they get feedback only infrequently. Larson et al. (2016) test this hypothesis in a recent …eld experiment. 3 They observe professional traders on a new trading platform. The traders only know that they participate in a beta test. All traders get an endowment that they can invest in a single risky asset. They can trade for ten trading days on the platform. On average, traders earned 1454 USD in this experiment, so the stakes were quite substantial. 3 Larson, Francis, John List, and Robert Metcalfe (2016): “Can myopic loss aversion explain the Equity Premium Puzzle? Evidence from a natural …eld experiment with professional traders,” NBER Working Paper 22605. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 16 / 22
Evidence on MLA from the …eld The outcome variable of interest is the share of the endowment that the traders invest into the risky asset. Frequent treatment: Traders can observe price changes every second. Infrequent treatment: Traders can observe price changes only every four hours. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 17 / 22
Evidence on MLA from the …eld The results provide strong evidence in favor of MLA. In the last 20 percent of the experiment, traders in the Infrequent treatment invest 36.4 percent of their portfolio, while traders in the Frequent treatment only invest 27.4 percent of their portfolio. The di¤erence in behavior between treatment groups develops over time. Traders in the Infrequent treatment earn 50 percent more pro…ts than traders in the Frequent treatment. Experience as a trader has no signi…cant e¤ect on behavior. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 18 / 22
Other Applications of Prospect Theory Insurance Sydnor (2010) studies the insurance decisions of 50.000 customers of a large home insurance company. 4 Households have to choose a deductible from a menu of four possibilities: 100 USD, 250 USD, 500 USD and 1.000 USD. Households who choose a 500 USD deductible pay an average premium of 715 USD a year, while the average premium for a policy with 1.000 USD deductible is only 615 USD. The annual claim rate is around 5 percent. Hence, households are ready to pay 100 USD a year to insure against a 5 percent chance of paying additional 500 USD in the event of a claim. Under EUT, this can only be rationalized by unreasonably high levels of risk aversion. 4 Sydnor, Justin (2010): “(Over)insuring Modest Risks,” American Economic Journal: Applied Economics 2(4), 177 - 199. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 5. Portfolio Choice 19 / 22
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