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on Utility Models and Prospect Theory |
| By: | Kevin Dowd (The University of Nottingham, UK); John Cotter (University College Dublin, Ireland) |
| Abstract: | Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their risk-aversion functions. To date there has been very little guidance on the choice of risk-aversion functions underlying spectral risk measures. This paper addresses this issue by examining two popular risk aversion functions, based on exponential and power utility functions respectively. We find that the former yields spectral risk measures with nice intuitive properties, but the latter yields spectral risk measures that can have perverse properties. More work therefore needs to be done before we can be sure that arbitrary but respectable utility functions will always yield ‘well-behaved’ spectral risk measures. |
| Keywords: | coherent risk measures, spectral risk measures, risk aversion functions |
| JEL: | G15 |
| Date: | 2011–06–24 |
| URL: | http://d.repec.org/n?u=RePEc:ucd:wpaper:2007/42&r=upt |
| By: | Kontek, Krzysztof |
| Abstract: | Cumulative Prospect Theory (Kahneman, Tversky, 1979, 1992) holds that the value function is described using a power function, and is concave for gains and convex for losses. These postulates are questioned on the basis of recently reported experiments, paradoxes (gain-loss separability violation), and brain activity research. This paper puts forward the hypothesis that perception utility is generally logarithmic in shape for both gains and losses, and only happens to be convex for losses when gains are not present in the problem context. This leads to a different evaluation of mixed prospects than is the case with Prospect Theory: losses are evaluated using a concave, rather than a convex, utility function. In this context, loss aversion appears to be nothing more than the result of applying a logarithmic utility function over the entire outcome domain. Importantly, the hypothesis enables a link to be established between perception utility and Portfo-lio Theory (Markowitz, 1952A). This is not possible in the case of the Prospect Theory value function due its shape at the origin. |
| Keywords: | Prospect Theory; value function; perception utility; loss aversion; gain-loss separability violation; neuroscience; Portfolio Theory; Decision Utility Theory. |
| JEL: | D81 G11 D87 C91 |
| Date: | 2011–06–20 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:31715&r=upt |
| By: | Kevin Dowd (The University of Nottingham, UK); John Cotter (University College Dublin, Ireland) |
| Abstract: | Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds that these risk measures have nice intuitive properties. It also discusses how they can be estimated using numerical quadrature methods, and how confidence intervals for them can be estimated using a parametric bootstrap. Illustrative results suggest that estimated exponential spectral risk measures obtained using such methods are quite precise in the presence of normally distributed losses. |
| Keywords: | limit orders, market orders, tail risks |
| JEL: | G15 |
| Date: | 2011–06–24 |
| URL: | http://d.repec.org/n?u=RePEc:ucd:wpaper:2007/46&r=upt |
| By: | Emmanuel PETIT (GREThA, CNRS, UMR 5113); Anna TCHERKASSOF (LIP/PC2S); Xavier GASSMANN (INRA) |
| Abstract: | Our experiment aims at studying the impact of self-esteem on risk-prone choices in an Allais-type decision context using hypothetical money. We use an Internet protocol in order to reach a large heterogeneous student population sample. An anticipated regret explanation for the certainty effect implies that self-esteem is a crucial psychological variable in what concerns risky decision, but only when the choice is between a safe option and a risky option. Thus, in our experiment, we hypothesize that low self-esteem people will choose more frequently the safe option (rather than the risky-prone option) than high self-esteem people, whereas low self-esteem and high self-esteem individuals will show the same pattern of choices between two different risk-based options. Our data confirm our hypothesis. Regarding risky choices preferences, we also observe that females, non economists and older people significantly exhibit safer choice preferences than other participants. We find also that men and students in economics are more likely to conform to expected utility theory than females and other social science students respectively. We then discuss what these findings mean for economic regret theory, and suggest that a complete theory of decision-making under risk should introduce both situational and motivational explanations of individual behaviour. |
| Keywords: | Allais paradox; Risk; Regret aversion; Self-esteem; Internet experiment; Gender differences |
| JEL: | C91 D81 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:grt:wpegrt:2011-25&r=upt |
| By: | John Cotter (University College Dublin, Ireland); Kevin Dowd (The University of Nottingham, UK) |
| Abstract: | This paper applies an AR(1)-GARCH (1, 1) process to detail the conditional distributions of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses the conditional distribution for these contracts to estimate spectral risk measures, which are coherent risk measures that reflect a user’s risk-aversion function. It compares these to more familiar VaR and Expected Shortfall (ES) measures of risk, and also compares the precision and discusses the relative usefulness of each of these risk measures in setting variation margins that incorporate time-varying market conditions. The goodness of fit of the model is confirmed by a variety of backtests. |
| Keywords: | Spectral risk measures, Expected Shortfall, Value at Risk, GARCH, clearinghouse. |
| JEL: | G15 |
| Date: | 2011–06–24 |
| URL: | http://d.repec.org/n?u=RePEc:ucd:wpaper:2006/16&r=upt |
| By: | John Cotter (University College Dublin, Ireland); Kevin Dowd (The University of Nottingham, UK) |
| Abstract: | This paper applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that reflect a user’s risk-aversion function. It compares these to VaR and Expected Shortfall (ES) risk measures, and compares the precision of their estimators. It also discusses the usefulness of these risk measures in the context of clearinghouses setting initial margin requirements, and compares these to the SPAN measures typically used. |
| Keywords: | Spectral risk measures, Expected Shortfall, Value at Risk, Extreme Value, clearinghouse |
| JEL: | G15 |
| Date: | 2011–06–24 |
| URL: | http://d.repec.org/n?u=RePEc:ucd:wpaper:2005/16&r=upt |
| By: | Günter Franke (Department of Economics, University of Konstanz, Germany); Harris Schlesinger (University of Alabama, USA); Richard C. Stapleton (University of Manchester, UK) |
| Abstract: | We examine the effects of background risks on optimal portfolio choice. Examples of background risks include uncertain labor income, uncertainty about the terminal value of fixed assets such as housing and uncertainty about future tax liabilities. While some of these risks are additive and have been amply studied, others are multiplicative in nature and have received far less attention. The simultaneous effect of both additive and multiplicative risks has hitherto not received attention and can explain some paradoxical choice behavior. We rationalize such behavior and show how background risks might lead to seemingly U-shaped relative risk aversion for a representative investor. |
| Keywords: | Derived risk aversion, Additive, multiplicative background risk |
| JEL: | D81 G11 |
| Date: | 2011–06–16 |
| URL: | http://d.repec.org/n?u=RePEc:knz:dpteco:1126&r=upt |
| By: | Michał Krawczyk (Faculty of Economic Sciences, University of Warsaw) |
| Abstract: | This study is a field experiment on loss aversion. The framing of scoring rules was differentiated in two exams at the University of Warsaw, with only half the students facing explicit penalty points in the case of giving an incorrect answer. Loss aversion predicts that less risk will be taken (less questions will be answered) when losses are possible but in fact, no treatment effect was observed. |
| Keywords: | loss aversion, framing, field experiments, gender differences |
| JEL: | C93 D81 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2011-13&r=upt |
| By: | Michał Krawczyk (Faculty of Economic Sciences, University of Warsaw) |
| Abstract: | This study makes use of an unusual opportunity to manipulate framing of a simple decision under uncertainty: whether or not to answer an exam question when unsure which answer is correct and a missing response is scored higher than an incorrect one. Two treatments were compared in a natural field experiment: one in which the decision was framed in terms of losses, and the other – in terms of gains. Some alternative theories of decision making under risk, notably prospect theory, propose that individuals display reflection effect, i.e. tend to be more risk-seeking in losses than gains. No such evidence was found: subjects were generally risk-averse and this disposition was not affected by treatment. |
| Keywords: | framing, reflection effect, field experiments |
| JEL: | C93 D81 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2011-14&r=upt |
| By: | John Cotter (University College Dublin, Ireland); Kevin Dowd (The University of Nottingham) |
| Abstract: | This paper presents non-parametric estimates of spectral risk measures applied to long and short positions in 5 prominent equity futures contracts. It also compares these to estimates of two popular alternative measures, the Value-at-Risk (VaR) and Expected Shortfall (ES). The spectral risk measures are conditioned on the coefficient of absolute risk aversion, and the latter two are conditioned on the confidence level. Our findings indicate that all risk measures increase dramatically and their estimators deteriorate in precision when their respective conditioning parameter increases. Results also suggest that estimates of spectral risk measures and their precision levels are of comparable orders of magnitude as those of more conventional risk measures. Running head: financial risk measures for futures positions. |
| JEL: | G15 |
| Date: | 2011–06–24 |
| URL: | http://d.repec.org/n?u=RePEc:ucd:wpaper:2006/13&r=upt |
| By: | Andrew Caplin; Daniel Martin |
| Abstract: | We introduce a rational choice theory that allows for many forms of imperfect perception, including failures of memory, selective attention, and adherence to simplifying rules of thumb. Despite its generality, the theory has strong, simple, and intuitive implications for standard choice data and for more enriched choice data. The central assumption is rational expectations: decision makers understand the relationship between their perceptions, however limited they may be, and the (stochastic) consequences of their available choices. Our theory separately identifies two distinct "framing" effects: standard effects involving the layout of the prizes (e.g. order in a list) and novel effects relating to the information content of the environment (e.g. how likely is the first in the list to be the best). Simple experimental tests both affirm the basic model and confirm the existence of information-based framing effects. |
| JEL: | D01 |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:17163&r=upt |
| By: | Wolfgang Höchtl (University of Innsbruck); Rupert Sausgruber (University of Innsbruck); Jean-Robert Tyran (University of Vienna) |
| Abstract: | Some people have a concern for a fair distribution of incomes while others do not. Does such a concern matter for majority voting on redistribution? Fairness preferences are relevant for redistribution outcomes only if fair-minded voters are pivotal. Pivotality, in turn, depends on the structure of income classes. We experimentally study voting on redistribution between two income classes and show that the effect of inequality aversion is asymmetric. Inequality aversion is more likely to matter if the “rich” are in majority. With a “poor” majority, we find that redistribution outcomes look as if all voters were exclusively motivated by self-interest. |
| Keywords: | redistribution; self interest; inequality aversion; median voter; experiment |
| JEL: | A13 C9 D72 |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1118&r=upt |