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on Utility Models and Prospect Theory |
| By: | Krzysztof Kontek (Artal Investments) |
| Abstract: | The paper presents a method for lottery valuation using the relative utility function. This function was presented by Kontek (2009) as “the aspiration function” and resembles the utility curve proposed by Markowitz (1952A). The paper discusses lotteries with discrete and continuous outcome distributions as well as lotteries with positive, negative and mixed outcomes providing analytical formulas for certainty equivalents in each case. The solution is similar to the Expected Utility Theory approach and does not use the probability weighting function – one of the key elements of Prospect Theory. Solutions to several classical behavioral problems, including the Allais paradox, are presented, demonstrating that the method can be used for valuing lotteries even in more complex cases of outcomes described by a combination of Beta distributions. The paper provides strong arguments against Prospect Theory as a model for describing human behavior and lays the foundations for Relative Utility Theory – a new theory of decision making under conditions of risk. |
| Keywords: | Lottery Valuation, Expected Utility Theory, Markowitz Hypothesis, Prospect / Cumulative Prospect Theory, Aspiration / Relative Utility Function |
| Date: | 2009–07–25 |
| URL: | http://d.repec.org/n?u=RePEc:wse:wpaper:39&r=upt |
| By: | Geert Bekaert (Columbia Business School, 3022 Broadway, New York, NY 10027, USA.); Marie Hoerova (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany.); Martin Scheicher (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany.) |
| Abstract: | Implied volatility indices should have information about risk parameters, once they are cleansed of the influence of normal volatility dynamics and macroeconomic uncertainty. Building on intuition from the dynamic asset pricing literature, we uncover unobserved risk aversion and fundamental uncertainty from the observed time series of the VIX and the credit spreads while controlling for realized volatility, expectations about the macroeconomic outlook, and interest rates. We apply this methodology to monthly data from both Germany and the US. We find that implied volatilities contain a substantial amount of information regarding risk aversion whereas credit spreads have a lot to say about both risk aversion and uncertainty. Moreover, there is a significant comovement in the German and US risk aversion. JEL Classification: G12, E44. |
| Keywords: | Economic uncertainty, Risk aversion, Time variation in risk and return, Credit spread, Volatility dynamics. |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20091037&r=upt |
| By: | Carolina Fugazza (CeRP-Collegio Carlo Alberto, Turin); Massimo Guidolin (Manchester Business School); Giovanna Nicodano (University of Turin and CeRP-Collegio Carlo Alberto, Turin) |
| Abstract: | Welfare gains to long-horizon investors may derive from time diversification that exploits non-zero intertemporal return correlations associated with predictable returns. Real estate may thus become more desirable if its returns are negatively serially correlated. While it could be important for long horizon investors, time diversification has been mostly investigated in asset menus without real estate and focusing on in-sample experiments. This paper evaluates ex post, the out-of-sample gains from diversification when equity REITs belong to the investment opportunity set. We find that diversification into REITs increases both the Sharpe ratio and the certainty equivalent of wealth for all investment horizons and for both classical and Bayesian (who account for parameter uncertainty) investors. The increases in Sharpe ratios are often statistically significant. However the out-of-sample average Sharpe ratio and realized expected utility of long-horizon portfolios are frequently lower than that of a one-period portfolio, which casts doubt on the value of time diversification. |
| Keywords: | real time asset allocation, real estate, ex post performance, predictability, parameter uncertainty |
| JEL: | G11 L85 |
| Date: | 2009–02 |
| URL: | http://d.repec.org/n?u=RePEc:crp:wpaper:82&r=upt |
| By: | Peter Duersch; Maroš Servátka (University of Canterbury) |
| Abstract: | This paper experimentally investigates whether risk-averse individuals punish less if the outcome of punishment is uncertain than when it is certain. Our design includes three treatments: Baseline in which the one-shot prisoner’s dilemma game is played; Certain Punishment in which the prisoner’s dilemma game is followed by a punishment stage allowing subjects to decrease the other player’s payoff by 2 Euros; and Uncertain Punishment in which subjects could decrease the other player’s payoff with a 50% probability by 1 Euro and with a 50% probability by 3 Euros. We find that in all cases the risk-averse subjects are equally likely to cooperate in the prisoner’s dilemma and equally likely to punish in the second stage in either of the two punishment treatments. |
| Keywords: | Experimental economics; prisoner’s dilemma; punishment; risk aversion; uncertainty |
| JEL: | C70 C91 |
| Date: | 2009–07–25 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:09/12&r=upt |
| By: | Kontek, Krzysztof |
| Abstract: | The paper presents an alternative interpretation of the experimental data published by Kahneman and Tversky in their 1992 study "Advances in Prospect Theory”, which describes the Cumulative version of their Prospect Theory from 1979. It was assumed that, apart from the operations made during the initial stage of problem resolution, which Prospect Theory defines as Editing (here generalized as Mental Adaptation), other mental transformations such as Prospect Scaling (resulting from Focused Attention) and Logarithmic Perception of Financial Stimuli should be considered when analyzing the experimental data. This led to the design of an explicit, simple and symmetric solution without the use of the probability weighting function. The double S-type function obtained (the aspiration function) resembles the utility curve specified by the Markowitz hypothesis (1952) and substitutes the fourfold pattern of risk attitudes introduced by Cumulative Prospect Theory. The results presented constitute a basis for negating Prospect Theory as a theory which correctly describes how decisions are made under conditions of risk and may signal a return to a description of people’s behavior that only relies on the utility-like function. |
| Keywords: | Prospect/Cumulative Prospect Theory; Markowitz Utility Hypothesis; Utility & Aspiration Functions; Mental Processes; Adaptation & Attention Focus |
| JEL: | D81 D01 C91 |
| Date: | 2009–03–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:16516&r=upt |
| By: | Arie Kapteyn; Federica Teppa |
| Abstract: | The paper investigates risk attitudes among different types of individuals. We use several different measures of risk attitudes, including questions on choices between uncertain income streams suggested by Barsky et al. (1997) and a number of ad hoc measures. As in Barsky et al. (1997) and Arrondel and Calvo-Pardo (2002), we first analyse individual variation in the risk aversion measures and explain them by background characteristics (both œobjective characteristics and other subjective measures of risk preference). Next we incorporate the measured risk attitudes into a household portfolio allocation model, which explains portfolio shares, while accounting for incomplete portfolios and fixed costs. Our results show that a measure based on factor analysis of answers to a number of simple risk preference questions has the most explanatory power. The Barsky et al. (1997) measure has less explanatory power than this theoretical measure. We provide a discussion of the reasons for this finding. Fixed costs turn out to provide an economically and statistically highly significant explanation for incomplete portfolios. |
| Keywords: | Risk Aversion; Portfolio Choice; Subjective Measures; Econometric Models; Fixed Costs. |
| JEL: | C5 C9 D12 G11 |
| Date: | 2009–07 |
| URL: | http://d.repec.org/n?u=RePEc:dnb:dnbwpp:216&r=upt |
| By: | Wolfgang Lemke (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany.); Thomas Werner (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany.) |
| Abstract: | We estimate time-varying expected excess returns on the US stock market from 1983 to 2008 using a model that jointly captures the arbitrage-free dynamics of stock returns and nominal bond yields. The model nests the class of affine term structure (of interest rates) models. Stock returns and bond yields as well as risk premia are affine functions of the state variables: the dividend yield, two factors driving the one-period real interest rate and the rate of inflation. The model provides for each month the `term structure of equity premia', i.e. expected excess stock returns over various investment horizons. Model-implied equity premia decrease during the `dot-com' boom period, show an upward correction thereafter, and reach highest levels during the financial turmoil that started with the 2007 subprime crisis. Equity premia for longer-term investment horizons are less volatile than their short-term counterparts. JEL Classification: E43, G12. |
| Keywords: | Equity premium, affine term structure models, asset pricing. |
| Date: | 2009–04 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20091045&r=upt |
| By: | Alexandre Souza (Departments of Economis, Banco Central do Brasil); Gabriel Porcile (Department of Economics, Universidade Federal do Paraná) |
| Abstract: | In the nonconventional economic literature decision processes are mainly analyzed on the basis of cognitive aspects (such as the existence of limited rationality) and institutional aspects (such as rules of thumb, institutions and conventions). The fuzzy logic, in turn, offers a form of treating the decision process when agents only have imprecise and subjective information in a context of complexity and uncertainty. This paper discusses the points of convergence and complementarities between the fuzzy logic and the theory of behavior based on limited rationality and rule-guided economic behavior. |
| Keywords: | complexity; uncertainty; decision; fuzzy |
| JEL: | B41 C45 D81 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:fup:wpaper:0080&r=upt |
| By: | Harin, Alexander |
| Abstract: | The article raises the question of possible existence of gaps, ruptures in the probability scale and of possible values of these ruptures. The calculations give 1/3 of the standard deviation as the minimal value of these ruptures for a number of standard distributions. |
| Keywords: | probability; probability scale; noises; |
| JEL: | C02 C1 C01 |
| Date: | 2009–08–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:16663&r=upt |