Decision-making under uncertainty – A field study of cumulative prospect theory

The presented research tests cumulative prospect theory (CPT, [Kahneman, D., Tversky, A., 1979. Prospect theory: An analysis of decision under risk. Econometrica 47, 263–291; Tversky, A., Kahneman, D., 1981. The framing of decisions and the psychology of choice. Science 211, 453–480]) in the financial market, using US stock option data. Option prices possess information about actual investors’ preferences in such a way that an exploitation of conventional option analysis, along with theoretical relationships, makes it possible to elicit investor preferences. The option data in this study serve for estimating the two essential elements of the CPT, namely, the value function and the probability weighting function. The main part of the work focuses on the functions’ simultaneous estimation under CPT original parametric specification. The shape of the estimated functions is found to be in line with theory. Comparing to results of laboratory experiments, the estimated functions are closer to linearity and loss aversion is less pronounced.     

Alternative utility functions: review,analysis and comparison

The paper reviews the development of von Neumann and Morgenstern (vNM) utility theory. Kahneman and Tversky’s (KT’s) prospect theory is introduced. The vNM utility function is compared and contrasted with KT’s value function. We prove the uniqueness of two popular utility functions. First, we show that all power utility functions possess constant RRA. And, we show that all exponential utility functions have constant ARA. The paper concludes by discussing applications, strengths and weaknesses of various utility functions.     

Non‐Monotonicity of the Tversky‐Kahneman Probability‐Weighting Function: A Cautionary Note

Cumulative Prospect Theory has gained a great deal of support as an alternative to Expected Utility Theory as it accounts for a number of anomalies in the observed behavior of economic agents. Expected Utility Theory uses a utility function and subjective or objective probabilities to compare risky prospects. Cumulative Prospect Theory alters both of these aspects. The concave utility function is replaced by a loss‐averse utility function and probabilities are replaced by decision weights. The latter are determined with a weighting function applied to the cumulative probability of the outcomes. Several different probability weighting functions have been suggested. The two most popular are the original proposal of Tversky and Kahneman and the compound‐invariant form proposed by Prelec. This note shows that the Tversky‐Kahneman probability weighting function is not increasing for all parameter values and therefore can assign negative decision weights to some outcomes. This in turn implies that Cumulative Prospect Theory could make choices not consistent with first‐order stochastic dominance.     

Prospect theory–based portfolio optimization: an empirical study and analysis using intelligent algorithms

The behaviourally based portfolio selection problem with investor’s loss aversion and risk aversion biases in portfolio choice under uncertainty is studied. The main results of this work are: developed heuristic approaches for the prospect theory model proposed by Kahneman and Tversky in 1979 as well as an empirical comparative analysis of this model and the index tracking model. The crucial assumption is that behavioural features of the prospect theory model provide better downside protection than traditional approaches to the portfolio selection problem. In this research the large-scale computational results for the prospect theory model have been obtained for real financial market data with up to 225 assets. Previously, as far as we are aware, only small laboratory tests (2–3 artificial assets) have been presented in the literature. In order to investigate empirically the performance of the behaviourally based model, a differential evolution algorithm and a genetic algorithm which are capable of dealing with a large universe of assets have been developed. Specific breeding and mutation, as well as normalization, have been implemented in the algorithms. A tabulated comparative analysis of the algorithms’ parameter choice is presented. The prospect theory model with the reference point being the index is compared to the index tracking model. A cardinality constraint has been implemented to the basic index tracking and the prospect theory models. The portfolio diversification benefit has been found. The aggressive behaviour in terms of returns of the prospect theory model with the reference point being the index leads to better performance of this model in a bullish market. However, it performed worse in a bearish market than the index tracking model. A tabulated comparative analysis of the performance of the two studied models is provided in this paper for in-sample and out-of-sample tests. The performance of the studied models has been tested out-of-sample in different conditions using simulation of the distribution of a growing market and simulation of the t-distribution with fat tails which characterises the dynamics of a decreasing or crisis market.     

Aggregate investor preferences and beliefs in stock market: A stochastic dominance analysis

This paper analyzes whether the market portfolio is efficiently related to benchmark portfolios formed on size, value, momentum and reversal with various utility theories by using stochastic dominance criteria. The results support the prospect theory including assumption of loss aversion at monthly and yearly horizons, which indicates the market utility is S-shaped, and steeper for losses than for gains. And, the findings do not provide convincing evidence for positive skewness preference. Therefore, it should probe into asset pricing model and financial puzzles by prospect theory preferences. It may thus be difficult for the market to benefit from the asset through its features on skewness or other higher order central moment. We also develop several bootstrap procedures with favorable properties in statistical size and power for testing stochastic dominance efficiency.     

A dynamic model of active portfolio management with benchmark orientation

This paper studies optimal dynamic portfolios for investors concerned with the performance of their portfolios relative to a benchmark. Assuming that asset returns follow a multi-linear factor model similar to the structure of Ross (1976) [Ross, S., 1976. The arbitrage theory of the capital asset pricing model. Journal of Economic Theory, 13, 342–360] and that portfolio managers adopt a mean tracking error analysis similar to that of Roll (1992) [Roll, R., 1992. A mean/variance analysis of tracking error. Journal of Portfolio Management, 18, 13–22], we develop a dynamic model of active portfolio management maximizing risk adjusted excess return over a selected benchmark. Unlike the case of constant proportional portfolios for standard utility maximization, our optimal portfolio policy is state dependent, being a function of time to investment horizon, the return on the benchmark portfolio, and the return on the investment portfolio. We define a dynamic performance measure which relates portfolio’s return to its risk sensitivity. Abnormal returns at each point in time are quantified as the difference between the realized and the model-fitted returns. Risk sensitivity is estimated through a dynamic matching that minimizes the total fitted error of portfolio returns. For illustration, we analyze eight representative mutual funds in the U.S. market and show how this model can be used in practice.     

Explaining investor preference for cash dividends

The well-known tendency of investors to favor cash dividends emerges quite naturally in two new theories of choice behavior [the theory of self-control due to Thaler and Shefrin (1981), and the version of prospect theory set out by Kahneman and Tversky (1979)]. Although our treatment is novel when viewed from the perspective of standard financial theory, it provides explanations for a phenomenon that has long been described as perplexing.     

A non-probabilistic approach to efficient portfolios

The notion of efficient portfolios is restated employing a novel approach to asset uncertainty, in which an uncertainty set conveys all information on asset returns. Based on the idea that a portfolio is a function mapping the asset returns to the portfolio return, the width of the image of the uncertainty set is used as a risk measure. The statement of the separation theorem is inherited. Furthermore, non-positive Value at Risk with 100% confidence is found in a class of efficient portfolios.     

The pricing of volatility risk in the US equity market

We analyze whether the pricing of volatility risk depends on the asset pricing framework applied in the tests, the specified volatility proxies, and the portfolio sorts used for spanning the asset universe. For this purpose, we compare the results using a macroeconomic and fundamental based asset pricing model using three proxies of volatility and uncertainty, using size/value sorted and industry sector portfolios. Our results reveal that the marginal pricing effect of the VIX volatility factor is strong and statistically significant throughout the models and specifications, while the effect of an EGARCH-based volatility factor is mixed, mostly smaller but with the correct sign. In most cases, the EGARCH factor does not impair the pricing effect of the VIX. The portfolio sorts have a substantial impact on the volatility premiums in both model frameworks. The size of the volatility risk premium is more uniform across the models if the industry sector portfolio sort is used. Finally, the size/value portfolio sort generates larger volatility risk premiums for both models.     

State Dependence Can Explain the Risk Aversion Puzzle

Risk aversion functions extracted from observed stock and optionprices can be negative, as shown by Aït-Sahalia and Lo(2000), Journal of Econometrics 94: 9–51; and Jackwerth(2000), The Review of Financial Studies 13(2), 433–51.We rationalize this puzzle by a lack of conditioning on latentstate variables. Once properly conditioned, risk aversion functionsand pricing kernels are consistent with economic theory. Todifferentiate between the various theoretical explanations interms of heterogeneity of beliefs or preferences, market sentiment,state-dependent utility, or regimes in fundamentals, we calibrateseveral consumption-based asset pricing models to match theempirical pricing kernel and risk aversion functions at differentdates and over several years.     

An alternative measure of the “world market portfolio”: Determinants, efficiency, and information content

The world market portfolio plays an important role in international asset pricing, but is unobservable in practice. We first propose a framework for constructing a market proxy that corresponds to the “market portfolio” of financial theory. We then construct this proxy, analyze its determinants and test its efficiency and explanatory power over the period 1975-2007 with respect to the return generating processes of a broad asset universe. We show that its major determinants are traded assets and that it is not efficient. However, it is significant for explaining individual asset returns over an asset universe that includes stocks, bonds, money markets and commodities. The explanatory information is incremental to what is available in traded asset prices and the significance of this information is robust with respect to diversified portfolios generated by factor analysis and to characteristic-sorted portfolios as well as to various model specifications, including the single-index model, the Fama-French (1992) three factor model for stocks, and various specifications of multi-index models hedged and unhedged for foreign currency risk.     

Portfolio insurance and prospect theory investors: Popularity and optimal design of capital protected financial products

Portfolio insurance strategies are used on both the institutional and the retail side of the asset management industry. While standard utility theory struggles to provide an explanation, this study justifies the popularity of portfolio insurance strategies in a behavioral finance context. We run Monte Carlo simulations as well as historical simulations for popular portfolio insurance strategies and benchmark strategies in order to evaluate the outcomes using cumulative prospect theory. Our simulation results indicate that most portfolio insurance strategies are the preferred investment strategy for a prospect theory investor. Moreover, the analysis provides insights into how portfolio insurance products should be designed and structured to meet the preferences of prospect theory investors as accurately as possible.     

Behavioral portfolio selection and optimization: an application to international stocks

The behavioral approach of decision making has emerged as a diversified solution in the presence of risk and uncertainty. Using the popular cumulative prospect theory as an objective function for portfolio selection, this study implements the classical mean–variance model to compare the portfolio performance of high behavioral stocks with that of stocks with lower behavioral values. Based on a sample of 37 international stocks over the period from October 1998 to November 2017, empirical results from D-vine pair copula GARCH-GEV indicate that the portfolio of high behavioral prospect stocks outperforms the portfolio of stocks with low behavioral scores. This finding may suggest that portfolios with high behavioral values coincide with rational efficiency sets.     

Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model

The paper develops a general discrete-time framework for asset pricing and hedging in financial markets with proportional transaction costs and trading constraints. The framework is suggested by analogies between dynamic models of financial markets and (stochastic versions of) the von Neumann–Gale model of economic growth. The main results are hedging criteria stated in terms of “dual variables” – consistent prices and consistent discount factors. It is shown how these results can be applied to specialized models involving transaction costs and portfolio restrictions.     

Disagreement and return predictability of stock portfolios

This paper provides evidence that portfolio disagreement measured bottom-up from individual-stock analyst forecast dispersions has a number of asset pricing implications. For the market portfolio, market disagreement mean-reverts and is negatively related to ex post expected market return. Contemporaneously, an increase in market disagreement manifests as a drop in discount rate. For book-to-market sorted portfolios, the value premium is stronger among high disagreement stocks. The underperformance by high disagreement stocks is stronger among growth stocks. Growth stocks are more sensitive to variations in disagreement relative to value stocks. These findings are consistent with asset pricing theory incorporating belief dispersion.     

Macroeconomic fundamentals and cryptocurrency prices: A common trend approach

Based on asset pricing theory, we posit and find that equity markets and cryptocurrency markets share a common fundamental. Our cointegration tests show that the most important asset pricing primitive, consumption, can serve as the common fundamental. We further show that additional macroeconomic factors, as well as uncertainty and sentiment, all play a role in explaining the deviation from fundamentals. To understand the linkage between equity markets, cryptocurrency markets, and the macroeconomy, we suggest the following three channels: (i) portfolio allocation decisions, (ii) intermarket order flows, and (iii) technological adaption expectations.     

Two Paradigms and Nobel Prizes in Economics: a Contradiction or Coexistence?

Abstract Markowitz and Sharpe won the Nobel Prize in Economics for the development of Mean‐Variance (M‐V) analysis and the Capital Asset Pricing Model (CAPM). Kahneman won the Nobel Prize in Economics for the development of Prospect Theory. In deriving the CAPM, Sharpe, Lintner and Mossin assume expected utility (EU) maximisation in the face of risk aversion. Kahneman and Tversky suggest Prospect Theory (PT) as an alternative paradigm to EU theory. They show that investors distort probabilities, make decisions based on change of wealth, exhibit loss aversion and maximise the expectation of an S‐shaped value function, which contains a risk‐seeking segment. Can these two apparently contradictory paradigms coexist? We show in this paper that although CPT (and PT) is in conflict to EUT, and violates some of the CAPM's underlying assumptions, the Security Market Line Theorem (SMLT) of the CAPM is intact in the CPT framework. Therefore, the CAPM is intact also in CPT framework.     

Options Trading and the CAPM

This article studies equilibrium asset pricing when agents facenonnegative wealth constraints. In the presence of these constraintsit is shown that options on the market portfolio are nonredundantsecurities and the economy's pricing kernel is a function ofboth the market portfolio and the nonredundant options. Thisimplies that the options should be useful for explaining riskyasset returns. To test the theory, a model is derived in whichthe expected excess return on any risky asset is linearly related(via a collection of betas) to the expected excess return onthe market portfolio and to the expected excess returns on thenonredundant options. The empirical results indicate that thereturns on traded index options are relevant for explainingthe returns on risky asset portfolios.     

Irreversible investment and discounting: an arbitrage pricing approach

This paper presents a unified approach to valuing investment projects under uncertainty, based on stochastic discount factors, by linking optimal stopping theory to the no-arbitrage principle in asset pricing. An investment threshold for the case where the discount factor and the project’s cash-flow both follow a geometric Brownian motion is derived. Comparative statics of the investment trigger are obtained adding to and clarifying on the uncertainty–investment debate. Finally, two different ways to obtain discount factors are illustrated: spanning assets and representative agent analysis. The link between the characteristics of these different approaches and the optimal investment policy is clarified.