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.     

Minority membership on boards of directors: the case for requiring pictures of boards in annual reports

Affirmative action and diversity continue to be contentious issues in the United States. Financial markets are still reeling from the effects of Enron, WorldCom and other corporate exemplars of corruption and malfeasance. The role of the board of directors in these scandals is the subject of serious and ongoing concern. Weak and/or ineffectual boards are often the consequences of “old-boy networks” and a lack of diversity in membership. This research study argues for an increased presence of gender and race diversity on boards of directors. Empirical evidence is presented that shows a significant increase in the presence of ethnic minorities and females when pictures of board members are included in annual reports. We suggest that requiring pictures of board members in annual reports and regulatory filings would result in a larger presence for gender and race diversity on boards of directors. This requirement is not a significant burden and merely represents compliance with the spirit and intent of the “full disclosure” principle.     

On the consequences of state dependent preferences for the pricing of financial assets

This paper introduces state dependent utility into the standard Mehra and Prescott [J. Monet. Econ. 15 (1985) 145] economy by allowing the representative agent's coefficient of relative risk aversion to vary with the underlying economy's growth rate. Existence of equilibrium is proved and its asymptotic properties analyzed. This generalization leads to level dependent marginal rates of substitution, a property that sharply distinguishes this model from the standard construct. For very low coefficients of relative risk aversion, the equilibrium risk free and risky security returns are demonstrated to have volatilities and an associated equity premium that substantially exceed what is found in the data. This provides a contrasting perspective on the classic “equity premium puzzle.”     

An analysis of the companies’ compliance with the EU disclosure requirements and corporate characteristics influencing it: A case study of Turkey

One of the factors shaping accounting disclosure of countries in Europe is the EU Fourth Directive (EUFD) which addresses individual company accounts. The EUFD has been claimed to have had an impact on accounting, including accounting disclosure, of not only the EU countries but also non-EU member European countries. Turkey is one of the non-EU member European countries claimed to be influenced by the EUFD and this study examined Turkish companies’ level of compliance with the disclosure requirements of the EUFD over the years (1986, 1987, 1991, 1992 and 1995), and assessed whether companies’ level of compliance had been influenced by their corporate characteristics, such as company size, listing status and industry type.Turkish companies’ level of compliance with the disclosure requirements of the EUFD was measured by an index (i.e. EUFD Disclosure Compliance Index—EUFDCDI). The index was developed by; constructing disclosure scoring sheet; obtaining annual reports of 61 sampled Turkish companies over the years; completing scoring sheet for each companies’ annual report; and creating disclosure index. The index (EUFDCDI) scores was, than, analysed for each year to assess the companies’ compliance with the EU disclosure requirements and both parametric and non-parametric test, were conducted to determine if there were significant changes in the extent of disclosure in compliance with the EUFD over the years. Furthermore, using the companies EUFDCDI score as dependent variable and corporate characteristics as independent variables, the Ordinary Least Square regression was run for each year to find out if the companies’ level of compliance with the EU disclosure requirements were influenced by their corporate characteristics.The results of this study revealed that Turkish companies’ compliance with the required disclosure by the EUFD varied within the range of 30–85%, but their compliance increased significantly from one year to another throughout the selected period. The results further revealed that listing status is one of the important corporate characteristics of the Turkish companies affecting their compliance with the EU disclosure requirements.     

Skewness Preference,Risk Taking and Expected Utility Maximisation

Available empirical evidence suggests that skewness preference plays an important role in understanding asset pricing and gambling. This paper establishes a skewness-comparability condition on probability distributions that is necessary and sufficient for any decision-maker's preferences over the distributions to depend on their means, variances, and third moments only. Under the condition, an Expected Utility maximizer's preferences for a larger mean, a smaller variance, and a larger third moment are shown to parallel, respectively, his preferences for a first-degree stochastic dominant improvement, a mean-preserving contraction, and a downside risk decrease and are characterized in terms of the von Neumann-Morgenstern utility function in exactly the same way. By showing that all Bernoulli distributions are mutually skewness comparable, we further show that in the wide range of economic models where these distributions are used individuals’ decisions under risk can be understood as trade-offs between mean, variance, and skewness. Our results on skewness-inducing transformations of random variables can also be applied to analyze the effects of progressive tax reforms on the incentive to make risky investments.     

Towards a rational strategy for the human settlement of space

This paper revisits the core issues of space policy from the viewpoint of optimal decision theory. First it argues for a metric: maximizing the probability that humans and their technology in space someday reach what Rostow called the “economic takeoff” point where autonomous growth becomes possible, not bound by the rate of growth on earth. Next it discusses three concrete requirements to reach that point: benefits to earth which exceed costs to earth, large and diverse enough “exports” from space to earth, and advancements in technology and infrastructure. Energy from space (ES) is now one of the most promising export possibilities, based on what was learned in the last open US government effort on that topic, “JIETSSP,” led jointly by NSF and NASA. I review several options for ES, and propose a new one which, while slightly riskier, offers real hope of electricity at a price that could compete with coal and fission-plus-enrichment.     

We don't need no fancy hedges! Or do we?

Hedging decisions in the real world often contradict the literature. We reverse-engineer the optimal hedging problem by identifying patterns of price behavior that warrant using strategies more sophisticated than variance minimization (MV). Historical time series of spot and futures prices for the crack spread components (crude oil, gasoline, and heating oil) are used to generate different patterns of price dependency. A copula approach is used to model the joint dependence between spot and futures price shocks of the three commodities. We find that minimizing a downside risk criterion (what actual hedgers do) leads to consistently better outcomes than MV, as measured by Expected Utility. This is especially true in scenarios corresponding to strong upward or downward price movements. We provide a simple decision heuristic for hedgers by identifying price patterns whereby using sophisticated strategies for multi-commodity hedging is optimal in practice.     

Stochastic CVP analysis as a gateway to decision-making under uncertainty

Although a substantial research literature on cost–volume–profit (CVP) analysis under uncertainty has accumulated since the seminal contribution of Jaedicke and Robichek [Accounting Review, 39 (1964), 917], this literature has been almost entirely ignored by authors of managerial and cost accounting textbooks. This is unfortunate because owing to the extreme simplicity of the basic deterministic CVP model, students are better able to understand the elements added by generalizing the model to an uncertainty situation. A CVP model that incorporated uncertainty would therefore provide a good entry point into the important but complicated topic of decision-making under uncertainty. This paper sets forth, analyzes and applies a CVP under uncertainty model specifically geared toward classroom instruction. It is a simpler model than many of those developed in the research literature, but it does incorporate one advanced component: an “economic” demand function relating the expected sales level to price. Price is neither a constant nor a random variable in this model but rather the firm's basic decision variable. The simplicity of the model permits analytical solutions for five “special prices”: (1) the highest price which sets breakeven probability equal to a minimum acceptable level; (2) the price which maximizes expected profits; (3) the price which maximizes a Cobb–Douglas utility function based on expected profits and breakeven probability; (4) the price which maximizes breakeven probability; and (5) the lowest price which sets breakeven probability equal to a minimum acceptable level. An example of application is presented in which the model is applied to pricing continuing education programs offered by Center for Management and Professional Development at the authors’ university.     

Mortgage prepayment with an uncertain holding period

A discrete-time-option pricing model is developed to value a mortgage and its embedded prepayment option when the effective life of the mortgage is a random variable with a probability distribution of known parameters. The model can be applied when the borrower's ex ante expectation of his tenure follows any probability distribution bounded to the left at zero. The Gamma distribution is used to illustrate the model.The pricing model is further applied to determine the conditions under which financially motivated prepayment is optimal. The results show that the certainty model understates the Interest Rate Differential needed to justify prepayment (IRD) for short Expected Holding Period (EHP) borrowers and overstates the IRD for long EHP borrowers. When the EHP is relatively long, the certainty model provides relatively good estimates of IRD during the beginning years of the mortgage life. Under most other conditions, the estimates of the certainty holding period model are biased.     

Self-Insurance, Self-Protection and Market Insurance within the Dual Theory of Choice

As demonstrated by Ehrlich and Becker [1972], Expected Utility Theory predicts that market insurance and self-insurance are substitutes, whilst surprisingly, market insurance and self-protection could be complements. This article examines the robustness of this conclusion, as well as its extensions under the Dual Theory of Choice [Yaari, 1987]. In particular, the non-reliability of self-insurance activities, background risk and asymmetric information are considered.