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.     

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.     

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.     

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.     

A Continuous Time Model to Price Commodity-Based Swing Options

On the commodity market there exist contracts which give the holder multiple opportunities to adjust delivery of the underlying commodity. These contracts are often named “Swing” or “take-or-pay” options. They are especially common on the electricity market.In this paper the price of a Swing option on commodities is investigated under the additional constraint of a recovery time between two different exercise times. We give an explicit characterization of the price function as the value function of a continuous stochastic impulse control problem and prove existence of an optimal control. We investigate the connection between the price function and the solution of a system of quasi-variational inequalities. Finally, we present a numerical algorithm for solving the quasi-variational inequalities, and give some numerical examples.JEL Classification: C61, C62, C63     

Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance

This paper presents a theoretically sound portfolio performance measure that takes into account higher moments of distribution. This measure is motivated by a study of the investor’s preferences to higher moments of distribution within Expected Utility Theory and an approximation analysis of the optimal capital allocation problem. We show that this performance measure justifies the notion of the Generalized Sharpe Ratio (GSR) introduced by Hodges (1998). We present two methods of practical estimation of the GSR: nonparametric and parametric. For the implementation of the parametric method we derive a closed-form solution for the GSR where the higher moments are calibrated to the normal inverse Gaussian distribution. We illustrate how the GSR can mitigate the shortcomings of the Sharpe ratio in resolution of Sharpe ratio paradoxes and reveal the real performance of portfolios with manipulated Sharpe ratios. We also demonstrate the use of this measure in the performance evaluation of hedge funds.     

Setting a fox to keep the geese — Does the comply-or-explain principle work?

The German Corporate Governance Code works according to the comply-or-explain principle. One of its recommendations was to publish the remuneration of the members of the executive board on an individual basis. We examine the characteristics of the firms that complied with the code requirement. Our results indicate that firms that paid higher average remunerations to their management board members were less likely to comply, whereas firms with higher Tobin's Q were more likely to comply. We also document a non-monotonic relation between ownership concentration and the probability of compliance that is consistent with standard corporate governance arguments.Due to the fact that the number of firms complying with the disclosure requirement was low, a new law was passed that mandates disclosure unless the shareholders' meeting (with a 75% majority) decides otherwise. We find that this “loophole” in the new legislation is exploited by smaller firms, firms with comparatively high levels of executive remuneration, and firms with concentrated ownership. We discuss the implications of our results for the effectiveness of the comply-or-explain regulation.     

The use of on-line summative assessment in an undergraduate financial accounting course

According to the Quality Assurance Agency [QAA (2006). Section 6: Assessment of students, Code of practice for the assurance of academic quality and standards in higher education. <http://www.qaa.ac.uk/>. Accessed 14.03.2007] “Assessment describes any processes that appraise an individual’s knowledge, understanding, abilities or skills” and is inextricably linked to a course or programme’s intended learning outcomes. Assessment also has a fundamental effect on students’ learning where it serves a variety of purposes including evaluation, feedback and motivation. Assessment also provides a performance indicator for both students and staff. Computer-aided assessment (CAA) offers an option for “sustainable assessment” and provides opportunities for creating innovative assessment practices that help engage students and increase their motivation for learning. This paper reports the findings of a qualitative study where a series of on-line summative assessments were introduced into a first-year financial accounting course. Feedback from students obtained from an evaluative survey and focus group interviews indicates that assessment played a significant role in the teaching/learning process. That is, students perceived a beneficial impact on learning, motivation, and engagement.     

Is There a Connection Between the Tax Administration and the Political Power?

This paper offers empirical evidence from Spain of a connection between the tax administration and the political power at the regional level. Firstly, the system of unconditional grants from the central layer of government provokes an “income effect” which disincentivises the efforts of the regional tax administration. Secondly, these efforts tend to be lower in those electoral districts where vote turnout is high, the margin to lose a parliamentary seat is narrow and their parliamentary representation is high, although the importance of these disincentives decreases according to the parliamentary strength of the incumbent. Finally, leftist governments, through the tax administration, tend to exert a greater effort in ensuring tax compliance.     

Liquidity protection versus moral hazard: the role of the IMF

A game between the IMF, a country and atomistic private investors is motivated by recent crises including that in Argentina. The one stage game has no Nash equilibrium in pure strategies. Considering an equilibrium in mixed strategies, conditions are derived on whether the IMF should exist. A “cooperative first best” may be supported in a repeated game by a “minimum punishment strategy” but breaks down as the probability of insolvency rises. Countries are likely to deviate in bad times placing the IMF in an “impossible position”. The international financial architecture (IFA) remains incomplete.     

Probability weighting and default risk: a possible explanation for distressed stock puzzles

This paper suggests incorporating investor probability weighting and the default risk of individual firms into a consumption-based asset pricing model. The extended model provides a unified explanation for several anomalous patterns observed in financial markets. The analysis addresses not only widely recognized asset pricing puzzles, such as the equity premium puzzle, but also less-studied anomalies on financially distressed stocks. The simulation, under which the model is calibrated according to U.S. historical data, shows that a combination of mild overweighting of probability on tail events and nonlinearity of equity values caused by default risk has the potential to resolve these patterns.     

Optimal derivatives: portfolios,payoffs and preferences

This article presents an extension to the growth optimal derivative that can accommodate risk preferences differing from those of logarithmic utility. Analysis of the optimal derivative provides interesting insights into the behaviour of power investors. We show that power investors under the real-world probability can be viewed as logarithmic investors under the myopic probability of Guasoni and Robertson [(2012). “Portfolios and Risk Premia for the Long Run.” Annals of Applied Probability, 22 (1), 239–284]. Furthermore, this intuition provides criteria for establishing whether fractional Kelly betting is optimal for power investors. Finally, the Black–Scholes model is used to demonstrate how the optimal derivative can be implemented and we show that our approach is consistent with classical techniques.     

Information Uncertainty and Expected Returns

This study examines the role of information uncertainty (IU) in predicting cross-sectional stock returns. We define IU in terms of “value ambiguity,” or the precision with which firm value can be estimated by knowledgeable investors at reasonable cost. Using several different proxies for IU, we show that (1) on average, high-IU firms earn lower future returns (the “mean” effect), and (2) price and earnings momentum effects are much stronger among high-IU firms (the “interaction” effect). These findings are consistent with analytical models in which high IU exacerbates investor overconfidence and limits rational arbitrage.This revised version was published online in August 2005 with a corrected cover date.     

The unethical practices of accountants and auditors and the compromising stance of professional bodies in the corporate world: Evidence from corporate Nigeria

Investors in Nigeria have lost several billions of dollars through the collusion of accountants and external auditors with companies’ management and directors to falsify and deliberately overstate companies’ accounts. As a consequence of unethical practices by accountants and auditors, which have resulted in the distress or occasionally the closure of companies, some indigenous Nigerian Managing Directors of multinational corporations such as Lever Brothers Nigeria Plc and Cadbury Nigeria Plc have been sacked and replaced with expatriates. Some companies placed under receivership have also lost billions of dollars due to professional misconduct by their official receivers. Contrary to the claim of ‘protecting the public interest,’ accountants and auditors may be partly responsible for cases of distress and closure of companies and banking institutions in Nigeria. However, the various Statutory Provisions and Acts relating to companies and professional bodies all place the responsibility on the accountants and auditors to detect and report to the regulators cases of suspected fraud and accounting malpractice. Through detailed consideration of cases of fraud, falsifications and deliberate overstatement of companies’ accounts, this paper examines the claim that the professional bodies are capable of protecting the public interest. It utilizes archival documents to provide evidence that suggests professional misconduct by accountants, particularly the members of the Institute of Chartered Accountants of Nigeria (ICAN). The paper provides further evidence that ICAN has been reluctant to either investigate or sanction its erring members. The paper posits that the reluctance or inability of the ICAN's “Investigation and Disciplinary Machinery” to either investigate or discipline the erring accountants and auditors suggests that whether by design or default, the ICAN's “Investigation and Disciplinary Machinery” operates to shield the activities of its erring members in accountancy firms from critical scrutiny.