Momentum strategies based on reward–risk stock selection criteria

In this paper, we analyze momentum strategies that are based on reward–risk stock selection criteria in contrast to ordinary momentum strategies based on a cumulative return criterion. Reward–risk stock selection criteria include the standard Sharpe ratio with variance as a risk measure, and alternative reward–risk ratios with the expected shortfall as a risk measure. We investigate momentum strategies using 517 stocks in the S&P 500 universe in the period 1996–2003. Although the cumulative return criterion provides the highest average monthly momentum profits of 1.3% compared to the monthly profit of 0.86% for the best alternative criterion, the alternative ratios provide better risk-adjusted returns measured on an independent risk-adjusted performance measure. We also provide evidence on unique distributional properties of extreme momentum portfolios analyzed within the framework of general non-normal stable Paretian distributions. Specifically, for every stock selection criterion, loser portfolios have the lowest tail index and tail index of winner portfolios is lower than that of middle deciles. The lower tail index is associated with a lower mean strategy. The lowest tail index is obtained for the cumulative return strategy. Given our data-set, these findings indicate that the cumulative return strategy obtains higher profits with the acceptance of higher tail risk, while strategies based on reward–risk criteria obtain better risk-adjusted performance with the acceptance of the lower tail risk.     

Limiting losses may be injurious to your wealth

Theory tells us that if return distributions are independent over time, an expected utility maximizing logarithmic-utility investor will almost surely accumulate the most long-run wealth. This paper examines the robustness of the result. Specifically, it examines the expected and unexpected long-run and short-run consequences of imposing Value at Risk and other loss constraints on power-utility investors with a numerical example and empirically in an asset-allocation setting covering the 1934–2008 period. In addition, it examines the expected and unexpected long-run consequences of imposing Conditional Value at Risk constraints on power-utility and prospect-theory (kinked linear-utility) investors.     

An empirical analysis of marginal conditional stochastic dominance

Stochastic dominance is a more general approach to expected utility maximization than the widely accepted mean–variance analysis. However, when applied to portfolios of assets, stochastic dominance rules become too complicated for meaningful empirical analysis, and, thus, its practical relevance has been difficult to establish. This paper develops a framework based on the concept of Marginal Conditional Stochastic Dominance (MCSD), introduced by Shalit and Yitzhaki (1994), to test for the first time the relationship between second order stochastic dominance (SSD) and stock returns. We find evidence that MCSD is a significant determinant of stock returns. Our results are robust with respect to the most popular pricing models.     

Optimal Portfolio Allocation under Higher Moments

We evaluate how departure from normality may affect the allocation of assets. A Taylor series expansion of the expected utility allows to focus on certain moments and to compute the optimal portfolio allocation numerically. A decisive advantage of this approach is that it remains operational even for a large number of assets. While the mean‐variance criterion provides a good approximation of the expected utility maximisation under moderate non‐normality, it may be ineffective under large departure from normality. In such cases, the three‐moment or four‐moment optimisation strategies may provide a good approximation of the expected utility.     

News and the cross-section of expected corporate bond returns

We study the cross-section of expected corporate bond returns using an inter-temporal CAPM (ICAPM) with three-factors: innovations in future excess bond returns, future real interest rates and future expected inflation. Our test assets are a broad range of corporate bond market index portfolios. We find that two factors – innovations about future inflation and innovations about future real interest rates – explain the cross-section of expected corporate bond returns in our sample. Our model provides an alternative to the ad hoc risk factor models used, for example, in evaluating the performance of bond mutual funds.     

Buffer stocks and precautionary savings with loss aversion

This paper reexamines buffer stocks and precautionary savings in the presence of loss aversion. We assume that agents are disappointment averse, as in Gul [Econometrica, 59 (1991) 667–686]. We show that the concavity of the marginal utility continues to determine precautionary saving, but its effect is of a second order magnitude (proportional to the square of the coefficient of variation) compared to the first order effect (proportional to the coefficient of variation) induced by loss aversion. We show that a stabilization fund that is rather small when agents are maximizing the conventional expected utility, turns out to be rather large with loss aversion.     

On the Theory of Rational Insurance Purchasing: A Note

The authors consider the optimal amount of insurance purchased by an individual who behaves according to the Hurwicz criterion of choice under uncertainty. Their results are compared with earlier results obtained in alternative frameworks (expected utility maximization and Savage's regret criterion). It is shown that a positive amount deductible is often suboptimal.     

Cross-sectional forecasts of the equity premium

If investors are myopic mean-variance optimizers, a stock's expected return is linearly related to its beta in the cross-section. The slope of the relation is the cross-sectional price of risk, which should equal the expected equity premium. We use this simple observation to forecast the equity-premium time series with the cross-sectional price of risk. We also introduce novel statistical methods for testing stock-return predictability based on endogenous variables whose shocks are potentially correlated with return shocks. Our empirical tests show that the cross-sectional price of risk (1) is strongly correlated with the market's yield measures and (2) predicts equity-premium realizations, especially in the first half of our 1927–2002 sample.     

MORE EVIDENCE ON EXPECTED VALUE-VARIANCE ANALYSIS VERSUS DIRECT UTILITY MAXIMIZATION

The theoretical difficulties of the expected value-variance (E-V) criterion are well known. A number of recent research efforts test the criterion's effectiveness in a publicly traded securities environment. In contrast, this research explores the performance of the E-V criterion using firm-specific, nontradeable investments such as those made by small firms. The empirical example in the study is a small family proprietorship with limited investment opportunities in agricultural production activities. Results indicate the E-V criterion performs well in selecting nontradeable investments that maximize expected utility. These results are consistent with results of earlier research dealing with tradeable securities.     

Sufficient conditions for expected utility to imply drawdown-based performance rankings

The least restrictive sufficient condition for expected utility to imply Sharpe ratio rankings is the location and scale (LS) property (see [Sinn, 1983] and [Meyer, 1987]). The normal, the extreme value, and many other distributions commonly used in finance satisfy this property. We argue that the LS property is also sufficient for expected utility to imply drawdown-based performance measure rankings, because for investment funds satisfying the LS condition, the Sharpe ratio and drawdown-based performance measures result in identical rankings. Hence, the same conditions that provide an expected utility foundation for the Sharpe ratio also provide a foundation for drawdown-based performance measures. We conclude that from a decision-theoretic perspective, drawdown-based performance measures are as good as the Sharpe ratio.     

Relation between time-series and cross-sectional effects of idiosyncratic variance on stock returns

Consistent with the post-1962 US evidence by Ang et al. [Ang, A., Hodrick, R., Xing Y., Zhang, X., 2006. The cross-section of volatility and expected returns. Journal of Finance 51, 259–299], we find that stocks with high idiosyncratic variance (IV) have low CAPM-adjusted expected returns in both pre-1962 US and modern G7 data. We also test in three ways the conjecture that IV is a proxy of systematic risk. First, the return difference between low and high IV stocks – that we dub as IVF – is a priced factor in the cross-section of stock returns. Second, loadings on lagged market variance and lagged average IV account for a significant portion of variation in average returns on portfolios sorted by IV. Third, the variance of IVF correlates closely with average IV, and the two variables have similar explanatory power for the time-series and cross-sectional stock returns.     

Triangulation of audit evidence in fraud risk assessments

Drawing on the triangulation framework of audit evidence ( and ), we experimentally test for the conditions, if any, under which financial-statement auditors alter their fraud-risk assessments based on whether external evidence provides positive or negative news about underlying business performance. We focus on the condition in which two kinds of management-controlled audit evidence – evidence from the financial statements and evidence from internal data depicting performance of a key business process – is contradicted by external evidence suggesting that a key business objective has not been attained. According to the triangulation framework, such contradictory external evidence should heighten auditors’ skepticism about the veracity of management-controlled evidence and increase their assessment of fraud risk.     

Utilitarianism and fairness in portfolio positioning

The paper introduces the theory of optimal positioning of financial products. It is illustrated in the context of long-term intertemporal portfolio allocation and can be applied for example to asset allocation funds. We embed this problem in location theory: the portfolio is optimized within the investors’risk aversion dimension. For the CRRA utility functions, we compute explicitly the distance functions. For the first (utilitarian criterion), the average utility of the investors is maximized. For the second one (fairness criterion), the choice of portfolio is optimized so that the average monetary loss due to the lack of customization is minimized. Given the distribution of investors’ risk aversion, we provide a solution method and an algorithm to optimally position standardized portfolio along one of these two criteria.     

Reinsurance and corporate taxation in the United Kingdom life insurance industry

There are two main tax-related arguments regarding the use of reinsurance – the income volatility reduction and the income level enhancement arguments. The income volatility reduction argument contends that firms facing convex tax schedules have incentives to hedge in order to reduce the volatility of their annual taxable income and thereby lower expected tax liabilities [Smith, C.W., Stulz, R.M., 1985. Optimal hedging policies. Journal of Financial and Quantitative Analysis 19, 127–140]. The income level enhancement argument, advanced by Adiel [Adiel, R., 1996. Reinsurance and the management of regulatory ratios and taxes in the property–casualty insurance industry. Journal of Accounting and Economics 22, 207–240], is more specific to hedging via reinsurance. This perspective holds that reinsurance enhances current reported earnings via the receipt of reinsurance commissions and so increases tax liabilities. Consequently, insurance firms with high marginal tax rates should use less reinsurance than those with low marginal tax rates if tax matters. Prior studies using data on financial derivatives have produced mixed results on the validity of the first argument, while Adiel (1996) finds the second argument insignificant in his study of the use of reinsurance by a sample of United States (US) property–liability insurance firms. This study tests the two tax-related arguments using 1992–2001 data for a sample of United Kingdom (UK) life insurance firms. We find that UK life insurers with low before-planning marginal tax rates tend to use more reinsurance; in contrast, tax convexity is found to have no significant impact on the purchase of reinsurance and so the volatility-reduction argument is not supported.     

Price discovery in currency markets

This paper examines the price discovery process in currency markets, basing its analysis on the pivotal distinction between the customer (end-user) market and the interdealer market. It first provides evidence that this price discovery process cannot be based on adverse selection between dealers and their customers, as postulated in standard models, because the spreads dealers quote to their customers are not positively related to a trade’s likely information content. The paper then highlights three factors familiar in the literature – fixed operating costs, market power, and strategic dealing – that may explain the cross-sectional variation in customers’ spreads. The paper finishes by proposing a price discovery process relevant to liquid two-tier markets and providing preliminary evidence that this process applies to currencies.     

Asset pricing with unforeseen contingencies

We investigate an economy of heterogeneous agents that cannot specify all exogenous welfare-relevant events and consequently view the impact of unforeseen contingencies as utility shocks. In this setting we characterize an appropriate market equilibrium concept when securities can trade only on demand- and price-contingent events. We establish the existence of an equilibrium for a class of parametric models in which aggregating taste shocks across agents can lead to nonconsumption pricing factors. To fit the stylized facts, (i) non consumption factors must dominate the pricing kernel and contribute to the variation of the wealth-consumption ratio, (ii) markets must be incomplete and the set of claims that are traded endogenously determined, (iii) agents’ preferences with respect to unforeseen contingencies must be non-expected utility, and, (iv) although non-consumption pricing factors can be conditionally uncorrelated with aggregate consumption shocks, they must be correlated with shocks to expected consumption growth.     

Horizon dependence of utility optimizers in incomplete models

This paper studies the utility maximization problem with changing time horizons in the incomplete Brownian setting. We first show that the primal value function and the optimal terminal wealth are continuous with respect to the time horizon T. Secondly, we exemplify that the expected utility stemming from applying the T-horizon optimizer on a shorter time horizon S<T may fail to converge to the T-horizon value as S↑T. Finally, we provide necessary and sufficient conditions preventing the existence of this phenomenon.     

Utility Functions

Abstract

This article is a self-contained survey of utility functions and some of their applications. Throughout the paper the theory is illustrated by three examples: exponential utility functions, power utility functions of the first kind (such as quadratic utility functions), and power utility functions of the second kind (such as the logarithmic utility function). The postulate of equivalent expected utility can be used to replace a random gain by a fixed amount and to determine a fair premium for claims to be insured, even if the insurer’s wealth without the new contract is a random variable itself. Then n companies (or economic agents) with random wealth are considered. They are interested in exchanging wealth to improve their expected utility. The family of Pareto optimal risk exchanges is characterized by the theorem of Borch. Two specific solutions are proposed. The first, believed to be new, is based on the synergy potential; this is the largest amount that can be withdrawn from the system without hurting any company in terms of expected utility. The second is the economic equilibrium originally proposed by Borch. As by-products, the option-pricing formula of Black-Scholes can be derived and the Esscher method of option pricing can be explained.     

A comparison of the estimates of expected utility and non-expected-utility preference functionals

This paper extends the literature on the estimation of expected utility and non-expected-utility preference functionals (and the consequent exploration of the superiority of non-expected-utility over expected utility preference functionals) to a comparison of two different ways (pairwise choice and complete ranking) of experimentally obtaining data on such preferences. What is revealed is that the magnitude of the subject error is clearly conditional on the elicitation method used and, rather alarmingly, that the preference functional apparently employed by the subject may also be conditional on the elicitation method.     

Prospect and Markowitz stochastic dominance

Levy and Wiener (J Risk Uncertain 16(2), 147–163, 1998), Levy and Levy (Manage Sci 48(10), 1334–1349, 2002; Rev Fin Stud 17(4), 1015–1041, 2004) develop the prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend their work on prospect stochastic dominance theory (PSD) and Markowitz stochastic dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Furthermore, we formulate the following PSD and MSD properties: hierarchy exists in both PSD and MSD relationships; arbitrage opportunities exist in the first orders of both PSD and MSD; and for any two prospects under certain conditions, their third order MSD preference will be ‘the opposite of’ or ‘the same as’ their counterpart third order PSD preference. By extending the work of Levy and Wiener and Levy and Levy, we provide investors with more tools to identify the first and third order PSD and MSD prospects and thus they could make wiser choices on their investment decision.