Risk aversion,prudence, and compensation

In a standard principal-agent setting, we use a comparative approach to study the incentives provided by different types of compensation contracts, and their valuation by managers with utility function u who are risk averse (u″<0) and prudent (u″′>0). We show that concave contracts tend to provide more incentives to risk averse managers, while convex contracts tend to be more valued by prudent managers. This is because concave contracts concentrate incentives where the marginal utility of risk averse managers is highest, while convex contracts protect against downside risk. Thus, managerial prudence can contribute to explain the prevalence of stock-options in executive compensation. However, convex contracts are not optimal when the principal is sufficiently prudent relative to the manager.     

(Non-)robustness of maximum likelihood estimators for operational risk severity distributions

The quality of operational risk data sets suffers from missing or contaminated data points. This may lead to implausible characteristics of the estimates. Outliers, especially, can make a modeler's task difficult and can result in arbitrarily large capital charges. Robust statistics provides ways to deal with these problems as well as measures for the reliability of estimators. We show that using maximum likelihood estimation can be misleading and unreliable assuming typical operational risk severity distributions. The robustness of the estimators for the Generalized Pareto distribution, and the Weibull and Lognormal distributions is measured considering both global and local reliability, which are represented by the breakdown point and the influence function of the estimate.     

An Extended Family of Financial-Risk Measures

Recalling the class of risk measures introduced by Stone [1973], the authors survey measures from different academic disciplines—including psychology, operations research, management science, economics, and finance—that have been introduced since 1973. We introduce a general class of risk measures that extends Stone's class to include these new measures. Finally, we give four axioms that describe necessary attributes of a good financial risk measure and show which of the measures surveyed satisfy these. We demonstrate that all measures that satisfy our axioms, as well as those that do not but are commonly used in finance, belong to our new generalized class.     

Reducing reporting risk: Designating foreign currency forward contracts as cash flow hedges

We present an example that compares the effects on earnings of designating a foreign currency forward contract as either a cash-flow or fair-value hedge of a foreign currency denominated receivable. Entities engaging in exchange transactions not denominated in their functional currency frequently enter into foreign currency forward contracts in order to mitigate their foreign exchange rate risk exposure. The aggregate effect on earnings of the transaction gain or loss on the foreign currency receivable and the gain or loss on the forward contract is known on the date the forward contract is initiated. The effect on each period’s earnings during the term of a forward contract designated as a cash-flow hedge is also known on the date the contract is initiated; whereas the effect on each periods’ earnings from a fair-value hedge cannot be determined until the respective balance sheet dates. Therefore, designating forward contracts as cash-flow hedges may suppress volatility in reported earnings compared to designating forward contracts as fair-value hedges. In addition, the reporting risk (the amount of uncertainty surrounding the pending measure of an item to be reported in the financial statements) is lower when a forward contract is designated as a cash-flow hedge relative to designating it as a fair-value hedge. This suggests foreign currency forward contracts designated as cash-flow hedges are more consistent with the purpose of hedge accounting: to mitigate the effects on earnings of applying different measurement criteria for the hedge and the hedged item.     

Applying Portfolio Change and Conditional Performance Measures: The Case of Industry Rotation via the Dynamic Investment Model

This paper applies portfolio change and conditional performance measures to assess the performance of the dynamic investment model in various industry-rotation settings spanning the 1934–1995 period. The dynamic investment model employs the empirical probability assessment approach in raw form. In addition, it incorporates three adjustments for estimation error: James–Stein, Bayes–Stein, and CAPM-based corrections. The tests are unanimous in their conclusion that the excess returns attained by the (unadjusted) historic, the Bayes–Stein, and the James–Stein estimators are (sometimes highly) statistically significant over the 1966–1995 and 1966–1981 sub-periods. This lends support to the idea that the joint empirical probability assessment approach based on the recent past, with and without Stein-based corrections for estimation error, contains information that can be profitably exploited. The relationship of these findings to the extant literature on momentum and contrarian strategies is addressed.     

Derivatives and systemic risk: Netting, collateral, and closeout

In the U.S., as in most countries with well-developed securities markets, derivative securities enjoy special protections under insolvency resolution laws. Most creditors are “stayed” from enforcing their rights while a firm is in bankruptcy. However, many derivatives contracts are exempt from these stays. Furthermore, derivatives enjoy netting and closeout, or termination, privileges which are not always available to most other creditors. The primary argument used to motivate passage of legislation granting these extraordinary protections is that derivatives markets are a major source of systemic risk in financial markets and that netting and closeout reduce this risk. To date, these assertions have not been subjected to rigorous economic scrutiny. This paper critically re-examines this hypothesis. These relationships are more complex than often perceived. We conclude that it is not clear whether netting, collateral, and/or closeout lead to reduced systemic risk, once the impact of these protections on the size and structure of the derivatives market has been taken into account.     

Interval Estimation of Actuarial Risk Measures

Abstract

This article investigates performance of interval estimators of various actuarial risk measures. We consider the following risk measures: proportional hazards transform (PHT), Wang transform (WT), value-at-risk (VaR), and conditional tail expectation (CTE). Confidence intervals for these measures are constructed by applying nonparametric approaches (empirical and bootstrap), the strict parametric approach (based on the maximum likelihood estimators), and robust parametric procedures (based on trimmed means).

Using Monte Carlo simulations, we compare the average lengths and proportions of coverage (of the true measure) of the intervals under two data-generating scenarios: “clean” data and “contaminated” data. In the “clean” case, data sets are generated by the following (similar shape) parametric families: exponential, Pareto, and lognormal. Parameters of these distributions are selected so that all three families are equally risky with respect to a fixed risk measure. In the “contaminated” case, the “clean” data sets from these distributions are mixed with a small fraction of unusual observations (outliers). It is found that approximate knowledge of the underlying distribution combined with a sufficiently robust estimator (designed for that distribution) yields intervals with satisfactory performance under both scenarios.     

On risk management problems related to a coherence property

Value at Risk has lost the battle against Expected Shortfall on theoretical grounds, the latter satisfying all coherence properties while the former may, on carefully constructed cases, lack the sub-additivity property that is in a sense, the most important property a risk measure ought to satisfy. While the superiority of Expected Shortfall is evident as a theoretical tool, little has been researched on the properties of estimators proposed in the literature. Since those estimators are the real tools for calculating bank capital reserves in practice, the natural question that one may ask is whether a given estimator of Expected Shortfall also satisfies the coherence properties. In this paper, we show that it is possible to have estimators of Expected Shortfall that do not satisfy the sub-additivity condition. This finding should motivate risk managers and quantitative asset managers to investigate further the properties of the estimators of the risk measures they are currently utilizing.     

Estimating Beta

This paper presents evidence that Ordinary Least Squares estimators of beta coefficients of major firms and portfolios are highly sensitive to observations of extremes in market index returns. This sensitivity is rooted in the inconsistency of the quadratic loss function in financial theory. By introducing considerations of risk aversion into the estimation procedure using alternative estimators derived from Gini measures of variability one can overcome this lack of robustness and improve the reliability of the results.     

Computing the market price of volatility risk in the energy commodity markets

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black–Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177–181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.     

Optimal capital and risk allocations for law- and cash-invariant convex functions

In this paper we provide a complete solution to the existence and characterization problem of optimal capital and risk allocations for not necessarily monotone, law-invariant convex risk measures on the model space L ^p for any p∈[1,∞]. Our main result says that the capital and risk allocation problem always admits a solution via contracts whose payoffs are defined as increasing Lipschitz-continuous functions of the aggregate risk. Filipović is supported by WWTF (Vienna Science and Technology Fund). Svindland gratefully acknowledges financial support from Munich Re Grant for doctoral students and hospitality of the Research Unit of Financial and Actuarial Mathematics, Vienna University of Technology. We thank Beatrice Acciaio and Walter Schachermayer for fruitful discussions and an anonymous referee for helpful remarks.     

Risk,partner selection and contractual control in interfirm relationships

This study examines firms’ use of partner selection and formal contracts as key approaches to manage transaction risk in interfirm relationships. We specifically examine the impact of transaction characteristics that generate transaction risk on (1) the importance placed on different selection criteria in the choice of collaboration partner, and (2) the complexity of contracts used to manage the collaboration. Survey data support that when confronted with greater risk from the transaction context, firms place more emphasis on trust-based and reputation-based selection criteria for partner choice and develop more complex (i.e., more inclusive and specific) contracts to manage the collaboration. Furthermore, our results show that partner selection mediates the effects of transaction characteristics on contract complexity, consistent with the argument that the information acquired during the partner selection process in response to risk facilitates the design of contracts to manage risk.     

The actual evaluation of school PFI bids for value for money in the UK public sector

Much of the literature on value for money (VFM) evaluation of private finance initiative (PFI) contracts has concentrated on the financial methodology of constructing the public sector comparator (PSC) and its limitations. In contrast, this paper focuses on examining how ‘PFI bids’ are actually evaluated for VFM in the case of three secondary school PFI contracts. It is a unique study which presents the Northern Ireland school PFI decision-making processes, within the broader UK context. It is based on the full business cases of three PFI schools and interviews with key actors involved in the PFI processes. This study shows that the methodology used to evaluate and benchmark the design, facilities management, financial and contractual aspects of PFI bids for VFM is subjective and problematic-changes in the assumptions used may easily shift the balance in favour of conventional procurement and/or competing private sector service providers. It further highlights the importance of risk transfer; how non-financial factors are taken into consideration; and the public sector's reliance on consulting firms and ‘accounting measures’ in the PFI decision-making processes.     

A Likelihood Ratio Test of Price Volatilities: Comparing Stock Index Spot and Futures

This paper uses three methods to estimate the price volatility of two stock market indexes and their corresponding futures contracts. The classic variance measure of volatility is supplemented with two newer measures, derived from the Garman-Klass and Ball-Torous estimators. A likelihood ratio test is used to compare the classic variance measure of price volatilities of two stock market indexes and their corresponding futures contracts during the bull market of the 1980s. The stock market volatilities of the Standard & Poor's 500 (S&P 500) and New York Stock Exchange (NYSE) indexes were found to be significantly lower than their respective futures price volatilities. Since information may flow faster in the futures markets than in the corresponding stock market, our results support Ross's information-volatility hypothesis. It was also noted that the NYSE spot volatility was lower than the S&P 500 spot volatility. If the rate of information flow and firm size are positively related, then the lower NYSE spot volatility is explained by the size effect. The futures price volatilities for the two indexes were insignificantly different from each other. With stock index spot-futures price correlations approaching unity, one implication of our results for index futures activity is that smaller positions in futures contracts may suffice to achieve hedging or arbitrage goals.     

Earnouts: The real value of disagreement in mergers and acquisitions

Earnout agreements link part of the payment for an acquired company to its future performance. Despite their option-like features, they cannot be valued using vanilla option-pricing methods. Two peculiar sources of risk affect these contracts: Bidder default before the earnout expiration (default risk) and potential litigation associated with earnouts (litigation risk). We developed an option-pricing model that encompasses these sources of risk, showing that counterparty and litigation risk can have a remarkable impact on earnout values. Our model's relevance is further enhanced by recent accounting standards that require contingent payments to be valued at fair value.     

Nominal contracting in a world of uncertainty

This paper evaluates corporate sensitivity to relative price risk and inflation risk and suggests how the existence of various nominal contracts, particularly debt and forward contracts, may modify firm behavior under uncertainty. By differentiating between the two types of price risk, this paper demonstrates the distinct risk reduction functions served by forward contracts and debt. Debt primarily protects against inflation risk whereas forward contracts can be used to protect against relative price risk. Complications arise, however, because forward contracts, which are denominated in nominal terms, also have an impact on the firm's degree of inflation risk.     

Zur Modellierung von Rückversicherungsverträgen in der dynamischen Finanzanalyse

In this paper we study the influence of Gaussian dependencies on the payoff of reinsurance contracts and the resulting effects on a non-life insurer's risk and return profile. To achieve this, we integrate different Gaussian dependencies and reinsurance contracts in a dynamic financial analysis (DFA) framework and conduct numerical tests within a simulation study. Depending on the reinsurance contract and the dependency employed, we find substantial differences in risk assessment for the ruin probability and for the expected policyholder deficit. The results have important implications for regulators and rating agencies that use these risk measures as a foundation for capital standards and ratings. Our results extend the findings of a recent working paper by Eling and Toplek (2008) with a detailed analysis of Gaussian dependencies under different reinsurance contracts.     

The predictive performance of the currency futures basis for spot returns

This paper investigates the predictive performance of the futures basis in directly forecasting currency spot returns and compares it with that of the one-month forward basis. We consider the settle prices of both front-month and nearby-month continuous futures contracts and find that the futures basis exhibits statistically and economically significant in-sample and out-of-sample forecasting power, which clearly exceeds that of the well-known forward basis. The empirical results show that spot returns correspond negatively to both the front-month futures basis and nearby-month futures basis. Furthermore, the futures basis reveals substantial economic value for investors in terms of sizable and tangible portfolio gains, which are consistent with statistical measures. The difference in the forecasting ability of the futures basis and forward basis can be explained by the level of exposure to the time-varying risk premium. Finally, we find that impacts of the futures basis on spot returns vary with time and experienced substantial structural changes during the Global Financial Crisis.     

Risk assessment for public–private partnership projects: using a fuzzy analytic hierarchical process method and expert opinion in China

Public–private partnerships (PPP) have been widely used in China to procure public facilities and services. Complicated problems in PPP projects in China arise because of a variety of risk factors. A proper risk assessment model is needed to identify risks and provide risk response strategies for future Chinese PPP projects. The fuzzy analytic hierarchy process (F-AHP) method provides the ability to solve complex risk assessment of PPP projects. Current risk assessment models are limited to PPP projects in specific countries and do not consider unique risks in China, especially political, economic, social, and legal risks. This paper designed a risk evaluation index system for PPP projects based on the Delphi expert investigation method, and then established an optimized risk evaluation model for PPP projects in China using the F-AHP method. The risks identified are confirmed by interviewing experts from Chinese local government departments, private enterprise, third-party intermediary consulting and regulatory agencies, and academic organizations. The results show that the risks that ranked among the top ten are closely related to China’s political and economic policies and relationships among stakeholders. It can be concluded that government authorities play a critical role in providing a favorable political, social, and economic environment and an effective institutional framework for PPP projects. Furthermore, it is also important to deal with relationships among stakeholders based on the public–private ‘win–win’ principle. This study provides risk response strategies, addressing key issues from eight aspects: an impeccable legal and regulatory framework; a central coordinating and regulating PPP authority; supportive governmental authorities; institutional capacity-building; favorable economic conditions and viability; community, partner, and moral accountability; clear division of responsibilities through contracts; and effective advisory management. These effective measures may be useful in reducing the adverse effects of risk for PPP projects in China.     

Guaranteed renewable life insurance under demand uncertainty

Guaranteed renewability (GR) is a prominent feature in many health and life insurance markets. We develop a model that includes unpredictable (and unobservable) fluctuations in demand for life insurance as well as changes in risk type (observable) over individuals' lifetimes. The presence of demand type heterogeneity leads to the possibility that optimal GR contracts may have a renewal price that is either above or below the actuarially fair price of the lowest risk type in the population. Individuals whose type turns out to be high risk but low demand renew more of their GR insurance than is efficient due to the attractive renewal price. This results in imperfect insurance against reclassification risk. Although a first‐best efficient contract is not possible in the presence of demand type heterogeneity, the presence of GR contracts nonetheless improves welfare relative to an environment with only spot markets.