On dynamic spectral risk measures,a limit theorem and optimal portfolio allocation

In this paper, we propose the notion of continuous-time dynamic spectral risk measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk measures in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may be considered to be (strongly) time-consistent continuous-time extensions of iterated spectral risk measures, which are obtained by iterating a given spectral risk measure (such as expected shortfall) along a given time-grid. Specifically, we demonstrate that any DSR arises in the limit of a sequence of such iterated spectral risk measures driven by lattice random walks, under suitable scaling and vanishing temporal and spatial mesh sizes. To illustrate its use in financial optimisation problems, we analyse a dynamic portfolio optimisation problem under a DSR.     

Risk-aversion concepts in expected- and non-expected-utility models

The non-expected-utility theories of decision under risk have favored the appearance of new notions of increasing risk like monotone increasing risk (based on the notion of comonotonic random variables) or new notions of risk aversion like aversion to monotone increasing risk, in better agreement with these new theories. After a survey of all the possible notions of increasing risk and of risk aversion and their intrinsic definitions, we show that contrary to expected-utility theory where all the notions of risk aversion have the same characterization (u concave), in the framework of rank-dependent expected utility (one of the most well known of the non-expectedutility models), the characterizations of all these notions of risk aversion are different. Moreover, we show that, even in the expected-utility framework, the new notion of monotone increasing risk can give better answers to some problems of comparative statics such as in portfolio choice or in partial insurance. This new notion also can suggest more intuitive approaches to inequalities measurement.     

Risk measures with the CxLS property

In the present contribution, we characterise law determined convex risk measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (Math. Finance 16:419–441, 2006), we show that these risk measures can be identified with a class of generalised shortfall risk measures. As a direct consequence, we are able to extend the results in Ziegel (Math. Finance, 2014, http://onlinelibrary.wiley.com/doi/10.1111/mafi.12080/abstract) and Bellini and Bignozzi (Quant. Finance 15:725–733, 2014) on convex elicitable risk measures and confirm that expectiles are the only elicitable coherent risk measures. Further, we provide a simple characterisation of robustness for convex risk measures in terms of a weak notion of mixture continuity.     

Robustness and sensitivity analysis of risk measurement procedures

Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a ‘risk measure’ that summarizes the risk of the portfolio. We define the notion of ‘risk measurement procedure’, which includes both of these steps, and introduce a rigorous framework for studying the robustness of risk measurement procedures and their sensitivity to changes in the data set. Our results point to a conflict between the subadditivity and robustness of risk measurement procedures and show that the same risk measure may exhibit quite different sensitivities depending on the estimation procedure used. Our results illustrate, in particular, that using recently proposed risk measures such as CVaR/expected shortfall leads to a less robust risk measurement procedure than historical Value-at-Risk. We also propose alternative risk measurement procedures that possess the robustness property.     

A value-of-information approach to measuring risk in multi-period economic activity

In this paper, we discuss measures of risk for uncertain outcomes of economic activity, which are based on the notion of the value of full information in stochastic programs. Information is measured in terms of σ-algebras. For multi-period income streams information is represented by filtrations, i.e. sequences of σ-algebras. The basic properties of our risk measures are multi-period coherence (“diversification decreases risk”), compound concavity (“random alternatives increase risk”) and convex monotonicity (“insurance decreases risk”).     

Noise sensitivity of portfolio selection under various risk measures

We study the sensitivity to estimation error of portfolios optimized under various risk measures, including variance, absolute deviation, expected shortfall and maximal loss. We introduce a measure of portfolio sensitivity and test the various risk measures by considering simulated portfolios of varying sizes N and for different lengths T of the time series. We find that the effect of noise is very strong in all the investigated cases, asymptotically it only depends on the ratio N/T, and diverges (goes to infinity) at a critical value of N/T, that depends on the risk measure in question. This divergence is the manifestation of a phase transition, analogous to the algorithmic phase transitions recently discovered in a number of hard computational problems. The transition is accompanied by a number of critical phenomena, including the divergent sample to sample fluctuations of portfolio weights. While the optimization under variance and mean absolute deviation is always feasible below the critical value of N/T, expected shortfall and maximal loss display a probabilistic feasibility problem, in that they can become unbounded from below already for small values of the ratio N/T, and then no solution exists to the optimization problem under these risk measures. Although powerful filtering techniques exist for the mitigation of the above instability in the case of variance, our findings point to the necessity of developing similar filtering procedures adapted to the other risk measures where they are much less developed or non-existent. Another important message of this study is that the requirement of robustness (noise-tolerance) should be given special attention when considering the theoretical and practical criteria to be imposed on a risk measure.     

CAPM and APT-like models with risk measures

The paper deals with optimal portfolio choice problems when risk levels are given by coherent risk measures, expectation bounded risk measures or general deviations. Both static and dynamic pricing models may be involved. Unbounded problems are characterized by new notions such as (strong) compatibility between prices and risks. Surprisingly, the lack of bounded optimal risk and/or return levels arises for important pricing models (Black and Scholes) and risk measures (VaR, CVaR, absolute deviation, etc.). Bounded problems present a Market Price of Risk and generate a pair of benchmarks. From these benchmarks we introduce APT and CAPM-like analyses, in the sense that the level of correlation between every available security and some economic factors explains the security expected return. The risk level non correlated with these factors has no influence on any return, despite the fact that we are dealing with risk functions beyond the standard deviation.     

A framework for the analysis of firm risk communication

In this paper, we propose a framework for the analysis of risk communication and an index to measure the quality of risk disclosure. Mainstream literature on voluntary disclosure has emphasized that quantity can be used as a sound proxy for quality. We contend that, in the analysis of the disclosure of risks made by public companies, attention has to be paid not only to how much is disclosed but also to what is disclosed and how.We apply the framework to a sample of nonfinancial companies listed in the ordinary market on the Italian Stock Exchange. To verify that the framework and synthetic index are not influenced by the two factors recognized in the literature as the most powerful drivers of disclosure behavior for listed companies, we use an OLS model. The regression shows that the index of disclosure quantity is not influenced either by size or industry. Thus, the synthetic measure can be used to rank the quality of the disclosure of risks.     

Which market integration measure?

This paper compares the dynamics of the financial integration process as described by different empirical approaches. To this end, a wide range of measures accounting for several dimensions of integration is employed. In addition, we evaluate the performance of each measure by relying on an established international finance result, i.e., increasing financial integration leads to declining international portfolio diversification benefits. Using monthly equity market data for three different country groups (i.e., developed markets, emerging markets, developed plus emerging markets) and a dynamic indicator of international portfolio diversification benefits, we find that (i) all measures give rise to a very similar long-run integration pattern; (ii) the standard correlation explains variations in diversification benefits as well or better than more sophisticated measures. These findings are robust to a battery of robustness checks.     

Beyond cash-additive risk measures: when changing the numéraire fails

We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on cash-additive risk measures, for which the eligible asset is a risk-free bond, on the grounds that the general case can be reduced to the cash-additive case by a change of numéraire. However, discounting does not work in all financially relevant situations, especially when the eligible asset is a defaultable bond. In this paper, we fill this gap by allowing general eligible assets. We provide a variety of finiteness and continuity results for the corresponding risk measures and apply them to risk measures based on value-at-risk and tail value-at-risk on L ^p spaces, as well as to shortfall risk measures on Orlicz spaces. We pay special attention to the property of cash subadditivity, which has been recently proposed as an alternative to cash additivity to deal with defaultable bonds. For important examples, we provide characterizations of cash subadditivity and show that when the eligible asset is a defaultable bond, cash subadditivity is the exception rather than the rule. Finally, we consider the situation where the eligible asset is not liquidly traded and the pricing rule is no longer linear. We establish when the resulting risk measures are quasiconvex and show that cash subadditivity is only compatible with continuous pricing rules.     

Political geography and stock returns: The value and risk implications of proximity to political power

We show that political geography has a pervasive effect on the cross-section of stock returns. We collect election results over a 40-year period and use a political alignment index (PAI) of each state's leading politicians with the ruling (presidential) party to proxy for local firms’ proximity to political power. Firms whose headquarters are located in high PAI states outperform those located in low PAI states, both in terms of raw returns, and on a risk-adjusted basis. Overall, although we cannot rule out indirect political connectedness advantages as an explanation of the PAI effect, our results are consistent with the notion that proximity to political power has stock return implications because it reflects firms’ exposure to policy risk.     

Is It Possible to Construct Derivatives for the Paris Residential Market?

Index-based derivatives markets are fast developing in Europe, the US and Asia. Both valuation based and transactions based indices are used as bases for these derivatives contracts. This paper addresses the issue of revision effects on key index parameters, and their implications for derivatives pricing and questions whether these indices may be suitable for derivatives. More specifically, we address the issue of the robustness of the price level, mean, and volatility estimates for two repeat sales real estate price indices: the classical Weighted Repeat Sales (WRS) method and a Principal Component Analysis (PCA) factorial method, as elaborated in Baroni et al. (J Real Estate Res, 29(2):137–158, 2007). Our work is an extension of Clapham et al. (Real Estate Econ, 34(2):275–302, 2006), with the aim of helping judge the efficiency of such indices in designing real estate derivatives. We use an extensive repeat sales database for the Paris (France) residential market. We describe the dataset used and compute the parameters (index price level, trend and volatility) of the indices produced over the period 1982–2005. We then test the sensitivity of these two indices to revisions due to additional repeat-sales transactions information. Our analysis is conducted on the overall Paris market as well as on sub-markets. Our main conclusion is that even if the revision problem may cause substantial concern for the stability of key parameters that are used as inputs in the pricing of derivatives contracts, the order of magnitude of revision on derivatives pricing is not sufficient to deter market participants when it comes to products such a swap contract or insurance contracts against severe losses. We also show that WRS and PCA react differently to revision. The impact of index revision is non negligible in estimating the index price level for both indices. This result is consistent with existing literature for the US and Swedish markets. Price level revision causes moderate concern when trading products such as index futures or price insurance contracts, but could deter option like products. We show that managing this price level revision risk is similar to delta hedging in standard option pricing theory. We also find that although revision impact on index trend can be important, the WRS method seems more robust than PCA. However, the trend revision impact order of magnitude for contracts such as total return swaps is low. Finally, revision influence on volatility estimates seems to have a modest impact on derivatives, and according to the robustness of the volatility estimate, the PCA factorial index seems to fare relatively better than the WRS index. Hence, our findings show that the factorial index could better sustain volatility based derivatives. We also show that whatever the index, managing this volatility revision risk is similar to vega hedging in option pricing theory.

Unbiased estimation of expected return using CAPM

Estimation of expected return is required for many financial decisions. For example, an estimate for cost of capital is required for capital budgeting and cost of equity estimates are needed for performance evaluation based on measures such as EVA. Estimates for expected return are often based on the Capital Asset Pricing Model (CAPM), which states that expected excess return (expected return minus the risk-free rate) is equal to the asset's sensitivity to the world market portfolio (β) times the risk premium on the “world market portfolio” (the market risk premium). Since the world market portfolio, by definition, contains all assets in the world, it is not observable. As a result, an estimate for expected return is commonly obtained by taking an estimate for β based on some index (as a proxy for the world market portfolio) and an estimate for the market risk premium based on a potentially different index and multiplying them together. In this paper, it is shown that this results in a biased estimate for expected return. This is undesirable since biased estimates lead to misallocation of funds and biased performance measures. It is also shown in this paper that the straightforward procedure suggested by Fama and MacBeth [J. Financ. Econ. 1 (1974) 43] results in an unbiased estimate for expected return. Further from the analysis done, it follows that, for an unbiased estimate, it does not matter what proxy is used, as long as it is used correctly an unbiased estimate for expected return results.     

Integrating market and credit risk: A simulation and optimisation perspective

We introduce a modelling paradigm which integrates credit risk and market risk in describing the random dynamical behaviour of the underlying fixed income assets. We then consider an asset and liability management (ALM) problem and develop a multistage stochastic programming model which focuses on optimum risk decisions. These models exploit the dynamical multiperiod structure of credit risk and provide insight into the corrective recourse decisions whereby issues such as the timing risk of default is appropriately taken into consideration. We also present an index tracking model in which risk is measured (and optimised) by the CVaR of the tracking portfolio in relation to the index. In-sample as well as out-of-sample (backtesting) experiments are undertaken to validate our approach. The main benefits of backtesting, that is, ex-post analysis are that (a) we gain insight into asset allocation decisions, and (b) we are able to demonstrate the feasibility and flexibility of the chosen framework.     

The materiality of country-specific geographic segment disclosures

SFAS 131 (1997) substantially changed geographic segment reporting in the United States by requiring disclosures to be made by individual foreign country when operations in an individual country are material. Although SFAS 14 (1976) provided a quantitative threshold for determining separately reportable segments, SFAS 131 provides no guidance for determining when operations in an individual country are material. In SAB 99 (1999), the SEC reminds firms that exclusive reliance on quantitative benchmarks to assess materiality is inappropriate; qualitative factors also should be considered.Using financial analysts as subjects, we conduct an experiment to examine two possible benchmarks for determining the materiality of operations in an individual foreign country: (1) the percent of total operations located in an individual country (a quantitative benchmark) and (2) the level of risk associated with the country in which the operations are located (a qualitative benchmark). The results indicate that across two regions both the magnitude of operations and the level of country risk significantly affect financial analysts’ judgments about firm risk. However, the effect that the magnitude of specific country operations has on risk assessment does not apply to countries of relatively high and relatively low risk. These results suggest that, although materiality is often evaluated in quantitative terms, the qualitative criterion of country risk may dominate in importance.     

Effect of cash flow risk on corporate failures,and the moderating role of earnings management and abnormal compensation

In this study, we find that United States firms' average cash flow risk (CFR) shows a significantly increasing trend over the past four decades or so. This does not portend well considering the significance of cash flows in maintaining a firm's financial health and going concern status. The CFR also increases dramatically for firms approaching financial distress or bankruptcy, suggesting its important role in predicting a firm's failure. Empirically, we find that CFR has a strong positive effect on a firm's financial distress likelihood. We also find that the association between CFR and financial distress is negatively moderated in firms with high earnings management and abnormal compensation. The results suggest that managers in firms with high CFR are more likely to use heuristics in form of earnings management. Thus, supporting the upper echelons theory related to managers under performance pressure. Meanwhile, consistent with the notion in the agency theory that financial incentives serve as effective monitoring mechanisms, compensation packages can incentivize better risk management practices and decrease the likelihood of a firm's failure. Our findings are also robust to alternative definitions of a firm's failure: financial constraints, presumed debt covenant violation and legal bankruptcy filings.     

Malmquist-type indices in the presence of negative data: An application to bank branches

In this paper we develop an index and an indicator of productivity change that can be used with negative data. For that purpose the range directional model (RDM), a particular case of the directional distance function, is used for computing efficiency in the presence of negative data. We use RDM efficiency measures to arrive at a Malmquist-type index, which can reflect productivity change, and we use RDM inefficiency measures to arrive at a Luenberger productivity indicator, and relate the two. The productivity index and indicator are developed relative to a fixed meta-technology and so they are referred to as a meta-Malmquist index and meta-Luenberger indicator. We also address the fact that VRS technologies are used for computing the productivity index and indicator (a requirement under negative data), which raises issues relating to the interpretability of the index. We illustrate how the meta-Malmquist index can be used, not only for comparing the performance of a unit in two time periods, but also for comparing the performance of two different units at the same or different time periods. The proposed approach is then applied to a sample of bank branches where negative data were involved. The paper shows how the approach yields information from a variety of perspectives on performance which management can use.     

Combining creativity and control: Understanding individual motivation in large-scale collaborative creativity

Recent research has shown that management control systems (MCS) can improve performance in contexts characterized by high levels of task uncertainty. This seems to conflict with a second stream of research, which argues that MCSs risk undermining the intrinsic motivation needed for effective performance in such settings. To solve this puzzle, we build on theories of perceived locus of causality and self-construal and develop an integrative model summarized in 15 propositions. To explicate our proposed solution and to show its robustness, we focus on the class of activities we call large-scale collaborative creativity (LSCC) - contexts where individuals face a dual challenge of demonstrating creativity and embracing the formal controls that coordinate their creative activities with others’. We argue that LSCC requires the simultaneous activation of intrinsic and identified forms of motivation, and simultaneously independent and interdependent self-construals. Against some scholarship that argues or assumes that such simultaneous combinations are infeasible, we argue that they can be fostered through appropriate attraction-selection-attrition policies and management control systems design. We also show how our propositions can enrich our understanding of motivation in other settings, where creativity and/or coordination demands are less pressing.     

Is information risk priced? Evidence from abnormal idiosyncratic volatility

We propose a new, price-based measure of information risk called abnormal idiosyncratic volatility (AIV) that captures information asymmetry faced by uninformed investors. AIV is the idiosyncratic volatility prior to information events in excess of normal levels. Using earnings announcements as information events, we show that AIV is positively associated with informed return run-ups, abnormal insider trading, short selling, and institutional trading during pre-earnings-announcement periods. We find that stocks with high AIV earn economically and statistically larger future returns than stocks with low AIV. Taken together, our findings support the notion that information risk is priced.     

Quantitative models for operational risk: Extremes,dependence and aggregation

Due to the new regulatory guidelines known as Basel II for banking and Solvency 2 for insurance, the financial industry is looking for qualitative approaches to and quantitative models for operational risk. Whereas a full quantitative approach may never be achieved, in this paper we present some techniques from probability and statistics which no doubt will prove useful in any quantitative modelling environment. The techniques discussed are advanced peaks over threshold modelling, the construction of dependent loss processes and the establishment of bounds for risk measures under partial information, and can be applied to other areas of quantitative risk management.¹