A model of optimal portfolio selection under liquidity risk and price impact

We study a financial model with one risk-free and one risky asset subject to liquidity risk and price impact. In this market, an investor may transfer funds between the two assets at any discrete time. Each purchase or sale policy decision affects the rice of the risky asset and incurs some fixed transaction cost. The objective is to maximize the expected utility from terminal liquidation value over a finite horizon and subject to a solvency constraint. This is formulated as an impulse control problem under state constraints and we characterize the value function as the unique constrained viscosity solution to the associated quasi-variational Hamilton–Jacobi–Bellman inequality. We would like to thank Mihail Zervos for useful discussions.     

Parameter risk in time-series mortality forecasts

The projection of mortality rates is an essential part of valuing liabilities in life insurance portfolios and pension schemes. An important tool for risk management and solvency purposes is a stochastic projection model. We show that ARIMA models can be better representations of mortality time-series than simple random-walk models. We also consider the issue of parameter risk in time-series models from the point of view of an insurer using them for regulatory risk reporting – formulae are given for decomposing overall risk into undiversifiable trend risk (parameter uncertainty) and diversifiable volatility. Particular attention is given to the contrasts in how academic researchers might view these models and how insurance regulators and practitioners in life offices might use them. Using a bootstrap method we find that, while certain kinds of parameter risk are negligible, others are too material to ignore. We also find that an objective model selection criterion, such as goodness of fit to past data, can result in the selection of a model with unstable parameter values. While this aspect of the model is superficially undesirable, it also leads to slightly higher capital requirements and thus makes the model of keen interest to regulators. Our conclusions have relevance to insurers using value-at-risk capital assessments in the European Union under Solvency II, but also territories using conditional tail expectations such as Australia, Canada and Switzerland.     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.     

Trading frenzies and their impact on real investment

We study a model in which a capital provider learns from the price of a firm's security in deciding how much capital to provide for new investment. This feedback effect from the financial market to the investment decision gives rise to trading frenzies, in which speculators all wish to trade like others, generating large pressure on prices. Coordination among speculators is sometimes desirable for price informativeness and investment efficiency, but speculators' incentives push in the opposite direction, so that they coordinate exactly when it is undesirable. We analyze the effect of various market parameters on the likelihood of trading frenzies to arise.     

Stroke--incidence, mortality, morbidity and risk

In the United States, 700,000 strokes, responsible for 165,000 deaths, occur each year. Worldwide, stroke is the 2nd leading cause of death. Stroke is a major health problem; and as the population ages, its significance will grow. This paper reviews the epidemiology of stroke, the identification of modifiable risk factors, and some of the options for intervention that can reduce stroke-related mortality and morbidity. Though the diagnosis and care of stroke patients has improved, mortality resultant from stroke remains significant, with only 50% 5-year survival in some clinical studies. The risk of stroke following a transient ischemic attack (TIA) or initial stroke is also significant-approximately 30% following either event. Stroke severity at onset and patient age are the most important factors for predicting prognosis. Stroke prevention focuses on management of the traditional cardiovascular risk factors especially control of blood pressure and smoking cessation. The role of diabetes and lipid control in stroke prevention continues to be studied. The optimum use of anticoagulation to reduce stroke risk has been explored by the Stroke in Patients with Atrial Fibrillation (SPAF) studies. Carotid endarterectomy is effective in stroke prevention for those with symptomatic carotid obstruction of 70%, but its role in other scenarios is less certain. Antiplatelet drugs continue to be an important therapy for the prevention of recurrent stroke. Centralized stroke centers that specialize in stroke diagnosis and care along with rapidly rendering appropriate treatment can improve mortality and morbidity of stroke by 20%.     

The impact of risk and uncertainty on expected returns

We study asset pricing in economies featuring both risk and uncertainty. In our empirical analysis, we measure risk via return volatility and uncertainty via the degree of disagreement of professional forecasters, attributing different weights to each forecaster. We empirically model the typical risk-return trade-off and augment these models with our measure of uncertainty. We find stronger empirical evidence for an uncertainty-return trade-off than for the traditional risk-return trade-off. Finally, we investigate the performance of a two-factor model with risk and uncertainty in the cross section.     

Detecting and modelling the jump risk of CO2 emission allowances and their impact on the valuation of option on futures contracts

Modelling CO₂ emission allowance prices is important for pricing CO₂ emission allowance linked assets in the emissions trading scheme (ETS). Some statistical properties of CO₂ emission allowance prices have been discovered in the literature ignoring price jumps. By employing real data from the ETS, this research first detects the jump risk using a jump test and then verifies jump effects in modelling CO₂ emission allowance prices by comparing the in-sample and out-of-sample model performance. We suggest a model which can capture the statistical properties of autocorrelation, volatility clustering and jump effects is more appropriate for modelling CO₂ emission allowance prices. We establish a general framework for pricing CO₂ emission allowance options on futures contracts with these properties and find that the jump risk significantly affects the value of the CO₂ emission allowance option on futures contracts. More importantly, we demonstrate that the dynamic jump ARMA–GARCH model can provide more accurate valuations of the CO₂ emission allowance options on futures than other models in terms of pricing error.     

Credit risk management at retail in Mexico: An econometric improvement in the selection of variables and changes in their characteristics

The early prediction of bad debtors for revolving credits in Mexico is a relevant issue today. The credit behavior econometric model proposed considers the changes in the characteristics of the consolidated accredited and provides better results than those obtained with the methodology utilized by the CNBV on provision matters. The results obtained show that the possibility of replacing the current model, minimizing the expected loss and increasing the ROA per financial institution at a national level by 2.20%, complies with the methodological criteria and the statistical tests in accordance with the Compiled Banking Regulation and Basel II guidelines on credit risk issues.     

Quantifying mortality risk in small defined-benefit pension schemes

A risk of small defined-benefit pension schemes is that there are too few members to eliminate idiosyncratic mortality risk, that is, there are too few members to effectively pool mortality risk. This means that when there are few members in the scheme, there is an increased risk of the liability value deviating significantly from the expected liability value, as compared to a large scheme. We quantify this risk through examining the coefficient of variation of a scheme's liability value relative to its expected value. We examine how the coefficient of variation varies with the number of members and find that, even with a few hundred members in the scheme, idiosyncratic mortality risk may still be significant. Next we quantify the amount of the mortality risk concentrated in the executive section of the scheme, where the executives receive a benefit that is higher than the non-executive benefit. We use the Euler capital allocation principle to allocate the total standard deviation of the liability value between the executive and non-executive sections. The results suggest that the mortality risk of the scheme should be monitored and managed within the sections of a scheme and not only on a scheme-wide basis.     

Portfolio selection with mental accounts and background risk

Das et al. (2010) develop a model where an investor divides his or her wealth among mental accounts with motives such as retirement and bequest. Nevertheless, the investor ends up selecting portfolios within mental accounts and an aggregate portfolio that lie on the mean–variance frontier. Importantly, they assume that the investor only faces portfolio risk. In practice, however, many individuals also face background risk. Accordingly, our paper expands upon theirs by considering the case where the investor faces background risk. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we show that these portfolios lie away from the mean–variance frontier under fairly general conditions. Third, we find that the composition and location of such portfolios can differ notably from those of portfolios on the mean–variance frontier.     

The impact of loan prepayment risk and deposit withdrawal risk on the optimal intermediation margin

Numerous studies have analyzed how a bank's intermediation margin varies with respect to such factors as credit quality, funding risk, bank capital, deposit insurance and other factors. However, these studies ignore the potential that loans tend to prepay if interest rates decline and deposits tend to be withdrawn if interest rates rise. Taking this very fundamental fact into account, we derive optimal loan rates and deposit rates when the bank is subject to loan prepayments and deposit withdrawals. Among other things, we find that greater volatility of interest rates tends to increase the margin. The strength of the correlation between the level of interest rates and the propensity to prepay loans (withdraw deposits) also plays an interesting role.     

如何建立岗位风险评价预警机制

近年来,岗位风险和案件预防已经成为困扰基层央行内部管理和发展的突出问题。目前,岗位风险和案件预防管理主要沿用以检查、教育为主的被动模式,而没有一套科学的岗位风险评价预警体系。如何对岗位风险进行判别和度量,对可能出现的风险及即将引发的后果进行客观准确的评价和预警,并采取相应的处置措施,实施全面可靠的风险控制,是基层央行亟待研究和解决的重大课题。     

On systematic mortality risk and risk-minimization with survivor swaps

A new market for so-called mortality derivatives is now appearing with survivor swaps (also called mortality swaps), longevity bonds and other specialized solutions. The development of these new financial instruments is triggered by the increased focus on the systematic mortality risk inherent in life insurance contracts, and their main focus is thus to allow the life insurance companies to hedge their systematic mortality risk. At the same time, this new class of financial contract is interesting from an investor's point of view, since it increases the possibility for an investor to diversify the investment portfolio. The systematic mortality risk stems from the uncertainty related to the future development of the mortality intensities. Mathematically, this uncertainty is described by modeling the underlying mortality intensities via stochastic processes. We consider two different portfolios of insured lives, where the underlying mortality intensities are correlated, and study the combined financial and mortality risk inherent in a portfolio of general life insurance contracts. In order to hedge this risk, we allow for investments in survivor swaps and derive risk-minimizing strategies in markets where such contracts are available. The strategies are evaluated numerically.     

The impact of imposing capital requirements on systemic risk

This paper examines the impact of imposing capital requirements on systemic risk. We use a static model on financial institutions’ risk-taking behavior to quantify the systemic risk in the cross-sectional dimension in both regulated and unregulated systems. Although imposing a capital requirement can lower individual risk, it simultaneously enhances systemic linkage within the system. By using a proper systemic risk measure combining both individual risk and systemic linkage, we show that systemic risk in a regulated system can be higher than that in an unregulated system. In addition, we analyze a sufficient condition under which the systemic risk in a regulated system is always lower.