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on Risk Management |
| By: | Stefan Thurner (Dept. of Mathematics, University of Vienna); J. Doyne Farmer (Sante Fe Institute); John Geanakoplos (Cowles Foundation, Yale University) |
| Abstract: | We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing," i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on "irrational behavior," such as trend following. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility gets high, making these extreme fluctuations even worse. |
| Keywords: | Systemic risk, Clustered volatility, Fat tails, Crash, Margin calls, Leverage |
| JEL: | E32 E37 G12 G14 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1745&r=rmg |
| By: | Gollier, Christian |
| Abstract: | This paper explores empirically the link between stocks returns Value-at-Risk (VaR) and the state of financial markets cycle. The econometric analysis is based on a simple vector autoregression setup. Using quarterly data from 1970Q4 to 2008Q4 for France, Germany and the United-Kingdom, it turns out that the k-year VaR of equities is actually dependent on the cycle phase: the expected losses as measured by the VaR are smaller in recession times than expansion periods, whatever the country and the horizon. These results strongly suggest that the European rules regarding the solvency capital requirements for insurance companies should adapt to the state of the financial market’s cycle. |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:ide:wpaper:20628&r=rmg |
| By: | Janda, Karel; Svárovská, Barbora |
| Abstract: | In this paper we first introduce microfinance institutions as an alternative investment instrument. We argue that beside socially responsible features of microfinance, there exists also significant portfolio enhancement opportunity in microfinance investments. Then we provide an overview of possible ways how to evaluate the correlation between microfinance related financial instruments and conventional financial market measures of risk and return. |
| Keywords: | Microfinance; Investment; Funds |
| JEL: | G11 G21 |
| Date: | 2009–12–21 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:19486&r=rmg |
| By: | Nathan Foley-Fisher; Bernardo Guimaraes |
| Abstract: | We empirically analyse the appropriateness of indexing emerging market sovereign debt toUS real interest rates. We find that policy-induced exogenous increases in US rates raisedefault risk in emerging market economies, as hypothesised in the theoretical literature.However, we also find evidence that omitted variables which simultaneously increase US realinterest rates and reduce the risk of default dominate the hypothesised relationship. We canonly conclude that it's not a good idea to index emerging market bonds to US real interestrates. |
| Keywords: | real interest rates, default, sovereign debt, identification through heteroskedasticity |
| JEL: | F34 G15 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:cep:cepdps:dp0952&r=rmg |
| By: | Grau-Carles, Pilar; Sainz, Jorge; Otamendi, Javier; Doncel, Luis Miguel |
| Abstract: | Traditional risk-adjusted performance measures, such as the Sharpe ratio, the Treynor index or Jensen's alpha, based on the mean-variance framework, are widely used to rank mutual funds. However, performance measures that consider risk by taking into account only losses, such as Value-at-Risk (VaR), would be more appropriate. Standard VaR assumes that returns are normally distributed, though they usually present skewness and kurtosis. In this paper we compare these different measures of risk: traditional ones vs. ones that take into account fat tails and asymmetry, such as those based on the Cornish-Fisher expansion and on the extreme value theory. Moreover, we construct a performance index similar to the Sharpe ratio using these VaR-based risk measures. We then use these measures to compare the rating of a set of mutual funds, assessing the different measures' usefulness under the Basel II risk management framework. -- |
| Keywords: | Mutual funds,performance measures,Value-at-Risk,extreme value theory |
| JEL: | G10 G11 G20 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:ifwedp:200954&r=rmg |
| By: | Li, Hui |
| Abstract: | Current CVA modeling framework has ignored the impact of stochastic recovery rate. Due to the possible negative correlation between default and recovery rate, stochastic recovery rate could have a doubling effect on wrong-way risk. In the case of a payer CDS, when counterparty defaults, the CDS value could be higher due to default contagion while the recovery rate may also be lower if the economy is in a downturn. Using our recently proposed model of correlated stochastic recovery in the default time Gaussian Copula framework, we demonstrate this double impact on wrong-way risk in the CVA calculation for a payer CDS. We also present a new form of Gaussian copula that correlates both default time and recovery rate. |
| Keywords: | Counterparty Risk, Credit Valuation Adjustment, Wrong-Way Risk, Default Time Copula, Gaussian Copula, Default Correlation, Stochastic Recovery, Spot Recovery, Credit Default Swap |
| JEL: | G13 |
| Date: | 2009–12–31 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:19684&r=rmg |
| By: | Tom Fong (Research Department, Hong Kong Monetary Authority); Laurence Fung (Research Department, Hong Kong Monetary Authority); Lillie Lam (Research Department, Hong Kong Monetary Authority); Ip-wing Yu (Research Department, Hong Kong Monetary Authority) |
| Abstract: | This paper assesses systemic linkages among banks in Hong Kong using the risk measure "CoVaR" derived from quantile regression. The CoVaR measure captures the co-movements of banks¡¯ default risk by taking into account their nonlinear relationship when the banks are in distress. Based on equity price information, our estimation results show that the default risks of the banks were interdependent during the recent crisis. Although local banks are generally smaller, their systemic importance is found to be similar to their international and Mainland counterparts, which may be due to a higher degree of commonality in the risk profile of local banks. Regarding the impact of external shocks on the banks, international banks are more likely to be affected by the equity price fall in the US market, while local banks are relatively more responsive to funding liquidity risk. |
| Keywords: | Value-at-Risk, Systemic Risk, Risk Spillovers, Quantile Regression |
| JEL: | G21 G14 |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:hkg:wpaper:0919&r=rmg |
| By: | Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Bertrand Hassani (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | Operational risk management inside banks and insurance companies is an important task. The computation of a risk measure associated to these kinds of risks lies in the knowledge of the so-called loss distribution function (LDF). Traditionally, this LDF is computed via Monte Carlo simulations or using the Panjer recursion, which is an iterative algorithm. In this paper, we propose an adaptation of this last algorithm in order to improve the computation of convolutions between Panjer class distributions and continuous distributions, by mixing the Monte Carlo method, a progressive kernel lattice and the Panjer recursion. This new hybrid algorithm does not face the traditional drawbacks. This simple approach enables us to drastically reduce the variance of the estimated value-at-risk associated with the operational risks and to lower the aliasing error we would have using Panjer recursion itself. Furthermore, this method is much less timeconsuming than a Monte Carlo simulation. We compare our new method with more sophisticated approaches already developed in operational risk literature. |
| Keywords: | Operational risk ; Panjer algorithm ; Kernel ; numerical integration ; convolution. |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00443846_v1&r=rmg |
| By: | Garita, Gus |
| Abstract: | This paper defines a risk-stability index (RSI) that takes into account the extreme dependence structure and the conditional probability of joint failure (CPJF) among risk factors in a portfolio. In combination, both the RSI and CPJF provide a valuable tool for analyzing risk from complementary perspectives; thereby allowing the measurement of (i) common distress of risk factors in a portfolio, (ii) distress between specific risk factors, and (iii) distress to a portfolio related to a specific risk factor. With an application to a financial system comprised of 18 banks from around the world, the results herein show that financial stability must be viewed as a continuum, since risk varies from period to period. The risk-stability index indicates that U.S. banks tend to cause the most stress to the global financial system (as defined herein), followed by Asian and European banks. The results also show that Asian banks seem to experience the most persistence of distress, followed by U.S. and European banks. The panel VAR results show that monetary policy should "lean against the wind", since it has a significant effect in reducing the (potential) instability of a financial system. |
| Keywords: | Conditional probability of joint failure; contagion; dependence structure; distress; multivariate extreme value theory; panel VAR; persistence |
| JEL: | F15 C10 E44 F36 |
| Date: | 2009–12–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:19611&r=rmg |
| By: | Arthur M. Berd; Robert F. Engle; Artem Voronov |
| Abstract: | We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation surface as a convenient tool for comparing portfolio credit loss generating models and pricing synthetic CDO tranches. Analyzing alternative specifications of the underlying dynamics, we conclude that the asymmetric models with TARCH volatility specification are the preferred choice for generating significant and persistent credit correlation skews. The characteristic dependence of the correlation skew on term to maturity and portfolio hazard rate in these models has a significant impact on both relative value analysis and risk management of CDO tranches. |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1001.0786&r=rmg |
| By: | Al Janabi, Mazin A. M. |
| Abstract: | Asset market liquidity risk is a significant and perplexing subject and though the term market liquidity risk is used quite chronically in academic literature it lacks an unambiguous definition, let alone understanding of the proposed risk measures. To this end, this paper presents a review of contemporary thoughts and attempts vis-à-vis asset market/liquidity risk management. Furthermore, this research focuses on the theoretical aspects of asset liquidity risk and presents critically two reciprocal approaches to measuring market liquidity risk for individual trading securities, and discusses the problems that arise in attempting to quantify asset market liquidity risk at a portfolio level. This paper extends research literature related to the assessment of asset market/liquidity risk by providing a generalized theoretical modeling underpinning that handle, from the same perspective, market and liquidity risks jointly and integrate both risks into a portfolio setting without a commensurate increase of statistical postulations. As such, we argue that market and liquidity risk components are correlated in most cases and can be integrated into one single market/liquidity framework that consists of two interrelated sub-components. The first component is attributed to the impact of adverse price movements, while the second component focuses on the risk of variation in transactions costs due to bid-ask spreads and it attempts to measure the likelihood that it will cost more than expected to liquidate the asset position. We thereafter propose a concrete theoretical foundation and a new modeling framework that attempts to tackle the issue of market/liquidity risk at a portfolio level by combining two asset market/liquidity risk models. The first model is a re-engineered and robust liquidity horizon multiplier that can aid in producing realistic asset market liquidity losses during the unwinding period. The essence of the model is based on the concept of Liquidity-Adjusted Value-at-Risk (L-VaR) framework, and particularly from the perspective of trading portfolios that have both long and short trading positions. Conversely, the second model is related to the transactions cost of liquidation due to bid-ask spreads and includes an improved technique that tackles the issue of bid-ask spread volatility. As such, the model comprises a new approach to contemplating the impact of time-varying volatility of the bid-ask spread and its upshot on the overall asset market/liquidity risk. |
| Keywords: | Economic Capital; Emerging Markets; Financial Engineering; Financial Risk Management; Financial Markets; Liquidity Risk; Portfolio Management; Liquidity Adjusted Value at Risk |
| JEL: | G32 |
| Date: | 2009–05–20 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:19498&r=rmg |
| By: | Bennani, Norddine; Maetz, Jerome |
| Abstract: | The market evolution since the end of 2007 has been characterized by an increase of systemic risk and a high number of defaults. Realized recovery rates have been very dispersed and different from standard assumptions, while 60%-100% super-senior tranches on standard indices have started to trade with significant spread levels. This has triggered a growing interest for stochastic recovery modelling. This paper presents an extension to the standard Gaussian copula framework that introduces a consistent modelling of stochastic recovery. We choose to model directly the spot recovery, which allows to preserve time consistency, and compare this approach to the standard ones, defined in terms of recovery to maturity. Taking a specific form of the spot recovery function, we show that the model is flexible and tractable, and easy to calibrate to both individual credit spread curves and index tranche markets. Through practical numerical examples, we analyze specific model properties, focusing on default risk. |
| Keywords: | stochastic recovery; CDO; correlation smile; base correlation; copula; factor model; default risk |
| JEL: | G12 C02 G13 G10 |
| Date: | 2009–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:19736&r=rmg |
| By: | Saibal, Ghosh |
| Abstract: | The article examines the determinants of banks’ charter value and its disciplining effect on bank risk-taking since the mid-1990s. The analysis indicates that deposit and loan market concentration exert a significant effect on charter value, suggestive of a strong link between competition and charter value. Among the traditional banking activities, bank size and efficiency are found to be important determinants of charter value. The disciplining effect of charter value is robust across several measures on bank risk. |
| Keywords: | banking; charter value; risk-taking; capital buffer; prudential regulation; India |
| JEL: | G21 |
| Date: | 2009–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:19543&r=rmg |
| By: | Etienne Bordeleau; Allan Crawford; Christopher Graham |
| Abstract: | The Basel capital framework plays an important role in risk management by linking a bank's minimum capital requirements to the riskiness of its assets. Nevertheless, the risk estimates underlying these calculations may be imperfect, and it appears that a cyclical bias in measures of risk-adjusted capital contributed to procyclical increases in global leverage prior to the recent financial crisis. As such, international policy discussions are considering an unweighted leverage ratio as a supplement to existing risk-weighted capital requirements. Canadian banks offer a useful case study in this respect, having been subject to a regulatory ceiling on an unweighted leverage ratio since the early 1980s. The authors review lessons from the Canadian experience with leverage constraints, and provide some empirical analysis on how such constraints affect banks' leverage management. In contrast to a number of countries without regulatory constraints, leverage at major Canadian banks was relatively stable leading up to the crisis, reducing pressure for deleveraging during the economic downturn. Empirical results suggest that major Canadian banks follow different strategies for managing their leverage. Some banks tend to raise their precautionary buffer quickly, through sharp reductions in asset growth and faster capital growth, when a shock pushes leverage too close to its authorized limit. For other banks, shocks have more persistent effects on leverage, possibly because these banks tend to have higher buffers on average. Overall, the authors' results suggest that a leverage ceiling would be a useful tool to complement risk-weighted measures and mitigate procyclical tendencies in the financial system. |
| Keywords: | Financial institutions; Financial stability; Financial system regulation and policies |
| JEL: | G28 G21 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocadp:09-15&r=rmg |
| By: | Arthur M. Berd; Roy Mashal; Peili Wang |
| Abstract: | In the second part of our series we suggest new definitions of credit bond duration and convexity that remain consistent across all levels of credit quality including deeply distressed bonds and introduce additional risk measures that are consistent with the survival-based valuation framework. We then show how to use these risk measures for the construction of market neutral portfolios. |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:0912.4614&r=rmg |
| By: | Luigi Zingales (University of Chicago Booth School of Business); Oliver Hart (Harvard University & NBER) |
| Abstract: | We design a new, implementable capital requirement for large financial institutions (LFIs) that are too big to fail. Our mechanism mimics the operation of margin accounts. To ensure that LFIs do not default on either their deposits or their derivative contracts, we require that they maintain an equity cushion sufficiently great that their own credit default swap price stays below a threshold level, and a cushion of long term bonds sufficiently large that, even if the equity is wiped out, the systemically relevant obligations are safe. If the CDS price goes above the threshold, the LFI regulator forces the LFI to issue equity until the CDS price moves back down. If this does not happen within a predetermined period of time, the regulator intervenes. We show that this mechanism ensures that LFIs are always solvent, while preserving some of the disciplinary effects of debt. |
| Keywords: | Banks, Capital Requirement, Too Big to Fail |
| JEL: | G21 G28 |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2009.124&r=rmg |
| By: | El Bouhadi, Abdelhamid; Achibane, Khalid |
| Abstract: | The uncertainty plays a central role in most of the problems which addressed by the modern financial theory. For some time, we know that the uncertainty under the speculative price varies over the time. However, it is only recently that a lot of studies in applied finance and monetary economics using the explicit modelling of time series involving the second and the higher moments of variables. Indeed, the first tool appeared in order to model such variables has been introduced by Engel (1982). This is the autoregressive conditional heteroskedasticity and its many extensions. Thus, with the emergence and development of these models, Value-at-Risk, which plays a major role in assessment and risk management of financial institutions, has become a more effective tool to measure the risk of asset holdings. Following the current financial debacle, we give the simple question about the progress and some achievements made in the context of emerging and pre-emergent financial markets microstructure which can sustain and limit the future fluctuations. Today, we know that the crisis has no spared any financial market in the world. The magnitude and damage of the crisis effects vary in the space and time. In the Moroccan stock market context, it was found that the effects were not so harmful and that the future of these markets faces a compromise or at least a long lethargy. Indeed, inspired by these events, our study attempts to undertake two exercises. In first, we are testing the ability of the nonlinear ARCH and GARCH models (EGARCH, TGARCH, GJR-GARCH, QGARCH) to meet the number of expected exceedances (shortfalls) of VaR measurement. In second, we are providing a forecasting volatility under the time-varying of VaR. |
| Keywords: | Market Microstructure; ARCH Models; VaR; Time-Varying Volatility; Forecasting Volatility; Casablanca Stock Exchange. |
| JEL: | G14 C53 C52 G18 C22 |
| Date: | 2009–12–20 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:19482&r=rmg |
| By: | Mitropoulos, Atanasios; Zaidi, Rida |
| Abstract: | We have assembled a unique loan-level performance dataset for mortgages originated in the UK to study the differences in default likelihood between loans of varying borrower and loan characteristics. We can broadly confirm the relevance of most commonly known riskfactors and find that most drivers of default for prime are also relevant for non-conforming, drivers of repossessions are largely similar to drivers of arrears and information on adverse borrower information dominates any other risk factor. Our study provides many more details and compares results with recent studies for the US and other European countries. |
| Keywords: | residential mortgages; loan defaults; consumer behaviour; logistic regression; United Kingdom |
| JEL: | D14 G21 |
| Date: | 2009–12–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:19619&r=rmg |
| By: | Delia Coculescu |
| Abstract: | We build a general model for pricing defaultable claims. In addition to the usual absence of arbitrage assumption, we assume that one defaultable asset (at least) looses value when the default occurs. We prove that under this assumption, in some standard market filtrations, default times are totally inaccessible stopping times; we therefore proceed to a systematic construction of default times with particular emphasis on totally inaccessible stopping times. Surprisingly, this abstract mathematical construction, reveals a very specific and useful way in which default models can be built, using both market factors and idiosyncratic factors. We then provide all the relevant characteristics of a default time (i.e. the Az\'ema supermartingale and its Doob-Meyer decomposition) given the information about these factors. We also provide explicit formulas for the prices of defaultable claims and analyze the risk premiums that form in the market in anticipation of losses which occur at the default event. The usual reduced-form framework is extended in order to include possible economic shocks, in particular jumps in the recoveries at the default time. This formulas are not classic and we point out that the knowledge of the default compensator or the intensity process is not anymore a sufficient quantity for finding explicit prices, but we need indeed the Az\'ema supermartingale and its Doob-Meyer decomposition. |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:0912.4312&r=rmg |
| By: | Ulrich Kirchner |
| Abstract: | We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied probability distributions. We argue that volatility is not risk, but uncertainty. Non-normal distributions combine the risk in the left tail with the opportunities in the right tail -- unifying the "risk premium" with the possible loss. Risk and reward must be part of the same picture and expected returns must include possible losses due to risks. We reinterpret the Black-Scholes pricing formulas as prices for maximum-entropy probability distributions, illuminating their importance from a new angle. Using these ideas we show how derivatives can be priced under "uncertain uncertainty" and how this creates a skew for the implied volatilities. We argue that the current standard approach based on stochastic modelling and risk-neutral pricing fails to account for subjectivity in markets and mistreats uncertainty as risk. Furthermore, it is founded on a questionable argument -- that uncertainty is eliminated at all cost. |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1001.1616&r=rmg |
| By: | Lall, Somik V.; Deichmann, Uwe |
| Abstract: | Today, 370 million people live in cities in earthquake prone areas and 310 million in cities with high probability of tropical cyclones. By 2050, these numbers are likely to more than double. Mortality risk therefore is highly concentrated in many of the world’s cities and economic risk even more so. This paper discusses what sets hazard risk in urban areas apart, provides estimates of valuation of hazard risk, and discusses implications for individual mitigation and public policy. The main conclusions are that urban agglomeration economies change the cost-benefit calculation of hazard mitigation, that good hazard management is first and foremost good general urban management, and that the public sector must perform better in generating and disseminating credible information on hazard risk in cities. |
| Keywords: | Banks&Banking Reform,Environmental Economics&Policies,Hazard Risk Management,Urban Housing,Labor Policies |
| Date: | 2009–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:wbk:wbrwps:5161&r=rmg |
| By: | Thomas Conlon; Heather J. Ruskin; Martin Crane |
| Abstract: | The cross correlation matrix between equities comprises multiple interactions between traders with varying strategies and time horizons. In this paper, we use the Maximum Overlap Discrete Wavelet Transform to calculate correlation matrices over different timescales and then explore the eigenvalue spectrum over sliding time windows. The dynamics of the eigenvalue spectrum at different times and scales provides insight into the interactions between the numerous constituents involved. Eigenvalue dynamics are examined for both medium and high-frequency equity returns, with the associated correlation structure shown to be dependent on both time and scale. Additionally, the Epps effect is established using this multivariate method and analyzed at longer scales than previously studied. A partition of the eigenvalue time-series demonstrates, at very short scales, the emergence of negative returns when the largest eigenvalue is greatest. Finally, a portfolio optimization shows the importance of timescale information in the context of risk management. |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1001.0497&r=rmg |