Mathematical Definition, Mapping, and Detection of (Anti)Fragility

SSRN Electronic Journal, 2000

Under the new capital accord stress tests are to be included in market risk regulatory capital calculations. This development necessitates a coherent and objective framework for stress testing portfolios exposed to market risk. Following recent criticism of stress testing methods our tests are conducted in the context of risk models, building on the VaR literature. First, to identify the most suitable risk models for stress testing, we apply an extensive back testing procedure that focuses on extreme market movements. We consider eight possible risk models including both conditional and unconditional models and four possible return distributions (normal, Student's t, empirical and normal mixture) applied to three heavily traded currency pairs using a sample of daily data spanning more than 20 years. Finding that risk models accommodating both volatility clustering and heavy tails are the most accurate predictors of extreme returns, we develop a corresponding model-based stress testing methodology. Our results are compared with traditional stress tests and we assess the implications for capital adequacy. On the basis of our results we conclude that the new recommendations for market risk regulatory capital calculation will have little impact on current levels of foreign exchange regulatory capital.

Fractile Graphical Analysis was proposed by Prashanta Chandra Mahalanobis (Mahalanobis, 1960) in a series of papers and seminars as a method for comparing two distributions controlling for the rank of a covariate through fractile groups. Mahalanobis used a heuristic method of approximating the standard error of the dependent variable using fractile graphs from two independently selected "interpenetrating subsamples." We revisit the technique of fractile graphical analysis with some historical perspectives. We a propose a new non-parametric regression method called Fractile Regression where we condition on the ranks of the covariate, and compare it with existing regression techniques. We apply this method to predict mutual fund in ‡ow distributions after conditioning on returns and to wage distribution after conditioning for educational quali…cations. Finally, we investigate large and …nite sample properties of fractile regression coe¢ cients both analytically and through Monte Carlo simulations.

2001

"The possibility that market participants are developing a degree of complacency or a feeling that (risk management) technology has inoculated them against market turbulence is admittedly somewhat disquieting. Such complacency is not justified. In estimating necessary levels of risk capital, the primary concern should be to address those disturbances that occasionally do stress institutional solvency-the negative tail of the loss distribution that is so central to modern risk management. As such, the incorporation of stress scenarios into formal risk modeling would seem to be of first-order importance. However, the incipient art of stress testing has yet to find formalization and uniformity across banks and securities dealers. At present, most banks pick a small number of ad hoc scenarios as their stress tests. And although the results of the stress tests may be given to management, they are, to my knowledge, never entered into the formal risk modeling process." -Alan Greenspan [2000] W hile VaR models have proven themselves to be very useful risk management tools, recent financial debacles have also highlighted their limitations-in particular, their excessive dependency on history or unrealistic statistical assumptions. The natural response to these limitations is for firms to resort to stress tests to complement the results of their VaR analyses. Stress tests are exercises to determine the losses that might occur under unlikely but plausible circumstances, and there has been a dramatic increase in the importance given to stress testing since the east Asian crisis and the LTCM affair. Indeed, many firms and regulators now regard stress tests as no less important than VaR methods for assessing a firm's risk exposure.

2016

Author(s): Khanom, Najrin | Advisor(s): Chauvet, Marcelle; Ullah, Aman | Abstract: The theme of this dissertation is the risk and return modeling of financial time series. The dissertation is broadly divided into three chapters; the first chapter focuses on measuring risks and uncertainty in the U.S. stock market; the second on measuring risks of individual financial assets; and the last chapter on predicting stock return. The first chapter studies the movement of the SaP 500 index driven by uncertainty and fear that cannot be explained by economic fundamentals. A new measure of uncertainty is introduced, using the tone of news media coverage on the equity market and the economy; aggregate holding of safe financial assets; and volatility in SaP 500 options trading. Major contributions of this chapter include uncovering a significant non-linear relationship between uncertainty and changes in the business cycle. An increase in uncertainty is found to be associated with drastic but sho...

Relatórios COPPEAD, 2001

Accurate forecasting of risk is the key to sucessful risk management techniques. Given the fat-tailed characterisitic of financial returns, the assumptions of modeling these returns with the thin-tailed Gaussian distribution is inappropriate. In this paper a more accurate VaR estimate is tested using the "stable" or "αstable" distribution, which allows for varying degrees of tail heaviness and varying degrees of skewness. Stable VaR measures are estimated and forecasted using the main Latin American stock market indexes. The results show that the stable modeling provides conservative 99% VaR estimates, while the normal VaR modeling significantly underestimates 99% VaR. The 95% VaR stable and normal estimates, using a window length of 50 observations, are satisfactory. However, increasing the window length to 125 and 250 observations worsens the stable and the normal VaR measurements.

2010

Portfolio risk estimation requires appropriate modeling of fat-tails and asymmetries in dependence in combination with a true downside risk measure. In this survey, we discuss computational aspects of a Monte-Carlo based framework for risk estimation and risk capital allocation. We review different probabilistic approaches focusing on practical aspects of statistical estimation and scenario generation. We discuss value-at-risk and conditional value-at-risk and comment on the implications of using a fat-tailed framework for the reliability of risk estimates.

Physica A: Statistical Mechanics and its Applications, 2001

We analyze the performance of RiskMetrics, a widely used methodology for measuring market risk. Based on the assumption of normally distributed returns, the RiskMetrics model completely ignores the presence of fat tails in the distribution function, which is an important feature of financial data. Nevertheless, it was commonly found that RiskMetrics performs satisfactorily well, and therefore the technique has become widely used in the financial industry. We find, however, that the success of RiskMetrics is the artifact of the choice of the risk measure. First, the outstanding performance of volatility estimates is basically due to the choice of a very short (one-period ahead) forecasting horizon. Second, the satisfactory performance in obtaining Value-at-Risk by simply multiplying volatility with a constant factor is mainly due to the choice of the particular significance level.

2019

Analysing the world banking sector, we realize that traditional risk measurement methodologies no longer reflect the actual scenario with uncertainty and leave out events that can change the dynamics of markets. Considering this, regulators and financial institutions began to search more realistic models. The aim is to include external influences and interdependencies between agents, to describe and measure the operationalization of these complex systems and their risks in a more coherent and credible way. Within this context, X-Events are more frequent than assumed and, with uncertainties and constant changes, the concept of antifragility starts to gain great prominence in comparison to others methodologies of risk management. It is very useful to analyse whether a system succumbs (fragile), resists (robust) or gets benefits (antifragile) from disorder and stress. Thus, this work proposes the creation of the Banking Antifragility Index (BAI), which is based on the calculation of a ...

Journal of Financial Econometrics, 2022

for their excellent discussions of our article, and for pointing out the possibility of extending our work in several research directions. The constructive discussions have raised some common issues (such as the Gaussianity assumption, and large cross-sections), which we opt to address first in the rejoinder, before providing our thoughts on the remaining comments. Overall, we concur with the thoughtful comments by our discussants, while we provide additional interpretations in this rejoinder.

Economic Modelling, 2015

Variance and downside risk are different proxies of risk in portfolio management. This study tests mean-variance and downside risk frameworks in relation to portfolio management. The sample is a highly volatile market; Karachi Stock Exchange, Pakistan. Factors affecting portfolio optimization like appropriate portfolio size, portfolio sorting procedure, butterfly effect on the choice of appropriate algorithms and endogeneity problem are discussed and solutions to them are incorporated to make the study robust. Results show that downside risk framework performs better than Markowitz mean-variance framework. Moreover, this difference is significant when the asset returns are more skewed. Results suggest the use of downside risk in place of variance as a measure of risk for investment decisions.