On the Necessity of Five Risk Measures

The banking systems that deal with risk management depend on underlying risk measures. Following the Basel II accord, there are two separate methods by which banks may determine their capital requirement. The Value at Risk measure plays an important role in computing the capital for both approaches. In this paper we analyze the errors produced by using this measure. We discuss other measures, demonstrating their strengths and shortcomings. We give examples, showing the need for the information from multiple risk measures in order to determine a bank's loss distribution. We conclude by suggesting a regulatory requirement of multiple risk measures being reported by banks, giving specific recommendations.Comment: 23 pages, 9 figure

Forecasting chaotic systems: The role of local Lyapunov exponents.

We propose a novel methodology for forecasting chaotic systems which is based on the nearest-neighbor predictor and improves upon it by incorporating local Lyapunov exponents to correct for its inevitable bias. Using simulated data, we show that gains in prediction accuracy can be substantial. The general intuition behind the proposed method can readily be applied to other non-parametric predictors.

Local Lyapunov exponents: Zero plays no role in Forecasting chaotic systems

We propose a novel methodology for forecasting chaotic systems which uses information on local Lyapunov exponents (LLEs) to improve upon existing predictors by correcting for their inevitable bias. Using simulated data on the nearest-neighbor predictor, we show that accuracy gains can be substantial and that the candidate selection problem identified in Guégan and Leroux (2009) can be solved irrespective of the value of LLEs. An important corollary follows: the focal value of zero, which traditionally distinguishes order from chaos, plays no role whatsoever when forecasting deterministic systems.Chaos theory, Lyapunov exponent, Lorenz attractor Rössler attractor, Monte Carlo Simulations.

Further evidence on the impact of economic news on interest rates

US interest rates’ overnight reaction to macroeconomic announcements is of tremendous importance when trading fixed income securities. Most of the empirical studies achieved so far either assumed that the interest rates’ reaction to announcements is linear or independent to the state of the economy. We investigate the shape of the term structure reaction of the swap rates to announcements using several linear and non-linear time series models. The empirical results yield several not-so-well-known stylized facts about the bond market. First, and although we used a daily dataset, we find that the introduction of non linear models leads to the finding of a significant number of macroeconomic figures that actually produce an effect over the yield curve. Most of the studies using daily datasets did not corroborate so far this conclusion. Second, we find that the term structure response to announcements can be much more complicated that what is generally found: we noticed at least four types of patterns in the term structure reaction of interest rates across maturities, including the hump-shaped one that is generally considered. Third, by comparing the shapes of the rates’ term structure reaction to announcements with the first four factors obtained when performing a principal component analysis of the daily changes in the swap rates, we propose a first interpretation and classification of these different shapes. Fourth we find that the existence of some outliers in the one-day changes in interest rates usually leads to a strong underestimation of the reaction of interest rates to announcements, explaining the different results obtained between high-frequency and daily datasets: the first type of study seems to lead to the finding of fewer market mover announcements.Macroeconomic Announcements; Interest Rates Dynamic; Outliers; Reaction Function; Principal Component Analysis

Portfolio Symmetry and Momentum

This paper presents a theoretical framework to model the evolution of a portfolio whose weights vary over time. Such a portfolio is called a dynamic portfolio. In a first step, considering a given investment policy, we define the set of the investable portfolios. Then, considering portfolio vicinity in terms of turnover, we represent the investment policy as a graph. It permits us to model the evolution of a dynamic portfolio as a stochastic process in the set of the investable portfolios. Our first model for the evolution of a dynamic portfolio is a random walk on the graph corresponding to the investment policy chosen. Next, using graph theory and quantum probability, we compute the probabilities for a dynamic portfolio to be in the different regions of the graph. The resulting distribution is called spectral distribution. It depends on the geometrical properties of the graph and thus in those of the investment policy. The framework is next applied to an investment policy similar to the Jeegadeesh and Titman's momentum strategy. We define the optimal dynamic portfolio as the sequence of portfolios, from the set of the investable portfolios, which gives the best returns over a respective sequence of time periods. Under the assumption that the optimal dynamic portfolio follows a random walk, we can compute its spectral distribution. We found then that the strategy symmetry is a source of momentum.Graph Theory, Momentum, Dynamic Portfolio, Quantum Probability, Spectral Analysis

Predicting Chaos with Lyapunov Exponents: Zero Plays no Role in Forecasting Chaotic Systems

We propose a nouvel methodology for forecasting chaotic systems which uses information on local Lyapunov exponents (LLEs) to improve upon existing predictors by correcting for their inevitable bias. Using simulations of the Rössler, Lorenz and Chua attractors, we find that accuracy gains can be substantial. Also, we show that the candidate selection problem identified in Guégan and Leroux (2009a,b) can be solved irrespective of the value of LLEs. An important corrolary follows : the focal value of zero, which traditionally distinguishes order from chaos, plays no role whatsoever when forecasting deterministic systems

Multivariate radial symmetry of copula functions: finite sample comparison in the i.i.d case

Abstract Given a d-dimensional random vector X = (X 1, . . ., X d ), if the standard uniform vector U obtained by the component-wise probability integral transform (PIT) of X has the same distribution of its point reflection through the center of the unit hypercube, then X is said to have copula radial symmetry. We generalize to higher dimensions the bivariate test introduced in [11], using three different possibilities for estimating copula derivatives under the null. In a comprehensive simulation study, we assess the finite-sample properties of the resulting tests, comparing them with the finite-sample performance of the multivariate competitors introduced in [17] and [1]

Detection of the industrial business cycle using SETAR models

In this paper, we consider a threshold time series model in order to take into account certain stylized facts of the industrial business cycle, such as asymmetries in the phases of the cycle. Our aim is to point out some thresholds under (over) which a signal of turning point could be given. First, we introduce the various threshold models and we discuss both their statistical theoretical and empirical properties. Especially, we review the classical techniques to estimate the number of regimes, the threshold, the delay and the parameters of the model. Then, we apply these models to the Euro-zone industrial production index to detect, through a dynamic simulation approach, the dates of peaks and troughs in the business cycle

Further evidence on the impact of economic news on interest rates

US interest rates’ overnight reaction to macroeconomic announcements is of tremendous importance when trading fixed income securities. Most of the empirical studies achieved so far either assumed that the interest rates’ reaction to announcements is linear or independent to the state of the economy. We investigate the shape of the term structure reaction of the swap rates to announcements using several linear and non-linear time series models. The empirical results yield several not-so-well-known stylized facts about the bond market. First, and although we used a daily dataset, we find that the introduction of non linear models leads to the finding of a significant number of macroeconomic figures that actually produce an effect over the yield curve. Most of the studies using daily datasets did not corroborate so far this conclusion. Second, we find that the term structure response to announcements can be much more complicated that what is generally found: we noticed at least four types of patterns in the term structure reaction of interest rates across maturities, including the hump-shaped one that is generally considered. Third, by comparing the shapes of the rates’ term structure reaction to announcements with the first four factors obtained when performing a principal component analysis of the daily changes in the swap rates, we propose a first interpretation and classification of these different shapes. Fourth we find that the existence of some outliers in the one-day changes in interest rates usually leads to a strong underestimation of the reaction of interest rates to announcements, explaining the different results obtained between high-frequency and daily datasets: the first type of study seems to lead to the finding of fewer market mover announcements

An econometric specification of monetary policy dark art

The classical Taylor rules usually do not yield the same estimation error when working in a monthly or a quarterly framework. This brings us to the conclusion that there must be something that monthly Taylor rules can capture and that the quarterly one cannot: we postulate that it simply boils down to the fact that the target rate's changes are irregularly spaced in time. So as to tackle this issue, we propose to split the target rate chronicle between changes in the target and the associated durations, that is the time spending between two changes in the target rate. In this framework, we propose to consider that changes in rate can be regarded as a real monetary policy decision, whereas the duration period between two changes can be related to a "wait and see" position or some fine tuning problematic. To show that both these features of monetary policy do not react to the same fundamentals, we propose an econometric understanding of the Fed's reaction function using a new model derived from financial econometrics that has been proposed by Engle and Russell (2005). We propose to model the changes in target rates with a classical ordered probit and the durations with an autoregressive conditional duration model. We extracted the Fed anticipations regarding inflation and activity using some factor based method, and used these factors as explanatory variables for the changes in rates and the related durations. We show that the target rate level, the scale of the change in target rate and the associated duration do not necessarily react to the same factors and if they do, the impact can be different. This empirical result supports the idea that durations and scale of the change in target rate deserve equal attention when modeling a Central Bank reaction function