A new theory of forecasting

This paper argues that forecast estimators should minimise the loss function in a statistical, rather than deterministic, way. We introduce two new elements into the classical econometric analysis: a subjective guess on the variable to be forecasted and a probability reflecting the confidence associated to it. We then propose a new forecast estimator based on a test of whether the first derivatives of the loss function evaluated at the subjective guess are statistically different from zero. We show that the classical estimator is a special case of this new estimator, and that in general the two estimators are asymptotically equivalent. We illustrate the implications of this new theory with a simple simulation, an application to GDP forecast and an example of mean-variance portfolio selection. JEL Classification: C13, C53, G11asset allocation, Decision under uncertainty, estimation, overfitting

CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles

Value at Risk has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. Despite its conceptual simplicity, its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions. Interpreting Value at Risk as a quantile of future portfolio values conditional on current information, we propose a new approach to quantile estimation that does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i.d. returns). The Conditional Value at Risk or CAViaR model moves the focus of attention from the distribution of returns directly to the behavior of the quantile. Utilizing the criterion from Regression Quantiles, and postulating a variety of dynamic updating processes we propose methods based on a Genetic Algorithm to estimate the unknown parameters of CAViaR models. We propose a Dynamic Quantile Test of model adequacy that tests the hypothesis that in each period the probability of exceeding the VaR must be independent of all the past information. Applications to simulated and real data provide empirical support to our methodology and illustrate the ability of these algorithms to adapt to new risk environments.

Market discipline, financial integration and fiscal rules: what drives spreads in the euro area government bond market?

This paper studies the determinants of interest rate spreads of euro area 10 year government bonds against the benchmark, the German bund, after the introduction of the euro. In particular, it pays attention to the question whether market discipline is advanced or obstructed by financial integration and by fiscal rules like the Stability and Growth Pact. We first argue that financial integration – by improving market efficiency – is instrumental for markets to exert their disciplinary role. Next, we discuss the relationships between market discipline and fiscal rules, arguing that these in principle may reinforce each other. Finally, we provide strong empirical evidence that spreads depend on the ratings of the underlying bond and to a large extent are driven by the level of short-term interest rates. JEL Classification: G12, G18, C23Bond spreads, Credit risk, liquidity risk

Finance and diversification

We study how financial market efficiency affects a measure of diversification of output across industrial sectors borrowed from the portfolio allocation literature. Using data on sector-level value added for a wide cross section of countries and for various levels of disaggregation, we construct a benchmark measure of diversification as the set of allocations of aggregate output across industrial sectors which minimize the economy’s long-term volatility for a given level of long-term growth. We find that financial markets increase substantially the speed with which the observed sectoral allocation of output converges towards the optimally diversified benchmark. Convergence to the optimal shares of aggregate output is relatively faster for sectors that have a higher "natural" long-term risk-adjusted growth and which exhibit higher information frictions. Our results are robust to using various proxies for financial development, to accounting for the endogeneity of finance, and to controlling for investor’s protection, contract enforcement, and barriers to entry. Crucially, the observed patterns disappear when we employ "naive" measures of diversification based on the equal spreading of output across sectors. JEL Classification: E32, E44, G11, O16diversification, Financial Development, Growth, Mean-variance efficiency, Volatility

The central bank as a risk manager: quantifying and forecasting inflation risks

In deciding the monetary policy stance, central bankers need to evaluate carefully the risks the current economic situation poses to price stability. We propose to regard the central banker as a risk manager who aims to contain inflation within pre-specified bounds. We develop formal tools of risk management that may be used to quantify and forecast the risks of failing to attain that objective. We illustrate the use of these risk measures in practice. First, we show how to construct genuine real time forecasts of year-on-year risks that may be used in policy-making. We demonstrate the usefulness of these risk forecasts in understanding the Fed's decision to tighten monetary policy in 1984, 1988, and 1994. Second, we forecast the risks of worldwide deflation for horizons of up to two years. Although recently fears of worldwide deflation have increased, we find that, as of September 2002, with the exception of Japan there is no evidence of substantial deflation risks. We also put the estimates of deflation risk for the United States, Germany and Japan into historical perspective. We find that only for Japan there is evidence of deflation risks that are unusually high by historical standards. JEL Classification: E31, E37, E52, E58, C22deflation, forecast, inflation, monetary policy, risk

Value at risk models in finance

The main objective of this paper is to survey and evaluate the performance of the most popular univariate VaR methodologies, paying particular attention to their underlying assumptions and to their logical flaws. In the process, we show that the Historical Simulation method and its variants can be considered as special cases of the CAViaR framework developed by Engle and Manganelli (1999). We also provide two original methodological contributions. The first one introduces the extreme value theory into the CAViaR model. The second one concerns the estimation of the expected shortfall (the expected loss, given that the return exceeded the VaR) using a regression technique. The performance of the models surveyed in the paper is evaluated using a Monte Carlo simulation. We generate data using GARCH processes with different distributions and compare the estimated quantiles to the true ones. The results show that CAViaR models perform best with heavy-tailed DGP. JEL Classification: C22, G22CAViaR, extreme value theory, Value at Risk

CAViaR: Conditional Value at Risk by Quantile Regression

Value at Risk has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. Despite its conceptual simplicity, its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions. Interpreting Value at Risk as a quantile of future portfolio values conditional on current information, we propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i.d. returns). The Conditional Value at Risk or CAViaR model moves the focus of attention from the distribution of returns directly to the behavior of the quantile. We postulate a variety of dynamic processes for updating the quantile and use regression quantile estimation to determine the parameters of the updating process. Tests of model adequacy utilize the criterion that each period the probability of exceeding the VaR must be independent of all the past information. We use a differential evolutionary genetic algorithm to optimize an objective function which is non-differentiable and hence cannot be optimized using traditional algorithms. Applications to simulated and real data provide empirical support to our methodology and illustrate the ability of these algorithms to adapt to new risk environments.

Modeling of strain-induced Pockels effect in Silicon

We propose a theoretical model to describe the strain-induced linear electro-optic (Pockels) effect in centro-symmetric crystals. The general formulation is presented and the specific case of the strained silicon is investigated in detail because of its attractive properties for integrated optics. The outcome of this analysis is a linear relation between the second order susceptibility tensor and the strain gradient tensor, depending generically on fifteen coefficients. The proposed model greatly simplifies the description of the electro-optic effect in strained silicon waveguides, providing a powerful and effective tool for design and optimization of optical devices.Comment: typos corrected in eq. 29 with respect to the published versio

Sensitivity analysis of volatility: a new tool for risk management

The extension of GARCH models to the multivariate setting has been fraught with difficulties. In this paper, we suggest to work with univariate portfolio GARCH models. We show how the multivariate dimension of the portfolio allocation problem may be recovered from the univariate approach. The main tool we use is the "variance sensitivity analysis", which measures the change in the portfolio variance as a consequence of an infinitesimal change in the portfolio allocation. We derive the sensitivity of the univariate portfolio GARCH variance to the portfolio weights, by analytically computing the derivatives of the estimated GARCH variance with respect to these weights. We suggest a new and simple method to estimate full variance-covariance matrices of portfolio assets. An application to real data portfolios shows how to implement our methodology and compares its performance against that of selected popular alternatives. JEL Classification: C32, C53, G15Dynamic Correlations, GARCH, risk management, Sensitivity Analysis