Conditional Dependency of Financial Series: The Copula-GARCH Model

We develop a new methodology to measure conditional dependency between time series each driven by complicated marginal distributions. We achieve this by using copula functions that link marginal distributions, and by expressing the parameter of the copula as a function of predetermined variables. The marginal model is an autoregressive version of Hansen’s (1994) GARCH-type model with time-varying skewness and kurtosis. Here, we extend, to a dynamic setting, the research that fo-cuses on asymmetries in correlation during extreme events. We show that, for many market indices, dependency increases subsequent to large extreme realizations. Furthermore, for several index pairs, this increase is stronger after crashes. Our model has many potential applications such as VaR measurement and portfolio allocation in non-gaussian environments.International correlation; Stock indices; Skewed Student-t distribution

The Allocation of Assets Under Higher Moments

We evaluate how deviations from normality may affect the allocation of assets. A Taylor expansion of expected utility allows us to focus on certain moments and to compute numerically the optimal portfolio allocation. A decisive advantage of our approach is that it remains operational even if a large number of assets is in-volved. We obtain that for small values of the risk-aversion parameter, non-normality does not alter significantly the optimal allocation. In contrast, when the investor is strongly risk averse and restricted to invest in risky assets, we also obtain significant changes in portfolio weights.Asset allocation; Stock returns; Non-normality; Utility function

Portfolio allocation in transition economies

Designing an investment strategy in transition economies is a difficult task because stock-markets opened through time, time series are short, and there is little guidance how to obtain expected returns and covariance matrices necessary for mean-variance portfolio allocation. Also, structural breaks are likely to occur. We develop an ad-hoc investment strategy with a flavor of Bayesian learning. An observation is that often an extreme event will herald a new state of the economy. We use this observation to re-initialize learning when unlikely returns materialize. By using a Cornell benchmark, we are able to show the usefulness of our strategy for certain types of re-initializations.mean-variance allocation; portfolio choice; transition economies

Conditional Asset Allocation under Non-Normality: How Costly is the Mean-Variance Criterion?

We evaluate how departure from normality may affect the conditional allocation of wealth. The expected utility function is approximated by a forth-order Taylor expansion that allows for non-normal returns. Market returns are characterized by a joint model that captures the time dependency and the shape of the distribution. We show that under large departure from normality, the mean-variance criterion can lead to portfolio weights that differ signifficantly from those obtained using the optimal strategy accounting for non-normality. In addition, the opportunity cost for a risk-adverse investor to use the sub- optimal mean-variance criterion can be very large.Volatility; Skewness; Kurtosis; GARCH model; Multivariate skewed Student-t distribution; Stock returns; Asset allocation; Emerging markets

Conditional Volatility, Skewness, and Kurtosis : Existence and Persistence

Recent portfolio choice, asset pricing, and option valuation models highlight the importance of skewness and kurtosis. Since skewness and kurtosis are related to extreme variations, they are also important for Value-at-Risk measurements. Our framework builds on a GARCH model with a conditional generalized-t distribution for residuals. We compute the skewness and kurtosis for this model and compare the range of these moments with the maximal theoretical moments. Our model, thus allows for time-varying conditional skewness and kurtosis. We implement the model as a constrained optimization with possibly several thousand restrictions on the dynamics. A sequential quadratic programming algorithm successfully estimates all the models, on a PC, within at most 50 seconds. Estimators, obtained with logistically-constrained dynamics, have different properties. We apply this model to daily and weekly foreign exchange returns, stock returns, and interest-rate changes. This finding is consistent with findings from extreme value theory. Kurtosis exists on fewer dates and for fewer series. There is little evidence, at the weekly frequency, of time-variability of conditional higher moments. Transition matrices document that agitated stares come as a surprise and that there is a certain persistence in moments beyond volatility. For exchange-rate and stock-market data, cross-sectionally and at daily frequency, we also document co-variability of moments beyond volatility.Garch; stock indices; exchange rates; interest rates; SNOPT; VaR

Testing for a Forward-Looking Phillips Curve. Additional Evidence from European and US data

The "New Keynesian" Phillips Curve (NKPC) states that inflation has a purely forward-looking dynamics. In this paper, we test whether European and US inflation dynamics can be described by this model. For this purpose, we estimate hybrid Phillips curves, which include both backward and forward-looking components, for major European countries, the euro area, and the US. Estimation is performed using the GMM technique as well as the ML approach. We examine the sensitivity of the results to the choice of output gap or marginal cost as the driving variable, and test the stability of the obtained specifications. Our findings can be summarized as follows. First, in all countries, the NKPC has to be augmented by additional lags and leads of inflation, in contrast to the prediction of the core model. Second, the fraction of backward-looking price setters is large (in most cases, more than 50 percent), suggesting only limited differences between the US and the euro area. Finally, our preferred specification includes marginal cost in the case of the US and the UK, and output gap in the euro area.Forward-looking Phillips curve, euro area, GMM estimator, ML estimator.

ML vs GMM Estimates of Hybrid Macroeconomic Models (With an Application to the "New Phillips Curve")

Many macroeconomic models (including the NKPC - "New Keynesian" Phillips Curve) involve hybrid equations, in which some variables depend on both their lags and leads. Hybrid models have produced conflicting empirical results: GMM (respectively ML) estimation find the forward- looking component to be large (small). A rationalization for this conflict is provided, allowing for two kinds of misspecifications (omitted dynamics and measurement error): we show analytically in a simple DGP that the GMM (ML) estimator overstates (understates) the size of the forward- looking component. Monte-Carlo experiments indicate this result has some generality. We use these findings to rationalize discrepancies observed in NKPC estimates.Rational-expectation model, GMM estimator, ML estimator, Inflation, New Phillips curve.

Aggregating Phillips curves

The New Keynesian Phillips Curve is at the center of two raging empirical debates. First, how can purely forward looking pricing account for the observed persistence in aggregate inflation. Second, price-setting responds to movements in marginal costs, which should therefore be the driving force to observed inflation dynamics. This is not always the case in typical estimations. In this paper, we show how heterogeneity in pricing behavior is relevant to both questions. We detail the conditions under which imposing homogeneity results in overestimating a backward-looking component in (aggregate) inflation, and underestimating the importance of (aggregate) marginal costs for (aggregate) inflation. We provide intuition for the direction of these biases, and verify them in French data with information on prices and marginal costs at the industry level. We show that the apparent discrepancy in the estimated duration of nominal rigidities, as implied from aggregate or microeconomic data, can be fully attributable to a heterogeneity bias. JEL Classification: C10, C22, E31, E52heterogeneity, Inflation persistence, marginal costs, New Keynesian Phillips curve

Assessing GMM Estimates of the Federal Reserve Reaction Function

Estimating a forward-looking monetary policy rule by the Generalized Method of Moments (GMM) has become a popular approach since the influential paper by Clarida, Gali, and Gertler (1998). However , an abundant econometric literature underlines to the unappealing small- samples properties of GMM estimators. Focusing on the Federal Reserve reaction function, we assess GMM estimates in the context of monetary policy rules. First, we show that three usual alternative GMM estimators yield substantially different results. Then, we compare the GMM estimates with two Maximum-Likelihood (ML) estimates, obtained using a small model of the economy. We use Monte-Carlo simulations to investigate the empirical results. We find that the GMM are biased in small sample, inducing an overestimate of the inflation parameter . The two-step GMM estimates are found to be rather close to the ML estimates. By contrast, iterative and continuous-updating GMM procedures produce more biased and more dispersed estimators.Forward-looking model, monetary policy reaction function, GMM estimator , FIML estimator , small-sample properties of an estimator .

Testing for differences in the tails of stock-market returns

In this paper, we use a database consisting of daily stock-returns for 20 countries to test for similarities between the left and right tail of returns as well as for cross-sectional differences. To mitigate the issue of dependency between stock returns, we estimate the distribution of extremes over subsamples of two months. We document a good fit of the model and show that the left and right tails of returns behave very similarly. Across countries, we find that extremes are located at different levels and that their dispersion varies. On the other hand, the tail index, characterizing large extreme realizations is found to be constant worldwide. Our results are not due to a lack of power. We also discuss the results from an economic point of view.extreme value theory; generalized extreme value distribution; emerging markets