Non-linear dependence and conditional heteroscedasticity in stock returns evidence from the norwegian thinly traded equity market

Abstract

The paper investigates the presence of non-linear dependencies in stock returns for the Norwegian equity market as it is very difficult to interpret the unconditional distribution of stock returns and its economic implications if the i.i.d. assumption is violated. Standard tests of non-linear dependence give strong evidence for the presence of non-linearity in raw returns. Modelling non-linear dependence must distinguish between models that are non-linear in mean and hence depart from the Martingale hypothesis, and models that are non-linear in variance and hence depart from independence but not from the Martingale hypothesis. Therefore, three non-linear models of asset returns are formulated applying ARMA-GARCH specifications for the conditional mean and variance equations. The paper goes on to answer which model has the necessary characteristics that are sufficient to account for most of the non-linear dependence. In the Norwegian equity market most of the non-linear dependence seems to be conditional heteroscedasticity. However, the most thinly traded assets still report significant non-linear dependence for all non-linear specifications. These results imply that the independence hypothesis can be rejected for all assets, portfolios and indices. Moreover, for thinly traded assets the Martingale hypothesis can also be rejected. The economic implications from the unconditional distributions of thinly traded assets are therefore very difficult to interpret and are unfamiliar territory for those who are accustomed to thinking analytically, intuitively and linearly.     

Selecting copulas for risk management

Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper, we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student’s t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student’s t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.     

Interest rate parity tests: Switzerland and some major western countries

This article reviews briefly the interest rate parity (IP) theory and possible divergences between covered interest rates on two assets denominated in different currencies. From direct IP tests involving pairs of assets denominated in Sfr., $, £ and DM, using monthly data on 3-month Treasury Bills and on 3-month Euro-deposits, it appears that the theory holds better for Euro-currency pairs of assets than for domestic pairs. Further investigation uncovers significant occurence of autocorrelation for domestic pairs, possibly indicating left-out explanatory factors in the standard IP formulation, and points to the non-normality of the distrbution of arbitrage margins, thus casting doubts on most statistical results in such tests.     

International exchange risk and asset substitutability

This paper estimates subsitutability/complementarity relations among financial assets denominated in foreign currencies. Utilizing a representative investor and a flexible functional form methodology, a mean-variance utility function was estimated and used to determine expected return and variance elasticities between assets in the world portfolio. The hypothesis that international assets are perfect substitutes was rejected. It was also found that relative changes in variance tended to have a bigger impact on asset demand than did relative changes in expected returns. Substituability/complementarity relationships were not strong except in specific cases where strong relationships were expected a priori.     

Insider trading,growth opportunities and the market reaction to new financing announcements*

Abstract

This paper explores the profitability of momentum strategies, by investigating if a momentum strategy is superior to a benchmark model once the effects of data-snooping have been accounted for. Two data sets are considered. The first set of data consists of US stocks and the second one consists of Swedish stocks. For the US data strong evidence is found of a momentum effect and hence the hypothesis of weak market efficiency is rejected. Splitting the sample in two parts, it is found that the overall significance is driven by events in the earlier part of the sample. The results for the Swedish data indicate that momentum strategies based on individual stocks generate significant profits. A very weak or no momentum effect can be found when stocks are sorted into portfolios. Finally, and perhaps most importantly, results show that data-snooping bias can be very substantial. Neglecting the problem would lead to very different conclusions.     

Cointegration analysis of the intensity of the ERM currencies under the European Monetary System

This paper examines the (long-run) intra-zonal elasticities between the spot exchange rates of the deutschemark and other major ERM currencies (French franc, Belgian franc, Dutch guilder, Danish krone, Italian lira and British pound) under the EMS. The findings show that under the fixed-but-adjustable rate system, the hypothesis of no cointegration can be rejected for all chosen ERM currency pairs and unit restriction on zonal elasticities can be accepted for almost all cointegrated currency pairs. On the other hand, under the fixed-rate system, Danish krone, Italian lira and British pound fail the cointegration test and the zonal elasticities for all cointegrated currency pairs are rejected to be unity. The study signifies less intense linkages of the ERM currencies without parity realignments. Finally, the deutschmark took the role of error-correcting process for one cointegrated currency pair under the fixed-but-adjustable-rate system, and it performed the same role for two pairs under the fixed-rate system. Hence, deutschmark should not be assumed a priori statistically exogenous under the EMS     

Modeling the contemporaneous duration dependence for high-frequency stock prices

This paper proposes a novel copula approach to model the contemporaneous duration dependence for high-frequency (HF) stock prices via the bivariate hazard function. This method is useful in understanding the mechanism through which the prices of financial assets jointly adjust to reflect new information. In the empirical analysis, we use the HF data on the APPLE and IBM stocks to illustrate the feasibility of our approach. In brief, the main findings are as follows: (1) there is a strong evidence of contemporaneous duration dependence between the prices of these stocks and (2) as a result the estimators of the bivariate hazard function are sensitive to the choice of copulas under our study.     

Can analysts predict rallies better than crashes?

We use the copula approach to study the structure of dependence between sell-side analysts’ consensus recommendations and subsequent security returns, with a focus on asymmetric tail dependence. We match monthly vintages of I/B/E/S recommendations for the period January–December 2011 with excess security returns during six months following recommendation issue. Using a mixed Gaussian–symmetrized Joe–Clayton copula model we find evidence to suggest that analysts can identify stocks that will substantially outperform, but not underperform relative to the market, and that their predictive ability is conditional on recommendation changes.     

Modeling the dependence structures of financial assets through the Copula Quantile-on-Quantile approach

This paper considers a new approach of analyzing asset dependence by estimating how the distributions (in particular, quantiles) of assets are related. Combining the techniques of quantile regression and copula modeling, I propose the Copula Quantile-on-Quantile Regression approach to estimate the correlation that is associated with the quantiles of asset returns, which is able to uncover obscure nonlinear characteristics in asset dependence. The estimation procedure proposed here can also be used for analyzing dependence structures in other settings, such as for studying how macroeconomic covariates are nonlinearly related by looking at the relationship between their quantiles.     

Weekly Pattern of Exchange Rate Risks: Evidence from Ten Asian-Pacific Currencies

This paper examines the day-of-the-week effect on the currency returns of ten Asian-Pacific countries and differs from previous studies in that it tests directly the effect on higher moments of currency returns. Using ten-year daily data, the results first show that currency returns are non-normally distributed, particularly with very large kurtosis. The hypothesis of equal higher moments (e.g., skewness or kurtosis or both) cannot be rejected by any pair of weekdays only for the Australian dollar. For the remaining nine currencies, the same hypothesis is rejected by at least one pair of weekdays. Six currencies reject the hypothesis in all pairs of weekdays, supporting the existence of the day-of-the-week effect on higher moments. Further analysis shows that Rogalski's effect exists on the higher moments of three currencies because the day-of-the-week effect exists only in non-January months. Sub-period analysis indicates that the weekly patterns on higher moments are quite consistent across two sub-periods for all currencies except the Taiwanese dollar. This revised version was published online in August 2006 with corrections to the Cover Date.     

Copula dynamics in CDOs

Values of tranche spreads of collateralized debt obligations (CDOs) are driven by the joint default performance of the assets in the collateral pool. The dependence between the entities in the portfolio mainly depends on current economic conditions. Therefore, a correlation implied from tranches can be seen as a measure of the general situation of the credit market. We analyse the European market of standardized CDOs using tranches of the iTraxx index in the periods before and during the global financial crisis. We investigate the evolution of the correlations using different copula models: the standard Gaussian, the NIG, the double-t, and the Gumbel copula model. After calibration of these models, one obtains a time varying vector of parameters. We analyse the dynamic pattern of these coefficients. That enables us to forecast future parameters and consequently calculate Value-at-Risk measures for iTraxx Europe tranches.     

The t copula with multiple parameters of degrees of freedom: bivariate characteristics and application to risk management

The t copula is often used in risk management as it allows for modeling the tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case. To overcome this problem, the grouped t copula was proposed recently, where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter. In this paper we propose the use of a generalized grouped t copula, where each group consists of one risk factor only, so that a priori grouping is not required. The copula characteristics in the bivariate case are studied. We explain simulation and calibration procedures, including a simulation study on the finite sample properties of the maximum likelihood estimators and Kendall's tau approximation. This new copula is significantly different from the standard t copula in terms of risk measures such as tail dependence, value at risk and expected shortfall.     

Dependence structure and extreme comovements in international equity and bond markets

Common negative extreme variations in returns are prevalent in international equity markets. This has been widely documented with statistical tools such as exceedance correlation, extreme value theory, and Gaussian bivariate GARCH or regime-switching models. We point to limits of these tools to characterize extreme dependence and propose an alternative regime-switching copula model that includes one normal regime in which dependence is symmetric and a second regime characterized by asymmetric dependence. We apply this model to international equity and bond markets, to allow for inter-market movements. Empirically, we find that dependence between international assets of the same type is strong in both regimes, especially in the asymmetric one, but weak between equities and bonds, even in the same country.     

Tail-dependence in stock-return pairs

The empirical joint distribution of return pairs on stock indices displays high tail-dependence in the lower tail and low tail-dependence in the upper tail. The presence of tail-dependence is not compatible with the assumption of (conditional) joint normality. The presence of asymmetric tail-dependence is not compatible with the assumption of a joint student-t distribution. A general test for one dependence structure versus another via the profile likelihood is described and employed in a bivariate GARCH model, where the joint distribution of the disturbances is split into its marginals and its copula. The copula used in the paper is such that it allows for the existence of lower tail-dependence and for asymmetric tail-dependence, and is such that it encompasses the normal or t-copula, depending on the benchmark tested. The model is estimated using bivariate data on a set of European stock indices. We find that the assumption of normal or student-t dependence is easily rejected in favour of an asymmetrically tail-dependent distribution. Copyright © 2002 John Wiley & Sons, Ltd.     

Estimating non-linear serial and cross-interdependence between financial assets

This paper proposes an approach based on copula families to determine shape and magnitude of non-linear serial and cross-interdependence between returns and volatilities of financial assets. It is evident the predominance of the student’s t copula in returns relationships. Association in tails is generally larger than the absolute. There is a fast decrease in association along time, but even after 5 days, there is still dependence between returns. For volatilities, Joe copula predominates in estimated bivariate relationships fit. Clayton copula rotated 180° (survival), Gumbel, BB6 and BB8 copulas also fit some relationships. The magnitude of lagged associations is larger for risks than returns. Persistence in the dependences is very high, and decreases very little after the first lag. The tail dependence has larger values than the absolute in most relationships. We present a practical application of the proposed approach, based on optimal investment allocation and risk prediction.     

A multivariate jump-driven financial asset model

We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behaviour of a series of stocks or indexes and to study a multi-firm, value-based default model. Starting from an independent Brownian world, we introduce jumps and other deviations from normality, including non-Gaussian dependence. We use a stochastic time-change technique and provide the details for a Gamma change. The main feature of the model is the fact that—opposite to other, non-jointly Gaussian settings—its risk-neutral dependence can be calibrated from univariate derivative prices, providing a surprisingly good fit.     

The shifting dependence dynamics between the G7 stock markets

The growing interdependence between financial markets has attracted special attention from academic researchers and finance practitioners for the purpose of optimal portfolio design and contagion analysis. This article develops a tractable regime-switching version of the copula functions to model the intermarkets linkages during turmoil and normal periods, while taking into account structural changes. More precisely, Markov regime-switching C-vine and D-vine decompositions of the Student’s t copula are proposed and applied to returns on diversified portfolios of stocks, represented by the G7 stock market indices. The empirical results show evidence of regime shifts in the dependence structure with high contagion risk during crisis periods. Moreover, both the C- and D-vines highly outperform the multivariate Student’s t copula, which suggests that the shock transmission path is as important as the dependence itself, and is better detected with a vine copula decomposition.     

The Euro and European financial market dependence

A time-varying copula model is used to investigate the impact of the introduction of the Euro on the dependence between 17 European stock markets during the period 1994–2003. The model is implemented with a GJR-GARCH-MA-t model for the marginal distributions and the Gaussian copula for the joint distribution, which allows capturing time-varying, non-linear relationships. The results show that, within the Euro area, market dependence increased after the introduction of the common currency only for large equity markets, such as in France, Germany, Italy, the Netherlands and Spain. Structural break tests indicate that the increase in financial market dependence started around the beginning of 1998 when Euro membership was determined and the relevant information was announced. The UK and Sweden, but not other European countries outside the Euro area, are found to exhibit an increase in equity market co-movement, which is consistent with the interpretation that these countries may be expected to join the Euro in the future.     

Score-driven copula models for portfolios of two risky assets

ABSTRACT

The precise measurement of the association between asset returns is important for financial investors and risk managers. In this paper, we focus on a recent class of association models: Dynamic Conditional Score (DCS) copula models. Our contributions are the following: (i) We compare the statistical performance of several DCS copulas for several portfolios. We study the Clayton, rotated Clayton, Frank, Gaussian, Gumbel, rotated Gumbel, Plackett and Student's t copulas. We find that the DCS model with the Student's t copula is the most parsimonious model. (ii) We demonstrate that the copula score function discounts extreme observations. (iii) We jointly estimate the marginal distributions and the copula, by using the Maximum Likelihood method. We use DCS models for mean, volatility and association of asset returns. (iv) We estimate robust DCS copula models, for which the probability of a zero return observation is not necessarily zero. (v) We compare different patterns of association in different regions of the distribution for different DCS copulas, by using density contour plots and Monte Carlo (MC) experiments. (vi) We undertake a portfolio performance study with the estimation and backtesting of MC Value-at-Risk for the DCS model with the Student's t copula.     

Modelling Co-movements and Tail Dependency in the International Stock Market via Copulae

This paper examines international equity market co-movements using time-varying copulae. We examine distributions from the class of Symmetric Generalized Hyperbolic (SGH) distributions for modelling univariate marginals of equity index returns. We show based on the goodness-of-fit testing that the SGH class outperforms the normal distribution, and that the Student-t assumption on marginals leads to the best performance, and thus, can be used to fit multivariate copula for the joint distribution of equity index returns. We show in our study that the Student-t copula is not only superior to the Gaussian copula, where the dependence structure relates to the multivariate normal distribution, but also outperforms some alternative mixture copula models which allow to reflect asymmetric dependencies in the tails of the distribution. The Student-t copula with Student-t marginals allows to model realistically simultaneous co-movements and to capture tail dependency in the equity index returns. From the point of view of risk management, it is a good candidate for modelling the returns arising in an international equity index portfolio where the extreme losses are known to have a tendency to occur simultaneously. We apply copulae to the estimation of the Value-at-Risk and the Expected Shortfall, and show that the Student-t copula with Student-t marginals is superior to the alternative copula models investigated, as well the Riskmetics approach.