Optimal futures hedging for energy commodities: An application of the GAS model

This paper applies generalized autoregressive score-driven (GAS) models to futures hedging of crude oil and natural gas. For both commodities, the GAS framework captures the marginal distributions of spot and futures returns and corresponding dynamic copula correlations. We compare within-sample and out-of-sample hedging effectiveness of GAS models against constant ordinary least square (OLS) strategy and time-varying copula-based GARCH models in terms of volatility reduction and Value at Risk reduction. We show that the constant OLS hedge ratio is not inherently inferior to the time-varying alternatives. Nonetheless, GAS models tend to exhibit better hedging effectiveness than other strategies, particularly for natural gas.     

A Portfolio Index GARCH model

This paper develops the structure of a parsimonious Portfolio Index (PI) GARCH model. Unlike the conventional approach to Portfolio Index returns, which employs the univariate ARCH class, the PI-GARCH approach incorporates the effects on individual assets, leading to a better understanding of portfolio risk management, and achieves greater accuracy in forecasting Value-at-Risk (VaR) thresholds. For various asymmetric GARCH models, a Portfolio Index Composite News Impact Surface (PI-CNIS) is developed to measure the effects of news on the conditional variances. The paper also investigates the finite sample properties of the PI-GARCH model. The empirical example shows that the asymmetric PI-GARCH-t model outperforms the GJR-t model and the filtered historical simulation with a t distribution in forecasting VaR thresholds.     

The emperor's new clothes: a critique of the multivariate t regression model

Zellner (1976) proposed a regression model in which the data vector (or the error vector) is represented as a realization from the multivariate Student t distribution. This model has attracted considerable attention because it seems to broaden the usual Gaussian assumption to allow for heavier-tailed error distributions. A number of results in the literature indicate that the standard inference procedures for the Gaussian model remain appropriate under the broader distributional assumption, leading to claims of robustness of the standard methods. We show that, although mathematically the two models are different, for purposes of statistical inference they are indistinguishable. The empirical implications of the multivariate t model are precisely the same as those of the Gaussian model. Hence the suggestion of a broader distributional representation of the data is spurious, and the claims of robustness are misleading. These conclusions are reached from both frequentist and Bayesian perspectives.     

Simple Stepwise Tests of Hypotheses and Multiple Comparisons

Holm's (1979) step-down and Hochberg's (1988) step-up procedures for tests of multiple hypotheses are simple to apply and are widely used. Holm's procedure controls the familywise error rate (FWE), while Hochberg's is more powerful. This paper investigates a step-down procedure (labelled CS) of Seneta & Chen (1997) which is a sharpening of Holm's, takes into account the degree of association between test statistics, and also controls the FWE. Computation for the CS procedure may be minimized by using the procedure as an adjustment to Holm's. The computational steps are detailed, and the adjustment is then illustrated by an application to a text-book example of multiple comparisons, in which step-wise procedures are shown to perform better than the usual Tukey T -comparison. Simulation investigations in a standard comparison with a control setting show that the CS step–down procedure is more powerful than Hochberg's step-up procedure and the procedure of Simes (1986), especially in regard to error rate, and not much less powerful than an optimal, but very specific, step-up procedure of Dunnett & Tamhane (1992).     

Quick consistency of quasi-maximum likelihood estimators in a multivariate poisson process

Recent results by the present author on quick consistency of quasi-maximum likelihood estimators of parameters in a multivariate Poisson process are strengthened at the cost of replacing the inverse continuity assumption with the strong uniform identifiability condition.     

A multivariate test of the covariance-co-skewness restriction for the three moment CAPM

This paper re-examines the importance of co-skewness in asset pricing using the multivariate testing procedure proposed by Gibbons (1982). This new approach allows for the testing of a share restriction derived from the Kraus and Litzenberger (1976) model which has been ignored in previous empirical studies. The results indicate that co-skewness is statistically significant in pricing risky assets and that the covariance risk is much more important in explaining the risk-return relationship than the co-skewness risk. However, the results also indicate that the Kraus and Litzenberger model does not adequately describe expected returns.     

An empirically derived taxonomy of retailer pricing and promotion strategies

Most research categorizes grocery retailers as following either an Every Day Low pricing (EDLP) or a High Low (Hi-Lo) pricing strategy at a store or chain level, whereas this paper studies retailer pricing and promotions at a brand-store level. It empirically examines 1,364 brand-store combinations from 17 chains, 212 stores and six categories of consumer package goods in five U.S. markets. Retailer pricing and promotion strategies are found to be based on combinations of four underlying dimensions: relative price, price variation, deal intensity and deal support. At the brand-store level, retailers practice five pricing strategies, labeled Exclusive, Moderately Promotional, Hi-Lo, EDLP, and Aggressive pricing. Surprisingly, the most prevalent pricing strategy is not Hi-Lo pricing strategy as is widely believed. It is one characterized by average relative brand price, low price variation, medium deal intensity, and medium deal support. The findings provide some initial benchmarks and suggest that retailers should closely monitor their competitors’ price decisions at the brand level.     

An inverted U‐shaped crude oil price return‐implied volatility relationship

We examined the return–volatility relationship for USO ETF oil price return and CBOE Crude Oil ETF Volatility Index, OVX. The data for the USO and OVX covers the period covering May 11, 2007 to February 28, 2013. Our OLS regression results suggest evidence of regular feedback and leverage effects. When we employ linear quantile regression techniques, we find evidence of regular and inverse feedback effects. The inverse feedback effects being noticeable in the upper quantile region of the oil return distribution. There is also support for a regular leverage effect in USO prices. We also examined the return–volatility relationship using quantile regression copula methods for measuring the degree of asymmetry in the relationships between the oil price return and implied volatility. The results of the analysis indicate, first, that there exists a negative relationship between contemporaneous oil VIX and USO ETF oil returns. Second, that the relationship between oil returns and implied volatilities depends on the quartile at which the relationship is being investigated. Third, there exists an inverted U-shaped dependency relationship between returns and implied volatilities across quantiles. Fourth, though an inverted U-shape exists, the shape is different from those observed in stock markets.     

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.     

Multivariate distributions characterized by a relationship between mean residual life and hazard rate

In this paper, we characterize some multivariate distributions based on a relationship between the multivariate hazard rate, as defined by Johnson and Kotz (1975) and Marshall (1975), and the multivariate mean residual life as defined by Arnold and Zahedi (1988). The results are extensions of the results obtained earlier by Roy (1989, 1990) and Ma (1996, 1997). Received July 1997