Panel quantile regressions for estimating and predicting the value‐at‐risk of commodities

• DOI: http://doi.org/10.1002/fut.22017
• Date: 01 September 2019
• Published date: 01 September 2019
• Author: František Čech,Jozef Baruník

Received: 27 September 2018

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Revised: 17 April 2019

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Accepted: 18 April 2019

DOI: 10.1002/fut.22017

RESEARCH ARTICLE

Panel quantile regressions for estimating and predicting

the value‐at‐risk of commodities

František Čech

1,2

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Jozef Baruník

1,2

1

Department of Macroeconomics and

Econometrics, Institute of

Economic Studies, Charles University,

Prague, Czech Republic

2

Department of Econometrics, Institute of

Information Theory and Automation,

Academy of Sciences of the Czech

Republic, Prague, Czech Republic

Correspondence

Jozef Baruník, Institute of Economic

Studies, Charles University, Opletalova

26, 110 00 Prague, Czech Republic.

Email: barunik@utia.cas.cz

Funding information

Czech Science Foundation, Grant/Award

Number: 16‐14151S; European Unions

Horizon 2020 Research and Innovation

Staff Exchange, Grant/Award Number:

681228

Abstract

Using a flexible panel quantile regression framework, we show how the future

conditional quantiles of commodities returns depend on both ex post and ex

ante uncertainty. Empirical analysis of the most liquid commodities covering

main sectors, including energy, food, agriculture, and precious and industrial

metals, reveal several important stylized facts. We document common patterns

of the dependence between future quantile returns and ex post as well as ex

ante volatilities. We further show that the conditional returns distribution is

platykurtic. The approach can serve as a useful risk management tool for

investors interested in commodity futures contracts.

KEYWORDS

implied volatility, panel quantile regression, realized volatility, value‐at‐risk

JEL CLASSIFICATION

C14, G17, G32, Q41

1

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INTRODUCTION

Commodities play an increasingly significant role in the asset allocations of institutional investors and, with the onset of

exchange‐traded funds, have become a regular asset class. Academic debate spurred by the developments has provided

valuable insights into the economics of commodity markets, as well as several crucial aspects, such as price forecasting,

risk measurement, or hedging. One of the main challenges faced by researchers is the fact that commodities are

nonhomogeneous assets, and their risk, as well as return, may differ substantially, as each commodity is driven by

specific supply and demand forces. A traditional economist’s view on an asset price being a stream of future discounted

expected cash flows is hence not directly applicable, and pricing of commodities is instead driven by short‐term

variations in the supply. In addition, exogenous factors, such as weather conditions, inventory levels, storage costs,

production shocks, and even geopolitical events, play a crucial role, rendering risk measurement a difficult task. In this

paper, we propose a simple, robust framework that can be used to model and forecast the value‐at‐risk (VaR) of

commodities semiparametrically without the need for traditional assumptions. Empirical results support our approach,

and we uncover stylized facts useful for investors and policy‐makers.

The complex nature of commodity pricing results in risk characteristics that are different from those of financial assets

such as stocks, bond, and currencies. Returns distributions—as measured by volatility, skewness, kurtosis, and empirical

quantiles—are different from traditional asset classes; hence, we need more flexible techniques to measure risk. Many

researchers have tried to model the VaR of commodities without reaching a consensus about the appropriate model. The

three main approaches used in the literature are useful but lack the ability to handle the complexity of commodity data.

First, RiskMetrics (Longerstaey & Spencer, 1996) does not necessarily capture the correct returns distribution conditional on

the changing volatility. Second, the historical simulations used by, for example, Cabedo and Moya (2003) have the opposite

J Futures Markets. 2019;39:1167–1189. wileyonlinelibrary.com/journal/fut © 2019 Wiley Periodicals, Inc.

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problem: They capture the empirical returns distribution but do not make it conditional on volatility. Third, more advanced

parametric models mostly built within the family of generalized autoregressive conditional heteroskedasticity (GARCH)

models improve fits (Aloui & Mabrouk, 2010; Chiu, Chuang, & Lai, 2010; Giot & Laurent, 2004; Hung, Lee, & Liu, 2008; Lux,

Segnon, & Gupta, 2016; Youssef, Belkacem, & Mokni, 2015); however, they require fat‐tailed distributions, long memory,

and other features that lead to heavy parameterization, making the approach less tractable.

Since the seminal work of Koenker and Bassett (1978), quantile regression models have been increasingly used in

many disciplines. Notable contributions in finance include that by Engle and Manganelli (2004), who were among the

first to use quantile regression and develop the conditional autoregressive VaR (CAViaR) model. Important for our

work, Žikešand Baruník (2016) show that various realized and implied volatility measures are useful in forecasting

quantiles of future returns without making assumptions about the underlying conditional distributions. The resulting

semiparametric model well captures conditional quantiles of financial returns in a flexible framework. Moving the

research focus toward the multivariate framework and concentrating on interrelations between quantiles of more

assets, White, Kim, and Manganelli (2015) pioneer the extension. A different stream of multivariate quantile regression‐

based literature concentrates on the analysis using factors (Ando & Bai, 2017; Chen, Dolado, & Gonzalo, 2016), but the

research is recent and awaits further development. Although the application of quantile regression to forecasting

quantiles of various economic variables is not new in finance, quantile regression has rarely been applied in the context

of commodities. Among the few applications, Li, Hurn, and Clements (2017) adapts quantile regression for forecasting

day‐ahead electricity load quantiles, and Reboredo and Ugolini (2016) studies the quantile dependence of oil price

movements and stock returns.

In this context, the work by Žikešand Baruník (2016) is important because it provides a link between future

quantiles of the returns distribution and its past variation. Despite the nonhomogeneous nature of commodities,

Christoffersen, Lunde, and Olesen (2019) uncover several stylized facts pointing to factor structure in volatility. Being

interested in future quantiles of commodity returns distributions, it is tempting to ask whether there is a common

structure in the quantiles of commodity returns. Inspired by our previous findings regarding financial markets (Čech &

Baruník, 2017), we hypothesize that there might be useful commonalities to be uncovered. In the quantile regression

setup, no similar study uncovers information captured in the panels of volatility series of commodity markets. Hence,

our work can possibly open new questions in modeling the VaR of commodity markets.

This paper contributes to the literature by identifying common patterns in the dependence between future quantiles

of commodity returns and ex post/ex ante volatility measures using a flexible panel quantile regression (PQR) approach.

Our simple yet robust modeling strategy utilizes all the advantages offered by PQR and commodity datasets. We

document interesting empirical regularities by controlling for otherwise‐unobserved heterogeneity among commodities.

In particular, we reveal common factors in volatility that have direct influences on the future quantiles of their returns.

Our research is important since the current literature contains little information about the potential of the uncertainty

factors in the precise identification of extreme‐tail events of the commodity returns distribution. More important, even

less is known about commonalities between more commodities in this respect. Our research attempts to contribute in

this direction.

In the first part of our empirical application, we study the behavior of energy (crude oil and natural gas), precious

metal (gold and silver), industrial metal (copper), agricultural (cotton), and food (corn) commodities during a period of

the global financial crisis. We document common effects of the ex post uncertainty measured by realized volatility on

the estimation of the VaR of commodities. We demonstrate these effects to be time‐varying; however, they do not

dramatically change when we compare the results from the nonoverlapping crisis and after‐crisis periods. In contrast to

our expectations, we document homogeneous behavior across commodities. Moreover, the conditional distribution of

the returns standardized by their realized volatility is platykurtic, in contrast to previous parametric studies, in which a

variety of GARCH models were used. To match the empirical data, GARCH models required a fat‐tailed distribution

(Charles & Darné, 2017; Cheong, 2009; Giot & Laurent, 2003; Marimoutou, Raggad, & Trabelsi, 2009) or combination

with extreme value theory (Youssef et al., 2015). Since commodities are considered to be relatively less risky compared

to financial assets (Bodie & Rosansky, 1980; Conover, Jensen, Johnson, & Mercer, 2010; Gorton & Rouwenhorst, 2006),

our findings are in line with those of Andersen, Bollerslev, Diebold, and Labys (2000), who document that returns of

financial assets standardized by their realized volatility are almost Gaussian. Our findings can be attributed to the

flexibility offered by the framework we use. Our model does not require an assumption about the distribution and

estimates the volatility nonparametrically.

In the second part, we employ option implied volatility as an ex ante measure of uncertainty and relate it to future

returns quantiles. Volatility implied by option prices reveals the market’s expectations and is often used as an ex ante

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