ریسک بازار در بازار کالا: یک رویکرد وار (ارزش در خطر)

We put forward Value-at-Risk models relevant for commodity traders who have long and short trading positions in commodity markets. In a 5-year out-of-sample study on aluminium, copper, nickel, Brent crude oil and WTI crude oil daily cash prices and cocoa nearby futures contracts, we assess the performance of the RiskMetrics, skewed Student APARCH and skewed student ARCH models. While the skewed Student APARCH model performs best in all cases, the skewed Student ARCH model delivers good results and its estimation does not require non-linear optimization procedures. As such this new model could be relatively easily integrated in a spreadsheet-like environment and used by market practitioners.

Managing and assessing risk is a key issue for financial institutions. The 1988 Basel Accord set guidelines for credit and market risk, enforcing the 8% rule or Cooke ratio. Regarding market risk, the total capital requirement for a financial institution is defined as the sum of the requirements for positions in equities, interest rates, foreign exchange and gold and commodities. This sum is a major determinant of the eligible capital of the financial institution based on the 8% rule. Because of this rather arbitrary 8% rule (which originates from credit risk) and the fact that diversification is not rewarded (computing the sum of the parts assumes a correlation of 1 across assets), the 1988 rules were much criticized by market participants and led to the introduction of the 1996 Amendment for computing market risk. This framework suggests an alternative approach as to how the market risk capital requirement should be computed, allowing the use of an internal model to compute the maximum loss over 10 trading days at a 99% confidence level. This set the stage for the so-called Value-at-Risk models, where a VaR model can be broadly defined as a quantitative tool whose goal is to assess the possible loss that can be incurred by a financial institution over a given time period and for a given portfolio of assets: ‘in the context of market risk, VaR measures the market value exposure of a financial instrument in case tomorrow is a statistically defined bad day’ (Saunders and Allen, 2002). VaR's popularity and widespread use in financial institutions stem from its easy-to-understand definition and the fact that it aggregates the likely loss of a portfolio of assets into one number expressed in percent or in a nominal amount in the chosen currency. Next to the regulatory framework, VaR models are also used to quantify the risk/return profile of active market participants such as traders or asset managers. Further general information about VaR techniques and regulation issues are available in Dowd, 1998, Jorion, 2000 and Saunders, 2000. Most studies in the VaR literature focus on the computation of the VaR for financial assets such as stocks or bonds, and they usually deal with the modelling of VaR for negative returns.1 Recent examples are the books by Dowd, 1998 and Jorion, 2000 or the papers by van den Goorbergh and Vlaar, 1999, Danielsson and de Vries, 2000, Vlaar, 2000 and Giot and Laurent, 2003. In this paper, we address the computation of the VaR for long and short trading positions in commodity markets. Quite interestingly, few papers deal with commodity markets and market risk management in this framework. Some recent work on the modelling of volatility and VaR in commodity markets include Kroner et al., 1994 and Manfredo and Leuthold, 1998. Thus, we model VaR for commodity traders having either bought the commodity (long position) or short-sold it (short position).2 In the first case, the risk comes from a drop in the price of the commodity, while the trader loses money when the price increases in the second case (because he would have to buy back the commodity at a higher price than the one he got when he sold it). Correspondingly, one focuses in the first case on the left side of the distribution of returns, and on the right side of the distribution in the second case. Note that this type of VaR modelling could be undertaken with a non-parametric model that would first model the quantile in the left tail of the distribution of returns, and then deal with the right tail. Our approach is, however, a pure parametric one, where we consider models that jointly deliver accurate VaR forecasts, i.e. both for the left and right tails of the distribution of returns. We first use the skewed Student APARCH model of Lambert and Laurent (2001) and show that this model accurately forecasts the 1-day-ahead VaRs for long and short positions in commodity markets. The empirical application focuses on aluminium, copper, nickel, Brent crude oil and WTI crude oil daily cash prices and cocoa nearby futures contracts. Because the RiskMetrics method is widely used by market practitioners, we also compute the relevant VaR measures in this framework. Not surprisingly, however, and because the distribution of returns is leptokurtic and (in some cases) skewed, the RiskMetrics method often does not deliver good results. In a second step, we introduce the skewed Student ARCH model as an alternative to both the skewed Student APARCH model and the RiskMetrics model. The skewed Student ARCH model has never been presented before and this new model combines features from the ARCH(p) model and the skewed Student density distribution. An important advantage of the skewed Student ARCH model is that its estimation does not require non-linear optimization procedures and could be routinely programmed in a ‘simple’ spreadsheet environment such as Excel. As such it is a good alternative to the RiskMetrics model (albeit more difficult to use) and it takes into account the fat tails and skewness features of the returns. The rest of the paper is organized in the following way. In Section 2 we briefly review the notion of risk management in commodity markets. Section 3 describes the data, while Section 4 presents the VaR models that are used in the empirical analysis. The empirical application for the six commodities is given in Section 5. Section 6 concludes and presents possible new research directions.

In this paper, we introduced Value-at-Risk models relevant for commodity traders who have long and short trading positions in commodity markets. Our time horizon is short-term as we focused on market risk at the 1-day time horizon. In an out-ofsample study spanning metal (aluminium, copper and nickel cash prices), energy (Brent crude oil and WTI crude oil cash prices) and agricultural commodities (cocoa nearby futures contracts), we assessed the performance of the RiskMetrics, skewed Student APARCH and skewed student ARCH models. While the skewed Student APARCH model performed best in all cases, the skewed Student ARCH model nevertheless delivered good results. An important advantage of the skewed Student ARCH model is that its estimation does not require numerical optimization procedures and could be routinely programmed in a ‘simple’ spreadsheet environment such as Excel. Several extensions of our study can be considered. The most obvious one is the ability of the models to correctly forecast out-of-sample VaR at a time horizon longer than 1 day. As mentioned in Section 2, commodity prices over the long-run are fundamentally determined by the economic cycles and availability of resources. Nevertheless, it could be interesting to assess the performance of our models in a 1-week or 1-month risk framework. Secondly, and with a very active market for commodity derivatives, implied volatility from short-term options (or options on futures) is readily available. Thus, one could look at the relevance of the additional information provided by the implied volatility and assess how it improves on the information given by the past returns in the APARCH specification, for example.22 See also Giot (2003) for a recent application to agricultural commodity markets.