The commodity futures contract is an agreement to deliver a specific amount of commodity at a future time . There are usually choices of deliverable grades, delivery locations and delivery dates. Hedging belongs to one of the fundamental functions of futures market. Futures can be used to help producers and buyers protect themselves from price risk arising from many factors. For instance, in crude oil commodities, price risk occurs due to disrupted oil supply as a consequence of political issues, increasing of demand in emerging markets, turnaround in energy policy from the fossil fuel to the solar and efficient energy, etc. By hedging with futures, producers and users can set the prices they will receive or pay within a fixed range. A hedger takes a short position if he/she sells futures contracts while owning the underlying commodity to be delivered; a long position if he/she purchases futures contracts.
The commonly known basis is defined as the difference between the futures and spot prices, which is mostly time-varying and mean-reverting. Due to such basis risk, a naïve hedging (equal and opposite) is unlikely to be effective. With the popularity of commodity futures, how to determine and implement the optimal hedging strategy has become an important issue in the field of risk management.
Hedging strategies have been intensively studied since the 1960s. One of the most popular approaches to hedging is to quantify risk as variance, known as minimum-variance (MV) hedging. This hedging strategy is based on Markowitz portfolio theory, resting on the result that “a weighted portfolio of two assets will have a variance lower than the weighted average variance of the two individual assets, as long as the two assets are not perfectly and positively correlated.”
MV strategy is quite well accepted, however, it ignores the expected return of the hedged portfolio and the risk preference of investors. Other hedging models with different objective functions have been studied intensively in hedging literature. Due to the conceptual simplicity, the value at risk (VaR) and conditional value at risk (C)VaR have been adopted as the hedging risk objective function.
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Table of Contents
1 Introduction
2 Hedging Strategies
2.1 Risk Measures
2.1.1 Standard Deviation and Its Variance
2.1.2 VaR and CVaR
2.2 Optimization of Hedging Objective Functions
2.2.1 Minimum Variance Hedge
2.2.2 Minimum (C)VaR Hedge
3 Modeling Conditional Return Distribution
3.1 Relationship between Futures and Spot Prices
3.2 GARCH Models
3.2.1 GARCH (1,1)
3.2.2 Elliptical Distribution
3.2.3 Multivariate GARCH
3.3 Regime Switching Models
3.3.1 Markov Chains
3.3.2 Mixture of Distributions
3.3.3 MRS-Model
3.3.4 MRS-GARCH Model
4 Implementation
4.1 Description of the Data and Their Properties
4.1.1 Testing for Normality
4.1.2 Testing for ARCH Effects
4.1.3 Testing for Stationarity
4.1.4 Testing for Cointegration
4.2 Parameter Estimation
4.3 Estimation Results
4.4 Hedge Ratios
4.5 Hedging Effectiveness of the Hedging Strategy
5 Conclusion and Future Outlook
Research Objectives and Key Topics
This thesis aims to estimate Minimum Variance Hedge Ratios (MVHR) and Min-(C)VaR hedge ratios using diverse econometric models and to conduct a comparative analysis of their empirical performance in a portfolio setting.
- Comparison of various econometric hedging models (GARCH, MRS, OLS).
- Application of risk measures including Variance, VaR, and CVaR.
- Evaluation of hedging effectiveness using empirical crude oil data.
- Implementation of dynamic hedging strategies versus static OLS benchmarks.
- Analysis of market regimes and their impact on hedge ratios.
Excerpt from the Book
3.2.1 GARCH (1,1)
The GARCH processes are generalized ARCH processes where the squared volatility is allowed to depend on previous squared volatilities, as well as previous squared values of the process. Empirical studies show that standard GARCH models highly outperform ARCH models.49
The standard GARCH (p,q) model introduced by Bollerslev (1986,1987) is specified as:
The simplest GARCH model is the GARCH (1,1), which takes the form:
where alpha0 is weight parameter for most recent squared residual and beta1 is weight parameter for variance predicted during this period. alpha0>0, alpha1>0 and beta1>0 are to ensure positive conditional variance.50 Alexander (2001) stated that the parameter estimates alpha1 and beta1 do have impact on volatility process: “The large beta1 indicate that shocks to the conditional variance take a long time to die out, so volatility is persistent. Large error coefficient alpha1 means that volatility reacts quite intensely to market movements, and so if alpha1 is relatively high and beta1 is relatively low then volatilities tend to be more spiky.”51
For one-step-ahead, volatility forecasting from GARCH (1,1) model is shown in
Summary of Chapters
1 Introduction: Defines commodity futures, explains the need for hedging against price risk, and outlines the thesis structure and research motivation.
2 Hedging Strategies: Introduces risk measures like Variance, VaR, and CVaR and details the optimization of objective functions for hedging.
3 Modeling Conditional Return Distribution: Discusses the statistical modeling of return distributions, specifically using GARCH and Regime Switching (MRS) models.
4 Implementation: Describes the empirical dataset, performs diagnostic tests (normality, stationarity, cointegration), and presents the parameter estimation and hedging results.
5 Conclusion and Future Outlook: Summarizes the key empirical findings and provides suggestions for potential future research extensions.
Keywords
Hedging, Commodity Futures, GARCH Models, Markov Regime Switching, Value at Risk, Conditional Value at Risk, Minimum Variance Hedge, Cointegration, Volatility, Risk Management, Crude Oil, Econometrics, Portfolio Optimization, Hedge Ratio, Hedging Effectiveness.
Frequently Asked Questions
What is the primary objective of this thesis?
The thesis aims to estimate and compare the empirical performance of Minimum Variance and Min-(C)VaR hedge ratios using several econometric models.
Which financial instruments are analyzed?
The study specifically focuses on crude oil spot and futures prices.
What research methodology is applied?
The author employs various econometric frameworks, including GARCH extensions (BEKK, CCC) and Markov Regime Switching (MRS) models, alongside a grid search method for hedge ratio selection.
What are the central thematic fields covered?
The research covers risk measures, hedging strategies, conditional return distribution modeling, and the empirical evaluation of hedging effectiveness.
What does the main part of the work entail?
The main part involves modeling the return distributions, estimating model parameters using crude oil data, and assessing the performance of different hedge ratios in an out-of-sample framework.
Which keywords best characterize this research?
Key terms include Hedging, GARCH, Markov Regime Switching, VaR, CVaR, Cointegration, and Volatility.
How is the path-dependency problem in MRS-GARCH models addressed?
The author discusses solving the path-dependency problem by employing a "recombining method" that collapses the conditional variances in each regime as suggested in the literature.
What did the empirical analysis regarding the static OLS model reveal?
The analysis showed that dynamic hedging models, while statistically sophisticated, did not significantly improve variance or VaR reduction compared to the static OLS model in the chosen dataset.
What is the significance of the HE/h* index mentioned?
This index accounts for both risk reduction and hedging costs, revealing that dynamic hedging strategies can be considerably more expensive than the simpler OLS approach.
Does the student's-t distribution improve model performance?
The study incorporates both normal and student's-t distribution assumptions for GARCH models to address potential tail risk, with BEKK-GARCH under the t-distribution performing above average.
- Quote paper
- Su Dai (Author), 2013, Hedging with Commodity Futures, Munich, GRIN Verlag, https://www.grin.com/document/264571
