# Energy Commodities: A Review of Optimal Hedging Strategies

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Hedging the Price Risk of Energy Commodities

#### 2.1. Hedging Tools for Managing Energy Commodities’ Price Risk

#### 2.1.1. Forward Contracts

#### 2.1.2. Futures Contracts

#### 2.1.3. Option Contracts

#### 2.1.4. Swap Contracts

## 3. Building the Optimal Hedging Strategy

_{F}assets in the futures market (short futures position), ${P}_{{S}_{t}}$ and ${P}_{{F}_{t}}$ denoting the spot and futures prices at a specific time t and ${r}_{{S}_{t}}$ and ${r}_{{F}_{t}}$ the net returns for a single period from $t-1$ to $t$, then the total return of the hedged portfolio ${r}_{h}$ is estimated as follows:

#### 3.1. The Minimum-Variance Hedging Strategy

#### 3.1.1. Estimation of the Minimum-Variance hedge ratio based on the OLS methodology

#### 3.1.2. Estimation of the Minimum-Variance Hedge Ratio based on Nonlinear Multivariate Garch Models

_{t}, in order to reasonably estimate all the parameters that are specified by the model, this can be diffic ult to investigate. Secondly, the large number of required parameters, as well as the demanding computational time, critically limit the model given the difficulty to consider more than two basic factors. As a result it is limited to a bivariate model [53].

#### 3.2. Hedging via the Expected Utility Maximization Methodology

#### 3.2.1. Measuring Risk Aversion

#### 3.2.2. Optimal Hedge Ratio Estimation based on Expected Utility Theory

#### 3.3. Alternative Hedging Strategies

## 4. State of the Art—Relevant Studies Using Hedging Strategies

#### 4.1. Optimal Hedging Strategies based on the Minimum Variance Methodology

#### 4.2. Incorporating the Elements of Risk Aversion and Expected Return into the Optimal Hedging Strategy

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Hedge position and the shape of portfolio variance [48].

**Table 1.**Risk analysis data—volatility under normal and crisis market conditions and sensitivity factors (adapted from [65]).

Commodity Name | Monthly Volatility (Normal Market) (%) | Monthly Volatility (Crisis Market) (%) | Annual Volatility (Normal Market) (%) | Annual Volatility (Crisis Market) (%) | Sensitivity Factors |
---|---|---|---|---|---|

Petroleum: average crude price | 8.1 | 24.6 | 28.1 | 85.2 | 1.72 |

Gasoline | 10.4 | 25.4 | 30.4 | 87.2 | 1.88 |

Natural gas | 5.8 | 20.6 | 20.0 | 71.2 | 0.14 |

Coal | 4.0 | 13.5 | 13.9 | 46.9 | 0.26 |

Gold | 3.3 | 12.5 | 11.3 | 43.2 | 0.18 |

Silver | 5.4 | 21.6 | 18.7 | 75.0 | 0.18 |

Copper | 6.2 | 20.0 | 21.5 | 69.2 | 0.48 |

Zinc | 6.1 | 24.9 | 21.3 | 86.4 | 0.34 |

Lead | 6.3 | 23.8 | 21.9 | 82.3 | 0.15 |

Aluminum | 5.8 | 32.6 | 20.0 | 133.1 | 0.31 |

Nickel | 8.9 | 22.2 | 30.7 | 76.9 | 0.54 |

Iron ore | 4.4 | 12.9 | 15.2 | 44.7 | 0.18 |

Phosphate rock | 2.3 | 21.7 | 8.1 | 75.2 | 0.01 |

Wheat | 5.1 | 15.1 | 17.7 | 52.3 | 0.08 |

Cotton | 4.9 | 12.6 | 17.0 | 43.5 | 0.14.9 |

Sugar | 2.1 | 11.0 | 7.3 | 38.2 | −0.05 |

Maize | 5.3 | 25.2 | 18.4 | 87.2 | −0.08 |

Tobacco | 1.8 | 4.9 | 6.2 | 16.8 | 0.01 |

Coffee | 8.0 | 37.1 | 27.6 | 128.6 | 0.04 |

Tea | 7.7 | 23.6 | 26.8 | 81.8 | 0.11 |

Rubber | 6.0 | 18.1 | 20.8 | 62.7 | 0.37 |

Wool | 4.7 | 16.5 | 16.4 | 57.3 | −0.02 |

All commodities | 3.6 | 12.3 | 12.5 | 42.5 | 1.00 |

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**MDPI and ACS Style**

Halkos, G.E.; Tsirivis, A.S. Energy Commodities: A Review of Optimal Hedging Strategies. *Energies* **2019**, *12*, 3979.
https://doi.org/10.3390/en12203979

**AMA Style**

Halkos GE, Tsirivis AS. Energy Commodities: A Review of Optimal Hedging Strategies. *Energies*. 2019; 12(20):3979.
https://doi.org/10.3390/en12203979

**Chicago/Turabian Style**

Halkos, George E., and Apostolos S. Tsirivis. 2019. "Energy Commodities: A Review of Optimal Hedging Strategies" *Energies* 12, no. 20: 3979.
https://doi.org/10.3390/en12203979