# Jet Fuel Price Risk and Proxy Hedging in Spot Markets: A Two-Tier Model Analysis

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Hedging

#### 2.2. Forecasting

## 3. Methodology

#### 3.1. Empirical Model 1—Fuel Hedging

_{1}) and the annual oil price changes (WTI) adjusted to U.S. consumer prices (X

_{2}) are the two independent variables. The reason for the integration of the economic growth rate into this simple regression analysis is to determine whether there is some multicollinearity that limits the effects of the energy (oil) price development on the shares of the airlines and, in turn, on the performance of the company. In addition, a simple linear regression analysis was performed for each airline if for only one independent variable a significant effect on the airline’s share performance (Y) was detected (Table 2).

_{1}= Annual world economic growth rate;

_{2}= Annual oil price development.

_{1}+ 0.253X

_{2}+ 8.833

^{2}). The F-test for the overall model is not significant at 0.120 (Table 4). This means that the hypothesis that the two independent variables have no influence on the dependent variable cannot be rejected. The p-value for the single independent variable X

_{2}is not significant (0.654), but the p-value for the economic growth rate X

_{1}is significant, which is at a confidence level of 95% (0.046) (Table 4). No collinearity can be measured between the two independent variables X

_{1}and X

_{2}.

_{1}) as the only independent variable (Table 5).

_{1}+ 9.564

^{2}) of Lufthansa’s share performance Y can be attributed to the annual world economic growth (X

_{1}). This influence is statistically significant (p-value = 0.042) (Table 5).

_{1}+ 0.177X

_{2}+ 8.546

^{2}) (Table 6). The F-test for the overall model is clearly not significant at 0.916 (Table 6); i.e., the hypothesis that the two independent variables have no influence on the dependent variable cannot be rejected. The p-value for the two individual independent variables X

_{1}and X

_{2}is not significant at a confidence level of 95% (0.679 and 0.907, respectively). No collinearity can be measured between the two independent variables X

_{1}and X

_{2}.

_{1}− 6.733X

_{2}+ 48.163

^{2}). The F-test for the overall model is not significant at 0.068 (narrow); i.e., the hypothesis that the two independent variables have no influence on the dependent variable cannot be rejected (Table 7). The p-value for the single independent variable X

_{2}is significant (0.022) at a 95% confidence level, while for the economic growth rate X

_{1}, the p-value at a 95% confidence level (0.841) is not significant. No collinearity can be measured between the two independent variables X

_{1}and X

_{2}.

_{2}is the only independent variable—was carried out.

_{2}+ 46.120

^{2}) of Air France’s share price development Y can be attributed to the annual oil price development X

_{2}. This influence is statistically significant (p-value = 0.020) (Table 8).

_{1}+ 0.004X

_{2}+ 4.978

^{2}). The F-test for the overall model is clearly not significant at 0.993; i.e., the hypothesis that the two independent variables have no influence on the dependent variable cannot be rejected (Table 9). The p-value for the two individual independent variables X

_{1}and X

_{2}is clearly not significant at a confidence level of 95% (0.915 and 0.995, respectively). No collinearity can be measured between the two independent variables X

_{1}and X

_{2}.

_{1}− 8.814X

_{2}+ 55.201

^{2}). The F-test for the overall model is significant at 0.034; i.e., the hypothesis that there is no influence of the two independent variables on the dependent variable can be rejected (Table 10). The p-value for the single independent variable X

_{2}is significant (0.015) at a 95% confidence level. And as for the economic growth rate X

_{1}, the p-value is not significant at a 95% confidence level (0.467). No collinearity can be measured between the two independent variables X

_{1}and X

_{2}.

_{2}is the only independent variable—was carried out (Table 11).

_{2}+ 60.661

^{2}) of the Delta Airlines share performance Y can be attributed to the annual oil price developments X

_{2}. This influence is statistically significant (p-value = 0.010) (Table 11).

_{1}− 9.941X

_{2}+ 64.097

^{2}). The F-test for the overall model is significant at 0.010; i.e., the hypothesis that there is no influence of the two independent variables on the dependent variable can be rejected at a 95% confidence level (Table 12). The p-value for the single independent variable X

_{2}is also very significant (0.008), and as for the economic growth rate X

_{1}, the p-value is not significant at a 95% confidence level (0.090).

_{1}and X

_{2}.

_{1}is the only independent variable—was carried out (Table 13).

_{2}+ 77.778

^{2}) of the United Airlines share performance Y can be attributed to the annual oil price developments X

_{2}. This influence is statistically significant (p-value = 0.011) (Table 13).

_{1}− 2.273X

_{2}+ 13.071

^{2}). The F-test for the overall model is not significant at 0.091 (narrow) (Table 14); i.e., the hypothesis that there is no influence of the two independent variables on the dependent variable cannot be rejected at a 95% confidence level. The p-values for the two independent variables, X

_{1}and X

_{2}, are not significant at a 95% confidence level (0.134 and 0.105, respectively).

_{1}and X

_{2}.

_{1}+ 1.446X

_{2}+ 6.074

^{2}). The F-test for the overall model is very significant at 0.000 (Table 15); i.e., the hypothesis that there is no influence of the two independent variables on the dependent variable can be rejected at a 95% confidence level. The p-value for the single independent variable X

_{2}is also very significant (0.000). And as for the economic growth rate X

_{1}, the p-value is not significant at a 95% confidence level (almost significant at 0.072).

_{1}and X

_{2}.

_{2}variable is the only independent variable (Table 16).

_{2}+ 8.366

^{2}) of the Cathay Pacific share performance Y can be attributed to the annual oil price developments X

_{2}. This influence is statistically very significant (p-value = 0.000) (Table 16).

_{1}+ 0.145X

_{2}+ 2.022

^{2}). The F-test for the overall model is significant at 0.046, which means that the hypothesis that there is no influence of the two independent variables on the dependent variable can be rejected (Table 17). The p-value for the single independent variable X

_{2}is not significant (0.610), and as for the economic growth rate X

_{1}, the p-value is significant at a 95% confidence level (0.015). No collinearity can be measured between the two independent variables X

_{1}and X

_{2}.

_{1}being the only independent variable—was carried out (Table 18).

_{1}+ 2.441

^{2}) of Finnair’s share performance Y can be attributed to the annual world GDP growth X

_{1}. This influence is statistically significant (p-value = 0.014) (Table 18).

_{1}− 0.109X

_{2}+ 2.766

^{2}). The F-test for the overall model is not significant at 0.437 (Table 19); i.e., the hypothesis that the two independent variables have no influence on the dependent variable cannot be rejected. The p-value for the single independent variable X

_{2}is not significant, and the p-value for X

_{1}is also not significant even at a confidence level of 95% (0.318 and 0.484, respectively). No collinearity can be measured between the two independent variables X

_{1}and X

_{2}.

_{1}− 5.939X

_{2}+ 63.147

^{2}). The F-test for the overall model is not significant at 0.514 (Table 20); i.e., the hypothesis that the two independent variables have no influence on the dependent variable cannot be rejected. The p-value for the two individual independent variables X

_{1}and X

_{2}is not significant at a confidence level of 95% (0.289 and 0.685, respectively). No collinearity can be measured between the two independent variables X

_{1}and X

_{2}.

_{1}+ 1.306X

_{2}+ 5.327

^{2}). The F-test for the overall model is significant at 0.011 (Table 21); i.e., the hypothesis that there is no influence of the two independent variables on the dependent variable can be rejected at a 95% confidence level. The p-value for the single independent variable X

_{2}is also significant (0.003). As for the economic growth rate X

_{1}, the p-value is not significant at a confidence level of 95% (0.581).

_{1}and X

_{2}.

_{2}is the only independent variable—was carried out (Table 22).

_{2}+ 6.153

^{2}) of the Singapore Airlines share performance Y can be attributed to annual oil price development X

_{2}. This influence is statistically very significant (p-value = 0.003) (Table 22).

_{1}+ 1.064X

_{2}+ 11.823

^{2}). The F-test for the overall model is not significant at 0.613 (Table 23); i.e., the hypothesis that the two independent variables have no influence on the dependent variable cannot be rejected. The p-value for the two individual independent variables X

_{1}and X

_{2}is not significant at a confidence level of 95% (0.972 and 0.331, respectively). No collinearity can be measured between the two independent variables X

_{1}and X

_{2}.

#### 3.1.1. Interpretation of Findings

#### 3.1.2. Testing the Hypotheses

^{2}) (Table 24).

^{2}= 0.644) (Table 24). Observing the effect of the two hedging variables on TobinsQ, which only affects the hedging for the second year (hedge2), there is a significant (95% confidence level) positive effect on TobinsQ, and the coefficient for hedge2 is 0.216 (Table 24).

^{2}, but the result should somehow be interpreted suspiciously, as hedge1 has relatively high multicollinearity (32.02). Therefore, the results should be considered invalid. Only testing for North American airlines (Southwest, Westjet, Air Canada, United Airlines, and Delta Air Lines), no significant influence of the hedging ratio on TobinsQ could be proven.

^{2}of 0.77 (Table 24).

^{2}of 0.115.

^{2}of 0.0184. Checking for low-cost as the dummy variable, the outcome for hedge2 is again highly significant with a positive coefficient of 0.366. R

^{2}of 0.748 suggests the high validity of the explanation. No significant influence of hedge1 or hedge2 on TobinsQ is found for legacy carriers, including fixed effects. Applying constantly hedged as a dummy variable for fixed-effects regression analysis, the variable hedge2 again yields a significant and positive effect on TobinsQ (coefficient = 0.363). R

^{2}has a high explanatory power at 0.8156 (Table 24).

#### 3.2. Model 2: Dynamic Capacity Forecasting

_{1}+ within the loop, it describes the inter-causal relationship of demand and frequency of approached routes. As both cause–effect relationships show a positive polarity, the closed feedback loop is characterised as reinforcing, which indicates growth. The second closed feedback loop in Figure 2 is labelled as R

_{2}+ and incorporates the cause–effect relationships of demand and airfare. Both relationships are assessed with a negative polarity. Nevertheless, the polarity of the whole loop is determined by adding the individual relationships. Therefore, in the case of R

_{2}+, the closed feedback loop is considered positive, as the addition of two negative relationships results in a positive loop, and thus, R

_{2}+ is considered a reinforcing loop. The third closed feedback loop, which is marked as B

_{1}-, considers the cause–effect relationship of the main input factors regarding capacity forecasting in Figure 2.

**H**

_{1a}.**H**

_{1b}.**H**

_{1c}._{1a}and H

_{2}are thus rejected.

#### Interpretation of Findings

_{1b}has already been considered above, as the result of the correlation analysis of the jet fuel costs p.g. and the jet fuel spot price p.g. (M) shows a strong positive correlation, along with 94% of the jet fuel costs p.g. being explained by the jet fuel spot price p.g. (M). The initial segment of hypothesis H

_{1a}has been accepted by correlation analysis. Additionally, based on the outcomes of the stock-flow diagram’s model simulation, it can be entirely accepted. With regards to hypothesis H

_{1c}, it was observed that there is no significant correlation between the jet fuel spot price p.g. (Q) and the average quarterly airfare. This is evident from the coefficient of determination, which indicates that only 47% of the average airfare’s fluctuations can be attributed to the jet fuel spot price p.g. (Q). However, the influence of fluctuations in jet fuel expenses on the mean airfare, as determined by the jet fuel spot price, was validated using the stock-flow diagram. Therefore, the reliability of considering the impact of risk on capacity forecasting is acknowledged. The absence of a notable association between the mean airfare and the spot price of jet fuel could be attributed to the limitations of the dataset employed, which exclusively encompasses quarterly average airfares within the domestic United States market. Consequently, varying outcomes concerning correlation could arise from conducting an analysis utilising an alternative dataset. However, with respect to the investigative methodology and the employed dataset, it is not possible to entirely accept hypothesis H

_{1c}.

## 4. Conclusions

#### 4.1. Limitations

#### 4.2. Practical Implications

#### 4.3. Proposals and Recommendations for Airlines

#### 4.4. Policy Recommendations for Policymakers

## Funding

## Conflicts of Interest

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**Figure 2.**Simplified Causal Feedback Loop Diagram regarding Airline Capacity Forecasting. Source: Author.

Year | Authors | Methodology | Key Findings |
---|---|---|---|

2002 | Carter, Rogers, and Simkins | Time series regression analysis | Airline stock value negatively correlated to rising jet fuel prices over time. Fuel hedging has a positive and statistically significant impact on airline business value. |

2004 | Cobbs and Wolf | Analytical model | Optimal hedging strategy for airlines using different derivatives based on price cycles. |

2006 | Morrell and Swan | Hedging may not significantly impact airline profitability or stock price in the long term. | |

2007 | Lee and Jang | Regression analysis | Firm-specific risk can be reduced through diversification and efficient cost structures. Airline size is positively linked to airline-specific systematic risk. |

2008 | Maher and Weiss | Regression analysis | Hedge score positively impacts cash flow and equity returns, especially post crisis. Fuel hedging does not fully protect airlines against adverse circumstances (e.g., 9/11). |

2012 | Cerny and Pelikan | Empirical analysis | The optimal hedge ratio can change during risk management strategy due to correlation shifts. |

2013 | Gerner and Ronns | Panel data analysis | Airlines with higher credit ratings have more hedging choices and engage in hedging during high fuel demand. |

2014 | Balu and Morad | Time series analysis | Developed a model to predict crude oil price volatility using historical data. |

2015 | Lim and Turner | Variance minimisation | The optimal hedge ratio for a portfolio can be determined by minimising variance in returns. |

2016 | Dafir and Gajjala | Literature review | Identified three types of risks in commodity trading relevant to the spot market. |

2017 | Jiang et al. | Time series analysis | Oil market recovery after shocks follows established patterns. |

2021 | Samunderu and Murahwa | Sensitivity analysis | GARCH model sensitivity in measuring risk in oil price distribution. |

Company | Beta_X1 | p-Value_X1 | Beta_X2 | p-Value_X2 | R-Squared |
---|---|---|---|---|---|

Lufthansa | 1.394 | 0.046 ** | 0.253 | 0.654 | 0.092 |

Southwest | 0.72 | 0.679 | 0.177 | 0.907 | −0.052 |

Air France | −0.653 | 0.841 | −6.733 | 0.022 ** | 0.108 |

Ryanair | −0.084 | 0.915 | 0.004 | 0.995 | −0.11 |

Delta Air Lines | 1.86 | 0.467 | −8.814 | 0.015 ** | 0.463 |

United Airlines | 4.53 | 0.09** | −9.941 | 0.008 ** | 0.56 |

Air Canada | 1.696 | 0.134 | −2.273 | 0.105 | 0.282 |

Cathay Pacific | 0.736 | 0.072 | −6.733 | 0.000 *** | 0.379 |

Finnair | 0.864 | 0.015** | 0.145 | 0.610 | 0.15 |

Qantas | 0.186 | 0.484 | −0.109 | 0.318 | −0.013 |

SAS | 15.297 | 0.289 | −5.939 | 0.685 | −0.039 |

Singapore Airlines | 0.264 | 0.581 | 1.306 | 0.003 *** | 0.209 |

WestJet | 0.038 | 0.972 | 1.064 | 0.331 | −0.058 |

Group | Airlines | Description |
---|---|---|

Group 1 | Delta Air Lines, United Airlines, Cathay Pacific, Singapore Airlines. | These airlines are significantly affected by changes in oil prices. Delta Air Lines and United Airlines experienced a negative impact, with their stock prices declining as oil prices rose. In contrast, Cathay Pacific and Singapore Airlines have a positive correlation, witnessing stock price increases with higher oil prices. |

Group 2 | Air France, Finnair. | Airlines in this group are moderately influenced by oil price changes. Air France shows a significant negative correlation between its stock performance and oil price changes. For Finnair, the relationship is less pronounced but still significant. |

Group 3 | Lufthansa, Southwest, Ryanair, Air Canada, Qantas, SAS, WestJet. | These airlines show no significant correlation between their stock performance and changes in oil prices. Additionally, their stock performance has an insignificant correlation with global economic growth. The impact of oil price changes and global economic growth on these airlines’ stock prices is relatively limited compared to those in group 1 and group 2. |

World GDP | 1.394 (0.662) ** | R^{2} | 0.092 |

Oil price | 0.253 (0.558) | F-Statistic | 2.322 |

constant | 8.833 (2.596) *** | Significance | 0.12 |

World GDP | 1.394 (0.651) ** | R^{2} | 0.121 |

Oil price | F-Statistic | 4.584 ** | |

constant | 9.564 (2.005) *** | Significance | 0.042 |

World GDP | 0.72 (0.177) | R^{2} | −0.052 |

Oil price | 0.177 (1.50) | F-Statistic | 0.089 |

constant | 8.546 (7.741) | Significance | 0.916 |

World GDP | −0.653 (3.236) | R^{2} | 0.108 |

Oil price | −6.733 (2.788) ** | F-Statistic | 2.937 ** |

constant | 48.163 (13.246) *** | Significance | 0.068 |

World GDP | R^{2} | 0.136 | |

Oil price | −6.696 (2.729) ** | F-Statistic | 6.020 ** |

constant | 46.120 (8.413) *** | Significance | 0.02 |

World GDP | −0.084 (0.735) | R^{2} | −0.11 |

Oil price | 0.004 (0.652) | F-Statistic | 0.007 |

constant | 4.978 (3.307) | Significance | 0.993 |

World GDP | 1.86 (2.438) | R^{2} | 0.463 |

Oil price | −8.814 (2.841) ** | F-Statistic | 5.313 ** |

constant | 55.201 (14.180) *** | Significance | 0.034 |

World GDP | R^{2} | 0.488 | |

Oil price | −8.979 (2.766) ** | F-Statistic | 10.534 ** |

constant | 60.661 (11.954) *** | Significance | 0.01 |

World GDP | 4.530 (2.386) ** | R^{2} | 0.56 |

Oil price | −9.941 (2.923) *** | F-Statistic | 8.004 ** |

constant | 64.097 (14.514) *** | Significance | 0.01 |

World GDP | R^{2} | 0.446 | |

Oil price | −10.724 (3.275) ** | F-Statistic | 9.838 ** |

Constant | 77.778 (14.146) *** | Significance | 0.011 |

World GDP | 1.696 (1.031) | R^{2} | 0.282 |

Oil price | −2.273 (1.263) | F-Statistic | 3.163 ** |

Constant | 13.071 (6.270) ** | Significance | 0.091 |

World GDP | 0.736 (0.394) ** | R^{2} | 0.379 |

Oil price | 1.446 0.337) *** | F-Statistic | 10.452 *** |

Constant | 6.074 (1.605) *** | Significance | 0 |

World GDP | R^{2} | 0.327 | |

Oil price | 1.401 (0.349) *** | F-Statistic | 16.086 *** |

Constant | 8.366 (1.077) *** | Significance | 0 |

World GDP | 0.864 (0.333) ** | R^{2} | 0.15 |

Oil price | 0.145 (0.280) | F-Statistic | 3.479 ** |

constant | 2.022 (1.311) | Significance | 0.046 |

World GDP | 0.861 (0.328) ** | R^{2} | 0.174 |

Oil price | F-Statistic | 6.878 ** | |

constant | 2.441 (1.017) ** | Significance | 0.014 |

World GDP | 0.186 (0.182) | R^{2} | −0.013 |

Oil price | −0.109 (0.135) | F-Statistic | 0.862 |

constant | 2.766 (0.789) *** | Significance | 0.437 |

World GDP | 15.297 (13.875) | R^{2} | −0.039 |

Oil price | −5.939 (14.341) | F-Statistic | 0.698 |

constant | 63.147 (68.542) | Significance | 0.514 |

World GDP | 0.264 (0.473) | R^{2} | 0.209 |

Oil price | 1.306 (0.406) *** | F-Statistic | 5.227 ** |

constant | 5.327 (1.937) ** | Significance | 0.011 |

World GDP | R^{2} | 0.227 | |

Oil price | 1.291 (0.401) *** | F-Statistic | 10.373 *** |

constant | 6.153 (1.235) | Significance | 0.003 |

World GDP | 0.038 (1.082) | R^{2} | −0.058 |

Oil price | 1.064 (1.061) | F-Statistic | 0.505 |

constant | 11.823 (5.269) ** | Significance | 0.613 |

All Airlines | Europe | America | Low−Cost | Legacy | Constant | Selective | |
---|---|---|---|---|---|---|---|

Model | Panel Data | Panel Data | Panel Data | Panel Data | Panel Data | Panel Data | Panel Data |

R^{2} | 0.644 | 0.803 | 0.5102 | 0.7774 | 0.7779 | 0.8222 | 0.3897 |

F-Statistik | 12.19 *** | 35.35 *** | 6.55 *** | 34.23 *** | 28.97 *** | 52.58 *** | 8.3 *** |

hedge1-lag1 | 0.0373 (−0.092) | −0.5381 (0.170) *** | 0.1225 (−0.131) | 0.0382 (−0.078) | −0.1193 (−0.075) | 0.0417 (−0.096) | 0.0449 (−0.136) |

hedge2-lag2 | 0.2168 (0.104) ** | 0.3937 (0.168) ** | 0.2057 (−0.118) ** | 0.04426 (0.098) *** | 0.1427 (−0.094) | 0.3488 (0.125) *** | 0.0036 (−0.084) |

OpMarg | 4.3491 (0.0766) ** | 6.0541 (0.701) *** | 3.9798 (1.517) ** | 5.0856 (0.541) *** | 5.1576 (0.430) *** | 1.1233 (−0.645) *** | |

Opln | −0.0001 (0.000) *** | 0.0001 (0.000) ** | 0.0000 (0.000) *** | ||||

NetIn | 0.0000 (0) ** | 0.0000 (0.000) *** | −0.0001 (0) ** | 0.0000 (0.000) *** | |||

RePa | 0.0000 (0.0000) ** | 0.0000 (0.000) *** | |||||

Fleet | 0.0001 0 | ||||||

CashRa | 0.3811 (0.110) *** | 0.3369 (0.114) *** | 0.2113 (0.098) ** | ||||

EquityRa | −0.5148 (0.118) *** | 0.4826 (0.143) *** | −0.8166 (0.096) *** | 0.3942 (0.123) *** | |||

Constant | 1.3867 (0.132) *** | 1.0236 (0.079) *** | 1.2861 (0.102) *** | 0.6945 (0.077) *** | 1.2749 (0.073) *** | 0.8271 (0.094) *** | 1.1555 (0.057) *** |

Model | Description |
---|---|

OpMarg | Operating margin of the airlines. |

OpLn | Natural logarithm of the airline’s total operating revenue. |

hedge1-lag1 | This variable is the lagged value of the hedging ratio (hedge1) from the first previous year. In econometrics, lagged variables are used to account for the effect of past values on current outcomes. |

hedge2-lag2 | Similar to hedge1-lag1, this variable is the lagged value of the hedging ratio (hedge2) from the second previous year. Using lagged variables can help capture the effect of hedging strategies from earlier periods on the current market value (TobinsQ) of the airline. |

NetLn | Similar to OpLn, this is the natural logarithm of the airline’s net income, which represents its total earnings after deducting all expenses. |

CashRA | Cash return on assets (CashRA) is a financial ratio that measures how efficiently a company generates operating cash flow from its total assets. It indicates the ability of the company to generate cash from its core business operations relative to its total asset base. |

EquityRa | Equity return on assets (EquityRa) is a financial ratio that measures the return on assets funded by shareholders’ equity. It indicates how effectively the company utilises its assets to generate returns for its shareholders. |

Constant: | This term represents the intercept or constant term in the regression equation. It accounts for the portion of TobinsQ that is not explained by the independent variables included in the model. |

All Airlines | Europe | America | Low−Cost | Legacy | Constant | Selective | |
---|---|---|---|---|---|---|---|

Model | Fixed Effects | Fixed Effects | Fixed Effects | Fixed Effects | Fixed Effects | Fixed Effects | Fixed Effects |

R^{2} | 0.3942 | 0.1151 | 0.0184 | 0.7494 | 0.2365 | 0.8103 | 0.0185 |

F-Statistik | 8954.49 *** | 2612.68 *** | 33,49 *** | 11,626.74 *** | 39,480.28 *** | 166.83 *** | 7284.66 *** |

hedge1-lag1 | 0.0646 (−0.127) | 0.2853 (−0.209) | 0.0562 (−0.106) | −0.1208 (−0.246) | −0.0167 (−0.105) | 0.1094 (−0.266) | −0.0464 (−0.18) |

hedge2-lag2 | 0.2788 (−0.130) ** | 1.0547 (0.059) *** | 0.1319 (0.036) ** | 0.3666 (0.055) *** | 0.0420 (−0.124) | 0.3640 (0.074) ** | 0.0182 (−0.159) |

OpMarg | 3.4223 (1.230) ** | 5.3719 (0.190) *** | 5.1708 (0.348) *** | ||||

Opln | 0.0000 0 | 0.0000 0 | |||||

NetIn | 0.0000 (0.0000) ** | 0.0000 (0.000) | 0.0000 (0.000) *** | ||||

CashRa | −0.3824 (−0.174) ** | ||||||

EquityRa | −0.8833 (0.198) *** | −0.4293 (−0.367) | |||||

Constant | 1.3677 (0.164) *** | 0.8432 (0.170) ** | 1.3116 (0.079) *** | 0.7520 (0.087) *** | 1.1455 (0.065) *** | 0.7937 (0.131) *** | 1.2364 (0.052) *** |

Variable | Value |
---|---|

Average airfare at t = 1 (in US-$) | 315.77 |

Monthly air passenger demand at t = 1 (people) | 49,757,124.00 |

Average number of seats on a plane | 180 |

Pass-through rate (in %) | 5 |

**Table 28.**The Correlation of the independent variable jet fuel spot price p.g. and the dependent variables jet fuel costs and average airfare.

Sample Standard Deviation | Sample Covariance | Sample Coefficient of Correlation | Coefficient of Determination | |
---|---|---|---|---|

Jet fuel spot price p.g. (M) d = 0 | 0.784797674 | |||

Jet fuel spot price p.g. (Q) d = 0 | 0.777465358 | |||

Jet fuel costs d = 0 | 0.76770914 | 0.5847151 | 0.97048739 | 0.94184579 |

Average airfare d = 0 | 28.99645346 | 13.216396 | 0.5862558 | 0.34369578 |

Jet fuel spot price p.g. (M) d = 3 | 0.799174 | |||

Jet fuel spot price p.g. (Q) d = 3 | 0.791104142 | |||

Jet fuel costs d = 3 | 0.76770914 | 0.575504637 | 0.93801713 | 0.879876136 |

Average airfare d = 3 | 28.99645346 | 15.39925295 | 0.671306901 | 0.450652955 |

Jet fuel spot price p.g. (M) d = 6 | 0.811981982 | |||

Jet fuel spot price p.g. (Q) d = 6 | 0.804338405 | |||

Jet fuel costs d = 6 | 0.76770914 | 0.521698348 | 0.836905375 | 0.700410607 |

Average airfare d = 6 | 28.99645346 | 16.05882491 | 0.688541426 | 0.474089296 |

Jet fuel spot price p.g. (M) d = 9 | 0.82620344 | |||

Jet fuel spot price p.g. (Q) d = 9 | 0.816916666 | |||

Jet fuel costs d = 9 | 0.76770914 | 0.474804289 | 0.748567422 | 0.560353186 |

Average airfare d = 9 | 28.99645346 | 15.96518357 | 0.673986624 | 0.454257969 |

Variable | Actual Value ($\overline{\mathit{A}}$) | Simulated Value ($\overline{\mathit{S}})$ | Error Rate |
---|---|---|---|

Monthly average airfare | 343.7889286 | 339.770814 | 0.011687737 |

Monthly air passenger demand | 54.239.240 | 54.087.453 | 0.002798481 |

Monthly number of flights | 747.616.46 | 747.708.13 | 0.00012261 |

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## Share and Cite

**MDPI and ACS Style**

Samunderu, E.
Jet Fuel Price Risk and Proxy Hedging in Spot Markets: A Two-Tier Model Analysis. *Commodities* **2023**, *2*, 280-311.
https://doi.org/10.3390/commodities2030017

**AMA Style**

Samunderu E.
Jet Fuel Price Risk and Proxy Hedging in Spot Markets: A Two-Tier Model Analysis. *Commodities*. 2023; 2(3):280-311.
https://doi.org/10.3390/commodities2030017

**Chicago/Turabian Style**

Samunderu, Eyden.
2023. "Jet Fuel Price Risk and Proxy Hedging in Spot Markets: A Two-Tier Model Analysis" *Commodities* 2, no. 3: 280-311.
https://doi.org/10.3390/commodities2030017