Time Varying Risk Aversion: An Application to Energy Hedging

Risk aversion is a key element of utility maximizing hedge strategies; however, it has typically been assigned an arbitrary value in the literature. This paper instead applies a GARCH-in-Mean (GARCH-M) model to estimate a time-varying measure of risk aversion that is based on the observed risk preferences of energy hedging market participants. The resulting estimates are applied to derive explicit risk aversion based optimal hedge strategies for both short and long hedgers. Out-of-sample results are also presented based on a unique approach that allows us to forecast risk aversion, thereby estimating hedge strategies that address the potential future needs of energy hedgers. We find that the risk aversion based hedges differ significantly from simpler OLS hedges. When implemented in-sample, risk aversion hedges for short hedgers outperform the OLS hedge ratio in a utility based comparison

A Utility Based Approach to Energy Hedging

A key issue in the estimation of energy hedges is the hedgers’ attitude towards risk which is encapsulated in the form of the hedgers’ utility function. However, the literature typically uses only one form of utility function such as the quadratic when estimating hedges. This paper addresses this issue by estimating and applying energy market based risk aversion to commonly applied utility functions including log, exponential and quadratic, and we incorporate these in our hedging frameworks. We find significant differences in the optimal hedge strategies based on the utility function chosen.Energy; Hedging; Risk Management; Risk Aversion; Forecasting

Hedging Effectiveness under Conditions of Asymmetry

We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail specific metrics to compare the hedging effectiveness of short and long hedgers using Oil futures contracts. The metrics used include Lower Partial Moments (LPM), Value at Risk (VaR) and Conditional Value at Risk (CVAR). Comparisons are applied to a number of hedging strategies including OLS and both Symmetric and Asymmetric GARCH models. Our findings show that asymmetry reduces in-sample hedging performance and that there are significant differences in hedging performance between short and long hedgers. Thus, tail specific performance metrics should be applied in evaluating hedging effectiveness. We also find that the Ordinary Least Squares (OLS) model provides consistently good performance across different measures of hedging effectiveness and estimation methods irrespective of the characteristics of the underlying distribution.Hedging Performance; Asymmetry; Downside Risk; Value at Risk, Conditional Value at Risk. JEL classification: G10, G12, G15. ____________________________________________________________________ John Cotter, Director of Centre for Financial Markets, Department of Banking and Finance, University College Dublin, Blackrock, Co. Dublin, Ireland, tel 353 1 716 8900, e-mail [email protected]. Jim Hanly, School of Accounting and Finance, Dublin Institute of Technology, tel 353 1 402 3180, e-mail [email protected]. The authors would like to thank the participants at the Global Finance Annual Conference for their constructive comments.

Hedging Effectiveness under Conditions of Asymmetry

We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail specific metrics to compare the hedging effectiveness of short and long hedgers using crude oil futures contracts. The metrics used include Lower Partial Moments (LPM), Value at Risk (VaR) and Conditional Value at Risk (CVAR). Comparisons are applied to a number of hedging strategies including OLS and both Symmetric and Asymmetric GARCH models. Our findings show that asymmetry reduces in-sample hedging performance and that there are significant differences in hedging performance between short and long hedgers. Thus, tail specific performance metrics should be applied in evaluating hedging effectiveness. We also find that the Ordinary Least Squares (OLS) model provides consistently good performance across different measures of hedging effectiveness and estimation methods irrespective of the characteristics of the underlying distribution.Hedging Performance; Asymmetry; Lower Partial Moments, Value at Risk, Conditional Value at Risk.

Re-evaluating Hedging Performance

Mixed results have been documented for the performance of hedging strategies using futures. This paper reinvestigates this issue using an extensive set of performance evaluation metrics across seven international markets. We compare the hedging performance of short and long hedgers using traditional variance based approaches together with modern risk management techniques including Value at Risk, Conditional Value at Risk and approaches based on Downside Risk. Our findings indicate that using these metrics to evaluate hedging performance, yields differences in terms of best hedging strategy as compared with the traditional variance measure. We also find significant differences in performance between short and long hedgers. These results are observed both in-sample and out-of-sample.Hedging Performance; Lower Partial Moments; Downside Risk; Variance; Semi- Variance; Value at Risk, Conditional Value at Risk

Time Varying Risk Aversion: An Application to Energy Hedging

Risk aversion is a key element of utility maximizing hedge strategies; however, it has typically been assigned an arbitrary value in the literature. This paper instead applies a GARCH-in-Mean (GARCH-M) model to estimate a time-varying measure of risk aversion that is based on the observed risk preferences of energy hedging market participants. The resulting estimates are applied to derive explicit risk aversion based optimal hedge strategies for both short and long hedgers. Out-of-sample results are also presented based on a unique approach that allows us to forecast risk aversion, thereby estimating hedge strategies that address the potential future needs of energy hedgers. We find that the risk aversion based hedges differ significantly from simpler OLS hedges. When implemented in-sample, risk aversion hedges for short hedgers outperform the OLS hedge ratio in a utility based comparison.Energy, Hedging, Risk Management, Risk Aversion, Forecasting

Hedging: Scaling and the Investor Horizon

This paper examines the volatility and covariance dynamics of cash and futures contracts that underlie the Optimal Hedge Ratio (OHR) across different hedging time horizons. We examine whether hedge ratios calculated over a short term hedging horizon can be scaled and successfully applied to longer term horizons. We also test the equivalence of scaled hedge ratios with those calculated directly from lower frequency data and compare them in terms of hedging effectiveness. Our findings show that the volatility and covariance dynamics may differ considerably depending on the hedging horizon and this gives rise to significant differences between short term and longer term hedges. Despite this, scaling provides good hedging outcomes in terms of risk reduction which are comparable to those based on direct estimation.Hedging Effectiveness; Scaling; Volatility Modelling, Forecasting

Hedging Effectiveness under Conditions of Asymmetry

We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail specific metrics to compare the hedging effectiveness of short and long hedgers using crude oil futures contracts. The metrics used include Lower Partial Moments (LPM), Value at Risk (VaR) and Conditional Value at Risk (CVAR). Comparisons are applied to a number of hedging strategies including OLS and both Symmetric and Asymmetric GARCH models. Our findings show that asymmetry reduces in-sample hedging performance and that there are significant differences in hedging performance between short and long hedgers. Thus, tail specific performance metrics should be applied in evaluating hedging effectiveness. We also find that the Ordinary Least Squares (OLS) model provides consistently good performance across different measures of hedging effectiveness and estimation methods irrespective of the characteristics of the underlying distribution

The use of administrative health care databases to identify patients with Rheumatoid Arthritis

Objective: To validate and compare the decision rules to identify rheumatoid arthritis (RA) in administrative databases. Methods: A study was performed using administrative health care data from a population of 1 million people who had access to universal health care. Information was available on hospital discharge abstracts and physician billings. RA cases in health administrative databases were matched 1:4 by age and sex to randomly selected controls without inflammatory arthritis. Seven case definitions were applied to identify RA cases in the health administrative data, and their performance was compared with the diagnosis by a rheumatologist. The validation study was conducted on a sample of individuals with administrative data who received a rheumatologist consultation at the Arthritis Center of Nova Scotia. Results: We identified 535 RA cases and 2,140 non-RA, noninflammatory arthritis controls. Using the rheumatologist's diagnosis as the gold standard, the overall accuracy of the case definitions for RA cases varied between 68.9% and 82.9% with a kappa statistic between 0.26 and 0.53. The sensitivity and specificity varied from 20.7% to 94.8% and 62.5% to 98.5%, respectively. In a reference population of 1 million, the estimated annual number of incident cases of RA was between 176 and 1,610 and the annual number of prevalent cases was between 1,384 and 5,722. Conclusion: The accuracy of case definitions for the identification of RA cases from rheumatology clinics using administrative health care databases is variable when compared to a rheumatologist's assessment. This should be considered when comparing results across studies. This variability may also be used as an advantage in different study designs, depending on the relative importance of sensitivity and specificity for identifying the population of interest to the research question

Letter to John Hodsdon, June 16, 1863

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