Testing Futures Market Efficiency and Optimal Hedge Ratio Estimation: Evidence from Futures and Options on RTS

This study investigates futures market efficiency and optimal hedge ratio estimation. First, cointegration between spot and futures prices is studied using Johansen method, with two different model specifications. If prices are found cointegrated, restrictions on cointegrating vector and adjustment coefficients are imposed, to account for unbiasedness, weak exogeneity and prediction hypothesis. Second, optimal hedge ratios are estimated using static OLS, and time-varying DVEC and CCC models. In-sample and out-of-sample results for one, two and five period ahead are reported. The futures used in thesis are RTS index, EUR/RUB exchange rate and Brent oil, traded in Futures and options on RTS.(FORTS) For in-sample period, data points were acquired from start of trading of each futures contract, RTS index from August 2005, EUR/RUB exchange rate March 2009 and Brent oil October 2008, lasting till end of May 2011. Out-of-sample period covers start of June 2011, till end of December 2011. Our results indicate that all three asset pairs, spot and futures, are cointegrated. We found RTS index futures to be unbiased predictor of spot price, mixed evidence for exchange rate, and for Brent oil futures unbiasedness was not supported. Weak exogeneity results for all pairs indicated spot price to lead in price discovery process. Prediction hypothesis, unbiasedness and weak exogeneity of futures, was rejected for all asset pairs. Variance reduction results varied between assets, in-sample in range of 40-85 percent and out-of sample in range of 40-96 percent. Differences between models were found small, except for Brent oil in which OLS clearly dominated. Out-of-sample results indicated exceptionally high variance reduction for RTS index, approximately 95 percent.

The effect of asymmetries on optimal hedge ratios

There is widespread evidence that the volatility of stock returns displays an asymmetric response to good and bad news. This article considers the impact of asymmetry on time-varying hedges for financial futures. An asymmetric model that allows forecasts of cash and futures return volatility to respond differently to positive and negative return innovations gives superior in-sample hedging performance. However, the simpler symmetric model is not inferior in a hold-out sample. A method for evaluating the models in a modern risk-management framework is presented, highlighting the importance of allowing optimal hedge ratios to be both time-varying and asymmetric.

Razão ótima de hedge em função do horizonte de hedge e da periodicicidade dos dados : uma aplicação no mercado de boi gordo brasileiro

As observações relatadas por Myers e Thompson, em seu artigo “Generalized Optimal Hedge Ratio Estimation” de 1989, foram analisadas neste estudo utilizando o boi gordo como a commodity de interesse. Myers e Thompson, demonstraram teórica e empiricamente, ser inapropriado o uso do coeficiente angular da regressão simples, dos preços à vista sobre os preços futuros como forma de estimar a razão ótima de hedge. Porém, sob condições especiais, a regressão simples com a mudança dos preços resultou em valores plausíveis, próximos àqueles determinados por um modelo geral. Este modelo geral, foi desenvolvido com o intuito de estabelecer os parâmetros para comparar as diferentes abordagens na estimativa da razão ótima de hedge. O coeficiente angular da reta da regressão simples e a razão ótima de hedge tem definições similares, pois ambos são o resultado da divisão entre a matriz de covariância dos preços, à vista e futuros e a variância dos preços futuros. No entanto, na razão ótima de hedge estes valores refletem o momento condicional, enquanto que na regressão simples são valores não condicionais. O problema portanto, está em poder estimar a matriz condicional de covariância, entre os preços à vista e futuros e a variância condicional dos preços futuros, com as informações relevantes no momento da tomada de decisão do hedge. Neste estudo utilizou-se o modelo de cointegração com o termo de correção de erros, para simular o modelo geral. O Indicador ESALQ/BM&F foi utilizado como a série representativa dos preços à vista, enquanto que para os preços futuros, foram utilizados os valores do ajuste diário dos contratos de boi gordo, referentes ao primeiro e quarto vencimentos, negociados na Bolsa Mercantil e de Futuros - BM&F. Os objetivos do presente estudo foram: investigar se as observações feitas por Myers e Thompson eram válidas para o caso do boi gordo brasileiro, observar o efeito do horizonte de hedge sobre a razão ótima de hedge e o efeito da utilização das séries diárias e das séries semanais sobre a estimativa da razão ótima de hedge. Trabalhos anteriores realizados com as séries históricas dos preços do boi gordo, consideraram apenas os contratos referentes ao primeiro vencimento. Ampliar o horizonte de hedge é importante, uma vez que as atividades realizadas pelos agentes tomam mais do que 30 dias. Exemplo disto é a atividade de engorda do boi, que pode levar até 120 dias entre a compra do boi magro e a venda do boi gordo. Demonstrou-se neste estudo, que o uso das séries semanais, é o mais apropriado, dado a diminuição substancial da autocorrelação serial. Demonstrou-se também, que as regressões com as mudanças dos preços, resultaram em estimativas da razão de hedge próximas daquelas obtidas com o modelo geral e que estas diminuem com o aumento do horizonte de hedge.

A taxa ótima de hedge no mercado brasileiro do boi gordo: uma abordagem com BEKK, DCC e BEKK com dummies de safra e entressafra

Esta dissertação tem três objetivos. O primeiro é encontrar o melhor método para se calcular a taxa ótima de “hedge” no mercado brasileiro do boi gordo. Para isso, foram testados cinco modelos: BEKK, DCC de Tse e Tsui (2002), DCC de Engle e Sheppard (2001), BEKK com dummy de safra e BEKK com dummy de entressafra. O segundo é calcular o diferencial de razões de “hedge” entre a safra e entressafra, pois a taxa de “hedge” na entressafra deve ser maior devido a uma maior incerteza sobre um possível choque de oferta, o que afetaria negativamente os custos dos frigoríficos. O terceiro e último objetivo é desvendar o porquê da literatura brasileira de taxa ótima de “hedge” estar encontrando estimativas muito pequenas das taxas quando comparadas às realizadas no mercado. Conclui-se que os modelos DCC’s são os que, no geral, obtém um desempenho melhor pelo critério de redução de variância e aumento do índice de Sharpe e que a taxa de “hedge” na entressafra não deve ser maior que na safra. Nota-se também que a quebra da expectativa intertemporal com a mudança de contratos faz com que a variância da série dos retornos futuros aumente muito, diminuindo assim a taxa de “hedge”.

Eficiência e razão de hedge: uma análise dos mercados futuro brasileiros de boi, café, etanol, milho e soja

This research aims to investigate the Hedge Efficiency and Optimal Hedge Ratio for the future market of cattle, coffee, ethanol, corn and soybean. This paper uses the Optimal Hedge Ratio and Hedge Effectiveness through multivariate GARCH models with error correction, attempting to the possible phenomenon of Optimal Hedge Ratio differential during the crop and intercrop period. The Optimal Hedge Ratio must be bigger in the intercrop period due to the uncertainty related to a possible supply shock (LAZZARINI, 2010). Among the future contracts studied in this research, the coffee, ethanol and soybean contracts were not object of this phenomenon investigation, yet. Furthermore, the corn and ethanol contracts were not object of researches which deal with Dynamic Hedging Strategy. This paper distinguishes itself for including the GARCH model with error correction, which it was never considered when the possible Optimal Hedge Ratio differential during the crop and intercrop period were investigated. The commodities quotation were used as future price in the market future of BM&FBOVESPA and as spot market, the CEPEA index, in the period from May 2010 to June 2013 to cattle, coffee, ethanol and corn, and to August 2012 to soybean, with daily frequency. Similar results were achieved for all the commodities. There is a long term relationship among the spot market and future market, bicausality and the spot market and future market of cattle, coffee, ethanol and corn, and unicausality of the future price of soybean on spot price. The Optimal Hedge Ratio was estimated from three different strategies: linear regression by MQO, BEKK-GARCH diagonal model, and BEKK-GARCH diagonal with intercrop dummy. The MQO regression model, pointed out the Hedge inefficiency, taking into consideration that the Optimal Hedge presented was too low. The second model represents the strategy of dynamic hedge, which collected time variations in the Optimal Hedge. The last Hedge strategy did not detect Optimal Hedge Ratio differential between the crop and intercrop period, therefore, unlikely what they expected, the investor do not need increase his/her investment in the future market during the intercrop

Eficiência e razão de hedge: uma análise dos mercados futuro brasileiros de boi, café, etanol, milho e soja

This research aims to investigate the Hedge Efficiency and Optimal Hedge Ratio for the future market of cattle, coffee, ethanol, corn and soybean. This paper uses the Optimal Hedge Ratio and Hedge Effectiveness through multivariate GARCH models with error correction, attempting to the possible phenomenon of Optimal Hedge Ratio differential during the crop and intercrop period. The Optimal Hedge Ratio must be bigger in the intercrop period due to the uncertainty related to a possible supply shock (LAZZARINI, 2010). Among the future contracts studied in this research, the coffee, ethanol and soybean contracts were not object of this phenomenon investigation, yet. Furthermore, the corn and ethanol contracts were not object of researches which deal with Dynamic Hedging Strategy. This paper distinguishes itself for including the GARCH model with error correction, which it was never considered when the possible Optimal Hedge Ratio differential during the crop and intercrop period were investigated. The commodities quotation were used as future price in the market future of BM&FBOVESPA and as spot market, the CEPEA index, in the period from May 2010 to June 2013 to cattle, coffee, ethanol and corn, and to August 2012 to soybean, with daily frequency. Similar results were achieved for all the commodities. There is a long term relationship among the spot market and future market, bicausality and the spot market and future market of cattle, coffee, ethanol and corn, and unicausality of the future price of soybean on spot price. The Optimal Hedge Ratio was estimated from three different strategies: linear regression by MQO, BEKK-GARCH diagonal model, and BEKK-GARCH diagonal with intercrop dummy. The MQO regression model, pointed out the Hedge inefficiency, taking into consideration that the Optimal Hedge presented was too low. The second model represents the strategy of dynamic hedge, which collected time variations in the Optimal Hedge. The last Hedge strategy did not detect Optimal Hedge Ratio differential between the crop and intercrop period, therefore, unlikely what they expected, the investor do not need increase his/her investment in the future market during the intercrop

Eficiência e razão de hedge: uma análise dos mercados futuro brasileiros de boi, café, etanol, milho e soja

This research aims to investigate the Hedge Efficiency and Optimal Hedge Ratio for the future market of cattle, coffee, ethanol, corn and soybean. This paper uses the Optimal Hedge Ratio and Hedge Effectiveness through multivariate GARCH models with error correction, attempting to the possible phenomenon of Optimal Hedge Ratio differential during the crop and intercrop period. The Optimal Hedge Ratio must be bigger in the intercrop period due to the uncertainty related to a possible supply shock (LAZZARINI, 2010). Among the future contracts studied in this research, the coffee, ethanol and soybean contracts were not object of this phenomenon investigation, yet. Furthermore, the corn and ethanol contracts were not object of researches which deal with Dynamic Hedging Strategy. This paper distinguishes itself for including the GARCH model with error correction, which it was never considered when the possible Optimal Hedge Ratio differential during the crop and intercrop period were investigated. The commodities quotation were used as future price in the market future of BM&FBOVESPA and as spot market, the CEPEA index, in the period from May 2010 to June 2013 to cattle, coffee, ethanol and corn, and to August 2012 to soybean, with daily frequency. Similar results were achieved for all the commodities. There is a long term relationship among the spot market and future market, bicausality and the spot market and future market of cattle, coffee, ethanol and corn, and unicausality of the future price of soybean on spot price. The Optimal Hedge Ratio was estimated from three different strategies: linear regression by MQO, BEKK-GARCH diagonal model, and BEKK-GARCH diagonal with intercrop dummy. The MQO regression model, pointed out the Hedge inefficiency, taking into consideration that the Optimal Hedge presented was too low. The second model represents the strategy of dynamic hedge, which collected time variations in the Optimal Hedge. The last Hedge strategy did not detect Optimal Hedge Ratio differential between the crop and intercrop period, therefore, unlikely what they expected, the investor do not need increase his/her investment in the future market during the intercrop

Dynamic hedging in Markov regimes

This dissertation proposes a bivariate markov switching dynamic conditional correlation model for estimating the optimal hedge ratio between spot and futures contracts. It considers the cointegration between series and allows to capture the leverage efect in return equation. The model is applied using daily data of future and spot prices of Bovespa Index and R$/US$ exchange rate. The results in terms of variance reduction and utility show that the bivariate markov switching model outperforms the strategies based ordinary least squares and error correction models.

Avaliação do mercado futuro do milho brasileiro como mecanismo de apoio à comercialização para os produtores de Goiás

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Agronomia e Medicina Veterinária, Programa de Pós-Graduação em Agronegócios, 2016.

Optimal hedging with higher moments

This study proposes a utility-based framework for the determination of optimal hedge ratios (OHRs) that can allow for the impact of higher moments on hedging decisions. We examine the entire hyperbolic absolute risk aversion family of utilities which include quadratic, logarithmic, power, and exponential utility functions. We find that for both moderate and large spot (commodity) exposures, the performance of out-of-sample hedges constructed allowing for nonzero higher moments is better than the performance of the simpler OLS hedge ratio. The picture is, however, not uniform throughout our seven spot commodities as there is one instance (cotton) for which the modeling of higher moments decreases welfare out-of-sample relative to the simpler OLS. We support our empirical findings by a theoretical analysis of optimal hedging decisions and we uncover a novel link between OHRs and the minimax hedge ratio, that is the ratio which minimizes the largest loss of the hedged position. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark

Hedge de crédito através de equity: uma análise empírica com uso de ativos corporativos brasileiros

Este trabalho tem como objetivo analisar os resultados de uma operação de hedge de um diversificado portfólio de crédito de empresas brasileiras através do uso de ativos de equity. Inicialmente, faz-se uma alusão aos principais aspectos teóricos da presente dissertação com suas definições e revisão bibliográfica. Posteriormente, são apresentados os parâmetros básicos da seleção da amostra utilizada e do período durante o qual tal estratégia de proteção será implementada.

Optimal Design of Permit Markets with an Ex Ante Pollution Target, August 2006

In this paper, we examine the design of permit trading programs when the objective is to minimize the cost of achieving an ex ante pollution target, that is, one that is defined in expectation rather than an ex post deterministic value. We consider two potential sources of uncertainty, the presence of either of which can make our model appropriate: incomplete information on abatement costs and uncertain delivery coefficients. In such a setting, we find three distinct features that depart from the well-established results on permit trading: (1) the regulator’s information on firms’ abatement costs can matter; (2) the optimal permit cap is not necessarily equal to the ex ante pollution target; and (3) the optimal trading ratio is not necessarily equal to the delivery coefficient even when it is known with certainty. Intuitively, since the regulator is only required to meet a pollution target on average, she can set the trading ratio and total permit cap such that there will be more pollution when abatement costs are high and less pollution when abatement costs are low. Information on firms’ abatement costs is important in order for the regulator to induce the optimal alignment between pollution level and abatement costs.

The Optimal Capital Structure of Banks: Balancing Deposit Insurance, Capital Requirements and Tax-Advantaged Debt

The capital structure and regulation of financial intermediaries is an important topic for practitioners, regulators and academic researchers. In general, theory predicts that firms choose their capital structures by balancing the benefits of debt (e.g., tax and agency benefits) against its costs (e.g., bankruptcy costs). However, when traditional corporate finance models have been applied to insured financial institutions, the results have generally predicted corner solutions (all equity or all debt) to the capital structure problem. This paper studies the impact and interaction of deposit insurance, capital requirements and tax benefits on a bankÇs choice of optimal capital structure. Using a contingent claims model to value the firm and its associated claims, we find that there exists an interior optimal capital ratio in the presence of deposit insurance, taxes and a minimum fixed capital standard. Banks voluntarily choose to maintain capital in excess of the minimum required in order to balance the risks of insolvency (especially the loss of future tax benefits) against the benefits of additional debt. Because we derive a closed- form solution, our model provides useful insights on several current policy debates including revisions to the regulatory framework for GSEs, tax policy in general and the tax exemption for credit unions.

Hedging under liquidity constraints

Although risk management can be justified by financial distress, the theoretical models usually contain hedging instruments free of funding risk. In practice, management of the counterparty risk in derivative transactions is of enhanced importance, consequently not only is trading on exchanges subject to the presence of a margin account, but also in bilateral (OTC) agreements parties will require margins or collateral from their partners in order to hedge the mark-tomarket loss of the transaction. The aim of this paper is to present and compare two models where the financing need of the hedging instrument also appears, influencing the hedging strategy and the optimal hedging ratio. Both models contain the same source of risk and optimisation criterion, but the liquidity risk is modelled in different ways. In the first model, there is no additional financing resource that can be used to finance the margin account in case of a margin call, which entails the risk of liquidation of the hedging position. In the second model, the financing is available but a given credit spread is to be paid for this, so hedging can become costly.

Anthropometric measures of increased central and overall adiposity in association with echocardiographic left ventricular hypertrophy

Left ventricular hypertrophy is an important predictor of cardiovascular risk and sudden death. This study explored the ability of four obesity indexes (body mass index, waist circumference, waist-hip ratio and waist-stature ratio) to identify left ventricular hypertrophy. A sample of the general population (n=682; 43.5% men) was surveyed to assess cardiovascular risk factors. Biochemical, anthropometric and blood pressure values were obtained in a clinic visit according to standard methods. Left ventricular mass was obtained from transthoracic echocardiogram. Left ventricular hypertrophy was defined using population-specific cutoff values for left ventricular mass indexed to height(2.7). The waist-stature ratio showed the strongest positive association with left ventricular mass. This correlation was stronger in women, even after controlling for age and systolic blood pressure. By multivariate analysis, the main predictors of left ventricular hypertrophy were waist-stature ratio (23%), systolic blood pressure (9%) and age (2%) in men, and waist-stature ratio (40%), age (6%) and systolic blood pressure (2%) in women. Receiver-operating characteristic curves showed the optimal cutoff values of the different anthropometric indexes associated with left ventricular hypertrophy. The waist-stature ratio was a significantly better predictor than the other indexes (except for the waist-hip ratio), independent of gender. It is noteworthy that a waist-stature ratio cutoff of 0.56 showed the highest combined sensitivity and specificity to detect left ventricular hypertrophy. Abdominal obesity identified by waist-stature ratio instead of overall obesity identified by body mass index is the simplest and best obesity index for assessing the risk of left ventricular hypertrophy, is a better predictor in women and has an optimal cutoff ratio of 0.56. Hypertension Research (2010) 33, 83-87; doi: 10.1038/hr.2009.188; published online 13 November 2009