A note on the hedging effectiveness of GARCH models

This note compares the hedging effectiveness of the conventional hedge ratio and time-varying conditional hedge ratios (of which GARCH ratio is a special case). It is shown that, in large sample cases, the conventional hedge ratio provides the best performance. For small sample cases, a sufficiently large variation in the conditional variance of the futures return is required to produce the opposite result. The result is due to the fact that the hedging effectiveness measure is based upon the unconditional variance; meanwhile, the conventional hedge ratio minimizes the unconditional variance and the conditional hedge ratio aims at minimizing the conditional variance.     

Comparison of Some Static Hedging Models of Agricultural Commodities Price Uncertainty

In static framework, many hedging strategies can be settled following the various hedge ratios that have been developed in the literature. However, it is difficult to choose among them the best the appropriate strategy according the to preference or economic behavior of the decision-maker such as prudence and temperance. This is so even with the hedging effectiveness measure. After introducing a hedging ratio that take into account the prudence and temperance of the decision maker, we propose a ranking based approach to measure the effectiveness using L-moment to classify hedge portfolios, hence hedge ratios, with regard to their performance. Moreover, we deal with the hedging issue in presence of quantity and rollover risks and derive an optimal strategy that depends upon the basis and insurance contract. Such hedging issue includes the relevant risks encountered in practice and we relate how insurance contract, specially designed for production risk could affect the futures hedge. The application on some agricultural futures prices data at hands shows that taking into account quantity and rollover risks leads to better hedging strategy based on the L-performance effectiveness measure.

     

Hedging for multi-period downside risk in the presence of jump dynamics and conditional heteroskedasticity

This study extends the one period zero-VaR (Value-at-Risk) hedge ratio proposed by Hung et al . (2005 Hung, JC, Chiu, CL and Lee, MC. 2005. Hedging with zero-Value at Risk hedge ratio. Applied Financial Economics, 16: 259–69.  [Google Scholar]) to the multi-period case and incorporates the hedging horizon into the objective function under VaR framework. The multi-period zero-VaR hedge ratio has several advantages. First, compared to existing hedge ratios based on downside risk, it has an analytical solution and is simple to calculate. Second, compared to the traditional Minimum Variance (MV) hedge ratio, it considers expected return and remains optimal while the Martingale process is invalid. Thirdly, hedgers may elect an adequate hedging horizon and confidence level to reflect their level of risk aversion using the concept of VaR. Pondering the occurrence of volatility clustering and price jumps, this study utilizes the ARJI model to compute time-varying hedge ratios. Finally, both in-sample and out-of-sample hedging effectiveness between one-period hedge ratio and multi-period hedge ratio are evaluated for four hedging horizons and various levels of risk aversion. The empirical results indicate that hedgers wishing to hedge downside risk over long horizons should use the multi-period zero-VaR hedge ratios.     

Dynamic hedging strategy in incomplete market: Evidence from Shanghai fuel oil futures market

This paper introduces a new incomplete index and establishes a new optimal hedging model. We find that when the market micro-noise is perfectly negatively correlated with the return of futures market, market incompleteness depends on the relative level of noise volatility. Especially when noise volatility is less than the futures market yield, noise volatility will be offset by return volatility. As a result, complete optimal hedging model emerges. As an aside, it is interesting to note that as different conditional variances derived from different volatility models being applied, the hedge performance tends to be basically consistent with subtle difference: DCC–GARCH model is more likely to execute the hedging with 1:1 ratio, while other multivariate GARCH models would give a hedging ratio with greater probability less than 1:1 and is less likely to be a perfect hedge. Therefore, we believe that a simpler econometric model might produce better empirical results.     

Optimal hedge ratio estimation and hedge effectiveness with multivariate skew distributions

This article proposes to use the three multivariate skew distributions (generalized hyperbolic distribution, multivariate skew normal distribution, and multivariate skew Student-t distribution) for estimating the minimum variance hedge ratio in a dynamic setting. Three criteria for measuring hedge effectiveness are employed: hedging instrument effectiveness, overall hedge effectiveness, and relative-to-optimal hedge ratio effectiveness (RHRE). Three portfolios of spot and futures series are formed for empirical analysis. The outcomes confirm that the three multivariate skew distributions are more helpful in deciding the minimum variance hedge ratio, especially the generalized hyperbolic distribution, than the symmetrical normal and Student-t distributions. This outperformance is significant especially at critical market moments and it is indicated by three hedge effectiveness measures. This advantage is held without the cost of lowering portfolio return. In addition, there is speculation possibility existing in the portfolio hedged by the traditional optimal hedge ratio and this potential can be detected especially by RHRE.     

PORTFOLIO SELECTION BETWEEN A MATURE MARKET AND SELECTED EMERGING MARKETS INDICES IN THE PRESENCE OF STRUCTURAL BREAKS

The paper examines the influence of the structural breaks on the optimal weights, hedge ratios and hedge effectiveness index (HEI) of risk‐minimizing portfolios composed of S&P500 and selected emerging markets’ indices from East Europe, Asia and South America. We employ a bivariate DCC‐EGARCH models without and with structural breaks and we find better estimation features when structural breaks are included in the model. However, we do not find evidence that insertion of structural breaks increases portfolio hedging performances. The differences that exist between optimal weights, hedge ratios and HEI values are so small that tangible economic benefit for international investors do not exist.     

Managing price risks using and local polynomial kernel forecasts

This study contributes to understanding price risk management through hedging strategies in a forecasting context. A relatively new forecasting method, nonparametric local polynomial kernel (LPK), is used to forecast prices and to generate ex ante hedge ratios. The selective multiproduct hedge based on the LPK price and hedge ratio forecasts is in general found to be better than continuous hedging, no hedging and alternative forecasting procedures. Selective multivariate hedging using the LPK is found to improve hog producer's expected returns. The findings indicate that combining hedging with forecasts, especially when using the LPK procedure, can improve price risk management.     

Imperfect Forward Markets and Hedging

This paper considers a hedging model of a risk-averse competitive firm facing output price uncertainty. Imperfections exist in forward transactions in that the firm faces a downward-sloping demand function for its forward sales. We show that the optimal output and hedge ratio of the firm are, in general, not separable, and are related in a deterministic manner. We also derive some economic implications of production and hedging decisions when firms differ in their attitudes towards risk. A more risk-averse firm is shown to produce less and hedge more than a less risk-averse firm.
(J.E.L.: D21, D81).     

Strategic use of futures and options by commodity processors

The impacts of input–output price relationships on end-users' demands for positions in futures and options are analyzed using a mean-variance portfolio model and applied to price risk management in the bread manufacturing industry. A production relationship was assumed between the input and resultant output, and correlation between the input and output prices were introduced into the portfolio model. The optimal hedge ratio can be either positive or negative depending upon the relationship between the input and output price standard deviation adjusted for production technology and input–output price correlation. Introduction of a call option into the portfolio (in addition to the futures) does not change the hedging demand for futures; however, the speculative component changes. The results show that the addition of input–output linear production and price correlation relationships would not justify a hedging role for options unless there is bias in the futures and/or options markets.     

Dynamic hedge ratio for stock index futures: application of threshold VECM

This study represents one of the first papers in stock-index-futures arbitrage literature to investigate the effects of arbitrage threshold on stock index futures hedging effectiveness by using threshold vector error correction model (hereafter threshold VECM). Moreover, in contrast to prior studies focusing on examining case studies involving mature stock markets, this study not only adopts US S&P 500 stock market as the sample but also adds an analysis of one emerging stock market, Hungarian BSI and examines the differences between them. Finally, this investigation employs a rolling estimation process to examine the impact of arbitrage threshold behaviours on the setting of futures hedging ratio. The empirical findings of this study are consistent with the following notions. First, arbitrage behaviour reduces co-movement between futures and spot markets and increases the volatility of both futures and spot markets. Second, this article denotes the outer regime of futures-spot market for the case of Hungarian BSI (US S&P 500) as a crisis (an unusual) condition. Moreover, arbitrage threshold behaviours make remarkable (unremarkable) shift on optimal hedge ratio between two different market regimes for the case of Hungarian BSI (US S&P 500). Finally, the framework involving regime-varying hedge ratio designed in this study provides a more efficient futures hedge ratio design for Hungarian BSI stock market, but not for US S&P 500 stock market.     

The hedging effectiveness of constant and time-varying hedge ratios using three Pacific Basin stock futures

This paper investigates the hedging effectiveness of Australian, Hong Kong, and Japanese stock futures markets. The traditional hedge and the minimum variance hedge ratios are all constant whereas the bivariate GARCH hedge ratio is time varying. The effectiveness of the hedge ratio is compared by investigating the out-of-sample performance of the three ratios. The whole sample consists of weekly returns from January 1990 to December 2000. Two 1-year, out-of-sample periods are used: January 1999 to December 1999 and January 2000 to December 2000. Results show that the time-varying GARCH hedge ratio outperforms the constant ratios in most of the cases. This is true using both out-of-sample periods.     

CROSS‐HEDGING OF EXCHANGE RATE RISKS: A NOTE*

This note studies the optimal production and hedging decisions of a competitive international firm that exports to two foreign countries. The firm faces multiple sources of exchange rate uncertainty. Cross‐hedging is plausible in that one of the two foreign countries has a currency forward market. We show that the firm's optimal forward position is an over‐hedge, a full‐hedge or an under‐hedge, depending on whether the two random exchange rates are strongly positively correlated, uncorrelated or negatively correlated, respectively.     

中国大豆期货市场最优套期保值比率的实证研究

在总结评述国际上成熟的最优套期保值比率估计方法的基础上,采用OLS、VAR、B-ECM、B-GARCH、ECM-B-GARCH五种模型和Lien提出的套期保值绩效衡量指标,对我国大豆期货市场的套期保值比率和套期保值绩效进行了实证研究。结果表明:对于中国大豆期货市场而言,按照OLS模型估计的最优套期保值比率进行动态套期保值能够最大程度地降低风险;基于VAR模型与B-ECM模型的结果次之;按照B-GARCH模型和ECM-B-GARCH模型估计的最优套期保值比率进行动态套期保值,风险降低程度最小。     

Risk Management Using Quasi–static Hedging

In this paper, we try to develop a comprehensive theory of risk management for illiquid trading instruments and exotics by examining the consequences of a quasi–static hedging strategy. In contrast to a static hedging strategy, in which an initial hedge once executed is kept in place for the life of the trade, and a dynamic hedging strategy, in which hedges are frequently adjusted over the life of the trade, a quasi–static hedging strategy utilizes hedge adjustments but tries to minimize the frequency. Almost all the examples studied in the framework introduced here take this minimization to the extreme by limiting hedge adjustments to at most one during the life of a trade. We examine the application of this approach to long–dated forwards, long–dated options and exotic options such as cliquet and barriers. The model we present for barriers is a new generation of the Derman–Ergener–Kani approach which combines the flexibility of the approach with a sizable increase in model independence.     

Multi-objective hedging model with the third central moment and the capital budget

The third central moment and the capital budget are two important factors in designing the optimal hedge strategy. This paper investigates the problem of futures hedging under the third central moment and the capital budget. Based on the multi-objective programming, a multi-objective hedging model with two important factors is proposed to manage this problem. Using the method of weighted sums, the multi-objective hedging model can be equivalently transformed into an ordinary single-objective programming. By solving the single-objective programming, we derive the optimal hedge ratio under the third central moment and the capital budget. Finally, an empirical example of hedging copper is given to illustrate the application of the proposed model. The results also show clearly the influence of the third central moment and the capital budget in the hedging decision.     

股指期货在风险管理中的应用

股指期货属于金融期货的一种,是以股票市场的股票价格指数为标的物的期货合约.在很多发达的股票市场乃至资本市场中,股指期货扮演着规避风险、套期保值的重要角色.在利用股指期货对股票组合进行套期保值时,可能面临各种风险,其中,基差风险是套期保值者面临的最主要风险.利用向量误差修正模型可以估计最小风险套期保值比,为投资者综合选择风险最小的套期保值策略提供了现实的、可操作的定量分析工具.     

Optimal hedging with currency forwards,calls, and calls on forwards for the competitive exporting firm facing exchange rate uncertainty

We extend the well-known full hedge theorems of the hedging literature to random profits that are nonlinear in the random exchange rate. This arises when production flexibility is added to the standard model of the risk-averse exporting firm, where all production decisions have to be made before the exchange rate is known. Hence, hedging with currency derivatives that provide a linear payoff in the exchange rate can no longer provide a perfect hedge. Therefore forward selling is replaced by writing a certain call portfolio. Adding delayed revenue to the model induces the firm to sell calls on forwards. Because our generalized full hedge proposition is proved for random profits that might as well decrease in the exchange rate, the result is applicable to certain types of importing firms, too. — Given the absence of speculative motives on the part of the firm, it turns out that long-term investments in capital goods are chosen in risk-neutral manner.     

Bootstrap methods for autocorrelation test with uncorrelated but not independent errors

By using bootstrap technique we investigate the properties of the Breusch [Breusch, T.S., 1978. Testing for autocorrelation in dynamic linear models. Australian Economic Papers 17, 334–355]–Godfrey [Godfrey, L.G., 1978. Testing for higher order serial correlation in regression equations when the regressors include lagged dependent variables. Econometrica 46, 1303–1310] autocorrelation tests in dynamic models with uncorrelated but not independent errors. In this paper we show that, under conditions when the errors are uncorrelated but not independent, even the best likelihood ratio test cannot achieve the asymptotic distribution under the null hypothesis of no autocorrelation. Standard bootstrap methods also fail to produce consistent results. To overcome this problem we applied several bootstrap testing methods for the same purpose and found the stationary bootstrap and Wild bootstrap with static model to perform adequately among the other bootstrap methods.     

The effectiveness of index futures hedging in emerging markets during the crisis period of 2008-2010: Evidence from South Africa

This article provides an assessment of the comparative effectiveness of four econometric methods in estimating the optimal hedge ratio in an emerging equity market, particularly the South African equity and futures markets. The article bases the effectiveness of hedging on volatility reduction and minimization of the coefficient of variation of hedged returns as well as risk-aversion-based utility maximization. The empirical analysis shows that the vector error-correction method and multivariate generalized autoregressive conditional heteroscedasticity methods are most effective over relatively long horizon, weekly and monthly hedging periods.     

Time and place where gold acts as an inflation hedge: An application of long-run and short-run threshold model

This study examines the short-run and long-run inflation hedging effectiveness of gold in the United States and Japan during the period of January 1971 to January 2010. Previous research has shown in the long-run that inflation tends to appropriately increase the price of gold in the U.S., leading to gold's popularity as an asset in portfolios to reduce the risk against sudden inflation. However, gold is only partially effective in hedging against inflation in Japan. This research found that the rigidity between the price of gold and the consumer price index affects the inflation hedging ability of gold in the long-run. The gold price is characterized by market disequilibrium induced by the price rigidity, causing the price of gold to be unable to response to changes in the CPI. To explore the inflation hedging ability of gold in the short-run, this study further examines the price rigidity in low and high momentum regime. It is found during the low momentum regimes that, gold return is unable to hedge against inflation in either the U.S. or Japan. However, during high momentum regimes, gold return is able to hedge against inflation in the U.S., while the price rigidity in Japan causes the price of gold to not fully hedge against inflation in the short-run.