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.     

Dynamic multiproduct optimal hedging in the soybean complex – do time-varying correlations provide hedging improvements?

Optimal multiproduct time-varying hedge ratios are determined – for a soybean complex – and their risk-mitigating impact is contrasted over single-commodity time-varying and naive hedge ratios. A parsimonious regime-switching dynamic correlation model is employed, with the estimated dynamic correlation matrix among prices varying between two different levels, and the time-varying correlations being applied to the multiproduct setting. Findings obtained are three-fold. First, there is significant evidence that estimated simultaneous correlations among different commodities’ prices (e.g. soybean spot and soybean meal futures) attain different values along the time series. Second, there is a substantial reduction in margin variance provided by the optimal multiproduct time-varying hedge ratios over single time-varying and naive hedge ratios, for both in- and out-of-sample data. Third, average optimal multiproduct time-varying hedge ratios for soybean and soybean meal (0.82 and 0.74, respectively; for out-of-sample data) are significantly below the naive full hedge ratio, providing risk mitigation at lower costs.     

Improving GARCH volatility forecasts with regime-switching GARCH

Many researchers use GARCH models to generate volatility forecasts. Using data on three major U.S. dollar exchange rates we show that such forecasts are too high in volatile periods. We argue that this is due to the high persistence of shocks in GARCH forecasts. To obtain more flexibility regarding volatility persistence, this paper generalizes the GARCH model by distinguishing two regimes with different volatility levels; GARCH effects are allowed within each regime. The resulting Markov regime-switching GARCH model improves on existing variants, for instance by making multi-period-ahead volatility forecasting a convenient recursive procedure. The empirical analysis demonstrates that the model resolves the problem with the high single-regime GARCH forecasts and that it yields significantly better out-of-sample volatility forecasts. First Version Received: November 2000/Final Version Received: August 2001     

Hedging against bunker price fluctuations using petroleum futures contracts: constant versus time-varying hedge ratios

The effectiveness of hedging marine bunker price fluctuations in Rotterdam, Singapore and Houston is examined using different crude oil and petroleum future contracts traded at the New York Mercantile Exchange (NYMEX) and the International Petroleum Exchange (IPE) in London. Using both constant and dynamic hedge ratios, it is found that in and out-of-sample hedging effectiveness is different across regional bunker markets. The most effective futures instruments for out of sample hedging of spot bunker prices in Rotterdam and Singapore are the IPE crude oil futures, while for Houston it is the gas oil futures. Differences in hedging effectiveness across regional markets are attributed to the varying regional supply and demand factors in each market. In comparison to other markets, the cross-market hedging effectiveness investigated in the bunker market is low.     

Simultaneously determined,time-varying hedge ratios in the soybean complex

Time-varying hedge ratios are derived which account for the dynamic characteristics of prices in the soybean complex. A multivariate generalized autogressive heteroskedastic (MGARCH) model, along with other conditional models, is used to specify the relevant covariance matrix. While the time-varying representations of the variance matrix are statistically appropriateex anteand ex posthedging effectiveness indicate that they provide minimal gain to hedging in terms of mean return and reduction in variance over a constant conditional procedure. Whether similar findings arise from other applications of GARCH models to optimal hedging is a question for further research.     

Estimating the optimal hedge ratio in the presence of potential unknown structural breaks

We propose a new approach in the estimation of the optimal hedge ratio that allows the hedge ratio to vary over time but without the necessity of frequently rebalancing the portfolio. We apply this in the context of the US and UK equity markets using weekly spot share prices and future share prices during the period 5 January 1999 to 29 September 2009. Our method is to test for cointegration in the presence of two potentially unknown structural breaks by determining the timing of each via the underlying data. The empirical findings reveal that the spot and future prices are strongly cointegrated in each market. The estimated parameters disclose that the optimal hedge ratio is not constant in case of the US and the UK. We find one negative and one positive shift in the optimal hedge ratio in the US. However, we find only one significant and positive shift in the optimal hedge ratio in the UK. The implication of these findings from the perspective of both investors as well as policy-makers is elaborated on in the main text.     

Is Beta-t-EGARCH(1,1) superior to GARCH(1,1)?

Statistical performance, in-sample point forecast precision and out-of-sample density forecast precision of GARCH(1,1) and Beta-t-EGARCH(1,1) models are compared. We study the volatility of nine global industry indices for period from April 2006 to July 2010. Competing models are estimated for periods before, during and after the United States (US) financial crisis of 2008. The results provide evidence of the superior out-of-sample predictive performance of Beta-t-EGARCH compared to GARCH after the US financial crisis.     

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.     

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.     

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.     

Hedging performance of REIT index futures: A comparison of alternative hedge ratio estimation methods

Futures contracts based on REIT market indices remain an under-researched topic, given their short history. This paper extends the literature by examining what hedge-ratio estimation method yields the most effective hedging performance of REIT futures. We include a wide range of commonly used methods and apply them to all four global markets which have developed REIT index futures (i.e., Australia, Europe, Japan & the U.S.). By adopting an out-of-sample analytical framework, our results show that there exist multiple methods in each market that can be considered best performers and the mix of best performers varies across markets. Furthermore, our results suggest that constant hedge-ratio methods are not necessarily inferior to their time-varying counterparts, and that a more complicated GARCH model does not necessarily lead to better performance than a more parsimonious one. Finally, only DCC and BEKK are found to rank consistently among the best performers across all four markets when we examine collectively the results using different out-of-sample periods. However, this does not mean that hedgers will always want to use them.     

Forecasting stock market volatility and information content of implied volatility index

This study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.     

Hedging and diversification across commodity assets

ABSTRACT

We investigate the conditional cross effects and volatility spillover between equity markets and commodity markets (oil and gold), Fama and French HML and SMB factors, volatility index (VIX) and bonds using different multivariate GARCH specifications considering the potential asymmetry and persistence behaviours. We analyse the dynamic conditional correlation between the US equity market and a set of commodity prices and risk factors to forecast the transmission of shock to the equity market firstly, and to determine and compare the optimal hedge ratios from the different models based on the hedging effectiveness of each model. Our findings suggest that all models confirm the significant returns and volatility spillovers. More importantly, we find that GO-GARCH is the best-fit model for modelling the joint dynamics of different financial variables. The results of the current study have implications for investors: (i) the equity market displays inverted dynamics with the volatility index suggesting strong evidence of diversification benefit; (ii) of the hedging assets gold appears the best hedge for the US equity market as it has a higher hedge effectiveness than oil and bonds over time; and (iii) despite these important results, a better hedge may be obtained by using well-selected firm sized and profitability-based portfolios.     

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.

     

Diversification and optimal hedges for socially responsible investment in Brazil

This study contributes to the literature on socially responsible investing by examining the diversification potential of commodities, specifically oil, gold and clean energy together with the Brazilian Corporate Sustainability Index (ISE). Multivariate GARCH models are used to model volatility spillovers and conditional correlation in pairs of stocks containing ISE. Specifically, A-BEKK and A-DCC models with spillovers are estimated. The models’ results are used to compute and analyze the optimal weights and hedge ratios for stock portfolio holdings. The greatest benefit from diversification is obtained through the acquisition of gold and then OVX.     

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.     

Modeling volatility and conditional correlations between socially responsible investments,gold and oil

Socially responsible investing (SRI) is one of the fastest growing areas of investing. While there is a considerable literature comparing SRI to various benchmarks, very little is known about the volatility dynamics of socially responsible investing. In this paper, multivariate GARCH models are used to model volatilities and conditional correlations between a stock price index comprised of socially responsible companies, oil prices, and gold prices. The dynamic conditional correlation model is found to fit the data the best and used to generate dynamic conditional correlations, hedge ratios and optimal portfolio weights. From a risk management perspective, SRI offers very similar results in terms of dynamic conditional correlations, hedge ratios, and optimal portfolio weights as investing in the S&P 500. For example, SRI investors can expect to pay a similar amount to hedge their investment with oil or gold as investors in the S&P 500 would pay. These results can help investors and portfolio managers make more informed investment decisions.     

Portfolio choice with high frequency data: CRRA preferences and the liquidity effect

This paper suggests a new approach for portfolio choice. In this framework, the investor, with CRRA preferences, has two objectives: the maximization of the expected utility and the minimization of the portfolio expected illiquidity. The CRRA utility is measured using the portfolio realized volatility, realized skewness and realized kurtosis, while the portfolio illiquidity is measured using the well-known Amihud illiquidity ratio. Therefore, the investor is able to make her choices directly in the expected utility/liquidity (EU/L) bi-dimensional space. We conduct an empirical analysis in a set of fourteen stocks of the CAC 40 stock market index, using high frequency data for the time span from January 1999 to December 2005 (seven years). The robustness of the proposed model is checked according to the out-of-sample performance of different EU/L portfolios relative to the minimum variance and equally weighted portfolios. For different risk aversion levels, the EU/L portfolios are quite competitive and in several cases consistently outperform those benchmarks, in terms of utility, liquidity and certainty equivalent.     

Hedging effectiveness comparisons: A note

This note examines the hedging effectiveness of three hedge strategies on twenty-four commodity and financial markets. Lien (Lien, D., 2005a, The use and abuse of the hedging effectiveness measure, International Review of Financial Analysis 14, 277–282, Lien, D., 2005b, A note on the superiority of the OLS hedge ratio, Journal of Futures Markets 25, 1121–1126.) suggest that, absent from estimation errors, the minimum variance (MV) hedge ratio attains the maximum post-sample hedging effectiveness when there is no structural change across estimation and comparison samples. When comparing the MV strategy with the naïve hedge ratio, we find sufficiently strong support for the conclusion. On the other hand, driven by estimation errors, weaker support is produced when comparing MV and error correction (EC) hedge strategy.     

基于ARIMA与GARCH模型的国际油价预测比较分析

在分析影响油价波动因素的基础上,利用1986年1月至2010年12月的WTI国际原油价格月度数据,分别建立ARIMA和GARCH模型对油价进行预测。并通过对2011年1月至2012年4月WTI原油价格进行外推预测,检验模型的预测效果。比较分析发现,在短期预测中,ARIMA和GARCH模型对油价的预测均比较准确,但当油价由于受到重大事件的影响而有较大波动时,模型的预测精度下降;在长期预测中,GARCH模型的预测效果优于ARIMA模型;整体来看,GARCH模型预测的精度高于ARIMA模型。因此,在国际油价预测中,用GARCH模型是比较合适的。