Constant Hedge Ratios Research Articles

A Primer on Hedging with Stock Index Futures

In this article, the authors discuss the various approaches and issues associated with hedging with stock index futures. The most common approach used in practice is based on minimizing the variance of the hedge within the mean-variance framework to obtain the optimal hedge ratio. In determining the optimal hedge ratio, consideration must be given to the basis risk to which a fund is exposed when using stock index futures. An optimal hedge ratio based on variance minimization is the slope coefficient estimated from an ordinary least squares (OLS) regression of the returns of the portfolio to be hedged on the returns of the stock index futures contract. The estimated slope coefficient is referred to as beta. The optimal hedge ratio can be further refined by adjusting for the beta estimated from an OLS regression of the return on the underlying stock index on the return on the stock index futures. A criticism of the OLS model is twofold. The first is that there are statistical issues in estimating beta using the basic OLS regression model. Several models that employ advanced econometric techniques have been proposed for estimating hedge ratios. The second criticism is that the OLS model assumes a constant hedge ratio, despite the theoretical and empirical evidence showing the hedge ratio should be time varying. Evidence suggests that employing advanced econometric models to estimate the slope coefficient offers little improvement in hedging effectiveness—and even if there is some improvement, the modeling cost may not justify the extra effort. As for the second criticism, the well-known autoregressive conditional heteroscedasticity (ARCH) and the generalized ARCH (GARCH) have been used to allow for time-varying hedge ratios. Although some studies have reported that ARCH and GARCH can improve hedge effectiveness, the effort may not be warranted due to the additional modeling as well as the time-varying hedge ratios involving rebalancing the portfolio periodically, which can add significantly to the cost of hedging.

The influence of the COVID-19 pandemic on the hedging functionality of Chinese financial markets

In this paper, we investigate both constant and time-varying hedge ratios in terms of the effectiveness of CSI300 index futures during the COVID-19 crisis. Using naïve, OLS and EC/ROLS strategies to estimate constant hedge ratios, results indicate that the CSI300 spot index presents decreased effectiveness using the naïve hedging strategy; however, increased effectiveness of OLS and EC hedge ratios are identified. Differential behaviour is identified when considering five newly introduced COVID-19 concept-based stock indices. Time-varying hedge ratios indicate the weakened effectiveness, ranging between 20% and 40% variance reduction. Evidence suggests that the capability of the CSI300 index futures to hedge against the risks of the COVID-19 is impaired, regardless of whether constant or time-varying hedge ratios are used. Such results provide important implications to both local and foreign investors in the Chinese stock market.

The hedging effect of green bonds on carbon market risk

This paper explores effective hedging instruments for carbon market risk. Examining the relationship between the carbon futures returns and the returns of four major market indices, i.e., the VIX index, the commodity index, the energy index and the green bond index, we find that the connectedness between the carbon futures returns and the green bond index returns is the highest and this connectedness is extremely pronounced during the market's volatile period. Further, we develop and evaluate hedging strategies based on three dynamic hedge ratio models (DCC-APGARCH, DCC-T-GARCH, and DCC-GJR-GARCH models) and the constant hedge ratio model (OLS model). Empirical results show that among the four market indices the green bond index is the best hedge for carbon futures and performs well even in the crisis period. The paper also provides evidence that the dynamic hedge ratio models are superior to the OLS model in the volatile period as more sophisticated models can capture the dynamic correlation and volatility spillover between the carbon futures and market index returns.

Futures Hedging in CSI 300 Markets: A Comparison Between Minimum-Variance and Maximum-Utility Frameworks

In this paper, we explore the hedging performance of CSI 300 stock index futures under the minimum-variance and maximum-utility framework. We employ ten commonly used econometric models including constant and dynamic ones. Our empirical results indicate that for all futures contracts none of the single model can outperform all other models out-of-sample. In general, the dynamic hedge ratio models are significantly superior to the constant hedge ratio models under the both frameworks in CSI 300 market. Further we obtain the most robust hedging effectiveness by combining OHRs from dynamic hedge models.

Razones de Cobertura Óptima para el Contrato Futuro sobre el Índice del Mercado Bursátil Mexicano: Un Enfoque GARCH Multivariado

This work compares different hedging strategies that use the Mexican Stock Exchange (MSE) Index futures contract traded at the Mercado Mexicano de Derivados – (Mexican Derivatives Market or MexDer), to minimize the impact of stock price fluctuations on the value of a well-diversified portfolio (the Mexican Stock Exchange Index, or IPC). We study the ex-post empirical performance of each using the daily closing contract’s price and the MSE Index for a period from December 30th, 1999, through December 30th, 2016. The set of hedging strategies we compare includes: a) a No-hedge strategy; b) a Naive hedge ratio (1 to 1); c) a constant hedge ratio, (obtained from an OLS); and d) a dynamic hedge ratio, obtained using a Constant Conditional Correlation Bivariate GARCH model, with Asymmetric Responses. Moreover, the sample period has four structural breaks, so the analysis is divided in five subperiods. The different strategies are compared using different risk measures: Value at Risk, Expected Shortfall and LAQ. In all cases, hedging effectively reduces the volatility of the portfolio, but the dynamic hedge ratio produces the best possible results, while the constant hedge ratio is a close second.

Futures hedging in crude oil markets: A comparison between minimum-variance and minimum-risk frameworks

Most of existing studies on crude oil futures hedging aim to minimizing the variance of hedged portfolio. In this paper, we evaluate the hedging performance in a different framework of minimum-risk and try to find the optimal hedge model. We employ a total of ten popular econometric specifications including three constant and seven dynamic hedge ratio models. Our results suggest that none of the models of interest can outperform all competitors in or out of sample for all futures contracts. The constant hedge ratio models perform better than the dynamic hedge ratio models under the min-V framework, but the situation overturns under the min-R framework with the DCC-GARCH performs best. More importantly, the equal-weighted combination of all constant and dynamic hedge ratios results in better out-of-sample performance than the combination of either type of hedge ratios only.

HEDGING EFFECTIVENESS OF CROSS-LISTED NIFTY INDEX FUTURES

This paper investigates the hedging effectiveness of cross-listed Nifty Index futures and compares the performance of constant and dynamic optimal hedging strategies. We use daily data of Nifty index traded on the National Stock Exchange (NSE), India and cross-listed Nifty futures traded on the Singapore Stock Exchange (SGX) for a period of six years from July 15, 2010 to July 15, 2016. Various competing forms of Multivariate Generalised Autoregressive Conditional Heteroscedasticity (MGARCH) models, such as Constant Conditional Correlation (CCC) and Dynamic Conditional Correlation (DCC), have been employed to capture the time-varying volatility. The results clearly depict that dynamic hedge ratios outperform traditional constant hedge ratios with the DCC–GARCH model being the most efficient with maximum variance reduction from the unhedged portfolio.

Some Like it Hedged

Foreign currency exposure is a by-product of international investing. When obtaining global asset exposure, investors also obtain the embedded foreign currency exposure. The impact of this foreign currency exposure on the return and the volatility of the institutional investor’s portfolio can be quite meaningful. For example, according to a Reuters’ article, the rise in the US dollar wiped out about $1 trillion in US pension fund assets (i.e., in the dollar value of the funds’ non-dollar-denominated assets) between mid-2014 and March 2015 (Chavez-Dreyfuss 2015). How to address this exposure has been a subject of much debate over the years. The seminal paper by Black (1989) argued for a “universal” hedge ratio for all investors. Perold and Schulman (1988) argued that US investors should completely hedge foreign currency exposure; another school of thought is that foreign currency exposure provides diversification benefits and should be left unhedged. Recently, Chen, Kritzman, and Turkington (2015) evaluated the impact of various currency-hedging strategies on a typical institutional investor portfolio. As expected, more-flexible strategies provide greater risk reduction, but there is no single best strategy ex ante, leaving investors to consider different risk–return trade-offs. Although no single best-practice solution exists for addressing foreign currency exposures, institutional investors have three main choices: 1. Do nothing (i.e., maintain unhedged foreign currency exposure). 2. Hedge passively (i.e., maintain a constant hedge ratio). 3. Hedge actively (i.e., vary the hedge ratio). The best solution will differ from institution to institution, but it comes down to two fundamental factors. First, the optimal solution depends on the importance of risk versus return and the institution’s tolerance for negative cash flow. Second, investors must decide whether they believe that currency managers are able to achieve a positive information ratio over the long term after fees and, importantly, whether they will be able to identify these currency managers. Before I address the available choices, I present the estimated impact of foreign currency exposure on institutional portfolios. In the following sections, I consider four different base currencies: the US dollar, Canadian dollar, euro, and Japanese yen.

Hedging efficiency of Atlantic salmon futures

ABSTRACTThis article examines the hedging properties of Atlantic salmon futures. Hedging is important because it allows for mitigation of the risk of adverse price changes in the spot market. We examine the hedging efficiency of three types of hedging strategies; unhedged, fully hedged and hedging using optimal hedging ratios. To find the optimal hedge ratio we use an estimated constant hedge ratio, optimal hedge ratios estimated with rolling 20-week and 52-week windows, and bivariate GARCH models. The results provide evidence that hedging using futures contracts listed on Fish Pool reduces risk for producers of farmed Atlantic salmon. The best hedging efficiency is achieved with a simple one-to-one hedge, closely followed by the bivariate GARCH approach.

Currency exchange rate risk hedging strategies using MXN/USD MexDer futures contracts

The use of futures contracts to hedge exchange rate risk rapidly gained importance after the Bretton Woods Agreement was abandoned in 1973. However, one of the technical difficulties of using futures contracts is the determination of the optimal hedge ratio that minimises risk. This work studies and compares eight possible hedging strategies to identify the optimal hedge ratio for a long position in US Dollar, from the perspective of a hedger whose currency of interest is the Mexican Peso. Two of the strategies use a constant hedge ratio (a naive 'one-to-one' strategy, and an OLS-based hedge ratio). The other six use bivariate GARCH models, including: a diagonal VECH model; a constant conditional correlation model; and a BEKK model. Results show that the OLS-based strategy outperforms the alternative strategies in terms of volatility reduction as measured by a hedging effective index (HEI), by value at risk (VaR) and conditional VaR (CVaR) criteria.

Econometric modeling for optimal hedging in commodity futures: An empirical study of soybean trading

The optimal hedge ratio (OHR) is basically based on the coefficient of the regression between the change in the spot prices and the change in price of the hedging instrument. The traditional constant hedge ratio based on the ordinary least square (OLS) technique has been avoided by the researchers being an inappropriate; it ignores the heteroscedasticity which often exists in price series. In other words, the hedge ratios will certainly vary over time as the conditional distribution between cash and futures prices changes. It has been recognized that time varying coefficient (TVC) model outperforms the static coefficient (SC). As an illustration, the future and spot price of Soybean have been considered for the contracts maturing in December, 2011; June, 2012; December, 2013; April, 2013. The hedge ratio has been estimated for all the contracts by using OLS method, GARCH-BEKK, GARCH-VECH and Kalman filter methodology.

M-GARCH Hedge Ratios and Hedging Effectiveness in Australian Futures Markets

This study deals with the estimation of the optimal hedge ratios using various econometric models. Most of the recent papers have demonstrated that the conventional ordinary least squares (OLS) method of estimating constant hedge ratios is inappropriate, other more complicated models however seem to produce no more efficient hedge ratios. Using daily AOIs and SPI futures on the Australian market, optimal hedge ratios are calculated from four different models: the OLS regression model, the bivariate vector autoaggressive model (BVAR), the error-correction model (ECM) and the multivariate diagonal Vcc GARCH Model. The performance of each hedge ratio is then compared. The hedging effectiveness is measured in terms of ex-post and ex-ante risk-return traHe-off at various forcasting horizons. It is generally found that the GARCH time varying hedge ratios provide the greatest portfolio risk reduction, particularly for longer hedging horizons, but hey so not generate the highest portfolio return.

Role of Indian Commodity Derivatives Market in Hedging Price Risk: Estimation of Constant and Dynamic Hedge Ratio, and Hedging Effectiveness

This  paper  examines  hedging  effectiveness  of  four  agricultural  (soybean,  corn,  castor seed and guar seed) and seven non-agricultural (gold, silver, aluminium, copper, zinc, crude oil  and,  natural  gas)  futures  contracts  traded  in  India,  using  VECM  and  CCC-MGARCH model to estimate constant hedge ratio and dynamic hedge ratios, respectively. We ind that agricultural  futures  contracts  provide  higher  hedging  effectiveness  (30-70%)  as  compared to  non-agricultural  futures  (20%).  In  the  more  recent  period,  the  hedging  effectiveness  of Indian futures markets has increased. When hedging effectiveness of non-agricultural Indian futures  contracts  with  the  world  spot  markets  (NYMEX  and  LME)  is  analyzed,  hedging effectiveness  increases  dramatically  which  indicates  the  fact  that  Indian  futures  contracts are more effective for hedging exposures to global prices. Other reasons of lower hedging effectiveness  of  Indian  futures  contracts  may  be  low  awareness  of  futures  markets  among participants,  high  transaction  costs  in  the  futures  markets,  policy  restrictions,  inadequate contract design, or high transaction costs in the spot market. These are, of course, expected birth pays for a nascent futures markets in an emerging economy. ");} // --> activate javascript

Hedging performance of Chinese stock index futures: An empirical analysis using wavelet analysis and flexible bivariate GARCH approaches

In this paper, we assess the hedging performance of the newly established CSI 300 stock index futures over some short hedging horizons. We use wavelet analysis as well as conventional models (naïve, ordinary least squares, and error-correction) to compute the constant hedge ratios. The constant conditional correlation (CCC) and dynamic conditional correlation (DCC) bivariate generalised autoregressive conditional heteroskedasticity (BGARCH) specifications are employed to calculate the time-varying hedge ratios. Overall, we find that the CSI 300 stock index futures can be an effective hedging tool. Among the constant hedge ratio models, the wavelet analysis yields the best in-sample hedging performance, though its out-of-sample hedging performance is similar to other models. Comparing the time-varying ratio models, the CCC BGARCH model is better in terms of in-sample hedging effectiveness while for out-of-sample hedging performance, the DCC model is better with short hedging horizons and CCC model is more favourable with long hedging horizons. Finally, the question whether time-varying ratios outperform constant ratios depends on the length of the hedging horizon. Short horizons favour BGARCH hedging models while long horizons favour constant hedging ratio models.

Dynamic hedge ratio estimations in the European Union Emissions offset credit market

Following the introduction of the European Union Emissions Trading Scheme in 2005, the size of the carbon market has been growing at a tremendous rate. To meet the emissions reduction targets, the regulated parties can choose to participate in the allowance-based market by purchasing the spot allowances. Commencing in 2008, the regulated parties are also allowed to purchase the offset credits to meet their allowance limit. Given the risky nature of the offset credits, this paper evaluates the hedging performance of dynamic hedge ratios for the carbon offset credit (certified emissions reduction) market in the EU-ETS. To the best of our knowledge, this paper is the first attempt to evaluate the hedging performance of dynamic and constant hedge ratios in the carbon offset credit market. Based on the variance reduction and utility improvement measurements, the findings generally support the use of static hedge ratios over the more sophisticated, dynamic hedge ratios.

A Simple Test of the Affine Class of Term Structure Models

Affine term structure models imply an affine relation between yields and factors, and between yields and yields. Hence, a necessary condition for the affine class to hold is that yield changes are linearly related to changes in as many other yields as the number of underlying risk factors. At the same time, yield changes should be unrelated to changes in nonlinear transformations of other yields. We test this hypothesis using weekly data on U.S. Treasury yields for the June 1961–December 2002 sample period. Bootstrap-adjusted tests lead to only weak rejections of the affine class, and a simulation shows that these tests have correct size and high power. Imposing the cross-equation restrictions deriving from a no-arbitrage affine term structure model leads to stronger rejections, but these stronger rejections have more to do with the no-arbitrage restrictions than with the implication of linearity. In an out-of-sample hedging exercise, the constant hedge ratios implied by the affine class generally outperform time-varying hedge ratios implied by nonlinear models.

Measuring the Hedging Effectiveness of Index Futures Contracts: Do Dynamic Models Outperform Static Models? A Regime-Switching Approach

This paper estimates linear and non-linear GARCH models to find optimal hedge ratios with futures contracts for some of the main European stock indexes. By introducing non-linearities through a regime-switching model, we can obtain more efficient hedge ratios and superior hedging performance in both in- and out-sample analysis compared with other methods (constant hedge ratios and linear GARCH). Moreover, the non-linear models also reflect different patterns followed by the dynamic relationship between the volatility of spot and futures returns during low and high volatility periods.

Hedging Effectiveness of Constant and Time Varying Hedge Ratio of the Copper in the London Metal Exchange

This paper evaluates different hedging strategies for copper futures contracts traded at the London Metal Exchange. We estimate dynamic and constant hedge ratio for futures contracts. Various models (Minimum variance hedge ratio, OLS regression model, VAR) are used to estimate constant hedge ratio. To estimate dynamic hedge ratio, we use BEKK and VARMGARCH models. This research provides an empirical comparison of different econometric technique in the context of hedging the market risk of copper traded at the London Metal Exchange. It is found that the VARMGARCH model estimates of time varying hedge ratio provide highest variance reduction. Besides, we examine the relation between hedging effectiveness and the maturity of the contract.

Hedge Ratio Stability and Hedging Effectiveness of Time‐Varying Hedge Ratios in Volatile Index Futures Markets: Evidence from the Asian Financial Crisis*

AbstractHedge ratio stability is especially important because hedgers are likely to use the estimate of historical hedge ratios to hedge future positions of their portfolios. One main purpose of the present study is to examine hedge ratio stability during the Asian financial crisis and post‐crisis, periods characterized by high price volatility, using the Nikkei 225, Hang Seng, and KOSPI 200 index futures contracts. Empirical results from the Hang Seng and the KOSPI 200 futures markets indicate that during the two periods of high price volatility, hedge ratios appeared to be unstable. Additionally, both in‐sample and out‐of‐sample evidences indicate that, for hedging effectiveness, the time‐varying hedge ratios clearly outperform the constant hedge ratios for the Hang Seng and the KOSPI 200 index futures, consistent with the findings of hedge ratio instability. The comparison results of different time‐varying hedge ratios support the conclusion that the bivariate error correction generalized autoregressive conditional heteroskedastic (1,1) model enhances hedging effectiveness compared to other time‐varying hedge ratios. Finally, this study examines the impact of hedge duration on hedging effectiveness and hedge ratios. The empirical results indicate that hedging effectiveness improves with increasing hedge duration.

Role of Indian Commodity Derivatives Market in Hedging Price Risk: Estimation of Constant and Dynamic Hedge Ratio and Hedging Effectiveness

This paper examines hedging effectiveness of four agricultural (Soybean, Corn, Castor seed and Guar seed) and seven non-agricultural (Gold, Silver, Aluminium, Copper, Zinc, Crude oil and Natural gas) futures contracts traded in India. We apply VECM and CCC-MGARCH model to estimate constant hedge ratio and dynamic hedge ratios respectively. We find that agricultural futures contracts provide higher hedging effectiveness (30-70%) as compared to non-agricultural futures (20%). In the more recent period, the hedging effectiveness of Indian futures markets has increased. When hedging effectiveness of non-agricultural Indian futures contracts with the world spot markets (NYMEX and LME) is analyzed, hedging effectiveness increases dramatically which indicates the fact that Indian futures contracts are more effective for hedging exposures to global prices. Other reasons of lower hedging effectiveness of Indian futures contracts may be low awareness of futures markets among participants, low participation of hedgers, high transaction costs in the futures markets, policy restrictions, lower number of delivery centers, inadequate contract design or high transaction costs in the spot market. These are, of course, expected birth pays for a nascent futures markets in an emerging economy.