SOM-Based Hedge Ratio Estimation with Hierarchical Cluster Resampling

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

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.

The present study examined the efficiency of commodity futures in price discovery and risk management for agricultural commodities in India. The price discovery function was examined by using Johansen's test of cointegration (1991), vector error correction model (VECM), Wald chi-square test, and Granger causality test. The risk-management function was examined by using ordinary least squares (OLS) method and VECM to estimate optimal hedge ratio (OHR) and hedge effectiveness (HE). The study used secondary data consisting of daily closing prices of spot and futures markets for a period of 10 years (2004 – 2013) for three agricultural commodities, that is, Chana, Chilli, and Turmeric, which are traded in National Commodity & Derivatives Exchange Ltd. (NCDEX). It was found that there is a long-run association between commodity spot and futures prices of Chana, Chilli, and Turmeric. The VECM results revealed that there is a long-run causality running from futures prices to spot prices, which enable the spot market to adjust its short-run deviations from long-run equilibrium path with nearly 2.17%, 2.78%, and 4.41% speed of adjustments in Chana, Chilli, and Turmeric, respectively. The Granger causality test results revealed that there is only a unidirectional causality from futures returns to spot returns of commodities - Chilli and Turmeric. However, in the case of Chana, there is a bidirectional causality between futures and spot returns. According to hedge ratios of OLS and VECM results, it was found that the commodity futures provide 50%, 56%, and 55% variance reduction in their spot prices of Chana, Chilli, and Turmeric, respectively. It is observed that the commodity futures are more effective in hedging, and the near month futures contracts are suitable for hedging.

This paper proposes a new econometric model for the estimation of optimal hedge ratios (HRs): the Kalman filter error-correction model (KF–ECM). When we construct a hedging model involving a stock index and its futures, the KF state-space model is used to extract the single best latent common trend between the stock index and its futures. After the best common trend has been obtained, we substitute it into an ECM to estimate the HR; therefore, the KF–ECM combines the merits of error correction and state-space hedge models. This paper uses daily data from the Taiwan Capitalization Weighted Stock Index and its futures from July 21, 1998 to March 27, 2019 to evaluate the hedging performance of the KF–ECM. The study uses a hedging effectiveness (HE) index to compare the performance of the KF–ECM with that of other hedging models, including ordinary least squares, generalized autoregressive conditional heteroscedasticity and cointegrating ECMs. The empirical results of testing both in-sample and out-of-sample data show the KF–ECM to be more effective than other hedging models. The results also demonstrate that, regardless of the financial crisis, the HE of the KF–ECM remains the highest among all the models.

The purpose of this study is to determine the extent to which canola (Brassica napus L. var. napus) is distinct from soybeans [Glycine max (L.) Merr.] from a marketing perspective. If the supply and demand fundamentals of canola are closely related to those affecting the soybean complex then, from a marketing standpoint, the two crops are substitutes because canola producers and merchandisers can employ marketing strategies similar to those for soybeans. The degree to which canola and soybeans are similarly affected by market fundamentals is measured here by conventional hedging effectiveness analyses. Relationships between canola prices and soybean, soybean oil, and soybean meal futures prices are estimated to determine whether soybean futures markets can be effectively used to crosshedge canola price risk [...]

Hedge 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.

A powerful method in the analysis of datasets where there are many natural clusters with varying statistics such as different sizes, shapes, density distribution, overlaps, etc., is the use of self-organizing maps (SOMs). However, further processing tools, such as visualization and interactive clustering, are often necessary to capture the clusters from the learned SOM knowledge. A recent visualization scheme (CONNvis) and its interactive clustering utilize the data topology for SOM knowledge representation by using a connectivity matrix (a weighted Delaunay graph), CONN. In this paper, we propose an automated clustering method for SOMs, which is a hierarchical agglomerative clustering of CONN. We determine the number of clusters either by using cluster validity indices or by prior knowledge on the datasets. We show that, for the datasets used in this paper, data-topology-based hierarchical clustering can produce better partitioning than hierarchical clustering based solely on distance information.

This paper employs the Kalman filter procedure to explore the impact of yield curve factors on the hedging of Japanese government bond (JGB) using treasury futures. Three parameters (i.e., level parameter, slope parameter, and curvature parameter) embedded in Nelson and Siegel (1987) are used to be the proxies of interest rate risk. The out-of-sample hedging performance is also provided by moving window technology. The empirical results indicate that there is a significant relationship between the optimal hedge ratio and the yield curve factors. However, the time varying hedge ratio that includes the yield curve variables from the information set would not provide good out-of-sample hedging effectiveness. But the out-of-sample results also demonstrate that the performance of the time varying hedge ratio with yield curve factors is better than hedge ratio with naive hedge or OLS model.

This paper investigates optimal futures hedge ratios in stock markets. We use univariate skewed t stochastic volatility (SV) models to capture the time-varying (TV) volatility of our data and set up Markov-switching (MS) copula models to derive the dynamic dependence structure. According to the variance minimization method, we obtain optimal hedge ratios for the CSI 300 Index spot and futures in China’s stock market. We examine the hedging performance of various models and compare their effectiveness with the most common dynamic copula hedging models, including Patton’s TV copula and Engle’s dynamic conditional correlation (DCC) copula models. The empirical results show that the proposed MS dynamic copula models derive better hedging effectiveness than the corresponding dynamic copula models. The hedge ratios constructed by the MS time-varying (MSTV) Gaussian copula model demonstrate the best performance in terms of variance reduction.

Based on a multilevel nonlinear mixed-effect model approach, a stand basal area model was developed for Cunninghamia lanceolata (Lamb.) Hook. plantations belonging to the National Forest Inventory in China. The database consists of 583 plots embracing 18 different blocks within three seed source sites in this study. Of the plots, 80% were randomly selected for model fitting and 20% were carried out for model validation. The modified Chapman–Richards and Schumacher models were evaluated to find a basic model. The explanatory variables included stand dominant height, stand age and total number of stems per hectare. After selection of the basic model, the fitting and predictive ability of a multilevel nonlinear mixed-effect model was analysed. Site-, block- and plot-level random-effects terms were assessed for their contributions to improve model prediction over the ordinary least squares (OLS) method widely used in forest management. In addition, within-plot variance–covariance structure was taken into account owing to the repeated measurements and hierarchical structure of the data set. When evaluating the predictive accuracy of the final model, the first measurement was used for estimation of random parameters. The Chapman–Richards model was finally selected for the basic model based on model-fitting statistics, and both the fitting model and validation data with site-, block- and plot-level random effects showed a substantial improvement compared with the OLS method. After taking into account a reasonable variance–covariance structure, the model performed better than the model developed using only random effects.

When using derivative instruments such as futures to hedge a portfolio of risky assets, the primary objective is to estimate the optimal hedge ratio (OHR). When agents have mean‐variance utility and the futures price follows a martingale, the OHR is equivalent to the minimum variance hedge ratio,which can be estimated by regressing the spot market return on the futures market return using ordinary least squares. To accommodate time‐varying volatility in asset returns, estimators based on rolling windows, GARCH, or EWMA models are commonly employed. However, all of these approaches are based on the sample variance and covariance estimators of returns, which, while consistent irrespective of the underlying distribution of the data, are not in general efficient. In particular, when the distribution of the data is leptokurtic, as is commonly found for short horizon asset returns, these estimators will attach too much weight to extreme observations. This article proposes an alternative to the standard approach to the estimation of the OHR that is robust to the leptokurtosis of returns. We use the robust OHR to construct a dynamic hedging strategy for daily returns on the FTSE100 index using index futures. We estimate the robust OHR using both the rolling window approach and the EWMA approach, and compare our results to those based on the standard rolling window and EWMA estimators. It is shown that the robust OHR yields a hedged portfolio variance that is marginally lower than that based on the standard estimator. Moreover, the variance of the robust OHR is as much as 70% lower than the variance of the standard OHR, substantially reducing the transaction costs that are associated with dynamic hedging strategies. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:799–816, 2003

This study analyzes the factors influencing Indonesia’s import value during the period 2021–2025 using the Ordinary Least Squares (OLS) method. To ensure the validity of the model, a series of classical assumption tests were conducted in accordance with the Best Linear Unbiased Estimator (BLUE) criteria, including tests for normality, multicollinearity, heteroscedasticity, and autocorrelation. The data were obtained from official publications of the Central Statistics Agency (BPS) and other relevant sources. The estimation results demonstrate that the independent variables, namely the exchange rate (X₁), national income (X₂), foreign exchange reserves (X₃), inflation rate (X₄), and interest rate (X₅), exert varying effects on Indonesia’s import value, with certain variables exhibiting significant influence while others remain insignificant. The model is free from violations of the classical assumptions, thereby meeting the criteria of the Best Linear Unbiased Estimator (BLUE). Keywords: Import Value, OLS, Classical Assumption Tests, Macroeconomics

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.

This research article primarily focuses on the estimation of parameters of a linear regression model by the method of ordinary least squares and depicts Gauss-Mark off theorem for linear estimation which is useful to find the BLUE of a linear parametric function of the classical linear regression model. A proof of generalized Gauss-Mark off theorem for linear estimation has been presented in this memoir. Ordinary Least Squares (OLS) regression is one of the major techniques applied to analyse data and forms the basics of many other techniques, e.g. ANOVA and generalized linear models [1]. The use of this method can be extended with the use of dummy variable coding to include grouped explanatory variables [2] and data transformation models [3]. OLS regression is particularly powerful as it relatively easy to check the model assumption such as linearity, constant, variance and the effect of outliers using simple graphical methods [4]. J.T. Kilmer et.al [5] applied OLS method to evolutionary and studies of algometry.

Hedging effectiveness is the proportion of price risk removed through hedging. Empirical hedging studies typically estimate a set of risk minimizing hedge ratios, estimate the hedging effectiveness statistic, apply the estimated hedge ratios to a second group of data, and examine the robustness of the hedging strategy by comparing the hedging effectiveness for this period to the period. This study focuses on the statistical properties of the in-sample and out-of-sample hedging effectiveness estimators. Through mathematical and simulation analysis we determine the following: (a) the R2 for the hedge ratio regression will generally overstate the amount of price risk reduction that can be achieved by hedging, (b) the properly computed hedging effectiveness in the hedge ratio regression will also generally overstate the true amount of risk reduction that can be achieved, (c) hedging effectiveness estimated in the out-of-sample period will generally understate the true amount of risk reduction that can be achieved, (d) for equal numbers of observations, the overstatement in (b) is less that the understatement in (c), (e) both errors decline as more observations are used, and (f) the most accurate approach is to use all of the available data to estimate the hedge ratio and effectiveness and to not hold any data back for hedge strategy validation. If structural change in the hedge ratio model is suspected, tests for parameter equality have a better statistical foundation that do tests of hedging effectiveness equality.