Hedging with Chinese commodity futures : evidence from 2010 to 2017

(1)

Hedging with Chinese commodity futures.

Evidence from 2010 to 2017.

MSc Finance: Asset Management track Manqin He 10621245

Date: 06/2017 Supervisor: dr. L. (Liang) Zou

(2)

2

Statement of Originality

This document is written by Manqin He who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

(3)

3

Abstract

This paper aims to analyze the optimal hedging strategy of Chinese commodity futures for the period from 2010 to 2017. Ten commodity products are analyzed and five hedging strategies including no-hedge, half-hedge, full-hedge, static(OLS) hedge ratio and dynamic(DCC-GARCH and DCC-EGARCH) hedge ratios are compared in this paper. Both normal and student-t distributions are applied for model specification and both in-sample analysis and out-of-sample analysis(90 trading days) are performed. In general, hedging is more effective for metal products with hedging

effectiveness of around 60 to 80 percent while for agricultural commodities, it is approximately 20 to 30 percent. OLS hedging strategy performs the best in most cases so dynamic hedge ratios obtained from DCC-GARCH models do not lead to better performance. In addition, models with normal distribution perform better than with student-t distribution and DCC-GARCH gives higher risk reduction than DCC-EGARCH. It is also notable that hedging performance is improved after imposing constraints on hedge ratios. Moreover, hedging performance is different in bull and bear market. Both for in-sample and out-of-sample analysis, bull market outperforms bear market in reducing variance while bear market is preferred for avoiding downside risk.

(4)

4

List of tables and figures

Table 1 Empirical evidence ... 15

Table 2 Empirical evidence for Chinese market ... 16

Table 3 Spot and futures sample series ... 23

Table 4 Futures contract information ... 24

Table 5 The underlying products for each commodity futures ... 24

Table 6 Summary statistics for spot and futures daily returns from Jan 1, 2010 to March 31, 2017, original prices are measured in Chinese Yuan ... 25

Table 7 Tests for GARCH models ... 26

Table 8 In-sample hedge ratios ... 29

Table 9 In-sample hedging performance ... 31

Table 10 In-sample hedge ratios(constrained) ... 32

Table 11 In-sample hedging performance(constrained) ... 32

Table 12 Out-of-sample hedge ratios ... 34

Table 13 Out-of-sample hedging performance ... 36

Table 14 Out-of-sample hedge ratios(constrained) ... 37

Table 15 Out-of-sample hedging performance(constrained) ... 38

Table 16 Bear and bull markets segmentations(in-sample) ... 39

Table 17 In-sample hedging performance in bear and bull markets(unconstrained) ... 41

Table 18 Bear and bull markets segmentations(out-of-sample) ... 44

Table 19 Out-of-sample hedging performance in bear and bull markets(unconstrained) ... 46

Figure 1 In-sample hedge ratios ... 29

Figure 2 Out-of-sample hedge ratios ... 35

Figure 3 Bear and bull markets segmentations(in-sample) ... 40

(6)

6

1 Introduction

Futures contracts are widely used to hedge the price risk. Compared to other hedging instruments, futures are exchange-traded and are with standardized contracts. Futures are therefore having lower counterparty risk and are more liquid than others. Chinese futures market has been developed rapidly since 2000. According to The 2016 Development Report on China's Futures Markets1

published by Shanghai Institute of Futures and Derivatives, the total trading value of Chinese futures has increased from approximately zero in 2003 to more than 500 trillion RMB in 2015. Moreover, the report also showed that the three main commodity futures exchanges in China have ranked the top three exchanges in the world with the highest trading volume of commodity futures and options. This rapid development worth attention and the aim of this paper is to analyze the optimal hedging strategies of Chinese commodity futures for the period from 2010 to 2017.

Hedging with futures contracts has been widely documented in academic studies. Many researchers tried to estimate the optimal hedge ratios by using different econometric models and then compare their hedging effectiveness to find out which strategy gives the best performance. However, their results are mixed and it is still unclear how to hedge optimally. One of the key concerns in futures hedging is the comparison between constant and dynamic hedge ratios. On the one hand, Kroner and Sultan(1993), Park and Switzer(1995) and Myers(2000) found empirical

evidence showing that time-varying hedging strategies outperformed constant strategies. In contrast, Lien, Tse and Tsui(2002), Byström(2003) and Copeland and Zhu(2006) found constant hedge ratios performed better. Besides, Byström(2003) argued that the costs of time-conditional hedging strategy will be too high since it needs to adjust hedge ratios on a daily basis. Hence, no agreement has been made on which strategy is better. The main question of this paper is therefore: do dynamic hedging strategies outperform constant hedging strategies in Chinese commodity market?

To answer the research question, ten commodity products including soybean meal, rapeseed meal, white sugar, palm olein, soybean oil, steel rebar, iron ore, silver, copper and nickel will be analyzed and I will compare five hedging strategies including no-hedge, half-hedge, full-hedge, static hedge ratio and dynamic hedge ratio in this paper. Static hedge ratio will be obtained from Ordinary Least Square(OLS) method and I will adopt DCC-GARCH and DCC-EGARCH to estimate dynamic hedge ratios. Both normal and student-t distribution will be applied in model specifications and both in-sample analysis and out-of-sample analysis(of 90 trading days) will be performed. I will use three criteria to measure the hedging performance, namely average daily return of the hedged

(7)

7

portfolio, variance reduction(HE) and downside risk(LPM) reduction. Moreover, in order to avoid taking speculative position and to avoid excessive trading, hedging performance of constrained hedge ratios will be also presented as well. Furthermore, similar to Chang, Lai and Chuang(2010), I will provide comparative results of hedging performance under increasing and decreasing price trend.

This paper contributes to the existing literatures in several ways. Firstly, researches on Chinese futures hedging strategy are limited and this paper can add evidence for Chinese commodity futures. To my best knowledge, only eight papers provide empirical evidence for the hedging

effectiveness of Chinese futures and only five of them are relevant for commodities. Previous studies are focusing on metal products including copper, aluminum and gold and this paper will add

evidence for agricultural products. Secondly, although EGARCH can solve the limitation of GARCH by allowing for asymmetric reaction in volatility, there are not many applications of EGARCH to

estimate hedge ratios. Only Awang, Azizan, Ibrahim and Said(2014) provides analysis for it and they found EGARCH(and OLS) are preferred over others. Moreover, this paper will combine DCC with EGARCH to model the conditional correlation and volatility. Only Kotkatvuori-Ö rnberg(2016) has applied DCC-EGARCH to estimate the optimal hedge ratios. He has compared between OLS, ECM, CCC-EGARCH, CCC-EGARCH with realized variance(RV), DCC-EGARCH and DCC-EGARCH with RV and found DCC-EGARCH with RV outperformed in most cases. Different from his work, this paper will focus on comparing DCC-GARCH with DCC-EGARCH. In addition, both normal and student-t

distributions will be used for model specifications. Last but not least, this paper also links to the work of Chang, Lai and Chuang(2010), who have found that the hedging performance is not parallel in different price patterns. Based on their work, I will separate the whole sample period into several bull and bear markets for each commodities and analyze the optimal hedging strategies under different price trends.

The remainder of this paper is organized as follows. Chapter 2 will briefly describe the development of futures hedging theory, provide background information about Chinese commodity and futures market, discuss the existing econometric models that can be applied to estimate the optimal hedge ratios and summarize relevant empirical studies. Chapter 3 will derive hypotheses based on literature review and then introduce in details about the methodology used in this paper. Chapter 4 will provide information about data source, summary statistics and all other relevant data descriptions. Chapter 5 and 6 will display the main results of this paper and the last chapter will give conclusions.

(8)

8

2 Literature review

This section presents relevant literatures on futures hedging and gives background information about Chinese market. This section starts with the development of futures hedging theory, followed by the current condition of Chinese futures market. Next, descriptions of ten commodity products analyzed in this paper are provided and the underlying factors that can cause price fluctuations in the spot market are discussed. Moreover, detailed information about the existing econometric methods that are used to derive the optimal hedge ratios are explained. Finally, empirical evidence from previous papers are summarized.

2.1 Futures hedging theory

The development of futures hedging theory has three stages(Ederington, 1979). Traditional hedging theory states that the motivation behind hedging is to avoid the price risk in the spot market by transferring the risk to speculators. Hedgers aim to offset the losses in the spot market by the gains received in the futures market. Theoretically, futures market is the forward spot market and futures price is the expected spot price. Therefore, the factors that can affect spot price will also influence futures price and the changes are similar in both markets. Moreover, because of the existence of arbitragers, the spot and futures price will gradually become the same when futures contracts approach expirations. Therefore, the implied hedging strategy under traditional hedging theory is simply taking an opposite position in the futures market with the same size and the same type of product as in the spot market(naïve strategy). However, the traditional hedging strategy is only effective when spot and futures markets are fully correlated and when no transaction costs are involved. While in practice, spot and futures markets are difficult to be fully correlated and the changes of spot and futures prices are usually not consistent. Working(1953) has introduced the concept of basis risk for hedging, which implies that the price changes in spot and futures markets are not parallel. He argued that the motivation behind hedging is not for risk minimizing but more importantly, to maximize the profit. Hedgers can choose the benchmark price, basis and terms of transaction by themselves and do not need to consider the actual spot price at the time of

transaction. In this way, hedgers can transfer their basis risk to other traders and receive profits at the same time. More recently, Ederington(1979) used the portfolio theory to explain hedging activities. From his perspective, hedging is equivalent as creating an investment portfolio by using both spot commodities and futures contracts and investors will determine the trading position to maximize the expected profit and to minimize the risk of that portfolio.

(9)

9

2.2 Chinese futures market

The common definition of hedging used in Chinese futures market is similar to the traditional hedging theory. According to The elements of futures brokerage contract2_{published by China}

Securities Regulatory Commission in 2013, hedging is defined as taking an opposite position of futures contracts to hedge the price risk in the spot market, with the same product type and an equal contract size(naïve hedging strategy). More recently, in 2015, Ministry of Finance of the People’s Republic of China has published The Temporary Regulations of Commodity Futures Hedging Accounting Treatment3_{to encourage futures hedging behavior. This document abolished the rigid}

requirement of 80%-125% hedging effectiveness and introduced a “rebalancing method” allowing firms to adjust hedge ratios to meet the required hedging effectiveness4_{. There are three main}

commodity futures exchanges in China, namely Dalian Commodity Exchange(DCE), Zhengzhou Commodity Exchange(ZCE) and Shanghai Futures Exchange(SHFE). All of their traded commodity futures are listed in Appendix 1. Ranked by the trading volume in 2015, the top five agricultural commodity futures in the global market are soybean meal(DCE), rapeseed meal(ZCE), sugar(ZCE), RBD palm olein(DCE) and soybean oil(DCE) futures. Similarly, the top five global metal commodity futures are steel rebar(SHFE), iron ore(DCE), silver(SHFE), copper(SHFE) and nickel(SHFE) futures.

2.3 Chinese commodity market

Chinese commodity market is important in the global market. The following paragraphs will describe in details about the situations of ten Chinese commodities and the underlying factors behind their price fluctuations. To start with, soybean oil is extracted from soybean and it is widely used for cooking. According to United States Department of Agriculture5_{, China is the largest production and}

consumption country for soybean oil. By the year of 2016/17, China accounts for 29 percent of the world production and 30 percent of the overall consumption of soybean oil. From 2012 to 2016, Chinese production of soybean oil has been increased by 33 percent and Chinese consumption has been increased by 28 percent. Soybean meal is the by-product of soybean after extracting soybean oil from it and the main use of soybean meal is to feed poultry. Similarly, China accounts for the largest share of total production and consumption of soybean meal. Several factors contribute to the price fluctuations of soybean oil and meal. Firstly, the supply of soybean can affect the production of

2_{http://www.cfachina.org/ZCFG/BMGZ/201608/t20160810_2053767.html}

3_{http://www.mof.gov.cn/zhengwuxinxi/caizhengwengao/wg2016/wg201602/201606/t20160601_2116319.html}

4_{http://www.shfe.com.cn/upload/20160816/1471335525810.pdf} 5_{https://apps.fas.usda.gov/psdonline/circulars/oilseeds.pdf}

(10)

10

soybean oil and meal and can further influence their prices. When the supply increases, the price of soybean oil and meal will decrease. Second underlying factor would be the price of the imported soybean. As shown in Appendix 3, the supply of soybean in China is heavily depending on the

imported soybean. Therefore, the price of imported soybean can affect the price of Chinese soybean oil and meal more significantly. Thirdly, the efficiency of soybean crushing will influence the supply of soybean oil and meal. If the crushing process is not efficient, oil factory will stop production and as a result, the price of soybean oil and meal will increase. Fourthly, due to the fact that soybean oil and meal are not easily storable for a long time, when the inventory increases, the price will

decrease. From the consumption side, the price of livestock is positively related to the price of soybean meal and the prosperity degree of restaurant industry is relevant for the price of soybean oil.

Palm oil is widely used for industrial purposes and in the food industry. As shown in Appendix 2, Indonesia and Malaysia are the main production country for palm oil, which accounts for 54 percent and 31 percent of the world production in the year of 2016/17. China is fourth largest consumption country(8%) and the third largest importing country(11%) for palm oil6_{. Same as}

soybean oil, supply, importing price, inventory and consumption are the key driven factors of palm oil price fluctuations.

Similar to soybean meal, rapeseed meal is extracted from rapeseed and is widely used as an aquatic or animal feed. As shown in Appendix 2, China is the second largest production and

consumption country of rapeseed meal in the world, which accounts for 25 percent of total production and 26 percent of total consumption. The main rapeseed production areas in China are located in Hubei, Jiangsu, Zhejiang, Jiangxi, Hunan and Chongqing provinces. Except for those factors that are mentioned for soybean meal and oil, some other elements could also influence the price of rapeseed meal. Firstly, since the end of 2008, Chinese government has introduced a state purchasing policy to support the minimum purchasing price of rapeseed and has continuously lifted the

purchasing price in the following years. Due to the higher price of raw materials, the price of rapeseed meal has been increased as well. Therefore, the state purchasing price of rapeseed is an important indicator for the price of movements of rapeseed meal. Secondly, since the last quarter of 2009, Chinese government has started to restrict the import of rapeseed and as a result, the supply of rapeseed meal has been decreased. To reduce the supply shortage, firms started to import rapeseed meal directly from other countries. In addition, importing of rapeseed meal in China is

(11)

11

exempt from import value-added tax. The competitive price of foreign rapeseed meal will reduce the demand of domestic rapeseed meal and will depress the price as well. Thirdly, the price fluctuations of rapeseed meal is also depending on the global demand and supply of oilseed market. If the world production of oilseed has declined and does not meet the demand, the domestic price of rapeseed meal will increase.

White sugar is usually made from sugarcanes and sugar beets and is an important material in food and pharmaceutical industry. Brazil and India are the two largest countries for producing sugar and the main productive areas in China are located in Guangxi and Yunnan provinces. As for demand, China is the third largest country in sugar consumption and accounts for 9 percent of the global consumption in the year of 2016/17(Appendix 2). According to the United States Department of Agriculture7_{, China has been the world largest importing country of sugar for the past five years from}

2012 to 2016. Expect for the factors mentioned previously, there are two extra features in Chinese market that play a role in the sugar price movements. Firstly, Chinese government has established “sugar reserves” since 1991 to stabilize the market. When there is supply shortage, government will increase supply by transferring sugar from reserves to the market. Secondly, Chinese festivals could influence the price of white sugar. For instance, the consumption of white sugar will be increased a few weeks before the spring festival or the mid-autumn festival and therefore the price of white sugar are usually higher during that period.

China also plays an important role in production and consumption of metal commodities. For iron ore, China is the third largest country in producing usable ore8_{and is the largest importer in}

2016(67.8% of total iron ore imports)9_{. For steel rebar, China accounts for almost 50 percent of both}

the world crude steel production and the global apparent steel use in 201510_{. According to the}

United States Geological Survey, China is the third biggest production country for copper and silver in 2016 and by the latest data provided on the World's Richest Countries website, China is the largest importer for both copper and nickel. Expect for supply, demand, economic situation, importing and exporting policies, price of substitutes, mining cost is another important factor that will influence the price of metal commodities. In addition, because silver is considered to be a safe-haven asset, global political status will also affect the price movements.

7_{https://apps.fas.usda.gov/psdonline/circulars/Sugar.pdf}

8_{https://minerals.usgs.gov/minerals/pubs/commodity/iron_ore/mcs-2017-feore.pdf} 9_{http://www.worldstopexports.com/iron-ore-imports-by-country/}

(12)

12

2.4 Econometric models

Different objective functions have been developed to estimate the optimal futures hedging strategy and the main method used in previous studies is to minimize the variance(MV hedge raito). Several econometric models can be applied for it. The conventional ordinary least squares(OLS) method is widely used to estimate static hedge ratio. Engle and Granger(1987) suggested that OLS method is wrongly specified when two time series are cointegrated and in this case, an error-correction term must be included. Based on this, Ghosh(1993) developed an error correction model(ECM) to estimate the optimal hedge ratio. Another limitation of OLS is when the residual series are

autocorrelated(Herbst, Kare and Marshall, 1993).To eliminate the serial correlation, bivariate-vector autoregression model(B-VAR) is proposed. Furthermore, vector error correction model(VECM) is developed from VAR to include the cointegration effect.

Engle(1982) proposed the autoregressive conditional heteroscedastic(ARCH) process for the case when heteroskedasticity is present. Bollerslev(1986) further developed generalized

ARCH(GARCH) models which can be used to estimate the optimal time-conditional hedge ratios. Based on the findings of Engle and Granger(1987) and Bollerslev(1986), Kroner and Sultan(1993) combined ECM and GARCH to develop ECM-GARCH model in order to capture the cointegration effect between spot and futures prices. Moreover, Bollerslev(1987) further improved GARCH models by allowing for conditionally student-t distributed errors.

However, GARCH models are forced to react symmetrically towards positive and negative information while in real situations, reactions are not necessary the same. In other words, bad news can cause more reaction in volatility than good news. To model the asymmetric reaction in volatility, Nelson(1991) proposed the exponential GARCH(EGARCH) and Glosten, Jagannathan and

Runkle(1993) developed GJR-GARCH. Another limitation of GARCH is that it implies high level of persistence. However, financial market is changing rapidly over time and if there are structural changes in conditional volatility, the implication of high persistence will be biased. To better capture the structural changes in volatility, Hamilton and Susmel(1994) introduced Markov Switching with ARCH models and Gray(1996) further generalized it into Markov Regime-Switching(MRS) GARCH models.

Compared to the univariate GARCH models described above, many multivariate GARCH models are proposed to not only estimate the conditional variance but also the time-conditional covariance matrix between spot and futures prices. Bollerslev, Engle and

Wooldridge(1988) developed VECH-GARCH and it is directly extended from the univariate GARCH models. Engle and Kroner(1995) further proposed BEKK-GARCH model and it is a restricted version

(13)

13

of VECH with less parameters. Moreover, Engle, Ng and Rothschild(1990) suggested factor GARCH model which assumes that asset returns are generated by some underlying factors and these factors are in line with autoregressive conditional heteroskedasticity. Based on this, Van der Weide(2002) introduced generalized orthogonal(GO) GARCH model.

Although empirical results showed that multivariate GARCH performs better than univariate GARCH, multivariate GARCH models need to include additional complicated parameters that are difficult to estimate. To simplify the process, Bollerslev(1990) introduced constant conditional correlation(CCC) GARCH model which assumes time-variant conditional variances and covariance while with time-invariant conditional correlations. However, the assumption is not in line with the dynamic correlation coefficient that can be observed from real financial data. Engle(2002) improved CCC-GARCH and introduced dynamic conditional correlation(DCC) GARCH model to allow time-varying correlations. His model divides the conditional covariance matrix into conditional variance and conditional correlation matrix and then parameterize them separately. DCC-GARCH is therefore easy to estimate while can describe volatility better than CCC. Furthermore, Cappiello, Engle, and Sheppard(2006) extended DCC to asymmetric generalized dynamic conditional correlation(ADCC) model and this model allows asymmetric reactions in conditional variances and correlations towards negative news or returns. Similarly, Storti(2008) proposed multivariate bilinear(BL) GARCH.

After deriving the optimal hedge ratio, is it important to test if the hedging is effective. Ederington(1979) estimated the minimum variance(MV) hedge ratio and tested for its effectiveness by calculating the percentage reduction for the variance of hedged portfolio, which has been widely used in many papers. However, this measure accounted for reducing both upside and downside risk while for hedgers, they only want to avoid downside risk. Bawa(1975) introduced the lower partial moment(LPM) as a measure of downside risk.

2.5 Empirical evidence

Empirically, Ederington(1979) was the first to prove that when the objective is to minimize the price risk, naïve hedging strategy is not optimal. Table 1 presents selected empirical evidences from previous studies. On the contrary to Ederington(1979), Wang and Yang(2015) compared the out-of-sample hedging performance between naïve and other minimum variance hedging strategies using 18 econometric models and 24 futures markets and found that it is difficult to outperform naïve hedge ratio. Lien, Tse and Tsui(2002) found the OLS hedge ratio estimated with daily rollover performed better than the constant-correlation vector-GARCH hedge ratios. They argued that GARCH models have high computational costs and hence is not optimal for hedging purpose. Baillie and Myers(1991) examined the hedge ratios estimated by bivariate GARCH model and reported that

(14)

14

the range of variance reductions is between 52 percent for cotton and 7 percent for coffee. In general, they found BGARCH outperformed constant hedge ratio, both for in-sample and out-of-sample analysis. Lien and Yang(2008) found empirical evidence showing that the basis(difference between spot and futures prices) effect in commodity markets on volatility is asymmetric. In other words, the positive basis has stronger effect on variance than the negative basis. They compared asymmetric BGARCH, symmetric BGARCH, conventional BGARCH and OLS and concluded that including the asymmetry effect can lead to larger risk reduction. Zhang and Choudhry(2015) analyzed the forecasting ability of six different GARCH models including bivariate GARCH, BEKK, GARCH-X, BEKK-X, Q-GARCH and GARCH–GJR with both normal and student-t distributions. They found BEKK-type models outperform for storable agricultural products while asymmetric GARCH models are preferred for non-storable commodities.

The empirical evidence of EGARCH is quite limited and only one paper studied the futures hedging performance with EGARCH. Awang, Azizan, Ibrahim and Said(2014) investigated the hedging performance of OLS, VECM, EGARCH and bivariate GARCH by applying them into the stock index futures markets in Malaysia and Singapore. They found OLS and EGARCH are preferred over others.

Previous results for DCC-GARCH are mixed. Chang, McAleer and Tansuchat(2011) compared the usefulness of crude oil hedging strategies using BEKK, CCC, DCC, and VARMA-GARCH models and found diagonal BEKK and DCC gave the best performance with 57 percent variance reduction for Brent and 81 percent for WTI. Basher and Sadorsky(2016) used DCC, ADCC and GO-GARCH to analyze the cross-hedging strategies for emerging market stock prices by using oil, gold, VIX, and bonds. They compared both normal and student-t distributions for DCC and found DCC with multivariate-t distribution had the best fit. As a result, all models are estimated with MVT and they concluded ADCC performed the best in most cases. Similarly, Toyoshima, Nakajima and Hamori(2013) applied DCC, ADCC and diagonal BEKK in analyzing the hedging performance of crude oil futures and concluded that DCC and ADCC outperformed BEKK. Pan, Wang and Yang(2014) added evidence for regime switching models. They developed a regime switching asymmetric DCC(RS-ADCC) model and compared its hedging performance with BEKK, CCC, DCC and RS-DCC. Variance reduction and utility are both considered to measure hedging effectiveness and they found RS-ADCC performed the best for out-of-sample period. Chang, Lai and Chuang(2010) have analyzed the hedging effectiveness of energy futures in different price scenarios and found hedging performance is better when the market experienced upward price trend. Meanwhile, they compared hedging performance between OLS, MD-GARCH, BEKK, CCC, ECM-MD, ECM-BEKK, ECM-CCC, and the state space model that allows for non-constant value in mean equation. They concluded that state space model ranked the highest

(15)

15

for in-sample analysis and CCC-GARCH and ECM-CCC models performed the best for out-of-sample analysis. Kotkatvuori-Ö rnberg(2016) combined DCC with EGARCH based on copulas method and compare the hedging performances for OLS, ECM, CCC-EGARCH, CCC-EGARCH with realized variance(RV) estimator, DCC-EGARCH and DCC-EGARCH with RV. He found DCC-EGARCH with RV outperformed in most cases.

Table 1 Empirical evidence

Paper Model Product Frequency

Baillie and Myers (1991)

OLS, Bivariate GARCH Beef, coffee, corn, cotton, gold, soybeans Daily

Lien, Tse and Tsui(2002)

OLS, VGARCH(both re-estimated on a day-by-day rollover)

British Pound, Deutchmark, Japanese Yen, soybean oil, wheat, crude oil, corn, cotton, NYSE composite, S&P 500

Daily

Lien and Yang(2008) Asymmetric BGARCH, Symmetric BGARCH, Conventional BGARCH, OLS

Corn, soybeans, cotton, coffee, frozen pork bellies, lean hog, heating oil, light sweet crude oil, copper, silver

Daily

Chang, Lai and Chuang(2010)

OLS, MD-GARCH, BEKK-GARCH, CCC-GARCH, ECM-MD, ECM-BEKK, ECM-CCC, state space model

Crude oil and gasoline Daily

Chang, McAleer and Tansuchat(2011)

CCC, VARMA-GARCH, DCC, BEKK and diagonal BEKK

Crude oil(Brent and WTI) Daily

Toyoshima, Nakajima and Hamori(2013)

DCC, ADCC and diagonal BEKK Crude oil(WTI) Daily

Awang, Azizan, Ibrahim and Said(2014)

OLS, VECM, EGARCH and bivariate GARCH Malaysia’s Kuala Lumpur Composite Index (KLCI) and Singapore’s Straits Times Index (STI)

Daily

Pan, Wang and Yang(2014)

RS-ADCC, BEKK, CCC, DCC and RS-DCC Cude oil (WTI), conventional gasoline (New York Harbor) and heating oil (New York Harbor)

Weekly

Wang and Yang(2015) OLS, VAR, VEC, Adj. VEC, FIVEC, BEKK, ABEKK, CCC, ACCC, DCC, ADCC, GARCH-copula, GJR-GARCH-copula, MRS-OLS, MRS-VAR, MRS-VEC, MRS-BEKK, MRS-DCC

Crude oil, heating oil, natural gas, gasoline, aluminum, copper, lead, tin, zinc, gold, silver, corn, soybeans, soybean oil, wheat, oats, cotton, sugar, British pound, Canadian dollar, Japanese yen, FTSE 100, NIKKEI 225, S&P 500

Weekly

Zhang and Choudhry(2015)

bivariate GARCH, BEKK GARCH, GARCH-X, BEKK-X, Q-GARCH and GARCH–GJR

Wheat, soybean, live cattle and live hogs Daily

Basher and Sadorsky(2016)

DCC, ADCC and GO-GARCH Hedging emerging market stock prices with oil, gold, VIX, and bonds

Daily

Kotkatvuori-Ö rnberg(2016)

OLS, ECM, CCC-EGARCH, CCC-EGARCH with realized variance(RV), DCC-EGARCH and DCC-EGARCH with RV

Australian dollar (AUD), Canadian dollar (CAD), euro (EUR), British pound (BP), and Japanese yen (JPY)

(16)

16

As for Chinese market, only eight papers analyzed the hedging performance for Chinese futures and Table 2 summarizes the key information of these papers. Hua(2007) used OLS, VECM and MGARCH models to study the hedging performance of the Chinese copper futures and reported that time-varying hedge ratio could give both the highest return and the greatest risk reduction. Lien and Yang(2008) analyzed the asymmetric basis effect on hedging strategies for Chinese copper and aluminum commodities and found asymmetric BFIGARCH model gave the best performance in most cases. Wen, Wei and Huang(2011) compared the hedging effectiveness of CSI 300 stock index futures by using OLS, the symmetric BGARCH, the asymmetric BGARCH and time-varying copulas and concluded that the hedge ratio estimated by OLS performed the best in variance reduction. Similarly, Hou and Li(2013) also analyzed the CSI 300 stock index futures. They found that almost all models could reduce the variance by more than 92%. They also stated that DCC-BGARCH performed better for short horizons while CCC-BGARCH outperformed for long horizons. Lau and Bilgin(2013)

constructed a model(DHRSS) which can incorporate the spillover effect and the size basis effect when estimating dynamic hedge ratios. They considered structural breaks, spillover effect and the basis effect in their study and found the symmetric GARCH model performed the best for both in-sample and out-of-in-sample analysis. They concluded that the hedging effectiveness of Chinse aluminum futures is not significantly affected by the return and volatility spillover. Chen, Zhuo and Liu(2016) analyzed the hedging effectiveness of gold futures in China and found ECM-GARCH is the most efficient model in estimating hedge ratio. Chen, Leung, Poon and Su(2016) studied the basis effect on futures hedging for Chinese copper and aluminum futures contracts by applying BGARCH-DCC, Symmetric BGARCH-DCC and Asymmetric BGARCH-DCC models. They found considering basis effect is important to improve hedging performance especially for the asymmetric model. Instead of mean-variance hedge ratio, Dai, Zhou and Zhao(2017) used parametric method to estimate the optimal hedge ratio that can minimize the lower partial moments. This method is more consistent with investors’ concern because it allows hedging strategy to minimize only the downside risk. Table 2 Empirical evidence for Chinese market

Paper Model Product Frequency Period

Hua(2007) OLS, VECM, MGARCH Copper Daily 2004-2006

Lien and Yang(2008) OLS, Asymmetric BFIGARCH, Symmetric BFIGARCH, BFIGARCH

Copper and aluminum Daily 1996-2004

Wen, Wei and Huang(2011) OLS, Symmetric BGARCH, Asymmetric BGARCH, DCC Gaussian copula, DCC Student-t copula

CSI300 stock index Daily 2010-2011

Lau and Bilgin(2013) DHRSS, Symmetric BGARCH, Conventional BGARCH

Aluminum Daily 1993-2010

Hou and Li(2013) OLS, error-correction, wavelet hedging model, CCC-BGARCH, DCC-BGARCH

(17)

17

Chen, Zhuo and Liu(2016) OLS, ECM, VECM, ECM-BGARCH Gold Daily 2014-2015

Chen, Leung, Poon and Su(2016)

BGARCH-DCC, Symmetric BGARCH-DCC and Asymmetric BGARCH-DCC

Copper and aluminum Daily 1999-2008

Dai, Zhou and Zhao(2017)

Parametric method to minimize lower partial moments

(18)

18

3 Methodology

This chapter presents the methodology applied in this paper. First part of the chapter briefly discusses the main research method and develops four hypotheses based on literature review. The following four sections specify the econometric models in details and the last section provides information about performance measurements that are used to examine the hypotheses.

3.1 Hypotheses

In this paper, five hedging strategies will be compared, namely no-hedge, half-hedge(hedge ratio is 0.5; long one commodity spot and short 0.5 futures), full-hedge(hedge ratio is 1; long one

commodity spot and short one futures), static(OLS) hedge ratio and dynamic(GARCH and DCC-EGARCH) hedge ratios. Both the Gaussian normal distribution and the Student t-distribution will be applied. Compared to the standard normality assumption, student t-distribution is better in

capturing leptokurtosis and the fat-tail phenomenon that could appear in financial data. For the out-of-sample analysis, I will use the testing period of 90 trading days(approximately four months) for each product. The static hedge ratio generated by OLS will be used directly in the out-of-sample period. As for GARCH-based models, in-sample parameters will be used to forecast the out-of-sample period’s optimal hedge ratios. Dynamic forecasting method will be used. Similar to Chang, Lai and Chuang(2010), I will provide additional results about the hedging performance in both bear and bull markets. Based on the literature review, the following four hypotheses can be developed. Hypothesis 1: time-variant hedge ratios outperform time-invariant hedge ratios.

Hypothesis 2: EGARCH-based models outperform GARCH-based models.

Hypothesis 3: Models with student-t distribution outperform models with normal distribution. Hypothesis 4: Hedging is more effective in the bull market than bear market and the whole period.

3.2 Derive MV hedge ratio

The return of the hedged portfolio is,

𝑟ℎ𝑒𝑑𝑔𝑒𝑑= 𝑟𝑠− ℎ𝑟𝑓

where 𝑟𝑠= ∆𝑆𝑡= ln(𝑆𝑡) − ln(𝑆𝑡−1) and 𝑟𝑓 = ∆𝐹𝑡= ln(𝐹𝑡) − ln(𝐹𝑡−1) are spot return and futures return which can be calculated by taking the differences between the natural logarithm of today and previous day’s prices. ℎ indicates hedge ratio.

(19)

19

Minimum variance hedge ratio can be derived by minimizing the risk of hedged portfolio and Johnson(1960) used variance to measure risk. The objective function is therefore to minimize

var(𝑟ℎ𝑒𝑑𝑔𝑒𝑑), which is equal to,

var(𝑟ℎ𝑒𝑑𝑔𝑒𝑑) = 𝑣𝑎𝑟(𝑟𝑠) + ℎ2𝑣𝑎𝑟(𝑟𝑓) − 2ℎ × 𝑐𝑜𝑣(𝑟𝑠, 𝑟𝑓)

By taking the first order conditions with respect to ℎ and set it equal to zero, we can obtain the optimal hedge ratio,

ℎ∗₌𝑐𝑜𝑣(𝑟𝑠, 𝑟𝑓) 𝑣𝑎𝑟(𝑟𝑓)

= corr(𝑟𝑠, 𝑟𝑓)

𝑠𝑡𝑑(𝑟𝑠) 𝑠𝑡𝑑(𝑟𝑓)

This paper will use OLS, DCC-GARCH(1,1) and DCC-EGARCH(1,1) to estimate optimal hedge ratio.

3.3 OLS

Ederington(1979) proposed the OLS method by running the following regression, 𝑟𝑠= 𝛼 + 𝛽𝑟𝑓+ 𝜀,

where the optimal hedge ratio is equal to the estimate coefficient of 𝛽.

3.4 DCC-GARCH(1,1)

The equations for GARCH(1,1) are,

𝜀𝑡 = 𝜎𝑡𝑣𝑡 𝑣𝑡|Ω𝑡−1~𝑁(0,1) 𝜎𝑡2= 𝜔𝑜+ 𝛽𝜎𝑡−12 + 𝛼𝜀𝑡−12

where 𝜎𝑡2 is the conditional variance and it is depending on three variables: the mean 𝜔𝑜 indicates the long term average; 𝜀𝑡−12 (ARCH term) is the news about volatility in the previous period, measured as the lag of squared residual from the mean equation and 𝛼(ARCH effect) measures the short-term persistency of shocks to returns; 𝜎𝑡−12 (GARCH term) is the previous period’s forecast variance and 𝛽 denotes GARCH effect. 𝜔𝑜, 𝛽 and 𝛼 are non-negative parameters and meets the condition of 𝛼 + 𝛽 < 1. Ω𝑡−1 is the information till t-1. {𝜀𝑡} is the GARCH process and 𝑣𝑡 denotes Gaussian white noise with unit variance.

(20)

20

𝑟𝑠,𝑡= 𝜇𝑠+ 𝜀𝑠,𝑡

σ𝑠,𝑡2 = 𝜔𝑠,0+ 𝛽𝑠σ𝑠,𝑡−12 + 𝛼𝑠ε𝑠,𝑡−12 𝑟𝑓,𝑡= 𝜇𝑓+ 𝜀𝑓,𝑡

σ𝑓,𝑡2 = 𝜔𝑓,0+ 𝛽𝑓σ𝑓,𝑡−12 + 𝛼𝑠ε𝑓,𝑡−12 only constant is included in the mean equation.

DCC-GARCH(1,1) has the following specifications, 𝑟𝑡|Ω𝑡−1~𝑁(0, 𝐻𝑡)

𝐻𝑡 ≡ 𝐷𝑡𝑅𝑡𝐷𝑡 𝐷𝑡 = 𝑑𝑖𝑎𝑔(√ℎ𝑖𝑡)

𝑟𝑡 is the return at time t conditional on information collected till t-1 and this conditional return follows a normal distribution with a mean of zero and a variance-covariance matrix of 𝐻𝑡. 𝐷𝑡 is the n × n diagonal matrix of time-varying volatility from univariate GARCH models. 𝑅𝑡 is the time-conditional correlation matrix. ℎ𝑖𝑡 is the variance of univariate variable i which can be obtained from GARCH process.

DCC-GARCH(1,1) involves two steps for estimation. First, estimate univariate GARCH(1,1) for each time series and obtain the conditional volatility for each series √ℎ𝑖𝑡 . Second, use the standard deviations from the first step to calculate the standardized residuals 𝑢𝑖,𝑡 = 𝜀𝑖,𝑡/√ℎ𝑖𝑖,𝑡 and then use these residuals to estimate the conditional correlations.

3.5 DCC-EGARCH(1,1)

The difference between GARCH and EGARCH is about how they model conditional variance. In the EGARCH(1,1) specifications, ln(𝜎𝑡2) = 𝜔𝑜+ 𝛽 ln(𝜎𝑡−12 ) + 𝛾 𝜀𝑡−1 √𝜎_𝑡−12 + 𝛼 [ |𝜀_𝑡−1| √𝜎_𝑡−12 − √ 2 𝜋]

where 𝜎𝑡2 is the conditional variance, 𝛽 measures the persistence of the conditional variance from the past and 𝛼 measures the GARCH effect. 𝛾 is the most important parameter in this model and it captures the asymmetry effect(or the leverage effect). When 𝛾 is equal to zero, the model is symmetric. When 𝛾 is negative, bad news can generate more volatility than good news. And when

(21)

21

𝛾 is positive, good news will generate more volatility. Compared to GARCH, 𝜎𝑡2 depends on both size and the sign of lagged residuals in EGARCH specifications.

3.6 Hedging performance measurements

According to Ederington(1979), hedging effectiveness will be measured as the percentage reduction in variance,

HE = 1 − 𝑉𝑎𝑟(ℎ𝑒𝑑𝑔𝑒𝑑 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜)

𝑉𝑎𝑟(𝑢𝑛ℎ𝑒𝑔𝑑𝑒𝑑 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜)

Lower partial moments(long spot and short futures) with threshold of zero percent will be used to measure the reduction of downside risk,

Downside risk reduction = 1 − 𝐿𝑃𝑀(ℎ𝑒𝑑𝑔𝑒𝑑 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜) 𝐿𝑃𝑀(𝑢𝑛ℎ𝑒𝑔𝑑𝑒𝑑 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜)

To capture both risk and return hedging performance, average daily return of the hedged and unhedged portfolios will be considered as well.

(22)

22

4 Data and sample statistics

Based on the trading volume ranking reported by Shanghai Institute of Futures and

Derivatives(2016), the five most actively traded agricultural commodity futures including soybean meal, rapeseed meal, white sugar, RBD palm olein, soybean oil and five metal commodity futures including steel rebar, iron ore, silver, copper, nickel are selected as sample commodity products. All data are collected from iFinD database with daily frequency. As shown in Table 3, spot price series used in this paper are the average spot price. Except for soybean oil and white sugar that need to calculate manually, all other series are directly downloaded from the database. There are two types of futures price series, namely active and continuous. Continuous futures prices are the prices of the nearest month contracts and are the most relevant indicators for spot prices. However, recent-month contracts usually are not the most active contracts in Chinese futures market. For instance, the most active futures for American agricultural products are often three-month, two-month or one-month before the delivery month while for Chinese agricultural products; it becomes nine-month, eight-nine-month, six-month or five-month before the delivery month11_{. Therefore, continuous}

and active futures contracts are different and it is important to choose the right futures price series. I compare these two series and select the one that is better correlated with spot series. As a result, I will use continuous futures price series for copper, nickel and silver while for the rest, I will use active series. Spot and futures prices are matched on a daily basis and original prices are expressed in Chinese Yuan. Full sample period ranges from Jan 1, 2010 to March 31, 2017. Due to the fact that some commodity futures are introduced after 2010 and also because some products are lack of spot price information, different commodities have different starting dates and I will include as many data as possible. For each commodity, the whole period will be separated into two sub periods: the most recent 90 trading days(approximately four months) will be used for out-of-sample analysis and the rest will used for in-sample analysis. Table 4 provides detailed information about futures

contracts for each products and Table 5 shows the underlying products for each commodity futures. Table 6 presents the summary statistics of the spot and futures daily return for the whole sample period. The mean return for almost all time series are negative indicating that for the selected sample period, commodity prices generally experienced a downward trend. Expect for rapeseed meal, soybean meal, steel rebar and white sugar, the skewness of both spot and futures daily returns for all the rest sample products are close to zero meaning that the data are approximately symmetric.Most of the skewness are negative, indicating that the size of the left-handed tail is larger than the right side. Kurtosis for all the time series are greater than zero so the sample data

(23)

23

have leptokurtic distribution. Furthermore, the kurtosis measures for all series are larger than three indicating that the distributions of the returns have thick tails. The Jarque-Bera test statistics of all returns reject the null hypothesis of normal distribution. Number of observations are different for each products but are the same for spot and futures series. Last column provides the correlation between spot and futures return for every commodities. A higher correlation usually leads to better hedging performance. Generally, spot and futures market are better correlated for metal

commodities and correlation is lower for agricultural products. Some residual-based tests need to be performed before applying GARCH models and Table 7 gives the results for two tests. Before the test, I need to run the OLS regression of spot return on futures return to get the residuals. Then Serial Correlation Lagrange multiplier(LM) test can be used to test the null hypothesis of serial

independence. All series reject the null hypothesis so their residuals are autocorrelated. The Heteroskedasticity Test is to test the null hypothesis of no ARCH effect. Except for iron ore, the test results for all other series are rejected at 1 percent level indicating that they have autoregressive conditional heteroskedasticity up to the fifth order in their residuals. Therefore, GARCH models are valid to use.

Table 3 Spot and futures sample series

Commodity Spot series Futures series Whole period In-sample

period

Out-of-sample period

Copper Average spot price: no.1 cathode copper(Cu_Ag>=99.95%) Futures settlement price(continuous): cathode copper From 2010/1/4 to 2017/3/31 From 2010/1/4 to 2016/11/17 From 2016/11/18 to 2017/3/31

Iron ore National average price: domestic iron ore(62%)

Futures settlement price(active): iron ore

From 2013/10/25 to 2017/3/31 From 2013/10/25 to 2016/11/10 From 2016/11/14 to 2017/3/31

Nickel Average spot price: no.1 electrolytic nickel(Ni99.90) Futures settlement price(continuous): nickel From 2015/3/30 to 2017/3/31 From 2015/3/30 to 2016/11/17 From 2016/11/18 to 2017/3/31 Palm olien Spot price: palm oil(24

degree): regional average

Futures settlement price(active): palm oil

From 2013/6/26 to 2017/3/31 From 2013/6/26 to 2016/11/17 From 2016/11/18 to 2017/3/31 Rapeseed meal

Spot price: rapeseed meal: national average

Futures settlement price(active): rapeseed meal

From 2013/7/23 to 2017/3/31 From 2013/7/23 to 2016/11/17 From 2016/11/18 to 2017/3/31 Silver Average spot price: no.1

silver(99.99%) Futures settlement price(continuous): silver From 2012/5/11 to 2017/3/31 From 2012/5/11 to 2016/11/17 From 2016/11/18 to 2017/3/31 Soybean meal

Spot price: soybean meal: regional average

Futures settlement price(active): soybean meal

From 2010/1/4 to 2017/3/31 From 2010/1/4 to 2016/11/17 From 2016/11/18 to 2017/3/31 Soybean oil Average spot price:

first-grade soybean oil*

Futures settlement price(active): soybean oil

From 2011/6/28 to 2017/3/31 From 2011/6/28 to 2016/11/17 From 2016/11/18 to 2017/3/31 Steel rebar Steel rebar: HRB400

20MM: national average price

Futures settlement price(active): Steel rebar

From 2010/1/4 to 2017/3/31 From 2010/1/4 to 2016/11/17 From 2016/11/18 to 2017/3/31

(24)

24

White sugar Average spot price: white sugar*

Futures settlement price(active): white sugar

From 2010/1/4 to 2017/3/31 From 2010/1/4 to 2016/11/17 From 2016/11/18 to 2017/03/31 Note: *The spot price of soybean oil is calculated manually by taking the average of the daily price from the following 28 cities: Dalian, Dandong, Tianjin, Qinhuangdao, Linyi, Rizhao, Boxing, Qingdao, Ningbo, Zhangjiagang, Wuhan, Changsha, Fuzhou, Xiamen, Guangzhou, Dongguan, Nanning, Guiyang, Kunming, Haerbin, Beijing, Weifang, Yantai, Nantong, Zhoukou, Zhenjiang, Lianyungang, Zhanjiang. *The spot price of white sugar is calculated manually by taking the average of the daily price from the following 41 cities: Liuzhou, Kunming, Dianwei, Dali, Nanning, Zhanjiang, Guangzhou, Shantou, Haikou, Shanghai, Hangzhou, Ningbo, Yiwu, Nanjing, Nantong, Hefei, Rizhao, Qingdao, Qingzhou, Fuzhou, Jinjiang, Chongqing, Chengdu, Guiyang, Changsha, Zhengzhou, Xinxiang, Zhoukou, Shangqiu, Wuhan, Xian, Taiyuan, Beijing, Tianjin, Langfang, Shijiazhuang, Ü rümqi, Hohhot, Harbin, Changchun, Bayuquan.

Table 4 Futures contract information

Product Contract Size Price Quote Tick Size Daily Price Limit Trading hours

(Beijing time)

Minimum Trade Margin

Copper 5 tons Yuan/ton 10 Yuan/ton 3% of last settlement price Monday to Friday, 9:00 a.m. to 11:30 a.m., 1:30 p.m. to 3:00 p.m. 5% of contract value Steel Rebar 10 tons Yuan/ton 1 Yuan/ton 3% of last

settlement price

5% of contract value Silver 15 kilograms Yuan/kilogram 1Yuan/kilogram 3% of last

settlement price

4% of contract value

Nickel 1 ton Yuan/ton 10 Yuan/ton 4% of last

settlement price

5% of contract value Soybean Meal 10 MT Yuan/MT 1 Yuan/MT 4% of last

settlement price

5% of contract value Soybean Oil 10MT Yuan/MT 2 Yuan/MT 4% of last

settlement price

5% of contract value RBD Palm Olein 10MT Yuan/MT 2 Yuan/MT 4% of last

settlement price

Iron Ore 100MT Yuan/MT 1Yuan/MT 4% of last

settlement price

5% of contract value Rapeseed Meal 10 tons Yuan/ton 1 Yuan/ton 4% of last

settlement price

5% of contract value White Sugar 10 tons Yuan/ton 1 Yuan/ton 4% of last

settlement price

Table 5 The underlying products for each commodity futures

Product Underlying products

Copper Standard products: 1# Standard Copper Cathode (Cu-CATH-2) as prescribed in the National Standard of GB/T467-2010, with Copper+Silver≥99.95%.

Steel Rebar Standard Products: As specified in Steel for Reinforcement of Concrete–Part 2: Hot-rolled Ribbed Bar, GB1499.2-2007, with designation of HRB400 or HRBF400 with a diameter of 16mm, 18mm, 20mm, 22mm, 25mm

(25)

25

Silver Standard Product: Prescribed in the National Standard of GB/T 4135-2002 IC-Ag99.99, with a fineness of no less than 99.99%

Nickel Standard products: nickel cathode as prescribed in the National Standard of GB/T 6516-2010 Ni9996, with the total content of nickel and cobalt > 99.96%.

Soybean Meal DCE Quality Specification for the Delivery of Soybean Meal (F/DCE D001-2006) Soybean Oil DCE Soybean Oil Futures Delivery Quality Standard(GB 1535 Soybean oil) RBD Palm Olein _{DCE RBD Palm Olein Delivery Quality Standard Melting Point≤24℃} Iron Ore DCE Iron Ore Delivery Quality Standards with Iron (Fe)=62.0%

Rapeseed Meal Benchmark delivery product: Grade 4 rapeseed meal conforming to “National Standard of the People’s Republic of China, Rapeseed Meal for Fodder Use” (GB/T 23726-2009)

White Sugar Grade 1 white sugar conforming to GB 317-2006

Sources: Shanghai Futures Exchange website; Dalian Commodity Exchange website; Zhengzhou Commodity Exchange website.

Table 6 Summary statistics for spot and futures daily returns from Jan 1, 2010 to March 31, 2017, original prices are measured in Chinese Yuan

Commodity Mean(%) Std. Dev.(%) Skewness Kurtosis Jarque-Bera JB Prob. Obs. Correlation

Copper S -0.0115% 1.1300% -0.2023 10.3495 3880.5395 0.0000 1719 0.93461 F -0.0104% 1.0945% -0.3027 7.2057 1293.1325 0.0000 1719 Iron ore S -0.0366% 0.5246% -0.1397 14.6492 4356.3605 0.0000 770 0.24587 F -0.0729% 2.0451% -0.9884 10.4105 1887.2648 0.0000 770 Nickel S -0.0441% 1.6033% -0.2982 5.4218 127.5230 0.0000 492 0.77415 F -0.0442% 1.6666% -0.1111 6.3500 231.0667 0.0000 492 Palm olien S -0.0009% 1.0915% 0.5811 90.0054 289601.8581 0.0000 918 0.48977 F -0.0109% 1.1097% 0.3627 6.4506 475.5688 0.0000 918 Rapeseed meal S -0.0207% 0.6803% 4.3531 53.5058 96747.5886 0.0000 884 0.39842 F 0.0028% 1.3757% -1.6953 28.2520 23910.7068 0.0000 884 Silver S -0.0343% 1.4527% -0.5585 13.3766 5396.1676 0.0000 1189 0.87599 F -0.0329% 1.3492% -0.3926 7.5486 1055.5623 0.0000 1189 Soybean meal S -0.0100% 0.7197% 1.6787 16.2119 13580.7901 0.0000 1754 0.44801 F -0.0044% 1.4331% -0.2533 28.5834 47852.7104 0.0000 1754 Soybean oil S -0.0344% 0.7647% -0.2214 23.4609 24031.1966 0.0000 1377 0.63606 F -0.0358% 0.9190% -0.1062 4.4590 124.7275 0.0000 1377 Steel rebar S -0.0033% 0.6809% 3.6334 52.8016 185542.4888 0.0000 1758 0.52779 F -0.0200% 1.1817% 0.4979 10.4981 4190.8158 0.0000 1758 White sugar S 0.0154% 0.4330% 3.2482 33.1371 69660.0477 0.0000 1759 0.53965 F 0.0084% 0.9952% -0.0536 9.6327 3225.1370 0.0000 1759

(26)

26

Table 7 Tests for GARCH models

Dependent variable Independent variable Serial Correlation LM(5) Heteroskedasticity Test: ARCH(5)

Daily spot return Daily futures return F-statistic Prob. Chi-Square F-statistic Prob. Chi-Square

Copper RS Copper RF 46.69 0.0000 18.04 0.0000

Iron ore RS Iron ore RF 13.92 0.0000 1.40 0.2208*

Nickel RS Nickel RF 33.93 0.0000 8.45 0.0000

Palm olien RS Palm olien RF 27.43 0.0000 118.84 0.0000

Rapeseed meal RS Rapeseed meal RF 12.46 0.0000 13.55 0.0000

Silver RS Silver RF 126.69 0.0000 59.11 0.0000

Soybean meal RS Soybean meal RF 11.70 0.0000 4.31 0.0007

Soybean oil RS Soybean oil RF 44.54 0.0000 284.09 0.0000

Steel rebar RS Steel rebar RF 82.33 0.0000 12.54 0.0000

White sugar RS White sugar RF 64.54 0.0000 14.10 0.0000

(27)

27

5 Results

This chapter provides in-sample and out-of-sample results including hedge ratios and hedging performance under both constrained and unconstrained scenarios.

5.1 In-sample results

Table 8 presents the optimal hedge ratios estimated for the in-sample period. In general, hedge ratios are higher for metal commodities. Copper and silver’s optimal hedge ratios are more than 90 percent and it is more than 70 percent with nickel. For palm olien and soybean oil, the ratios

estimated by different methods are all around 50 percent. Hedge ratios for iron ore is extremely low at approximately 5 percent which indicating that the iron ore futures price is not well correlated with its spot price. Moreover, it is notable that the ratios are generally higher when applying DCC-EGARCH(with student-t distribution). For instance, the optimal hedge ratios for soybean meal are less than 50 percent for other models while it is more than 60 percent when estimated by DCC-EGARCH(student) method. For silver, the ratio is even higher than 1. Figure 1 plots the conditional and unconditional hedge ratios for different commodities. It is notable that most of the ratios are moving around the OLS hedge ratios. However, for some certain type of products, the estimated ratios are varying a lot across different models and in most cases, DCC-EGARCH(student) is the most widely moved one. For instance, the figure of palm olien shows that the conditional hedge ratios estimated by DCC-EGARCH with student-t distributions deviate a lot from other models, especially for the period starting from the end of 2015. In addition, there are extremely high ratios occurring sometimes. Taking the most distinctive one as an example, the model DCC-EGARCH(student) has estimated a very high ratio of more than 60 for steel rebar. This is due to the very low correlation between spot and futures prices and the very high level of standard deviation of spot return on that day. Table 9 shows the hedging performance for the in-sample period. For copper, OLS method performs the best in variance reduction(86.78%) while DCC-EGARCH(student) performs the best in reducing downside risk(61.25%). In addition, full hedge can increase the mean return by 0.016 percent. For iron ore, fully hedged portfolio leads to the highest mean return but will increase the risk by 1158.56 percent. The most effective strategy is estimated by DCC-GARCH(norm) and it can reduce the variance by 7 percent. OLS performs the best in LPM reduction of 37.17 percent. For nickel, DCC-GARCH(student) ranked the highest in increasing return, DCC-GARCH(norm) is more effective in minimizing variance(62.11%) and full hedge has the best performance in LPM

reduction(78.21%). For palm olien, DCC-EGARCH(norm) has the highest mean return, OLS hedged portfolio can reduce the variance by 23.26 percent and DCC-EGARCH(norm) can decrease the downside risk by 33.89 percent. For rapeseed meal, all hedging strategies will worsen the return

(28)

28

performance, DCC-GARCH(student) has the best hedging effectiveness of 18.06 percent and half hedge is the only strategy that reduce the downside risk by more than 50 percent. For silver, fully hedged portfolio gives the highest mean return and performs the best in reducing LPM(91.92%) while OLS hedging strategy has the highest hedging effectiveness of 76.7 percent. For soybean meal, DCC-EGARCH(student) can increase the mean return by 43.11 percent, DCC-EGARCH(norm) performs the best in variance reduction(30.29%) and DCC-GARCH(student) is able to lessen the downside risk by 33.92 percent. For soybean oil, full hedge has the best performance in increasing return(112.99%) and in avoiding downside risk(12.68%) while OLS performs better in variance reduction(39.55%). For steel rebar, fully hedged portfolio gives the highest mean return(178.17%) while OLS hedge has the best performance in reducing both variance and LPM(by 25.14% and 28.48% respectively). Lastly for white sugar, all strategies will reduce the mean daily return and DCC-GARCH(norm) gives the highest hedging effectiveness of 28.64 percent. DCC-GARCH(student) perform better in downside risk reduction. To summarize, considering the expected mean return, fully hedged portfolio gives better performance in most cases and OLS hedging strategy performs better in variance reduction. In terms of downside risk, the difference between hedging strategies are not significant and the naïve

strategy performs slightly better than others. When comparing GARCH and EGARCH, DCC-GARCH gives better performance in risk reduction for both normal distribution and student-t

distribution. And when comparing between two distributions, normal distribution performs better in reducing risk. It is also notable that the hedging effectiveness is in general higher for copper, silver and nickel while hedging is relatively not effective for iron ore, for which the highest variance reduction is even below ten percent.

Since excessive hedging indicates bearing more leverage risk and short selling is considered to be taking a speculative position, in this paper I also present results with hedge ratios that are constrained between 0 and 1. Table 10 shows that constrained hedge ratios for the in-sample period. OLS hedge ratios remain the same and expect for certain commodities, the ratios did not change a lot in general. For copper and silver, the hedge ratios are reduced by approximately 0.02 and 0.03 for all models. For palm olien and white sugar, the average hedge ratio estimated by

DCC-EGARCH(student) has been decreased by 0.03. For steel rebar, the ratios are 0.05 and 0.06 lower for DCC-EGARCH(norm) and DCC-EGARCH(student). Based on the constrained hedge ratios, in-sample results are re-calculated in Table 11. Generally, the mean return has been reduced due to lower hedge ratios. Hedging effectiveness is improved or remains the same for all products. For copper, the variance reduction for conditional hedging strategies has been increased by approximately 1 to 3 percent but OLS hedge is still the most effective strategy. LPM reduction for DCC-EGARCH(student) is 1 percent lower but it is still the highest in reducing downside risk. For rapeseed meal, hedging

(29)

29

performance of DCC-EGARCH(norm) has been improved by 4 percent for variance reduction and 53 percent for LPM reduction. For silver, both hedging effectiveness and LPM reduction have been improved by around 3 and 6 percent and instead of full hedge, DCC-EGARCH(student) performs the best in reducing downside risk. For steel rebar, hedging performance has been improved a lot for all GARCH models and instead of OLS, DCC-EGARCH(norm) is ranked the highest in variance reduction for 30.26 percent and DCC-GARCH(norm) performs the best in downside risk reduction(41.54 percent). For white sugar, hedging effectiveness of DCC-EGARCH(norm) has been improved by 4.79 percent and has become the best model in reducing variance. The overall conclusion remains unchanged for constrained scenario.

Table 8 In-sample hedge ratios

Commodity OLS DCC-GARCH(norm) DCC-EGARCH(norm) DCC-GARCH(student) DCC-EGARCH(student)

Copper 0.9582 0.9737 0.9679 0.9795 0.9742 Iron ore 0.0703 0.0705 0.0674 0.0591 0.0901 Nickel 0.7505 0.7278 0.7599 0.7427 0.7322 Palm olien 0.4863 0.5427 0.5773 0.6684 0.7478 Rapeseed meal 0.1981 0.1873 0.1853 0.1482 0.1456 Silver 0.9458 0.9436 0.9375 0.9107 1.0355 Soybean meal 0.2241 0.3216 0.3196 0.4859 0.6562 Soybean oil 0.5204 0.5323 0.5382 0.6065 0.6163 Steel rebar 0.2990 0.1843 0.2649 0.1699 0.2550 White sugar 0.2294 0.2191 0.2392 0.2027 0.5101

Note: hedge ratios for DCC-GARCH(norm), DCC-EGARCH(norm), DCC-GARCH(student) and DCC-EGARCH(student) are the daily average hedge ratios.

Figure 1 In-sample hedge ratios

0 .5 1 1 .5 2

01jul2010 01jan2012 01jul2013 01jan2015 01jul2016 date

no full

ols dcc garch(n)

dcc egarch(n) dcc garch(t) dcc egarch(t)

Copper in-sample hedge ratios

0 .2 .4 .6 .8 1

01jan2014 01jan2015 01jan2016 date

no full

ols dcc garch(n)

(30)

30 0 .5 1 1 .5

01apr2015 01oct2015 01apr2016 01oct2016

date

no full

ols dcc garch(n)

Nickel in-sample hedge ratios

0

.5

1

.5

01jul2013 01jul2014 01jul2015 01jul2016 date

no full

ols dcc garch(n)

Palm olien in-sample hedge ratios

0 .5 1 1 .5 2

01jul2013 01jul2014 01jul2015 01jul2016 date

no full

ols dcc garch(n)

Rapeseed meal in-sample hedge ratios

0 .5 1 1 .5 2

01jul2012 01jul2013 01jul2014 01jul2015 01jul2016 date

no full

ols dcc garch(n)

Silver in-sample hedge ratios

-. 5 0 .5 1 1 .5

no full

ols dcc garch(n)

Soybean meal in-sample hedge ratios

0

1

2

3

4

01jan2011 01jul2012 01jan2014 01jul2015 date

no full

ols dcc garch(n)

Soybean oil in-sample hedge ratios

0

20

40

60

no full

ols dcc garch(n)

Steel rebar in-sample hedge ratios

-2

0

2

4

6

no full

ols dcc garch(n)

(31)

31

Table 9 In-sample hedging performance

no half full ols dcc garch(n) dcc egarch(n) dcc garch(t) dcc egarch(t)

Copper Mean(%) -0.0170% -0.0091% -0.0011% -0.0017% -0.0022% -0.0014% -0.0019% -0.0016% HE 66.94% 86.61% 86.78% 83.30% 83.90% 84.84% 85.62% LPM reduction 47.81% 60.13% 60.70% 36.06% 52.12% 52.37% 61.25% Iron ore Mean(%) -0.0722% -0.0341% 0.0041% -0.0669% -0.0671% -0.0665% -0.0694% -0.0721% HE -242.29% -1158.56% 6.65% 7.00% 6.59% 1.25% -11.77% LPM reduction 36.61% -190.78% 37.17% 36.12% 35.75% 34.76% 34.54% Nickel Mean(%) -0.0303% -0.0176% -0.0050% -0.0113% -0.0077% -0.0055% 0.0031% -0.0018% HE 54.75% 54.80% 61.62% 62.11% 60.20% 60.42% 60.31% LPM reduction 54.59% 78.21% 71.88% 71.28% 66.96% 67.09% 65.49% Palm olien Mean(%) 0.0138% 0.0117% 0.0097% 0.0118% 0.0223% 0.0242% 0.0136% 0.0161% HE 23.25% -2.69% 23.26% 20.22% 18.66% 17.74% 6.71% LPM reduction 32.22% 29.00% 32.17% 32.55% 33.89% 32.34% 33.42% Rapeseed meal Mean(%) -0.0231% -0.0241% -0.0252% -0.0235% -0.0283% -0.0275% -0.0287% -0.0253% HE -20.35% -236.75% 15.39% 12.82% 11.36% 18.06% 15.07% LPM reduction 52.52% -67.17% 48.48% 42.29% -12.53% 40.37% 41.99% Silver Mean(%) -0.0397% -0.0205% -0.0014% -0.0035% -0.0110% -0.0054% -0.0073% -0.0035% HE 59.66% 76.44% 76.70% 72.71% 74.02% 76.08% 74.12% LPM reduction 61.25% 91.92% 90.26% 81.68% 85.16% 90.60% 88.56% Soybean meal Mean(%) -0.0052% -0.0045% -0.0038% -0.0049% -0.0070% -0.0083% -0.0044% -0.0030% HE -10.38% -221.35% 20.15% 29.48% 30.29% 19.71% -12.72% LPM reduction -172.06% -1173.10% 17.45% 28.59% 23.44% 33.92% -16.52% Soybean oil Mean(%) -0.0278% -0.0121% 0.0036% -0.0115% -0.0132% -0.0121% -0.0118% -0.0132% HE 39.49% 5.97% 39.55% 37.84% 26.94% 34.68% 26.80% LPM reduction 9.03% 12.68% 8.25% 8.03% 7.34% 7.74% 6.65% Steel rebar Mean(%) -0.0162% -0.0018% 0.0126% -0.0076% -0.0173% -0.1395% -0.0181% -0.2014% HE 13.78% -112.99% 25.14% 19.43% -9078.56% 24.02% -17660.42% LPM reduction -49.91% -567.90% 28.48% -259.21% -319326.92% -118.92% -637211.51% White sugar Mean(%) 0.0162% 0.0109% 0.0056% 0.0137% 0.0118% 0.0094% 0.0109% 0.0094% HE -11.07% -291.19% 28.32% 28.64% 27.88% 26.31% -72.72% LPM reduction -224.72% -1164.95% -41.05% -26.43% -48.89% -21.20% -557.09%

(32)

32

Table 10 In-sample hedge ratios(constrained)

Commodity OLS DCC-GARCH(norm) DCC-EGARCH(norm) DCC-GARCH(student) DCC-EGARCH(student)

Copper 0.9582 0.9545 0.9497 0.9660 0.9578 Iron ore 0.0703 0.0706 0.0674 0.0594 0.0901 Nickel 0.7505 0.7278 0.7590 0.7410 0.7317 Palm olien 0.4863 0.5427 0.5771 0.6683 0.7159 Rapeseed meal 0.1981 0.1847 0.1842 0.1482 0.1456 Silver 0.9458 0.9088 0.9150 0.9001 0.9684 Soybean meal 0.2241 0.3216 0.3196 0.4862 0.6527 Soybean oil 0.5204 0.5313 0.5363 0.6030 0.6124 Steel rebar 0.2990 0.1826 0.2126 0.1690 0.1961 White sugar 0.2294 0.2180 0.2335 0.2017 0.4760

Note: hedge ratios for DCC-GARCH(norm), DCC-EGARCH(norm), DCC-GARCH(student) and DCC-EGARCH(student) are the daily average hedge ratios.

Table 11 In-sample hedging performance(constrained)

no half full ols dcc garch(n) dcc egarch(n) dcc garch(t) dcc egarch(t)

Copper Mean(%) -0.0170% -0.0091% -0.0011% -0.0017% -0.0026% -0.0028% -0.0022% -0.0021% HE 66.94% 86.61% 86.78% 86.42% 86.48% 86.37% 86.45% LPM reduction 47.81% 60.13% 60.70% 60.52% 60.23% 60.60% 60.71% Iron ore Mean(%) -0.0722% -0.0341% 0.0041% -0.0669% -0.0670% -0.0665% -0.0696% -0.0721% HE -242.29% -1158.56% 6.65% 7.00% 6.59% 1.28% -11.77% LPM reduction 36.61% -190.78% 37.17% 35.95% 35.75% 33.13% 32.91% Nickel Mean(%) -0.0303% -0.0176% -0.0050% -0.0113% -0.0077% -0.0062% 0.0022% -0.0024% HE 54.75% 54.80% 61.62% 62.11% 60.75% 60.75% 60.71% LPM reduction 54.59% 78.21% 71.88% 71.28% 66.96% 67.09% 65.49% Palm olien Mean(%) 0.0138% 0.0117% 0.0097% 0.0118% 0.0223% 0.0243% 0.0136% 0.0116% HE 23.25% -2.69% 23.26% 20.22% 18.68% 17.75% 12.42% LPM reduction 32.22% 29.00% 32.17% 32.55% 33.89% 32.34% 32.74% Rapeseed meal Mean(%) -0.0231% -0.0241% -0.0252% -0.0235% -0.0283% -0.0250% -0.0287% -0.0253% HE -20.35% -236.75% 15.39% 15.12% 14.97% 18.06% 15.07% LPM reduction 52.52% -67.17% 48.48% 42.29% 40.45% 40.37% 41.99% Silver Mean(%) -0.0397% -0.0205% -0.0014% -0.0035% -0.0130% -0.0091% -0.0085% -0.0063% HE 59.66% 76.44% 76.70% 76.23% 76.52% 76.44% 76.69% LPM reduction 61.25% 91.92% 90.26% 88.38% 91.61% 90.61% 92.05% Soybean meal Mean(%) -0.0052% -0.0045% -0.0038% -0.0049% -0.0070% -0.0083% -0.0067% -0.0075% HE -10.38% -221.35% 20.15% 29.48% 30.29% 21.41% -5.24% LPM reduction -172.06% -1173.10% 17.45% 28.59% 23.44% 33.99% 23.61%

Hedging with Chinese commodity futures : evidence from 2010 to 2017