“The measurement of tracking errors of commodity ETFs in China”

This paper presents the first study on the measurement and determinants of tracking errors using the daily figures for gold exchange-traded funds (ETFs) in China. This study employs three methods to measure tracking errors – one that involves calculating the absolute error measure, one that involves calculating the differences between the standard deviation of the benchmark index and that of the ETF, and a regression analysis of empirical returns. In general, the results suggest that the tracking errors of these ETFs in China are lower than those of equity-based ETFs in Hong Kong, the United States, and Australia. We also observe that distinct ETFs have different determinants. Our results provide valuable insight for both institutional and retail investors, as well as opportunities for them to be exposed to a wide range of commodity ETFs in China.


Introduction ©
The development of exchange-traded funds (ETFs) provides opportunities for both institutional and retail investors to be exposed to a wide range of asset classes.
A bulk of the existing studies focus on the tracking errors of equity-based ETFs using distinct approaches. Using S&P 500 Index data, Frino et al. (2004) examined the exogenous determinants of tracking errors and observed that such errors are significantly influenced by index revisions, share issuances, spin-offs, share repurchases, index replication strategy and fund size. They also found a seasonal pattern in tracking errors, consistent with the finding of Frino and Gallagher (2001). Chu (2011) studied the magnitude and determinants of ETF tracking errors using daily data in the Hong Kong stock market and found that the tracking error in Hong Kong is higher than those in the United States and Australia. Avellaneda and Zhang (2010) studied the price behavior equity-leveraged ETFs in different sectors and found minimal one-day tracking errors among the most liquid equity ETFs.
Commodities are unique in part because physical assets cannot be stored easily owing to the extra costs for warehousing. Thus, futures-based commodity ETFs may fail to track their reference indices perfectly. The commodity is also countercyclical with stocks and bonds; studies observed that it is significantly negatively correlated with both bonds and equities, implying that an appropriate allocation to commodities enhances portfolio performance (Jensen et  The contribution of this study is to measure the determinants and magnitude of the tracking error for commodity ETFs in China, from 05 January 2015 to 29 February 2016. To the best our knowledge, this study is the first to investigate all four existing gold ETFs in China. Existing studies paid more attention to equity-based ETFs in either the United States or European countries rather than in emerging countries. Following Pope and Yadav (1994) and Shin and Soydemir (2010), this study employed three different approaches to estimate tracking errors in order to obtain robust results.
The rest of the paper is organized as follows. Section 2 presents the data sources and provides an overview of the development of commodity ETFs in China. Section 3 describes the empirical approaches used to estimate the tracking errors as well as its determinants. Section 4 discusses the empirical findings, and Section 5 provides the conclusions and some directions for future research.

The development of commodity ETFs in China
The development of gold ETFs enables investors to allocate some of their assets to gold without directly buying physical gold. Gold ETFs in China first emerged on 24 June 2013, developed by GuoTai Fund Management Company, and the country has since become the largest gold consumer in the world. The Shanghai Gold Exchange facilitates spot gold exchange. Table 1 shows that the trading volume of spot gold in China has significantly increased along with the trading amount, suggesting that investors have become more focused on gold investments, which, in turn, makes this study important and timely.
The commodity ETFs used in this study are HuaAn Gold ETF, GuoTai Gold ETF, Bosera Gold ETF, and E Fund Gold ETF 1 . The ETF prices were collected from the Wind Database, created by Wind Information Co., Ltd., a financial data provider in China. Since the commodity ETFs in China emerged later than those in developed countries, all four commodity ETFs track the gold spot price at the Shanghai Gold Exchange, which is also the source of the gold spot price in this study. All of the data reflect daily observations for each trading day from 05 January 2015 to 29 February 2016. Figure 1 shows the performance of the existing gold ETFs in China. All four ETFs showa similar trend, with very small variations, and have a net asset value (NAV) between 2.00 and 2.65. However, even such small variations would have a large impact on the ETF returns.

Three methods for tracking error estimation
This section reviews the possible sources of tracking errors and the methods for analyzing such errors. The tracking error, ceteris paribus, is zero if the index fund perfectly aligns with the benchmark index. However, in practice, an ETF's performance in tracking the index is affected by a few factors, such as management fees and administrative/ operating expenses, different compositions of the index fund and the index, and trading costs (Frino and Gallagher, 2001;Drenovak et al., 2014). Thus, the tracking error is non-zero in practice, as was observed by many empirical studies (see for example, Murphy and Wright, 2010).
Several articles explored important issues in tracking error measurement. Roll (1992) provided a criterion for analyzing ETF performance. The approaches for tracking error estimation were well documented in the academic literature (e.g. Pope and Yadav, 1994;Shin and Soydemir, 2010). This study employs three methods to measure the tracking errors. One of the traditional methods involves calculating the absolute error measure, which is defined as the average absolute value of the difference between the returns of the benchmark index and index fund. The measure can be described as follows.
where R f,t represents the return of index fund f at time t, while R x,t is the return of its underlying gold at time t.
The second method of tracking error estimation involves calculating the standard deviation of the difference inreturns of benchmark index and that of the ETF. The variance equation can described as follows. , where t denotes the time period. R f,t represents the return of index fund f at time t, while R x,t is the return of its underlying (Gold) at time t. We can rewrite equation (2) as: The third method of tracking error estimation involves a regression analysis of empirical returns, based on the following linear model:

Results
We begin with estimating the tracking error using the absolute error method (TE 1 ). From Figure 2, which presents the TE 1 variation of all the gold ETFs, it is clear that the highest tracking error occurs in January 2015. The reason behind this phenomenonis that the Bosera Gold ETF cannot accurately track the increasing return of spot goldin January 2015, which result in that its tracking errors are ten times higher than other three ETFs.  Table 2 reports the empirical results of the tracking error estimation using the three methods.
We first consider the full sample, that is, the sample for the entire study period. The daily tracking error based on the first estimation method (calculating the absolute error measure) (TE 1 ) ranges from 0.0024% to 0.0273% across all ETFs. The daily tracking error based on the second method (calculating the standard deviation of return differences) (TE 2 ) ranges from 0.0035 % to 0.05%. Meanwhile, the daily tracking error based on the third method(regression analysis of empirical returns) (TE 3 ) ranges from 0.0027% to 0.0499%, and the coefficient of the benchmark index, as expected, is very close to one and the R 2 and is nearly 100%. The tracking error of the gold ETFs in China is generally lower than those of equity-based index ETFs in Hong Kong (0.39%), Australia (0.0074%), and the United States (0.039%) (Chu, 2011 Pope and Yadav's (1994) idea that if β is not exactly equal to one, the order of the ETFs in terms of the magnitude of tracking error may be different. Pope and Yadav (1994) also pointed out that if the relationship between the benchmark index return and Gold ETF return is not linear, the third method may overestimate the tracking error.
Finally, we examine the determinants of tracking errors for each gold ETFs and the results are reported in Table 3. Our results show that the tracking-error determinants differ with products. Trading amount and volume generally have insignificant effects on daily tracking errors. The exception is GuoTai Gold ETFs whose trakcingerror performance displayed a negative relationship with trading volume, but positive with trading amount. The fund size is negatively correlated for HuaAn Gold ETF's tracking error, whereas it is positively correlated for that of Bosera Gold ETF. None of the three determinants had a significant impact on E Fund Gold ETF. Our results are slightly different from previous findings that show fund size as significantly negatively correlated with tracking errors of equity-based ETFs (Grinblatt and Titman, 1989;Chu, 2011). Our results conclude that various ETFs have different determinants.

Conclusion
ETFs have provided both institutional and retail investors with new opportunities to be exposed to a wide array of commodities. This study is the first to examine the measurement and determinants of tracking errors using daily data for gold ETFs   Note: Coefficients are expressed as percentages; t-statistics are reported in parentheses; *indicates significance at 10% level, while **indicates significance at 5% or better.