key: cord-0073097-inrr88qx
authors: Saha, Kunal; Madhavan, Vinodh; Chandrashekhar, G. R.
title: Effect of COVID-19 on ETF and index efficiency: evidence from an entropy-based analysis
date: 2022-01-07
journal: J Econ Finan
DOI: 10.1007/s12197-021-09566-4
sha: f8636b9b060476ebfc0047dc5cffa2a0f0cc1fce
doc_id: 73097
cord_uid: inrr88qx

We examine the informational efficiency of domestic equity ETFs vis-a-vis their underlying market indices during the COVID-19 pandemic. To do so, we employ a multiscale entropy-based methodology. Our findings indicate that the informational efficiency of all ETFs as well as the indices fall sharply during the COVID induced market crash in February-March 2020. Having said so, we find disproportionate deterioration in market efficiency of ETFs and indices pertaining to USA and Canada as compared to those of China, Hong Kong and Taiwan. Interestingly, ETFs and indices pertaining to certain developed markets were found to be less efficient than their emerging market counterparts even during the pre-covid timeline. Lastly, there is a discernible difference between the efficiency of ETFs vis-a-vis their underlying indices. These findings should nudge investors to exercise caution while dealing with ETFs, for domestic ETFs do not exactly mimic the dynamics of their underlying indices.

should follow a random walk (Fama 1965) . The rise in popularity of index based Exchange Traded Funds (ETFs) over the last decade, may be attributed to the belief that markets are indeed efficient and hence active investments strategies cannot consistently beat the market. ETFs also offer additional benefits over mutual funds which include lower expense ratio and reduced tax incidence.

Studies that examine ETF efficiency in the context of Efficient Market Hypothesis usually employ traditional econometric methodologies such as regression and cointegration (Xu et al. 2017 (Xu et al. , 2019 Huang et al. 2021) . However, irregularities such as long memory, self-similarity and other non-linear phenomenon have also been reported in financial time series data of ETFs and equity indices (Zhu and Bao 2019; Saha et al. 2020; Caporale et al. 2020) .

The current COVID-19 pandemic adversely affected markets across the globe. It has been earlier observed that financial crises can affect different markets to varying degrees (Lim et al. 2008) . This study contributes to the literature on market efficiency in the following ways. First, we examine the level of informational efficiency of domestic ETFs and their respective underlying equity indices using an entropy based methodology. In doing so, we compare the degree of efficiency of developed vis-a-vis emerging market ETFs and underlying indices. Second, we examine the impact of covid-19 crisis on the informational efficiency of ETFs and underlying indices. While prior studies have used entropy based measures to examine efficiency across different assets (Alvarez-Ramirez et al. 2012; Ortiz-Cruz et al. 2012 ), we employ a recently proposed "refined composite multiscale fuzzy entropy" (RCMFE) algorithm that is more accurate and stable, especially for shorter temporal scales (Azami et al. 2017 ).

Entropy measures the extent of disorder in a system. In the context of information theory, higher values of entropy for a time series process corresponds to higher levels of efficiency (Gulko 1999) . A drop in market prices induced by a market crash creates a trend, that reduces entropy and thereby, informational efficiency. The first step in this analysis is to calculate the entropy of the dataset using the RCMFE method (Azami et al. 2017 ). Next, we use the informational efficiency index as proposed by Wang and Wang (2021) . A brief description is provided here.

From a time series y = y 1 , y 2 , … , y N , a de-meaned vector is created as

Here, m denotes the embedding dimensions which define the count of samples in every vector. The separation between two vectors is given by:

When this distance is lesser than a given tolerance r, a match occurs. This degree of similarity is measured by the for the level r and entropy power n. Next, the fuzzy entropy of the time series (y) is estimated as:

where the function m is given by Further, the RCMFE measures the entropy at various time scales that are used to arrive at the multi-scale market efficiency. These can be understood as being daily, weekly or monthly. For these, a coarse-graining procedure is employed to extract variations at all scales. For every time scale factor , separate coarse-grained series are created as z ( ) u |(u = 1, … , ) = {y ( ) u,1 , y ( ) u,1 , …} , with mean as RCMFE improves upon previous measures of entropy by extracting more information from the data since it allows for overlapping windows at every . This is implemented by calculating fuzzy entropy for all time scales and then averaged over u = 1, … , to get average ̄m and ̄m +1 . Subsequently, the RCMFE is calculated as:

Asset returns should follow Gaussian white noise in a completely efficient market. Hence, the index of informational market efficiency [ I IME ( ) ] is calculated for all time scales as:

with ( ) depicting the upper bound entropy of 5000 Monte Carlo simulations of Gaussian white noise samples. For I IME ( ) < 100% , the asset can be interpreted as partially or fractionally efficient. Table 1 provides the names of the domestic equity ETFs and their respective underlying indices that are considered for this study. We retrieve log returns of daily closing prices of each ETF and its index from January 2018 to April 2021 from Bloomberg. For this study, we chose the largest (by assets under management) domestic ETFs from various markets which fully replicate their indices without derivatives or leverage. This is done to prevent confounding factors at the time of interpreting results.

At the outset, we check the descriptive statistics of the log returns time series data of ETFs and their indices. We use the descriptive statistics data to compare the change from the pre-crash period (Jan 2018 to Jan 2020) to post-crash period (Apr 2020 to Apr 2021). We exclude the period of the crash from February to March 2020 since the volatility was very high during this period. However, even after removing these months of date, we can see that the descriptive statistics, especially the skewness and kurtosis changed markedly in the post crash period compared to the pre-crash period. The following Table 2 shows the details.

(4) 

The entropy based efficiency estimation results are presented and discussed at two levels. First, a full sample (static) analysis of the informational efficiency of each ETF and its underlying index is undertaken. Next, COVID-19 outbreak's impact on the dynamic informational efficiency is estimated using a rolling window approach. Figure 1 shows informational efficiency estimates for the static sample across all the chosen time scales ( = 1, … , 30 ). The drop in I IME ( ) for increasing values of across all markets is due to decline in underlying entropy as time scale ( ) increases. This is due to the reduction of "pattern richness" after filtering the time series using the coarse-graining procedure. These findings are in line with prior studies using entropy methods on various markets (Ortiz-Cruz et al. 2012; Wang and Wang 2021) . A comparison of various panels lead to novel findings. We see that the efficiency index of ETFs and indices from USA and Canada are consistently lower than other markets. On the other hand, ETFs and indices from China, Hong Kong, Taiwan and Japan are seen to be more efficient than remaining markets. We also see that in many cases, the efficiency levels of ETFs do not exactly mimic the level of efficiency of the underlying indices.

A rolling window methodology is used to measure the time-varying efficiency for both the ETFs and their underlying indices. Here, we relax the implicit assumption that the efficiency level is constant over time. As the economic environment evolves over time and as unforeseen shocks like covid-19 pandemic unfold, a rolling window analysis helps us examine the time varying nature of efficiency. Should the efficiency levels be stable over time, then the rolling window estimates would not vary much. On the other hand, any instability or change in the efficiency level over time will be captured by the dynamic rolling window estimates (Zivot and Wang 2003) . In line with precedence in literature, we use the rolling window length of 252 days (Wang and Wang 2021) . The rolling window analysis begins with the estimation of efficiency index, I IME ( ) for the first window period of 252 daily log return values. Then the window is moved forward based on the chosen value of . For = 1 , the rolling windows moves forward a day. Figure 2 shows the daily ( = 1 ) informational efficiency plots of all ETFs and their underlying indices.

Quite a few observations stand out. First, as expected, the efficiency drops during Feb-March 2020 when COVID-19 spread rapidly across the world. In addition, more interesting findings can also be gleaned. The fall in informational efficiency was the most for ETFs and indices from Canada and USA, while the ETFs and indices from China, Hong Kong, Japan, South Korea and Taiwan saw the least drop. Another notable observation is that the level of informational efficiency of several developed markets are lower than other cases even in the pre-covid days. Moreover, we see that in several cases, the efficiency plots of the ETFs and their indices do not coincide, especially after the march 2020 crash (Australia, Germany, New Zealand and Taiwan). An encouraging observation is that the level of informational efficiency is seen to increase towards the end of the plots, suggesting that market imperfections have reduced over time.

We compare the relative efficiency of ETFs and the Indices based on the average of rolling efficiency index values before and after the Covid-induced market crash (Feb-Mar 2020). While the covid-induced market crash impacted all ETFs and their underlying indices, the magnitude of impact was different for different countries. Tables 3 and 4 show the average efficiency index values for all the ETFs. Of all the ETFs considered for this study, the ETFs of Brazil and Canada appear to be the most affected by the covid induced market crash. Also, the USA based ETF was among the relatively least efficient ones in both the timelines.

Similarly, Tables 5 and 6 show the average efficiency index values for all the underlying indices. While the results for the indices are qualitatively similar to their ETFs, a few notable exceptions stand out. The Indian equity Index shows a higher level of relative efficiency than its ETF, especially in the pre-crash timeline. For the post-crash timelines, indices of Germany, Eurozone and New Zealand were relatively more efficient than their ETFs.

A visual illustration of the findings pertaining to Tables 3 to 6 is made available in Fig. 2 , which shows the dynamic nature of informational efficiency of all the ETFs and indices.

A potential factor behind the relative efficiency of ETFs in the pre-crash timeline could be the differential taxation rules in various geographies. 1 It may be noted that ETFs generate capital gains during rebalancing or creation / redemption process. (Shadforth et al. 2020; Ramachandran and Saha 2020) . Further, emerging markets across the globe offer tax friendly policies towards non-resident institutional investors (Blitz et al. 2012 ). On the other hand, investors in developed markets resort to trading ETFs so as to take advantage of various taxation loopholes such as tax loss harvesting and redemption in kind (Bouchey et al. 2016; Mider et al. 2019) . Consequently, it is very likely that the relative ranking of ETFs is a function of differential taxation and regulatory environment across geographies. The findings of this study in-connection with relative efficiency levels are, to some extent, in alignment with Morningstar's recent Regulation and Taxation Scorecard for various economies (Pettit et al. 2020 ).

This study analyses the informational efficiency of domestic ETFs and their underlying indices across various markets during the COVID-19 outbreak. We estimate informational efficiency using a refined multiscale entropy-based efficiency index. This methodology is used to measure static and dynamic efficiency of the ETFs and their underlying indices. The takeaways from this study are as follows. First, COVID-19 led to a decline in efficiency of all ETFs and their indices. This inference is based on the rolling window estimations that capture the relative efficiency of ETFs and their underlying indices over time. These findings are in line with literature that have examined the impact of crises on financial markets (Lim et al. 2008; Ortiz-Cruz et al. 2012) . Further, the efficiency of ETFs and their indices revert to pre-crash levels since Jan-Feb 2021. This transient deterioration in efficiency levels followed by subsequent reversion of the same is in alignment with Adaptive Market Hypothesis (Lo 2012) and is indicative of agents exhibiting lower rationality during market turbulence. The drop in efficiency during COVID may be attributed to increased fear among investors (Subramaniam and Chakraborty 2021). Second, developed markets exhibit relatively lower levels of efficiency than most other emerging markets during the covid-19 induced market crash. Put differently, not all domestic ETFs were equally impacted by the covid-19 crisis. The magnitude of drop in efficiency could be due to the degree of distrust in governments. For instance, Engelhardt et al. (2021) reported that volatility of equity markets in hightrust countries was significantly lower than low-trust countries during covid. Third, ETFs and indices pertaining to several developed markets were found to be less efficient than their emerging market counterparts even during the pre-covid timeline. As stated earlier, we believe that differential taxation on ETFs across the globe may be a contributory factor in this regard. Fourth, our findings indicate that not all domestic ETFs considered for this study exactly mimic the dynamics of the underlying indices. In conclusion, these findings should nudge investors to deal with domestic ETFs on a case-to-case basis.

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Relative efficiency of equity ETFs: an adaptive market hypothesis perspective

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Covid-19 fear index: does it matter for stock market returns?

Covid-19 and financial market efficiency: Evidence from an entropy-based analysis

Does ETF trading affect the efficiency of the underlying index?

The sidedness and informativeness of ETF trading and the market efficiency of their underlying indexes

Multifractality, efficiency and cross-correlations analysis of the american ETF market: Evidence from SPY, DIA and QQQ

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We thank participants at the 28 th Global Finance Conference 2021 for valuable comments. In addition, we are grateful to the editor and two anonymous reviewers for their constructive comments and suggestions that helped us improve the paper. All remaining errors are ours.Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

The data that support the findings of this study are available from Bloomberg but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of Bloomberg and the source code for analysis associated with the current submission is available at https:// doi. org/ 10. 1007/ s11517-017-1647-5.

The authors declare that they have no conflict of interest.