Bachelor Economics and Business: Economics and finance
Bachelor Thesis: Finance
Pricing the spread: An empirical study of ETF premiums stemming from
differences in liquidity between the ETF and its underlying assets.
Student:
Lars van den Enk
Student ID:
10441506
Supervisor:
P.F.A. Tuijp
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1. Introduction
In this paper, I will research whether the liquidity, defined as the bid-ask spread, plays an important factor in the premiums paid for exchange traded funds (ETFs). To answer this question I have looked at relationship between ETF and asset liquidity, to find out whether there is a relationship with the premium paid for the fund. As ETF's are becoming more popular, and investing in a more diverse set of assets, including cross country and illiquid assets, the price setting mechanism of these funds has become more complicated (Hilliard, 2014). These developments raise new questions about ETF pricing. The popularity of exchange traded funds has soared since its introduction in the United States in 1993 and Europe in 1999 (Hasbrouck, 2003). Since 2008 exchange traded funds are also allowed to be actively managed by fund managers in the United States, which will attract interest from a broader group of investors (Hilliard, 2014). These funds have generally started as index trackers when first launched and quickly established themselves, because they filled the gap between the existing closed and open end mutual funds with which they share several characteristics.
In general, an ETF is a bundle of assets composed of bonds, stocks or commodities, which can be sold over the market, just like a closed-end mutual fund. The key difference to such a fund is the ability to redeem the ETF share to the financial institution at the end of a trading day or a specified period for its underlying assets or vice versa, providing the underlying portfolio to the institution in exchange for a new ETF share. The option to redeem the ETF resembles the option investors in open ends funds have when, they want to sell their share, but are unable to find a buyer. Even though the redemption option is more complicated than simply returning the share the issuant, this feature does insure investors that the market price of an ETF does not differ much from its net asset value (NAV). This feature makes the ETF an attractive substitute for closed mutual funds, which can have wide variation in premiums and discounts (Lee, Shleifer and Thaler, 1990).
When prices for an ETF share are established on the market by demand and supply, this price may also, like a closed end mutual fund, differ from the underlying NAV. This phenomenon would theoretically lead to arbitrage opportunities when investors would exploit the pricing difference by buying or selling the underlying stocks for the fund and vice versa. Because an ETF can be redeemed often, in contrast with closed end mutual funds which can only be redeemed when eliminated or open-ended, the premium should not exist over a long period of time. In theory, this arbitrage shouldn’t exist on such a liquid market at all, which raises questions about the correlation between market liquidity and pricing deviations from the net assets value (Ackert and Tian, 2008). Some papers, like Ackert and Tian (2008) have found a correlation between the liquidity of the ETF and the
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premium/discount paid for it. They found that very low liquidity funds generally traded at discount to their net asset value.
Others, like Hilliard (2014) have looked at the premiums paid for cross country ETFs where the fund might contain assets trading on international stock markets. When the prices of these assets are not available to set the fund’s net asset value, the pricing of the ETF becomes more complicated. This reasoning was based on the idea that having to redeem the fund for international shares, which might not be traded at that moment, would increase the costs of redemption to the authorized participant, as more unknown factors come into play. This article suggested the premium stemmed from the liquidity issue of buying these cross country underlying assets to issue a new ETF.
In this paper I look at a sample of ETF characteristics and their portfolio holdings over the period 2002-2015. This data is obtained from the CRSP mutual fund database. To investigate the effect of liquidity and liquidity difference between the underlying assets on the fund's premium, I performed two regression analyses. In the first regression analysis I analyzed the effect of several fund specific variables relating to liquidity on the funds premium. The second regression included variables which were related to the funds underlying portfolio. These variables all had to do with the liquidity which could be observed from these assets.
The results from these regression analyses were in support of the research question, as the liquidity factors seems to play an important part in the ETF premium. From the second regression, the difference in bid-ask spreads between the fund and the underlying assets had a statistically significant impact on the funds premium. Other liquidity factors ,like volume and turnover ratio added to the regressions, did not generate significant results.
This evidence supports several liquidity based studies on ETF premiums, like the research performed by Ackert and Tian (2008) who found that ETFs trading in low liquidity markets, measured by the high spread in this research, are often traded at a low premium or discount and also corresponds with the same type of research performed on closed end mutual funds (Datar, 2002). The result shown by the spread difference supports evidence that the market liquidity for their underlying assets might play an important role in the price setting of traded funds (Chan, Jain and Xia, 2008).
From this study we can conclude that several liquidity factors play an important role in ETF pricing. This research was limited however because the database used to gather the sample only offered quarterly data on the funds net asset value, prohibiting the study from using daily or intraday premiums, which are preferable. The simple regression might also not reflect the reality as several
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variables might be over represented due to omitted variable bias. The results from this study might nonetheless be used for more in depth investigation of the subject.
In section 2 of this paper I will start with an explanation of the ETF share creation and redemption mechanism and review several papers on written on ETFs and the liquidity of closed-end mutual funds. Section 3 will focus on the data gathering process and the manipulations made to allow for the research, of which the empirical method will be discusses in section 4. I will explain the results in section 5 and end with a conclusion and discussion in section 6.
2. Literature review
As this research focuses on the liquidity of ETFs it is important to understand the mechanic behind the redemption of an ETF which was discusses above, because it is this option which has a great effect on liquidity, and poses a stark contrast with closed end mutual fund liquidity.
When a company wants to create a new ETF or increase the number of ETF to meet demand, it can create these by buying the underlying assets from the market. It could do so itself, but this process is mostly done by an authorized participant (AP), which can be a large financial company or a market maker. When these assets are acquired, the ETF company will hold them and in return will generate a block of ETF shares with the same total value. The exchange from assets to ETFs are priced at net asset value and are usually issued in blocks of 50,000 shares.
If a trader would want to create an ETF tracking the S&P500 for example, it would order an authorized participant to buy the index’s underlying stocks at the correct weight, and exchange these for an ETF share at net asset value to the participant. This example of an ETF is popularly known as a Spider (SPDR), and is widely traded throughout the world. Other examples for ETFs tracking indexes are Diamonds, which track the Dow Jones index and cubes (QQQ) which track the Nasdaq-100 index. After the creation of the fund, the authorized participant can sell the stock on the market, trading it like one would trade common stock. Because it trades on the market, excess demand might drive the price of the ETF above that of its net asset value. When people are willing to pay a premium on the ETF, the authorized participant can make an arbitrage profit from this movement. It can buy new blocks of shares and exchange these for new ETF at the company who issues them, and sell them on the market to make the profit on the difference, called the premium. This process also works the other way around, when the fund is underpriced. The participant can buy the ETF on the market, redeem them to the issuing company for the underlying assets, and sell those to make a profit.
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This mechanism insures that the ETF price will not differ much from NAV, because the authorized participant can theoretically make arbitrage profits when they arise. In reality, the AP incurs several costs for this creation/redemption process like trading spread and commissions, including a fee for the ETF issuing company. Because the AP can usually only redeem or create new ETFs at the end of trading days it cannot exploit all pricing differences which occur during the day. These facts allow the fund price to slightly differ from the net asset value, as the AP will not intervene, because it might not make an arbitrage profit.
There are several papers which have looked into the general efficiency of ETFs in terms of their tracking error to their index, the price setting abilities of ETFs and ETF liquidity. I will summarize some below:
A paper by Engle and Sarkar (2006) looked into the premium paid for ETF’s, based on end of day and intraday prices. They found that, in general, premiums were very small and only lasted several minutes. They included domestic and international funds and found a that the premiums were significantly higher but also persisted over longer periods of times, often spanning days or weeks. They offered several explanations for this difference including different tax regimes, trading costs and an interruption factor for the redemption process of the fund. This interruption exist because international shares may not directly traded as other stock markets might be closed at the time the arbitrage opportunity might exist for the authorized participant. This inability to directly use the redemption mechanism to its full effect might have strong implications for the premium.
Focusing further on international equity, Hilliard (2014) modelled the ETF premiums using the Ornstein-Uhlenbeck model augmented by jumps. She looks whether fund specific variables belonging to domestic and international ETFs affected the parameters and found that domestic fund were very efficient and showed almost no long term premium. The international ETFs showed persisted difference in pricing between the fund and its underlying assets. The outcome of several of these studies into the ETF premiums do suggest that not only fund specific characters, but also asset characteristics might play an important part in the price setting of an ETF.
One important question would be whether there is a difference in premium observed for funds which trade a different set of assets. As transparency and liquidity seem to play important parts in the investor’s ability to observe the right price for and ETF, wouldn’t the underlying assets and their characteristics have a significant impact on the pricing of ETFs?
I haven’t found many articles which take this subject into much depth for ETF’s, apart from cross-country ETFs, but literature written on closed-end mutual funds did offer inspiration for this
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study. A paper by Chan, Jain and Xia (2008) studies the effect that market liquidity has on the premium of a closed end mutual fund. They did not only look at the market liquidity of the host market, where the funds are traded, but also at the liquidity of the home market, where the underlying assets are traded. They found that fund premium increases when the host market has a high level of liquidity, which corresponds with research done for ETFs (Ackert and Tian, 2008). They also found that market liquidity for the home market had a significant impact on the funds premium. The less liquid this market, the higher the premium. This seems to rather logical, as an investor might be willing to pay something extra for a bundle of illiquid assets which would normally have liquidity constraints when traded separately.
3. Data
This section discusses the data used for this research. 3.1 CRSP Mutual fund database
From the CRSP Mutual Fund database, two sections were used. The Fund Summary, to get a total of 1440 exchange traded funds which were classified as such using the "et_flag" variable. Because of this restriction, data gathering started in 2002. All these funds traded nearly exclusively in equity, as I required the funds to hold at least 95% in common stock. Through the fund summary several important variables were obtained, like the net assets value and several fund identifiers which were used in the next process of gathering the underlying assets from the Mutual fund Database and fund prices the Monthly Stock File. The underlying assets from the portfolio holdings database were matched with the ETFs from the fund summary by removing all funds which did not have a corresponding CRSP identifier (CRSP_Portno)
3.2 CRSP Monthly Stock File
Using the fund's identifier, CRSP_Portno, several other variables were obtained using the monthly stock file. From this file I was able to obtain the ETF market price, bid and ask prices, volume of which I give a summary below.
3.3 Data Manipulations
These databases had to be merged using Stata13. Starting out with 17,190 observations the merging process, which excluded variables not found in the fund summary. These observations would be
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missing their net asset value if kept, which is undesirable if one wants to measure and research the premium paid on this value.
In the monthly stock files, the variable price was denoted as the positive closing price of that day if this price is available. If not, the price given is the average between the bid and the ask prices of that trading day, denoted by CRSP as a negative value. For research purposes, I have used these values as if they were positive, by commanding Stata to give the absolute values of price when it was in really negative. This change was made for 629 observations on a total of 17,190 (3,7%).
More observations were dropped during the generation of new variables. In several observations, prices, market, bid and/or ask were missing. These observations were dropped since it is undesirable to generate the premiums when these variables are missing in this research. After dropping the observations in which these variables were missing, the total number of observations was 13,318, summarized below:
In Table 1 we have the three variables that were obtained from the fund summary: Turnover ratio (turn_ratio), management fees (mgmt_fee) and the expense ratio (exp_ratio). From the Monthly Stock file, three other variables were added: The funds price (fprc), the NAV (fnav) and the funds trading volume (fvol). Together with the bid and ask prices from the Monthly Stock file, the ETF premium and ETF spread were obtained. The fund spread was generated from the database using the following formula:
Table 1 Descriptive statistics. This table contains the data obtained from the CRSP Monthly stock file and the mutual fund
database. In total, the sample contains 15307 quarterly observations from 2001 until 2015 from 1440 exchange traded funds. All variables are attributed to the ETFs. The ETF premium, spread, expense ratio and management fees are given in percentages.
Variable Description Mean Std. Dev. Min Max Observations
fprc Price 45.88977 28.7142 1.93 343.43 15307 fnav NAV 45.87535 28.71433 1.97 343.71 15307 fpremium Premium -0.04655% 0.0133463 -0.188251 0.7574789 15307 fspread Bid-ask spread 0.32609% 0.0095354 -0.0018413 0.6471534 15307 fvol Trading volume in dollars 373101.4 2705674 0 8.82e+07 15307 turn_ratio Turnover ratio -0.4651697 8.919476 -99 8.35 13318 mgmt_fee Management fees 0.323031% 0.5547727 -10.808% 1.328% 13318
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2
/
)
(
100
Bid
Ask
Bid
Ask
Fundspread
. (1)With this formula the fundspread was generated, denoted in percentages of the average between the bid and ask prices. The higher the spread in percentages, the lower the liquidity of the asset. Here the spread is given for the ETF share, but the same principle applies to the asset spreads used in the regression. Using the spread as a liquidity measure comes from the idea that the seller of the asset will have to significantly lower its price before a potential buyer is willing to take over the asset. This way I will circumvent the problems of comparing spread of assets which are in a different price range. For the ETF premium I used the following formula:
NAV NAV price
m
Fundpremiu 100 . (2)
With this formula, the premium is denoted in a percentage of the net asset value. Just like the spread, denoting its value in percentages overcomes problems with differences in assets values. A negative premium means that the fund trades at a discount.
From the Portfolio Holdings dataset, holdings from the ETFs were obtained starting in 2002 until 2015. Using the asset identifier (permno) I used the Monthly stock file to obtain the ask an bid prices for the portfolio’s assets. Merging these data gave a new dataset with 6,610,833 observations after the data was aligned with the portfolio numbers from the fund summary.
Table 2 Descriptive Statistics. This table contains data on the underlying assets from the portfolio holdings database in the period
2002-2015. All data, except observations, are given in percentages.
Variable Description Mean Std. Dev. Minimum Maximum Observations
aspread The bid-ask
spread of the asset .16472 0.62347 -1.68361 184.6154 6,610,833 percent_tna Assets weight in portfolio .3577891 1.243824 -.1.34 224.26 6,611,461 TWAspread Bid-ask spread of underlying portfolio .08915 0.11863 0.11155 .93808 30,286
Table 2 shows the unmatched portfolio underlying asset data for all the available 1,440 ETFs. With the asset spread (aspread) and the weight of an asset in its portfolio (percent_tna) the underlying portfolio spread (TWAspread) was generated. One thing which stands out immediately, is that the underlying
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portfolio spread seems to be lower than the ETF spread calculated above from the fund summary. In this stage however, I’m comparing two different datasets over different periods of time, so that other factors might skew the results.
After the merging process of the final set was completed, the research was performed on the remaining 6,587 observations:
Table 3 Descriptive statistics. This table contains the merged data on which the regressions in section 4 will be performed.
The set contains merged data from the two tables provided above and the sample stems from the period 2001-2015. And f in front of the variable states the variable explains something about an ETF.
Variable Description Mean Std. Dev. Min Max Obs
fpremium
Fund
premium -.000875 .0067504 -.188251 .1480267 7,336
fspread Fund spread .003562 .0111979 -.0018035 .6471534 7,336
exp_ratio Expense ratio -0.0046635 0.002361 0.0001 0.0417 6,587
fmgmt_fee Management fees .3191351 .5204397 -10.808 1.328 6,587 fturn_ratio Turnover ratio -.15552 7.342.324 -99 8.35 6,587 fvol Trading volum 380105.9 3033614 0 8.82e+07 7,336 Spreaddifference Difference in spreads .0027229 .010965 -.0378501 .6416338 7,336 TWAspread Spread of the underlying portfolio 0.0008391 0.001722 -.0011155 0.040331 7,336
aspread Asset spread 0.0008994 0.0025978 -0.0115607 0.0115607 7,336
In Table 3 the final data is summarized which I used for my regressions. The variables fund spread, premium and portfolio spread were obtained earlier and the variables shown above are the result from merging the two datasets summarized previously. The spread difference was calculated from the difference between the fund spread and the underlying portfolio spread:
pread
portfolios
Underlying
Fundspread
erence
Spreaddiff
(3)Several observations can be made which may be of interest. The premiums paid for the ETFs are negative, meaning that, in general, they trade on a discount. This result corresponds with most studies into ETF premiums (Engle and Sarkar, 2006). The liquidity of the fund is also lower than that of the underlying portfolio, resulting in a positive spread difference. This result stands in contrast to my expectations, as I expected the fund’s liquidity to be higher that the underlying portfolio. It does seem to support the thesis hypothesis however , as the bigger the spread difference, the lower the premium investors are willing to pay for the fund.
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4. Empirical method
In this paper I will be reviewing the liquidity of EFTs and the impact from the liquidity difference between its underlying assets on its pricing. I will do this by measuring both the bid-ask spread on the funds and its underlying assets as described in the data section. Working with two regressions to examine the funds liquidity and that of its underlying portfolio I will try to answer the thesis question stated in the introduction: Does the difference in spreads between the fund and its underlying assets impact the price setting of an ETF, and thereby it’s premium on net asset value?
4.1 Testable hypotheses and regressions
To answer the research question I used two main hypotheses:
Hypothesis 1: The bid-ask of the ETF fund has a negative impact on the premium paid for the fund. My assumption is that this effect is negative because traders are willing to pay a premium for a liquid fund. In this study, I measure the liquidity of the fund with the bid-ask spread: The higher the spread, the lower the liquidity. To test this hypothesis I have used the following regression:
.
5 4 3 2 1 it it it it it itFees
Management
io
Expenserat
tio
Turnoverra
Volume
Fundspread
m
Fundpremiu
(4)This regression uses the ETF spread as the explanatory variable for the premium, controlling for several fund specific characteristics like trading volume in trillions of dollars, turnover ratio, fund expenses and management fees, as these variables might also impact the ETF premium. Vinay (2001) studied the liquidity effect on premiums for closed end mutual funds and included several values into its regression like spreads, trading volume and turnover rates.
Hypothesis 2: The difference in the ETF spread and the asset weighed spread of the funds underlying portfolio have a negative impact on the premium paid for the ETF.
To test this hypothesis I use the ETF premium as the dependent variable and the difference in bid-ask spreads as the explanatory variable. Just like the regression above, several controlling variables which might impact the funds liquidity have been added. For this regression, the asset spreads of the underlying portfolio were also used, resulting in the regression below:
it it it it it it it it it it
d
Assetsprea
Fees
Management
io
Expenserat
tio
Turnoverra
Volume
Fundspread
erence
Spreaddiff
m
Fundpremiu
7 6 5 4 3 2 1 . (5)10
The reason to look at these underlying assets more closely, comes from the analyses made by other researchers like Chan, Jain and Xia (2008). Their study suggested that not only the liquidity of the fund, but also that of their underlying assets, might play role in setting the premium. Their results showed that illiquidity in the home market, where the assets are traded, had a positive effect on the premium paid for the fund. Looking at the difference between the home and the host market, where the ETF is traded, might offer a new insight on ETF pricing.
5. Empirical results
From the regressions discussed above, the following results were generated using Stata. Using the larger database of 13,318 observations, I performed the first regression (4), using the fund premium as dependable variable and the fund specific variables as explanatory variables. The second model was estimated using the second regression (5) for which I added two extra explanatory variables related to the underlying assets of the ETF. The results were the following:
Table 4 Empirical results. This table contains the empirical results of the regression above (4 and 5). For model 1 13318
were used in the regression, for model 2 the number is 6587. The level of significance is shown by the asterisks: Three asterisks denotes significance at 1%, two at 5% and one at 10%. The variable Bfvol is trading volume given in trillions of dollars. fpremium Model 1 N=13,318 Model 2 N=6,587 fspread -0.1260759*** (0.0195615) -0.0855869*** (0.143688) exp_ratio 0.1476967*** (0.0535648) 0.0415318 (0.0343935) mgmt_fee -0.0005036** (0.0002218) -0.0005118*** (0.0001522) turn_ratio -7.08e-06 (.0000135) -0.000012 (0.0000107) Bfvol 34.65019 (42.90167) 45.3299* (25.52341) Spreaddifference -0.2258563*** (0.0501124) aspread -0.0625895* (0.03726) _cons -0.0006944*** (0.00018919)
From Table 4, model 1, the fund spread is statically significant and the coefficient, more than 1200 basis points, is large enough for the variable to make a significant difference on the ETF premium. These results provide evidence in favor of my first hypothesis, which states the ETF bid-ask spread has a negative impact on the funds premium. Similar results were found by Acker and Tian (2008) in a research which also observed a negative relationship for liquidity and fund premium for exchange
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traded funds, and a study by Datar (2001) which observes the effect of liquidity on the premiums paid for closed end mutual funds. Two other variables, the management fees and the expense ratio, used in the regression were also statically significant, but showed contradicting coefficients. The management fees are the costs investors pay to the fund managers, while the expense ratio includes all costs paid for the fund, like the 12b-1 fee.
Model 2 shows the results from the second regression (formula 4). The spread difference also seems to be statistically significant. For every point of difference in the bid-ask spread between the fund and its underlying portfolio, the fund premium increases 22,6% according to the results. It must be kept in mind that the spread difference is denoted in absolutes, while its value is normally relatively small: The variable mean is 0.0027 from Table 3. The liquidity of the home market, the asset spread, seems to be statistically insignificant, contrasting with the research performed by Chan, Jain and Xia (2008). This difference in results may have been caused by the fact that my study also included the difference between the home and host market, represented by the spread difference.
As management fees and expense ratio’s also seem to play a significant role in the funds premium, as they are both significant in model 1 and the management fees are significant in model 2, it might be interesting to see whether these cost have an influence on the underlying assets. The next regression uses the expense ratio and the management fees associated with holding the ETF as explanatory variables on the asset spread.
it it it
it
it
ExpenseRat
io
Management
Fee
d
Assetsprea
1
2
(6)Table 5 Empirical results. This table obtains the results for regression (6). The data was obtained from the same sample
as the first model, and used over the same period. The expense ratio and management fees are both costs for holding the fund. The level of significance is shown by the asterisks: Three asterisks denotes significance at 1%, two at 5% and one at 10%. aspread Model 3 N=13,138 exp_ratio .0536422 *** (0.0117571) mgmt_fee 0.0001185** (0.0000533)
The results from Table 5 are statistically significant and raise new questions about the relationship between asset liquidity and the managerial costs. If illiquid assets might demand a premium, which is
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suggested by some studies (Chan, Jain and Xia, 2008), investors might tolerate higher costs to obtain these funds.
6. Conclusion and Discussion
The results from this study seems to support that the premiums paid on ETFs are strongly related with liquidity factors, whether they are specific to the fund or to its underlying assets. Several aspects of this study could be improved, especially the observation interval. Although the final regression was performed on 6,587 observations, these were taken over 13 years, in which market situations might have changed, skewing results. Observations taken on a daily basis are preferable, as this interval also allows a study to investigate whether relationship between variables changes over time, as technological progress and changing market situations might have a different impact on these variables.
For new research, looking into the data composition of ETFs to explain their premiums might be a relevant topic. From the result analysis, I found that management fees and expense ratios did have an impact on the liquidity level of these assets, while these two variables also had influence on the fund’s premium. Looking into different levels of liquidity of the underlying assets could be a proper expansion into understanding the price setting mechanism of ETFs. This research can be viewed as a starting exploration to offer new insights in ETF pricing which have currently been overlooked. Because of the limitations on the data sample and the research method, more in depth research would however be needed to make strong conclusions about the relationship between liquidity and ETF premiums.
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References
Ackert, L. F. and Tian, Y. S. (2008), Arbitrage, Liquidity, and the Valuation of Exchange Traded
Funds. Financial Markets, Institutions & Instruments, 17: 331–362.
Chan, J.S.P. Jain, R. Xia. Y. (2008) Market segmentation, liquidity spillover, and closed-end country
fund discounts Journal of Financial Markets Volume 11, Issue 4, November 2008, Pages 377–399
Engle, R. and Sarkar, D. (2006) Premiums-Discounts and Exchange traded funds The Journal of Derivatives
Hasbrouck, J. (2003), Intraday Price Formation in U.S. Equity Index Markets. The Journal of Finance, 58: 2375–2400.
Hilliard, J (2014) Premiums and discounts in ETFs: An analysis of the arbitrage mechanism in domestic
and international funds The Global Finance journal Volume 25, Issue 2, 2014, Pages 90–107
Lee, C. Shleifer, A. and Thaler, R.H. (1990) Anomalies: Closed-End Mutual Funds The Journal of Economic Perspectives, Vol. 4, No. 4 (Autumn, 1990), pp. 153-164
Datar, V. (2001) Impact of liquidity on premia/discounts in closed-end funds The Quarterly Review of Economics and Finance Vol. 41 Issue 1 2001
