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I am doing a little study on the relationship between ETF prices and NAVs. Using intraday tick data, I take the mid prices of an ETF and compare them to the NAVs that I compute from the mid prices of the constituents of the ETF's creation basket (including a cash component).

For some ETFs, the two curves (ETF mid price and NAV) are pretty much on top of each other. For other ETFs, however, there seems to be a gap between the two curves, and the gap is almost constant throughout the day and even multiple days. Here are some examples. Per comments, I added bid and ask in the second plot (DJD).

DIA shows no gap. DJD shows a constant gap.

Is there any reasonable explanation for such a gap? Or, does it indicate a problem in my data or formula? One argument I hear is that an ETF might trade at a premium or a discount if its constituents are illiquid. If there is a liquidity issue, wouldn't it just widen the spread? Why would it shift the mid point? Any insight would be appreciated.

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  • $\begingroup$ Could it be something that relates to the replication strategy (physical vs. synthetic)? The latter could include (total return-)swap costs? $\endgroup$
    – simzoor
    Jun 9, 2021 at 6:35
  • $\begingroup$ I've looked at only physical ETFs so far. For example, DJD has a significant gap while DIA does not. I will see if I can add some plots. $\endgroup$
    – spark
    Jun 9, 2021 at 13:04
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    $\begingroup$ The plots are for one day (5/26/2021). On the x axis, 05-26 10 means 5/26 10am. But the gaps indeed has persisted for many days as you may be able to check separately. $\endgroup$
    – spark
    Jun 9, 2021 at 17:36
  • $\begingroup$ Thank you for clarifying the time axis. I will delete my previous comment. $\endgroup$
    – nbbo2
    Jun 9, 2021 at 17:48
  • $\begingroup$ Most likely you're missing some cash component $\endgroup$
    – LazyCat
    Jun 9, 2021 at 20:26

1 Answer 1

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This definitely happens in the real world, in fact it is the basis for the very popular trade called ETF arbitrage. There are many reasons that this happens, the primary being that you haven't actually looked at the correct prices to assess the presence of an arbitrage- in order to actually perform creation or redemption of the ETF in a zero risk fashion, you need to be able to immediately buy the ETF at ask and sell the components of the basket at bid or vice versa- you can't generally trade at midpoints with any degree of reliability. This means that when you're looking at the NAV of the ETF, you should consider every value between the NAV computed with only basket asks and NAV comuted with only basket bids as potentially reasonable prices.

Beyond that, there are some fundamental reasons for gaps, a big one being dividends. Generally, ETFs will pay dividends with some regular cadence, say monthly or quarterly, but their components will be paying dividends with their own cadences. This can lead to the ETF accumulating a cash balance which is not part of it's redemption basket between it's own dividend intervals, and which will generally be factored into the fair value of the ETF.

Also in regard to liquidity, some ETFs that have some highly illiquid components might price those components in a different way than the market as a whole does. You see this a lot with bond ETFs, which tend to trade a lot more than their underlyings. It's possible that market participants have collectively priced one of the constituents at a meaningfully lower or higher value than what you see on the book, either for fundamental reasons or because if you were to actually perform creation or redemption you would realistically need to pay a premium or a discount to actually get enough shares to perform the trade- and these types of discounts can be systematically lopsided. Some shares for example might be easily available to purchase but might be hard to borrow, or have very high borrow costs which also need to be factored in.

Edit

I just noticed that the gap you observed for DJD lasted not for days or weeks but years. That type of gap is probably caused by having a problem in your basket data. Did you update the basket every day in your test, or is it possible that the basket changed at the time when you started to observe the difference?

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  • $\begingroup$ The plots are for one day. On the x axis, 5-26 10 means 5/26/2021 10am. $\endgroup$
    – spark
    Jun 9, 2021 at 17:38
  • $\begingroup$ Thanks for your answers. Re your 1st point, I changed the second plot to show bid/ask. The gap is smaller now but still there. Perhaps this gap is not big enough to warrant a creation process? $\endgroup$
    – spark
    Jun 9, 2021 at 17:47
  • $\begingroup$ The existence of ETF arbitrage is precisely why I suspected that an ETF price should always fluctuate around its NAV. So I don't quite follow your 2nd point (dividend). As long as there is an agreement to exchange ETF and basket, shouldn't the arbitrage bring the two close to each other. I don't see why dividend is a factor. $\endgroup$
    – spark
    Jun 9, 2021 at 17:55
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    $\begingroup$ Well there are two different "NAVs" to keep in mind- the real NAV of the ETF as a company, and the value of the redemption basket. The two may not be the same sometimes- such as when an ETF has accumulated a certain amount of dividends from it's holdings. In the case that these amounts have diverged, then a share of the ETF has a value above what you would expect just from the value of redeeming the etf- notably the value of the claim on the undistributed dividends. $\endgroup$
    – deftfyodor
    Jun 9, 2021 at 22:20
  • $\begingroup$ If the ETF value has diverged from the value of the basket (I call it creation basket and you call it redemption basket - I presume the two are identical), wouldn't the creation/redemption process bring them back in line? Where does the arbitrage operate? Between ETF and basket NAV or between ETF and holdings NAV? I am thinking basket NAV. $\endgroup$
    – spark
    Jun 10, 2021 at 0:55

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