Why Paired Leveraged and Inverse ETNs Do Not Hedge Each Other

# Why aren't ETNs always listed with an inverse ETN?


# Why aren't ETNs always listed with an inverse ETN?












Exchange Traded Notes (ETNs) are often issued to give buyers exposure to an index that cannot be easily constructed from liquid securities. (If an index can be constructed from liquid securities it is more common for sponsors to offer a tracking mutual fund or Exchange Traded Fund.)

Sometimes sponsors will offer an ETN and its inverse in pairs. For example:

- UBS ETRACS - ProShares Daily 3x Long Crude ETN (NYSE: WTIU)

- UBS ETRACS - ProShares Daily 3x Inverse Crude ETN (NYSE: WTID)

To first order, these ETN pairs offset each other. This is a benefit to the sponsor, since open interest in one is a free hedge to the other. It is also a benefit to buyers, because without the inverse ETN someone who wanted to hedge the other direction would have to pay borrow costs to sell the other one short. (Which is something that even the most sophisticated investor can't do in, say, an IRA.)

Given the benefits I see, there must be some cost or obstacle I don't see to issuing ETNs in pairs because it is relatively uncommon. So what are reasons that ETNs are not more often – or always – issued in pairs?

## Answer by Lliane (score 3)

https://quant.stackexchange.com/a/51194

The reverse 3x ETN and the daily 3x ETN are not inverse to each other due to convexity and they do not offset each other.

Let's say you have 1 million AUM in each (i.e. the ETN delta is +3 million for the 3x and -3 million for the -3x), and the market moves twice by + 5%.

End of day 1 :

- 3x = 1.15 million, etn needs to go long 3.45 million delta (buy +300k delta)

- -3x = 0.85 million, etn needs to go short 2.55 million delta (buy back -300k delta)

End of day 2 :

- 3x = 1.3225 million, etn needs to go long 3.9675 million delta (buy (3.9675-(1.3225-1.15)-3.45) = 345k delta)

- -3x = 0.7225 million, etn needs to go short 2.1675 million delta (buy back (2.1675-(0.7225-0.85)-2.55) = 255k delta)

As you can see if you sell both the 3x and the -3x, you need to hedge daily because of the convexity (and your gamma is in the same direction (you need to buy when market going up and sell when market going down)). It's actually a classic job interview question, and there was a lot of discussion revolving about that gamma during the VIX ETN blowups (both ETN and inverse ETN had to buy more and more vol).

## Answer by Chris (score 1)

https://quant.stackexchange.com/a/51193

I think the primary obstacle is the costs involved/potential revenue offered for distributors. ETNs are already uncommon and their market isn't the same as standard equity ETFs; inverse ETNs even moreso.

Your proposed benefits also don't hold up. In this case, ProShares doesn't care about hedging, they're just trying to attract assets to get their bps. And the inverse ETN is about 40 bps more expensive, so it's not really a slam dunk to buy the ETN versus simply shorting the underlying futures.

Even if ProShares is able to charge 10x what they do for standard ETFs, the assets aren't 10x so there isn't a reason to offer them--looks like WTIU is at about \$12M with WTID about half that. 'Successful' ETFs typically garner in excess of \$500M.