Short & ultra-short ETFs paradox

[Cutten]

Consider the following trade:

Go long the normal ETF (e.g. SPY, FXI)
Go long the short ETF

Now if the two ETFs have perfect inverse tracking, and normal ETF goes up 100%+, you have a risk-free profit, since your long in the short ETF cannot fall below zero.

Second, look at the "turbocharged" short ETFs such as FXP. Now the problem is magnified. Just go long $10k in FXI, and go long $5k in FXP. If the FXI goes up or down more than 50%, you have a risk-free profit.

So, can anyone explain this apparent paradox? First person to give the right answer gets a cookie.

 

[dtrader98]

Seems like a good hedging strategy
on the surface. Assume you had 5% daily gains on SPY from this day forward (fantasy, yes, but for hypothetical purposes...) and had invested $1 in each etf since SH's inception. It would ideally look like this.

Plus side is your cumulative gain would be in the black while hedged, and the SH would take a long time to get to zero as the effect of each doulble is to only half the short etf.

Negatives are you also lose a lot of the compounded power of the long only etf.
SPY only had 225% gain, hedged index had only 80% net gain.

Still looks reasonable. However, nothing great is free. This assumes they are always perfectly correlated at the 5% incremental gains. Anyone who thoroughly looks over the daily tracking of the ETFs will find they diverge quite a bit, which leads to very erroneous divergence on the longer term performance. There have been some etfs studies that have shown one index to go up say 8% long term, while the single and double etfs/long and short were wildly off over the same period.

This also doesn't take into account cap gains distributions, nor other expense fees. So while on the surface, it looks like a great strategy, one has to use very detailed variables to look at the long run benefits. No lunches are free in this industry.

 

[crgarcia]

First it is highly unlikely an index will go up/down 50% or more in a reasonable amount of time, it make take many years.

Most leveraged ETFs invest about 98% in short term T-Bills, and the other 2% in futures.

So by going long one / short other at most you may gain the T-Bills rate, less futures cost of carry, less commission costs.

 

[dtrader98]

One more scenario, using perfectly "ideal" inversely correlated indexes. $1 ea investment. Long ETF cruises along, and cumulative gain breezes up, while short decays. One day, long takes a 99% (10sigma) hit:eek: . Because the weight of the cumulative index is hit so hard, the doubling of the short index is not enough to overcome the impact and balance the total net loss to zero. End result: the strategy was not "risk-free" as the net hedged index balance went from $2 to 50 cents.

 

[Corelio]

Quote from Cutten:

Consider the following trade:

Go long the normal ETF (e.g. SPY, FXI)
Go long the short ETF

Now if the two ETFs have perfect inverse tracking, and normal ETF goes up 100%+, you have a risk-free profit, since your long in the short ETF cannot fall below zero.

Second, look at the "turbocharged" short ETFs such as FXP. Now the problem is magnified. Just go long $10k in FXI, and go long $5k in FXP. If the FXI goes up or down more than 50%, you have a risk-free profit.

So, can anyone explain this apparent paradox? First person to give the right answer gets a cookie.

There is no paradox here.
The answer to your apparent "paradox" is called asymmetry of returns.

 

[captain_trips]

Quote from Cutten:

....short ETF cannot fall below zero.

perhaps not ~ but can....

reverse split
reverse split
reverse split

etc.
etc.

this might tie up your capital a lot longer than you intended for minimal or no gains

plus this is starting to sound like a synthetic (long put + long stock = long call) as you're obviously hoping that the underlying goes UP to realize any return. Why not simply buy the etf/index where it is and enjoy the ride

dtrader also makes an interesting "catastrophe scenario" observation.

 

[Cutten]

Quote from Corelio:

There is no paradox here.
The answer to your apparent "paradox" is called asymmetry of returns.

The question remains - a fully hedged position appears to be offering a potential profit (in the event of a 50%+ gain) whilst giving full protection on the downside. In your view, where is the risk in this position.