Bad “good ideas”

Single or double, and now even triple short ETF have become pretty popular. Advantage: they offer new ways to bet on the downside of multiple markets, not always easily accessible. So for small investors, they seem to be a good idea.

And they are… for short term trading. But not for long-term investment. For example, this is the S&P 500 versus SDS, the double short S&P ETF, since August 2007:

S&P 500 : down 25%, SDS : … down 22.5%! Almost as bad!

Worse, it is normal. It is due to the gamma of the ETF. Usually associated with options, this term is appropriate here : when you “normally” short a stock or an index, the variation in US$ of your exposure matched perfectly the variation of the underlying you are selling. For example, if you short the S&P 500 at 1,000, you are short $1,000 (to make it simple). Let’s say the S&P drops by 10% the next day. It’s value is 900, and your remaining exposure $900 (you also have $100 of unrealized profit). In this case, you have no gamma, your exposure varies exactly with the underlying price.

In the case of an inversed ETF and an index at 900, your ETF would be valued at $1,100 ($1,000 + 10% x 1,000). You are now short the S&P 500 at 900 for a net exposure of $1,100, not $900. This increase of $200 is due to the positive gamma, ie increasing short exposure when the underlying moves down. Said differently, you are now short 1.22 time the S&P, rather than 1.

In the case of the double short, the effect of the gamma is even bigger. With an index at 900, you now have an exposure of $1,000 + 2×10%*$1,000 = $1,200. So you increased your short exposure by $300 and are now short 1.33 time the S&P.

Now if the market rebounds by 10% the next day, your simple short ETF would be worth $1,100 – 10% x 1,100 = $990, while the index is only back to 990. So you would have lost 1% while the index would have lost 1%. With a double, you would have lost 2%. Repeat the same process (with smaller daily variations) for a few months and you have an almost certain loosing proposition, even if the underlying goes your way. On top of that, you are getting shorter and shorter as the market moves down, which is exactly at the wrong time, as the probability of a rebound (even just a technical one) increases.

So here again, just for the eyes, the long term effect of a large positive gamma associated with a short position (graph of UHPIX, the double short Hong Kong index, versus its benchmark – inversed) :

PS: This effect is also true with double or triple long ETF.