I love Exchange Traded Funds (ETF). In theory. In practice they are being abused by issuers and traders alike (see Beware of systemic risk in ETF). But that’s another topic. Today let’s take a look what can happen with inverse ETF through the compounding effect.

I like inverse ETF (i.e. SH) on the stock market, because if I am wrong (market goes up), my problem gets smaller (ETF goes down). If I had sold short the market (i.e. SPY or via futures) my problem would get bigger.

Of course this “advantage” comes at a certain cost in form of a potential performance drag. To make it clear, let’s look at 4 simple examples:

Example A: Index drops 10%, then fully recovers on day 2 (+11.11%). The inverse ETF however ends ups on a level 2.22% lower than on day one. Why? The increase on day 1 is 10 points (or 10%), but the decrease on day 2 (11.11%) is 12.22 points in absolute terms, since the percentage drop is calculated based on a higher base (11.11% of 110 = 12.22).

Example B: Index rises 10%, then retraces fully on day 2 (-9.09%). The inverse ETF drops 10%, then recovers 9.09%. The ETF ends up 1.82% lower. Why? The %-increase is calculated on a lower basis (90), yielding only an 8.18 point (9.09% of 90) increase on day 2.

Example C and D look at identical percentage changes with opposite direction. In example C, the index first drops, then recovers (example D the opposite). In both cases, the ETF and the index end up having the same percentage changes from day 1 to day 3.

Conclusion: In a sideways market, the inverse ETF will have performance drag. For levered (twice, triple) ETF the effect will be magnified.

The levered ETF (i.e. SDS) has another disadvantage: it even has performance drag in a sideways market if the daily ups and downs are identical in percentage terms. Here, we let the S&P 500 decline 1%, then go up 1%, etc. for 460 days:

Over the course of 2 years (approximately) SPX and SH perform similar, while SDS underperforms.

Now let’s do same with 5% down, followed by 5% up days:

The levered inverse ETF gets atomized (-90%). While investors in levered ETF wish for high volatility in the short term (provided they got the direction right) it clearly hurts them in the longer term.

Now, let’s look at a sideways market in absolute terms: 2% down, 2.04% up the following day:

The numbers speak for themselves; SH and SDS both suffer badly.

But now let’s say the S&P 500 index goes to 400, as some people (including myself) believe (a normalization of corporate profit margins and a 10 times earnings multiple almost gets you there without a stretch). The market does it by declining 1%, followed by a 0.5% increase the following day:

Whoopsie! Compound growth starts showing up. Why? Theoretically, the index can decline 1% each day for an infinite amount of time (even at SPX 400 it can go down another percent).

And what would happen if this 1% down, 0.5% up pattern goes on for 5 years?

Anybody who had bought just one SDS would be multi-millionaire! Of course, with the SPX at 2 points markets would have stopped functioning for a long time.