Inverse exchange-traded fund

Inverse and leveraged inverse ETFs tend to have higher expense ratios than standard index ETFs,[2] since the funds are by their nature actively managed; these costs can eat away at performance.

In a market with a long-term upward bias, profit-making opportunities via inverse funds are limited in long time spans.[3] In addition, a flat or rising market means these funds might struggle to make money. Inverse ETFs are designed to be used for relatively short-term investing as part of a market timing strategy.

An inverse ETF, like any leveraged ETF, needs to buy when the market rises and sell when it falls in order to maintain a fixed leverage ratio. This results in a volatility loss proportional to the market variance. Compared to a short position with identical initial exposure, the inverse ETF will therefore usually deliver inferior returns. The exception is if the market declines significantly on low volatility so that the capital gain outweighs the volatility loss. Such large declines benefit the inverse ETF because the relative exposure of the short position drops as the market fall.

Since the risk of the inverse ETF and a fixed short position will differ significantly as the index drifts away from its initial value, differences in realized payoff have no clear interpretation. It may therefore be better to evaluate the performance assuming the index returns to the initial level. In that case an inverse ETF will always incur a volatility loss relative to the short position.

As with synthetic options, leveraged ETFs need to be frequently rebalanced. In financial mathematics terms, they are not Delta One products: they have Gamma.[4]^:87–91

The volatility loss is also sometimes referred to as a compounding error.

If one invests $100 in an inverse ETF position in an asset worth $100, and the asset's value changes the first day to $80, and the following day to $60, then the value of the inverse ETF position will increase by 20% (because the asset decreased by 20% from 100 to 80) and then increase by 25% (because the asset decreased by 25% from 80 to 60). So the ETF's value will be $100*1.20*1.25=$150. The gain of an equivalent short position will however be $100–$60=$40, and so we see that the capital gain of the ETF outweighs the volatility loss relative to the short position. However, if the market swings back to $100 again, then the net profit of the short position is zero. However, since the value of the asset increased by 67% (from $60 to $100), the inverse ETF must lose 67%, meaning it will lose $100. Thus the investment in shorts went from $100 to $140 and back to $100. The investment in the inverse ETF, however, went from $100 to $150 to $50.[5]

An investor in an inverse ETF may correctly predict the collapse of an asset and still suffer heavy losses. For example, if he invests $100 in an inverse ETF position in an asset worth $100, and the asset's value crashes to $1 and the following day it climbs to $2, then the value of the inverse ETF position will drop to zero and the investor would completely lose his investment. If the asset is a class such as the S&P 500, which has never increased by more than 12% in one day, this would never have happened.

For instance, between the close of November 28, 2008 and December 5, 2008, the iShares Dow Jones US Financial (NYSE: IYF) moved from 44.98 to 45.35 (essentially flat, properly an increase of 0.8%), so a double short would have lost 1.6% over that time. However, it varied greatly during the week (dropping to a low of 37.92 on December 1, a daily drop of 15.7%, before recovering over the week), and thus the ProShares UltraShort Financials (NYSE: SKF), which is a double-short ETF of the IYF moved from 135.05 to 117.18, a loss of 13.2%.

Given that the index follows a geometric Brownian motion and that a fraction ${\displaystyle x}$ of the fund ${\displaystyle A_{t}}$ is invested in the index ${\displaystyle S_{t}}$, the volatility gain of the log return can be seen from the following relation.

${\displaystyle \Delta \ln(A_{t})=x\Delta \ln(S_{t})+(x-x^{2})\sigma ^{2}{\frac {\Delta t}{2}}}$

where ${\displaystyle \sigma ^{2}}$ is the variance of the index process and the last term on the right hand side constitutes the volatility gain. We see that if ${\displaystyle x<0}$ or ${\displaystyle x>1}$, as is the case with leveraged ETFs, the return of the fund will be less than ${\displaystyle x}$ times the index return (the first term on the right hand side).[6]^:394