Not my area of finance, so I'm just here to learn. The article below would appear to support Arebelspy. Response?

http://news.morningstar.com/articlenet/article.aspx?id=271892

Edit: In case my question is unclear, it appears to show that you are only guaranteed that the hedge/offset works for a short period. Is this wrong?

Interesting.

I looked at a

Proshares 2x long S&P500 prospectus, and indeed it says that returns beyond one day will differ from 2x S&P500. The article you linked says that the way it differs will result in a decay.

But I think this is the effect that smedleyb wants. If you can short an ETF that's guaranteed to go down because of the decay described in the Morningstar article, then you win. So far, we've thought of two risks: (1) what if the market swing is so dramatic that it wipes out one of the funds and then some, and (2) what if you can't find shares to keep it going? I'm guessing there are other risks that are harder to pinpoint.

(The rest of this post is about trying to figure out the leveraged ETF decay effect.)

I'm still trying to wrap my brain around the decay effect. I found an NYU paper that goes more in depth:

Path-dependence of Leveraged ETF returns (pdf)

"[R]eturns of the LETFs have predominantly underperformed the static leveraged strategy. This is particularly the case in periods when returns are moderate and volatility is high. LETFs outperform the static leveraged strategy only when returns are large and volatility is small."

In the LETF case, you buy shares of the LETF. In the static leveraged strategy, you borrow to buy shares, then sell shares and pay back the loan.

I figured looking at a 2-day time period might help. Ignoring fees, suppose the market has return r

_{1} on one day and r

_{2} on the next day so that the total 2-day return is (1+r

_{1})*(1+r

_{2})=(1+r

_{TOT}). For a particular total return, you can solve for r

_{2} in terms of r

_{1}.

r_{2}=(1+r_{TOT})/(1+r_{1})-1

The 2x LETF return will be (1+2*r

_{1})*(1+2*r

_{2})-1, while the static leveraged return would be 2*(1+r

_{TOT})-2. If you difference those two, you can find out what you stand to gain or lose by buying the LETF rather than buying on margin, just due to volatility. Making r

_{1} the dependent variable, and plotting the gain/loss for several r

_{TOT} (shown in the legend) gives you this:

The peaks occur where r

_{1}=r

_{2}, that is, if volatility is low. You do better with the LETF only when both day's returns are the same sign as the total return, and the loss from different signs is greater than the gain when they are the same. Those two things together could account for the significance of the decay noted in the Morningstar article. Also, The LETF advantage is only significant for large total returns. This seems to match the above statement from the NYU paper.