Building a Long-Volatility ETF Portfolio

As I've discussed before, the nature of the VIX and its technical dangers provide a large disincentive to ETF issuers. In the absence of a VIX ETF, however, other options do exist that allow you to effectively purchase volatility. Transaction costs remain a large issue in any such endeavor, and so I have constructed what is most likely the simplest option.

The most VIX-correlated ETFs on the market are, nearly without expection, ProShares Ultra or UltraShort ETFs. It is likely that ProShares or their managing counterparty is using volatility contracts of some type in the management of these products. As a result, one of the most efficient proxies to volatility is to purchase equal amounts of the UltraShort S&P500 ProShares (SDS), and the Ultra S&P500 ProShares (SSO). This portfolio yields the following returns against the VIX:

click to enlarge

The daily log-return correlation squared here is 74%, and the weekly log-return correlation squared is 73%. However, as I've noted in previous analysis, the cumulative return series diverge temporarily without failure. The daily cumulative log-return correlation squared is 64%, and drops to 58% when moving to weekly cumulative log-returns.

Comments

[kkin365]

Excellent analysis. Well done.

[hillcrestln]

Fascinating. What is the left scale? Surely that is not tenths of a percentage point. And from the June low to the August peak (close) the VIX roughly doubled, which doesn't seem to be what this is showing.

[MichaelBommarito]

There's a typo/word omission in there - you should *hold* equal amounts of SDS and SSO, though you should hold SDS long and SSO short.

hillcrest, I almost always calculate log-return, and so the left-scale is cumulative log-return. Log-return is nearly identical to standard return for small values, but diverges for larger returns. A 100% increase is log(1+1) = log(2) = 0.6931 in log-return, whereas this would simply be 1.0 for price return. The difference has to do with the utility of returns, and although there isn't a strictly correct answer, many sophisticated calculations are much cleaner in log-return.

[wdr65]

What is the fundamental thesis behind this pair trade? Is there something about the construction of these Proshares ETFs that allows volatility (vix) to be isolated? Is this nothing more than a great data-mining find?

[ig0r]

very simple guys, volatility rises when prices fall (lots of reasons, google it, for example: corporations get more leveraged as equity values fall relative to debt, this increases risk of bankruptcy)