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Hedging by Directly Replicating VIX


Clayton
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(@clayton)
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Joined: 11 months ago

After retirement I want to make a portfolio that's mostly equities but uses a sub-portfolio of options to buy/hold into implied volatility so I either profit or lose less during crashes.  Someone posted a similar idea but involving derivatives of VIX (VXX, VIXY, etc.).

In portfoliovisualizer I found a preliminary Sharpe portfolio with VTSMX=85% and ^VIX=15% from 1992-Present month-to-month with Mean=13.7% SD=9.9% compared to just VTSMX=100% at Mean=11.3% SD=15%

The various VIX products however yield poor results when attempting the same strategy.  It's likely because they don't have the resolution to profit from sudden spikes before reversion.

I read the paper below which shows the math behind a static replication of implied volatility.  Section IV onward gets more into the concept.

http://eprints.lse.ac.uk/67036/7/Martin_What%20is%20the%20expected%20return%20on%20the%20market_published_2017%20LSERO.pdf

Based on the mathematical definition of the VIX as a 1 month expiry long strangle across the full range of strikes (realistically a discrete approximation of this) with weights inversely proportional to the square of the strike at each option.  According to the paper ^VIX should actually be the square root of the payout so the optimal portfolio would end up being around VTSMX=96% VIX^2=4%.  It's like adding salt to food.

Implementing this seems too good to be true.  I read that long strangles have a lot of issues with time decay.  Can anyone verify if the payout as reflected in that paper already incorporates time decay or will I have to do some weird daily turnover of these options to avoid decay? Definitely interesting.

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earlyretirementnow.com
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Joined: 6 years ago

You cannot "buy" the ^VIX in a portfolio. You can only go long (buy) futures on the VIX and they can have a performance that might be vastly different from simulating the "returns" of the VIX spot. So, I'm surprised that portfoliovisualizer even allows you to simulate a "VIX" portfolio position. It's not proper. The futures return will be impacted by the term structure of the VIX futures contract and you will likely have much lower returns from the futures than from the spot because the VIX term structure is in "contango" most of the time. You can eliminate the astronomically high expense ratio of some of the VIX-based ETFs and ETNs, by trading the VIX futures yourself. But you cannot overcome the contango problem in the VIX that way. The contango has to exist because of the strong diversification property of the VIX.

You can simulate the Variance of the S&P500 returns (=VIX-squared) through a portfolio of puts/calls. It's actually the definition of the VIX. It's not really meant to be implemented that way, certainly not for us retail investors. Also, the square/sqrt relationship does not mean that the target portfolio weight should be the sqrt of 15%. The long-VIX portion should be calibrated very carefully. It has to depend on the current VIX level and the level of contango in the term structure. It's something I've thought about previously but I haven't truly mastered it (yet).

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Clayton
Posts: 2
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(@clayton)
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Posted by: @earlyretirementnowcom

You can simulate the return of the Variance of the S&P500 returns (=VIX-squared) through a portfolio of puts/calls. It's actually the definition of the VIX. It's not really meant to be implemented that way, certainly not for us retail investors.

Thanks for your reply.  You lost me on two points.

What's the proper implementation for such a puts/calls portfolio if not to replicate buying into VIX?  It just seemed to make sense that if you recreate the portfolio that defines VIX then you can buy/hold into VIX directly just by definition.

Since it's just an options portfolio why would that be inaccessible to retail investors?

If this doesn't work then I'll consider the futures products.   

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earlyretirementnow.com
(@earlyretirementnowcom)
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@clayton

The VIX-squared (expected variance of the S&P 500) is the (weighted) sum of the OTM put and call contract prices. In order to replicate this, you'd have to buy every single put with a strike below the current S&P value and every single Call with a strike above the current S&P value. That's a lot of trading. Probably not feasible for retail investors.

Also, we're still confusing two things: 1) the construction/calculation of the VIX index (as described above) and 2) replicating the month/month returns of the VIX index. The two are completely different animals. That options portfolio will not necessarily give you the performance of the VIX or even the VIX^2. If the VIX goes up from 25 to 30 (a 20% increase) but the S&P500 stays at the same level as before, then all your options expire worthlessly and you have a -100% return in your options portfolio, very different from your VIX increase.

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