Wed, Apr 20, 2011 | Jared Woodard
The team at FT Alphaville have been on a tear recently, analyzing all manner of VIX-related issues and potential problems. I’ve linked to those posts below, and they’re definitely worth reading even though I don’t agree with everything there.
Here are two worries about pricing and replication of VIX products that leave me unmoved. First, the matter of replicating the spot VIX index.
As Theo Casey of Futures and Options World has discussed before, it’s actually impossible to replicate the Vix, making convergence arbitrage rather an impossibility. ["What is the fair value of a VIX future?"]
Theo’s post has a quote from Jeremy Wien (a name you should recognize if you follow the VIX space): “the spot VIX itself cannot be realistically replicated, as the execution/bid-offer costs are too high, and rolling the two strips every single day would be a logistical nightmare.” That’s exactly right. While it’s a step too far to say that it is “impossible” to replicate the spot VIX index, it’s certainly impractical to do so.
But: who cares? The spot VIX index is just a statistic. It’s an artificial construction. I can’t imagine why any investor, whether hedging or speculating, would want to replicate the VIX index as opposed to, say, buying or selling a few puts or calls at a handful of relevant strikes. To see why the replication of the spot VIX index is a non-issue, let’s imagine that I create and publicize a new volatility index I’ll call WVIX (Woodard Volatility Index): this index takes the implied volatilities of OTM options with deltas closest to 15 and 40 in the two nearest series and weights them to achieve a rolling 30-day window. I think WVIX would track VIX and VXO pretty closely. And you could replicate it each day by adjusting your exposure to no more than 8 option legs – not a load of fun, but not impossible, either. But why would you ever want to replicate WVIX? I just made it up, after all.
Maybe you actually like WVIX and want to have it in your portfolio; great. WVIX2 doubles the number of strikes used – adding strikes at deltas of 5 and 30 (let’s say); WVIX3 triples the strikes used. Eventually, for some value of n, WVIXn is indistinguishable from VIX (let’s call that value d, because you can’t distinguish it). In no nearby possible world is there an investor for whom VIX is a more desirable fantasy asset than WVIXd-1 (and arguably no investor would be better served by a replicated VIX than by WVIX) because the added informational content in the more complex variations does not offset logistical hassles and transaction costs. This is all just to say that I don’t think anyone is worse off in the absence of a spot VIX that can’t be easily replicated: all the features that might make someone want to trade a spot VIX product (e.g. the mean reverting nature of volatility, sensitivity to the skew curve, etc.) can be captured in myriad other ways, and more efficiently so.
Second, on the turtles-all-the-way down worry about VIX futures:
And as Chris Cole of Artemis Capital Management has reminded us, there’s no denying the fact that Vix futures are and always will be derivatives of derivatives, meaning they’re at least twice removed from any underlying fundamentals.
So does this make them extra susceptible to reflexivity and the feedback loop? Many argue yes. [ibid]
“Derivatives of derivatives” sounds bad until you realize that AAPL stock – or any of the plainest vanilla financial assets you can imagine – is also a derivative of a derivative of a derivative. The behavior of technology consumers, the odds of a strike in a sweatshop in China, the vicissitudes of global transport chains – these are all unknowable variables upon which AAPL earnings depend. And the price of an AAPL share is a derivative not just of those earnings, but also of the psychology and expectations of other market participants, the price of money, the skill of Steve Jobs’s doctors, and etc. unto eternity. If there are feedback loops and reflexivity in VIX products, those effects are of a piece with the reflexivity inherent in modern financial markets. Cf. the work of Donald MacKenzie, esp. An Engine, Not a Camera. Some of us don’t like the ethereality of it all, and are worried that in this crazy new world, as the prescient man said, “all that is solid melts into air.” But the uncanny qualities of Cthulhu-style capitalism aren’t unique to VIX futures.
I also want to insist on the difference between the spot VIX index and the tradable VIX products, the futures and options. The spot VIX index cannot by definition have an effect – reflexive or otherwise – on anything over and above the effects of changes in the prices of SPX options. That’s just a tautology. Whether the existence and prices of VIX futures and options could create feedback effects is an empirical matter; it’s possible, but the evidence so far is weak and difficult to isolate from other factors.
Moreover, while the limits to arbitrage are certainly greater in VIX products than they are elsewhere, it’s not the case that VIX futures are some kind of free-standing, purely fantastical construction. If the VIX futures for May expiration trade, let’s say, at 40, but the average implied volatility of SPX options expiring in June is around 20%, I know that arbitrageurs will come in and sell the VIX futures, buy the SPX options, and bring the two closer into line (because my friends and I will be among them).
You can object that the “closer into line” figure is not as tight as you might find in other markets – like the difference between the SPY ETF and S&P 500 futures – but my reply is that it’s plenty close for all practical purposes: May VIX futures traded recently at 18.45; June SPX options have an average IV of 16% or so. That difference is just as likely an effect of the persistent volatility risk premium as it is a by-product of anything more strange or worrisome. I see no reason to regard the popularity of VIX products – especially when used for hedging – as an independent reason for worry. On the contrary, if 2008 taught us anything, it’s that the still-widespread mythology of unhedged buy-and-hold investing is a far more dangerous illusion. Unhedged stock portfolios tend to get dumped at precisely the wrong times, and that implicit short gamma bias of ordinary investors is much more worrisome than the curiosities of VIX futures pricing models.