Vexed Vix February 24, 2011 at 10:09 am
FT alphaville asks Can you trust the Vix?
The answer rather depends on what you mean by ‘trust’. ‘Can you trust the price of VIX futures to provide the markets’ best estimate of what realised S&P volatility will be?’ is a different and more difficult question to ‘Can you trust the the price of VIX futures to reflect the price at which people are willing to buy and sell VIX futures?’. The connection between the first and second of these is problematic, as we will see.
Why might the price of a Futures contract on a commodity reflect the expectation of the spot price in the future? Because if not, the naive argument goes, you can buy or sell the spot vs. the Future and profit from that difference. That is all very well if you can indeed do both transactions, and if your arbitrage bound includes the costs of doing that (i.e. storage of the commodity or its borrow cost, interest on borrowed or invested money, and so on). But how do you take a position in volatility?
The simple answer is to trade an option. If you delta hedge (at least in the Black-Scholes world), your P/L is a function of the difference between the vol you paid, implied, and the vol that is realised. If the VIX suggests vol is going to be higher than you think it is, and if you believe that the VIX will reflect implieds in the future, then sell an option and delta hedge to the VIX expiry.
Unfortunately that doesn’t work that well as the sensitivity of the option to volatility is a function of spot. It’s like buying a commodity then finding there is a different amount in the warehouse every day. This isn’t helpful. Moreover the VIX prices off the whole volatility smile not just the at-the-moneys, so even if you knew what the at-the-money level was going to be at expiry, you would still be exposed to smile. You could just trade the vol (or var) swap, but that’s OTC so there is a significant amount of infrastructure needed to do the trade.
The other alternative is to take some risk. Let’s look at the VIX curve. It is, as Alphaville notes, in steep contango. If we were to view this as wrong, then we would want to sell the VIX futures and hope that volatility will be lower at expiry than the future predicts. Who would be the other side in this trade? Well, dealers who are short volatility through selling options can hedge by buying the VIX, and they might be keeping the curve in contango. It is much more common to worry about being short vol than long as the OTC equity derivatives business tends to be more about selling options than buying them, so often the industry position is structurally short. What all this means is that there is a good reason for the VIX curve to be in contango, and a good reason to just keep rolling a futures position front or second month vs. one year. If it were me, then, I’d forget the no arb arguments – the arb is too hard to get on, and there is too much money on the other side for it to come in – and just play the curve.