VIX – SPY Hedged Trade

It is a strange argument that stock charts from the Great Depression have some predictive value today. In the Striking Price article in Barrons over the weekend, Steven Sears quotes McMillan Research saying that there is an 89% correlation with 1938 so any pullback in the market will be short and shallow.

Even if that argument doesn’t convince, he does mention an interesting trade, which is to buy September 30 or 32.50 VIX (Chicago Board Options Exchange volatility index) puts and hedge with at the money SPY (ETF that tracks the S&P 500, whose implied volatility is measured by VIX) puts. What happens is, if the VIX drops as the market rises, the VIX puts make money, but the SPY puts lose value. If the market drops, the SPY puts increase in value, but the VIX puts lose value.

Now the question is, how much of each to buy?

Vega

What we have to look at is, for a move of, say, ten points down in the S&P 500 (which is equal to one point in the SPY) which would make our SPY puts more valuable, how much would VIX drop, which would make the VIX puts less valuable?

How much would the value of the SPY puts increase for a 1 point drop in SPY? Since their delta is near -0.5, they would increase in value by half a dollar.

That is one piece we need.

We need to figure out how much the VIX puts drop in value when SPY drops. To do that we use the SPY vega. Vega of SPY is 0.12 so the change in the implied volatility of SPY would be given by the change in the SPY option value divided by the option’s vega, or 0.5 / 0.12 or 4% for a 1 point drop in SPY. But this is 4% of the implied volatility. Since the implied volatility is 27, this gives a change of the implied volatility of 4% of 27 which is about 1. So the implied volatility would go from 27 to 28.

This change is the underlying that moves the VIX puts. So since the VIX 30 puts have a delta of -0.7, that would change the value of the VIX puts by (-0.7) * (1) = -0.7

So it is these two changes in value that we want to hedge. It looks like we would need about 7 SPY puts for every 5 VIX puts (7 SPY * 0.5 + 5 VIX * (-0.7) = 0).

Where Does The Profit Come From?

One way to figure that out is to look at the vega of the SPY puts and compare it to the delta of the VIX puts. That way, we are looking at the change in the value of the SPY puts when their implied volatility changes (that is what vega measures), and comparing that to the change in the VIX puts when its underlying (the implied volatility of the SPX index) changes.

The vega is the change in the value of the option for a small change in the implied volatility. For the 99 or the 98 SPY put, vega is $0.12 and the delta of the September 30 VIX put is -$0.71. For the September 32.50 VIX put the delta is -$0.89. So we would have to buy six times as many SPY puts as VIX puts. That would make us immune to movements in the implied volatility.

If we bought 7 SPY for every 5 VIX, we would profit from the change in implied volatility calculated above. The VIX puts are six times as sensitive to changes in implied volatility of the SPX as the SPY puts are. If the S&P implied volatility drops, the vega measures the change for the SPY while it is delta that changes the value of the VIX puts.