Calculus Of Anxiety

We just aired this piece I did about the "fear index" which does actually measure anxiety about the stock market. (Surprisingly, it's not as high now as it was during the 1987 crash.)

You can see what the fear levels are right now. And here's the other measure of anxiety that comes up in the story, the Ted Spread.

In the piece I glossed over how the fear index was actually calculated, which is pretty fascinating. An explanation after the jump.

The fear index, known as the VIX, is a gauge of how far people think the stock market thinks might have moved at the end of the next 30 days. It's a measure of expected future "volatility."

(To be precise, you take the VIX number and divide by sqrt(12). The 12 there is for 12 months in the year. Then look at the number you get. The VIX is saying that there is a roughly 2/3 chance the swing over the next 30 days will be less than that number. So if the VIX is 20, that means it's predicting that 30 days from now the stock market might be 5.7% higher or lower. It might be more or less. But it's saying there is a 2/3 chance it will be in that range. The 2/3 comes from plus or minus one standard deviation, if you ever learned about the bell-curve and all that stuff.)

Whew. Anyway the VIX is calculated from the price of what amounts to insurance policies that protect people against declines in the stock market. How much are people willing to pay, to guarantee that they won't lose money if the market drops?

Those insurance policies are financial instruments you may have heard — options. For a fee, you get the "option" to buy something at a locked-in price on a certain day in the future. The VIX index looks at options on the S&P 500 index fund, so they really are insurance policies on the general movement of the stock market.

So how does this get you to the expected magnitude of stock market swings 30 days out, the measure of fear and uncertainty?

Well, it makes sense that what people think will happen should effect the options price. If you worry that the market might swing 50 percent then you will really want insurance, and the person selling it is probably also worried and so will charge you a bunch. On the other hand if most people think stocks might only swing by a couple percent, well the insurance will be cheaper.

So the options price does have the fear mixed in. But that's not all. There are four other things that also effect the price (the date option can be exercised on, the price of the S&P, dividends paid on the S&P, the "risk free rate of interest".) So the formula to figure out the fear part has to factor out all the other stuff.

The full details are here, in a paper by Bob Whaley who devised the thing. More on the history here.

Whew, that seems like a lot of work right? It doesn't end there.

As I pointed out in the story you can actually bet on what will happen to the VIX. Which is sort of like being able to buy and sell fear. Interestingly, in order to do that you have to create another complex financial instrument, another option, based on the VIX.

Which is kind of funny to think about. You do all this work to extract the VIX from options prices, then you go and create a new option based on the VIX itself.

Whaley told me the properties of the VIX are still being studied. He says it might one day make up just another thing in people's investment portfolios. Bonds, Stocks, and Fear.

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