The Alito Volatility Index

Time for a really geeky post! Feel free to skip if you’re a mathphobe.
As I’ve mentioned before, I’m a fan of TradeSports.com. This Web site let’s investors buy “futures contracts” on real world events. In addition to many sports and political events, they also have contracts on the nomination of Judge Samuel Alito to the Supreme Court.
There are currently two sets of contracts on Alito. One is simply “Will Alito Be Confirmed?” That contract is currently running at 94.5%. So the market seems pretty confident that he’ll pass.
The other is a set of six contracts asking how many votes will he get (over 40, 50, 60, 70, 80 and 90).
What I find interesting in these markets is that you can look at two different contracts and find an “implied contract” for a separate event.
For example, Donald Luskin and I discovered that during the (brief) Meirs nomination, the contract for her getting more than 50 votes was trading much higher than the contract for her passing. The reason is that the number-of-votes contract was only if she came up for a vote. That means that there was an “implied withdrawal contract.” (Details here.) And withdraw she did.
These sorts of number games are actually quite common on Wall Street. That’s exactly what the volatility index (or VIX) is. It tells us the implied volatility of the S&P 500. In options pricing, volatility is a key variable. So we can look at the price an option and work backward to the volatility number that traders are using.
Personally, I don’t take these futures markets too seriously. Mostly, I think they’re just for fun. Real markets need to be much more liquid. Also, there’s too great a temptation for partisan interference.
Having said that, we can look at the futures for how many votes the market believes that Judge Alito will get. Plus, we can find some interesting observations.
Let’s look at two of the contracts: Alito receiving over 60 votes, and Alito receiving over 70 votes. The contract that Alito will get over 60 votes is priced at yesterday’s close at 74, meaning that the market believes that there’s a 74% chance the Judge Alito will get 60 or more votes. The 70+ vote contract is currently priced at 16.
Using these two numbers we can find the market’s mean and standard deviation for Judge Alito’s final confirmation vote. (Warning: math ahead!)
Here’s what we do:
Since there’s a 74% chance the Alitio will get 60 or more, the normal distribution tells us that a 74% chance is equal to the mean plus 0.64 standard deviations. A 16% chance works out to the mean minus 0.99 standard deviations. So the 10 votes between 60 and 70 is equal to 1.63 standard deviations. Ten divided by 1.63 equals 6.1 senators which is the standard deviation. That’s our Alitio Volatility Index, or ALIX (copyright, me!).
The mean number of votes is 60 + (0.64*6.1) or 63.9. So the market believes that Judge Alito will get 63.9 “aye” votes with a standard deviation of 6.1 senators. Assuming a normal distribution, this means that there’s a 68.3% chance that Alito’s vote total will fall between 57.8 and 70 votes.
Here’s a chart of the implied standard deviation of the Alito vote. This line will probably fall as senators gradually make up their minds:

Here’s the mean vote (black line). The red lines represent plus and minus one standard deviation:

I downloaded the price data off TradeSports’ Web site. You can download my excel file here.
Since the vote on Judge Alito will eventually come (assuming these windbags finally stop talking), the standard deviation number should gradually fall. This can happen even though the mean doesn’t change much. Every day on Wall Street, billions of dollars is invested in volatility. There are investors who don’t give a fig where the market goes, but they’re passionate that it does it smoothly (or erratically).
(Technical note: The real VIX is a weighted-average of several options contracts. I’m only using the 60+ and 70+ contracts.)
It seems that there’s a fairly solid bloc of about 35 votes dead set against Judge Alitio. However, the one-standard-deviation-below-the-mean line has nudged up a little since the hearings started. This may indicate that a few “maybe” votes have drifted over to the “aye” camp.
See, I told you this was a geeky post.
Update: Thanks, Ramesh! The 60+ contract moved up to 75 (a recent high), and the 60+ contract is now up to 22. That moves the mean vote total up to 64.7 with a standard deviation of 6.9 votes.

Posted by Eddy Elfenbein on January 12th, 2006 at 5:43 am

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