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Good Economic News for the Holidays: Volatility Is Down—A Commentary by Ian Ayres ’86

The following commentary was published in The New York Times on December 24, 2008.

Good Economic News for the Holidays: Volatility Is Down
By Ian Ayres ’86

One of the most important but underreported financial indicators is the CBOE’s Volatility Index (^VIX), which measures the market’s expectation of future volatility in stock prices. (The CBOE has written a nice technical white paper describing how it is calculated, here.) Traditionally, the annualized volatility of the S&P 500 has been 20 percent, but last month when I went to give a talk on retirement investment at Columbia, the VIX was standing at an apocalyptic 80 percent. The huge drop in stock prices is bad, but it would be a lot better if the market thought that the major gyrations were mostly in our past.

So the good news is that the volatility index has retreated to 45 percent:

Now, 45 percent is still more than twice what it “should” be. But it’s at least moving in the right direction. When it drops below 30 percent, it will be a strong indication that the market correction is complete and we’re back to business as usual.

A group of “chartists” — and I use that term disparagingly — attach a more mystical meaning to the recent decline, relating it to the “golden ratio” and Fibonacci sequence. For example, an article last week on Reuters trumpeted “US-VIX falls below key Fibonacci retracement level” :

The CBOE Volatility Index .VIX fell more than 10.7 percent to as low as 44.50, below a key 61.8-pct Fibonacci retracement level of its surge from late August to late October. Traders could next eye 42.16, the interim high seen shortly after the Lehman collapse.

Why is 61.8 percent key? It comes from the Fibonacci sequence of numbers — which starts with 0, 1 and then adds the two proceeding terms, so it’s 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. A very cool property of the sequence is that the ratio of any number greater than 5 in the sequence divided by the subsequent number in the sequence comes close to 61.8 percent (the reciprocal of the golden ratio).

Chartists look for FIBs. After a major price movement, technical analysts (i.e., chartists, people who think they can predict future stock price given the curve of its past prices) look for reversals equaling 61.8 percent, 50 percent, 38.2 percent, and 23.6 percent as moments where the price is more likely to change again (or not, if the price is powering through to another FIB). Why are these other percentages FIBs? 38.2 percent = 61.8 percent squared, and 23.6 percent = 61.8 percent cubed. Fifty percent isn’t really related to Fibonacci at all, but chartists think they see it in the data.

The golden ratio may exist in nature and art, but Fibonacci retracement strikes me as nonsense on stilts as applied to finance. I’m not as convinced by the short-term, random-walk hypothesis as I was in the days before programmed trading. But there is no reason in the world why Fibonacci retracement should characterize the pricing of a competitive market for information.