Sunday, August 17, 2008

Implied Volatility vs. Next Year's S&P Return

You can download the VIX index, daily, from 1986. I took all these datapoints, and grouped them into deciles. I then looked at the average 12 month ahead returns within those deciles. The results are in the graph above, and show that there is no clear relationship between volatility and future index returns, at least over the past 20 years.

It's standard in theory to assume that higher anticipated systematic volatility increases the expected return. Many researchers have documented this is not so (eg, Glosten, Nelson), but Christian Lundblad took the innovative approach of going back to 1836 and showing that under certain assumptions, you could not reject the hypothesis that return is positively related to volatility. Clearly, he tortured the data into talking. If the effect is this subtle, it is meaningless for driving behavior. I reminds William Sharpe's interview, where he notes that they were incredibly naive to think returns would be the same as expected returns, as if the failure of beta is due to a small sample variation in the CRSP data--an anomalous 80 year draw.

6 comments:

karl k said...

The VIX is not a predictor; it is a correlative.

It is the thermometer of the market; it's involved in taking the temperature of price volatility right then(or rather 30 days in advance, as it is trying to predict the vols of next months S&P), not whether the patient is going to get a whole lot better or whole lot sicker.

It tells us what we already know, but it isn't, or never has been, diagnostic.

Eric Falkenstein said...

In practice I agree. However, current theory from any general equilibrium model implies higher anticipated volatility should increase expected returns.

karl k said...

Eric, right. As you point out, it's the premise that is flawed.

All you have to do is watch the implied volatility of ITM options for any given stock at earnings time. Typically, it goes up, as market makers try to gauge how earnings -- either way -- will affect the stock price, and the associated options. Higher vols mean a higher anticipated price swing -- EITHER way.

In the end, implied volatility has nothing to do with WHERE a stock will wind up, but rather what's the risk of how FAR it will end up from where it is now.

The direction it goes is basically made moot.

Anonymous said...

1836? cool. i'm sure they traded a lot of volatility those days and it's quite relevant to today's float. seriously, does anyone know any, any quantitative approach I should focus my studies on? I have yet to see one that's predictive, but please do share. thx

shittingalpha said...

Have you checked how predictive it is over the next 30 days?

Anonymous said...

I actually think buying stock at very low VIX (<15) is a pretty good strategy, of course sometimes you go for years waiting for that to happen...