May you live in uninteresting times.

Market volatility has become a thing of the past. To wit, the S&P 500 (over the past 15 trading days) is trading in its narrowest range in history.

(Click on image to enlarge)

The VIX, the so-called “Fear Index,” is lower than 99% of historical readings. 

(Click on image to enlarge)

What are investors afraid of these days? You guessed it: the lack of fear. When volatility inevitably rises, investors are worried that will mean the end of the road for stocks.

This is not the first time they’ve had this concern. We have dispelled the myth that low volatility means stocks have to go down (it does not) a number times in the past few years. But the myth lives on.

(Click on image to enlarge)

So let’s try a different approach and talk about probabilities. If volatility rises from here (as is likely), what are the odds that the S&P 500 will post a positive return?

The answer: it depends. On what? Time frame.

If volatility rises tomorrow, the S&P 500 has a 12% chance of being up (based on historical data going back to January 1990). But if volatility rises over the next 3 years, the S&P has a 72% chance of rising.

(Click on image to enlarge)

Why the huge difference?

Time frame. As the time period lengthens, the relationship between stocks and changes in volatility weakens. The correlation between the percentage change in the VIX and percentage change in the S&P 500 goes from highly negative at 1 day (-0.70) to only slightly negative at 3 years (-0.08).

Why is this the case?

Because of path.

Saying that volatility is higher today than 3 years ago tells you nothing about the path. The path could very well have been up, up, up until the very end of the 3 year period when volatility finally spiked and stocks gave back some of their gains. Or the path could have been down, down, down with a surge upward near the end to bring stocks higher on a 3-year basis with higher volatility.

There are an endless array of paths over 3-year periods for both volatility and the stock market. But as stocks rise more than they fall and have higher odds of rising the longer the time frame, long-term compounding often trumps short-term volatility.

The compounding from 54% of all days being positive (with average daily gains equivalent to average daily losses) leads to 66% of 6-month periods and 81% of all 3-year periods being positive. The VIX is only telling you about implied volatility today. And while implied volatility a year from now may be higher than today, that doesn’t necessarily mean stocks will be lower. In fact, more often than not they are still higher (upper right quadrant in chart below).

(Click on image to enlarge)

Up until now, we’ve only discussed direction, not magnitude. What if the VIX doubles over the next year? Surely that would preclude gains in the S&P 500, right?

Wrong. Such an increase would make positive returns less likely, but far from impossible. Historically (using weekly data), the S&P 500 has actually been higher 34% of the time over a one-year period in which the VIX doubles. We saw this most recently from August 2014 to August 2015 when the VIX spiked 144% but the S&P 500 still managed a gain of 1.2%. Prior to this, we saw positive returns from 2006-07 with the VIX doubling as well as 1997-1998 and 1996-1997. The lesson here: path matters.

(Click on image to enlarge)

The counter to these benign scenarios are the many instances from 2007 to 2008 where the VIX doubled and losses occurred. If you’re fearful of a volatility spike today this is likely the scenario that is coming to mind.

So what happens from here when volatility rises?

Let’s summarize:

• If it rises over the next day/week/month, stocks are likely to be down.
• If it rises over the next 3 months, it’s a coin flip as to what stocks will do.
• If it rises over the next year, stocks are still likely to be higher but with lower odds than if volatility were to fall.
• If it rises substantially (+100% or more, very limited sample size) over the next year, stocks are likely to be down (66% chance) but there are examples (1996-98, 2006-07, 2014-15) where stocks were still up.
• If it rises over the next 5 years, it seems to have no impact at all on the odds of a higher/lower stock market (84% chance of a higher S&P 500 versus 82% in all 5-year periods).

Should you care what happens when volatility rises in the coming months? That depends entirely on your time frame. If you’re a short-term trader that is short volatility or leveraged long stocks, a rise in volatility over the next few months would likely cause significant pain. But if you’re a diversified investors with a horizon of 20-30 years, a short-term rise in volatility is the best thing that could happen, as it would likely provide an opportunity to add to your investments at lower prices.

When it comes to both volatility and markets, time frame is everything.