e 16 is the square root of 256, the approximate number of trading days in a year. 30 divided by 16 is 1.875, which means that a 30 VIX equates to roughly 1.9% daily moves in the S&P. To translate the VIX into a monthly vol number, we can divide it by 3.46, which is the square root of 12. 30 divided by 3.46 is about 8.7 and this means that a 30 VIX is suggesting we could see a monthly move in the S&P of as much as 8.7% higher or lower—in about 68% of cases.
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| S&P 500 Volatility: What does the VIX at 20 mean? |
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| By Kevin Cook |
Most investors are familiar with the unique negative correlation of the CBOE S&P 500 Volatility Index (VIX) and the S&P 500. In essence, when one goes up, the other is usually headed down in a classic relationship based on levels of market fear or complacency. But one under-the-radar aspect of the VIX that can make it more useful is its relationship to time. And there is a handy rule of thumb that every professional options trader learns early in their training to help them remember: volatility is proportional to the square root of time.
Say what? Yes, this involves some math, as most dealings with statistics and probability do. But contrary to that complicated mouthful about square roots and what not, this is some of the simplest math you will ever do with options, so don’t worry. First, let’s just review what a volatility number is measuring so we are on the same page.
Vol Refresher
Volatility is always expressed as the annualized standard deviation of price movement, whether actual historical price moves for some past period, or potential price moves implied by option prices. For instance, a stock with a historical volatility of 30% for some past period, say six months, means that in that past period the stock moved as if it was likely to trade for another 12 months within a range of 30% higher or lower from the current price, with a 68% probability. In other words, past price action tells you statistically how volatile a stock is and what its most probable price distribution is going to be.
If a $50 stock has a six month historical volatility of 30% and we are content using that number as a measure of future price movement—and thus as a gauge of future investment risk—we could assume that our stock will be within $35 and $65 one year from now, about 68% of the time. This “68%” business is just basic statistics—one standard deviation being defined as what is probable within a distribution of results in 68.27% of cases.
And since the mean for stock volatility is always the current stock price, we simply determine what price moves the volatility implies are probable. Two standard deviations for our $50 stock at a 30% vol gives us a price range of $20 to $80, with about 95% probability. Below are some graphics that illustrate these basic dynamics of statistics as applied to stock volatility.
 Click on image to enlarge!
 Click on image to enlarge!
Translating the VIX into daily and monthly moves
The VIX is built from a formula that blends the implied volatility of S&P 500 options traded at the CBOE. Implied volatility is simply the vol that comes from reversing the option pricing formula. Instead of putting historical volatility—or some guesstimate about future vol—into the pricing model to tell us what a fair price for an option should be, we put in a price that an option is currently trading at and the model spits out a volatility. In this way, options prices “imply” the volatility that market participants are expecting based on what they are paying for puts and calls.
A VIX reading of 30% tells us that the S&P 500 is expected to be 30% higher or lower one year from now, with a 68% probability. So how do we take that 30% VIX reading and turn it into a daily or monthly volatility that might give us a better idea of what to expect in the near term? By following the handy rule of thumb that “vol is proportional to the square root of time.”
And all this means is we divide the annualized vol number by the square root of the time period we are interested in. For instance, if we want to convert 30% into a daily vol measure, we divide by roughly 16. Why 16? Because 16 is the square root of 256, the approximate number of trading days in a year. 30 divided by 16 is 1.875, which means that a 30 VIX equates to roughly 1.9% daily moves in the S&P. To translate the VIX into a monthly vol number, we can divide it by 3.46, which is the square root of 12. 30 divided by 3.46 is about 8.7 and this means that a 30 VIX is suggesting we could see a monthly move in the S&P of as much as 8.7% higher or lower—in about 68% of cases.
The bottom line: when the VIX is between 30 and 35, the very liquid S&P options market is pricing in the likelihood of roughly 2% moves every day. And for monthly moves that means between 9 and 10% swings. While most investors do not care for this kind of volatility, options traders love it. As the S&P seems to have found some footing this week above key support near 1,015, the VIX has fallen below 30 and, as this trend will likely continue, option pros will be finding ways to sell volatility as fear subsides from the market.
Hopefully this has helped you understand better what the VIX means and encouraged you to learn more about how to use it to benefit from market volatility.
To read more from Kevin, please visit his page on ONN.TV |
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