The 5 year implied volatility on the S&P 500 is currently 29%. The math to take an annual standard deviation or volatility metric and convert it to a daily standard deviation is rather simple:
Number of trading days in a year = ~ 252
Daily Standard Deviation = Annual Standard Deviation/Sqrt(252)
In the case of a 5 year implied volatility of 29%, this translates into a daily standard deviation of 1.82%. If we believe that the distribution of returns follows a normal distribution, this means that 33% of the trading days for the next five years will have returns that are greater than or less than +/- 1.82%. This is a whole lot of movement over the next 5 years. To put this into perspective, we can look at the trailing 1 month, 1 year and 5 year realized volatilities since 1928:
One month realized volatility is….volatile. One year is less so and five year could almost be described as smooth. Take a look at the red line and find the periods where 5 year realized volatility traded above 20%. During the great depression, a period after the internet bubble and the recent period since the global financial crisis. What about 29%? Great depression exclusively.
This is by no means proof that 29% five year implied volatility is expensive – merely that it is historically rare. We could believe that the next ten years will be more volatile than the last ten and possibly more volatile than the great depression. I do not currently believe in that outcome. I personally believe that we happen to price risk with a very short memory. When looking at the last 70 years since 1940, the 3rd quarter of 2011 had the 5th largest number of trading days that were +/-2.5% or more. I believe that recent experience has a larger impact on the implied volatility term structure than a pure forecast of the next five years of market realized volatility.
As a quick reference for putting volatility into perspective, take a look at Bill Luby’s Rule of 16:
Using the rule of 16 and the 1/3 trading days time frame, the following translations should be committed to memory:
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- VIX of 16 – 1/3 of the time the SPX will have a daily change of at least 1%
- VIX of 32 – 1/3 of the time the SPX will have a daily change of at least 2%
- VIX of 48 – 1/3 of the time the SPX will have a daily change of at least 3%
