In our previous post we introduced the concept of using the ViX as a market gauge, and its practical use in terms of setting volatility based stop-losses and calculating the daily range.
Since we focused on the daily standard deviation of the SP500, we'll focus here and expand the ViX-formulae by calculating the standard deviations for different time-frames.
Monthly; ViX value/sqrt 9
Weekly; ViX-value/sqrt 36
Daily; ViX-value/sqrt 252
Hourly; ViX value/sqrt 6048
Minute; ViX value/sqrt 362880
Second; ViX value/ sqrt 21772800
It is important to note that these calculations are based on the amount of active trading days in a year, approximately 252, whilst the ViX itself is calculated by using a whole calendar year, consisting of 365 days.
If we calculate with 365 days we assume that trading occurs continuously, which excludes a weekend-effect, meaning that all trading days are considered being the same irrespective if it is monday, friday, Thanksgiving (or any other holiday*). None of these values result in totally perfect calculations as each of them have their unique advantages and disadvantages.
For simplicities sake we'll stick to 252 trading days as that provides an intuitive basis and a very close approximation to what we're trying to achieve - calculating standard deviations, despite this caveat.
From a practical standpoint it becomes increasingly complex and costly to backtest datasets and timeframes that are under a daily period, as this type of data usually comes with a cost, as it has to be purchased.
The daily data-set for the SP500 and the ViX in our previous post came from investing.com which offers its data for free.
An hourly, minute and second standard deviation can be useful for daytraders, and scalpers alike, as well as constructing certain algorithms (mean-reversion strategies, trendfollowing strategies etc*) that trade on these time-frames, as it provides a clear view of stop-loss levels, and profit-taking levels.
Furthermore, this concept stretches itself not only to the ViX and the SP500, but also to other asset-classes where volatility is easily gauged.
Volatility indices for stocks, bonds, currencies can be easily found by browsing Google, and the same calculations apply as we have presented.