Gold and the Eight Standard Deviation Move

Nothing gets me more excited than talking about implied volatility and the forward looking aspect of volatility indexes. On Thursday (before the storm in gold prices) the SPDR Gold Shares ETF (GLD) closed at 151.05 and the CBOE Gold ETF Volatility Index (GVZ) closed at 15.29. GVZ is a 30 day implied volatility measure, but is quoted at an annualized number. 15.29 can be interpreted as the implied volatility of GLD option prices as indicated as an annualized range for GLD of 15.29% higher or lower over the next 30 days. This range is also interpreted as one standard deviation which we learned in statistics class and never escape in the options world. This annualized number can also be narrowed all the way down to a single day. The formula that accomplishes this –

Price × Implied Volatility × Square Root(Days/252)

In the case of GLD based on Thursday’s close a one day standard deviation price change for Friday would have been –

151.05 × .1529 × Square Root(1/252) = 1.45

As even the most casual of market observers knows on Friday GLD dropped 7.10 to close at 143.95. We can be determined how many standard deviations, based on the Thursday closing prices of GVZ and GLD, this 7.10 move represents. This math is pretty easy –

7.10 / 1.45 = 4.88

So Friday was a 4.88 standard deviation move in the price of gold. For simplicity sake let’s call it a five standard deviation move. Statistically we get a five standard deviation move approximately once every 4,776 years. So we should not expect another move like this out of the price of gold until May 17, 6789. That is the first (and probably the last) time I will every use the number 6789 as a year.

So today’s move is a bit early. Friday GLD closed at 143.95 and GVZ went out at 21.32. Based on Friday’s close a one day one standard deviation move is 1.93. As I write this GLD is quoted at 134.40 down 9.55 which converts to a move of 4.93 standard deviations. Let’s call that a five standard deviation move as well.

Finally, we can convert the Thursday gold market prices to tell us what a two day one standard deviation move would entail. Using my HP-12C I got a two day one standard deviation move of 2.05. Currently the two day price change in GLD is 16.65 which can be converted to just over eight standard deviations. I wanted to share what this comes to, but the table I use only goes up to seven standard deviations. Let’s just say the sun is expected to burn out first.

  • http://www.facebook.com/wkbeaty William Keith Beaty

    Are you sure that formula is correct —> 151.05 x .1529 / Square Root (1 / 252) = 1.45 Regardless of how you order the terms I can’t get 1.45?

  • http://www.facebook.com/rarhoads Russell Rhoads

    Trust me, I always appreciate my math being checked you are correct the formula should read – (151.05 x .1529) x square root (1/252) = 1.45 (rounded of course). Shoot me an email at rhoads@cboe.com with your address and I’ll get you some CBOE swag!

  • Phil

    Stats are supposed to reflect reality.
    It is well known that standard deviation is useless for exceptional event, especially for stock quotes.
    The Gaussian probability curve is not reflecting reality of occurence.

    Another type of probability curve must be used, with a slower slope on the extremes.
    There are numerous articles on the subject on internet.

    • http://www.cboe.com/ Russell Rhoads, CFA

      This is exactly the point I’m making when I wrote this. Although it is all we have to work with, the markets do not care about or adhere to statistical models.