On Monday to illustrate how much of an outlier the move in GLD was over Friday last week and Monday I created an illustration of how rare the price action in GLD was. The statement was, “the sun is expected to burn out” before we would witness another price move of that magnitude. The full blog with that statement can be found at the link at the end of this blog. This statement has been taken a bit out of context as it related to what the option market was pricing in last Thursday, not the absolute price changes that occurred in the gold market. On the close last Thursday the CBOE Gold Volatility Index (GVZ) finished the day at 15.29. This number is the 30 day implied volatility as indicated by the pricing of a wide number of options on GLD. This can also be converted to depict how much price movement in GLD with a certain amount of statistical certainty is being indicated over a period of time. The formula to do this is –
Price x Implied Volatility x Square Root (Days /252)
Using Thursday’s closing for GLD (151.05) and GVZ (15.29) this translated into a single day move of
151.05 x .1529 x Square Root (1/252) = 1.45 (rounded)
So the option market was pricing in that the following day (Friday) there is 68.2% certainty that GLD would close between up 1.45 and down 1.45. Statistically this is known as a one standard deviation move. Statistically a two standard deviation move would be up or down 2.90 (2 x 1.45) and this would be expected to occur 95.4% of days. Finally a three standard deviation move would have been up or down 4.35 and would have been expected to occur 99.7% of trading days.
Taking that three standard deviation move into account this means that 1 day out of every 370 GLD is expected move more than 4.35. Remember this 4.35 is based on implied volatility of .1529. If the implied volatility was higher the result would be a larger three standard deviation move.
For instance as I write this GVZ is quoted at 28.60. Using 28.60 and combining it with Thursday’s close of 151.05 would give us the following result –
151.05 x .2860 x Square Root (1/252) = 2.70 (rounded again)
1 Standard Deviation = 2.70
2 Standard Deviations = 5.40
3 Standard Deviations = 8.10
On Friday GLD closed down 7.10 which will fall between a two and three standard deviation move. This would be more reasonable than the almost five standard deviation move we experienced last Friday. The big move for GLD was on Monday. I have been looking at what Thursday’s market indicated and then what happened over the two trading days following Thursday. On Monday GVZ closed at 34.48. Applying that to Thursday’s GLD close yields the following for a two day move for the price of GLD –
151.05 x .3448 x Square Root (2/252) = 4.65 (rounded again)
1 Standard Deviation = 4.65
2 Standard Deviations = 9.30
3 Standard Deviations = 13.95
4 Standard Deviations = 18.60
5 Standard Deviations = 22.95
This puts the two day move somewhere between a four and five standard deviation move based on the very high closing level of GVZ on Monday. A four standard deviation move is expected every 15,787 trading days (62 ½ years). A five standard deviation move is expected once in every 1,744,278 trading days (6,921 years). So even using the adjustment based on GVZ’s Monday close the two day move was a rarity.
The point behind all this is that a twenty dollar move may occur again in the future and the sun will still be shining. Although it may not be a sunny day for anyone caught on the wrong side of the move. This twenty dollar move may not be the statistical outlier that we experienced recently. That will depend on option pricing and implied volatility indicated by that pricing.