On the 12th Day of Volness …, from Kim Zussman
My true love gave to me,
A black eye and a kiss you'll see.
Daily range is high when volatility spikes, and decays over time. Yesterday was day 12 since the 4% decline in stocks. Checking the SPY intraday high/low as range (actually (H/L)-1), I used linear regression to measure the rate of decline. Here is a plot of SPY daily range since 2/27/07 (inclusive):
One might argue that range or volatility decay is not linear since it cannot progress continuously downward. In fact tests using quadratic regression showed better RSQ by adding **2 term, though linear term explained most of the variance. For simplicity the 1st 12 days are modelled as linear.
As a check on the current daily range decline against historics, I repeated regressions of the intraday range vs. the day following (analogous) declines; defined as 1day cl-cl drop worse than -3%, preceded by 5 days without a drop worse than -1% (SPY since 1993). Here is a table of the regression slopes and T-values for the range vs. the day following big declines, by year:
Yr slope t
2007 -0.0011 -1.8
2003 -0.0001 -0.2
2002 -0.0018 -2.4
2000 -0.0019 -2.8
1998 -0.0027 -1.5
1997 -0.0004 -0.9
1996 -0.0018 -2.4
It looks like the current change in range lies mainly in the plain, and is consistent with prior such events.
Bernd Dittmann adds:
As Kim outlined, both daily volatilities and daily high-low ranges decline after a spike. I estimated for the S&P 500 between Jan 03, 2000 and today a simple garch based on daily returns rather than daily range. The equation of the conditional variance ("h") seems to be consistent with his findings: Its regressor of lag 1 is 0.9276. A one-off vola spike (with subsequent error terms of the equation of the mean being zero) feeds through the model and decays as shown below:
day h
1 0.9276
2 0.8604
3 0.7981
4 0.7404
5 0.6868
6 0.6370
7 0.5909
8 0.5481
9 0.5084
10 0.4716
11 0.4375
12 0.4058
13 0.3764
14 0.3492
15 0.3239
This yields a similar picture as declines in daily high-low ranges.