Mar

15

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.


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