Do Markets Get More Volatile After Going Up? from Kim Zussman
One possibility is that markets get more volatile after they go up.
Using SPY (93-present), checked daily close-close returns, as well as range defined as (H-L) / (H+L)/2
Then sorted c-c returns into down or up, and checked the next day's range. Here is the comparison of mean range for days following those
either down or up:
Two-sample T for range nxtD vs range nxt U
N Mean StDev SE Mean
range nxtD 1872 0.0039 0.00309 0.000072 T=8
range nxt U 2187 0.0032 0.00230 0.000049
Indeed volatility after down is larger
To check whether the size of down or up moves has an effect on tomorrow's range, here is a regression of next day's range vs prior
day's return, just for prior days which were down:
Regression Analysis: range nxtD versus c-c D
The regression equation is
range nxtD = 0.00239 - 0.182 c-c D
Predictor Coef SE Coef T P
Constant 0.0024 0.00008 29.69 0.000
c-c D -0.1819 0.00623 -29.17 0.000
S = 0.00256647 R-Sq = 31.3% R-Sq(adj) = 31.2%
As expected, the bigger the down yesterday the bigger today's range. Here is the same regression, only for yesterdays which were up:
Regression Analysis: range nxt U versus c-c U
The regression equation is
range nxt U = 0.00250 + 0.0949 c-c U
Predictor Coef SE Coef T P
Constant 0.002498 0.00006 41.17 0.000
c-c U 0.094886 0.00503 18.85 0.000
S = 0.00213147 R-Sq = 14.0% R-Sq(adj) = 13.9%
So both for up and down yesterdays, the larger moves mean bigger range the following day. However the effect is more pronounced for down
days with 31% of variance explained vs 14% for up days. Of course
this can also be explained by persistence of volatility.