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.


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