# Do Markets Get More Volatile After Going Up? from Kim Zussman

March 14, 2009 |

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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1. Anton Johnson on March 17, 2009 8:04 pm

Here are data to determine whether price direction has an impact next period StDev, or vice-versa. I used 20-day non-overlapping periods to complement my trading style.

S&P 500 Daily data

Begin 6/25/1985 x= StDev for period
End 3/16/2009 y= % price change for period

Price Change influence on StDev (StDev are more recent 20 day periods)
Correl -36.31% R-Sq 13.38% y= -0.1637x + 0.0

StDev influence on Price Change (Price are more recent 20 day periods)
Correl -6.80% R-Sq 0.38% y= -0.0278x + 0.0094

Coincident
Correl -14.52% R-Sq 1.80% y= -0.0606x + 0.0149

2. Chris Monoki on March 17, 2009 9:15 pm

Thank you for the observation. It has worth.

I’ve noticed something similar, but I apologize for not posting the stats. First, volatility comes in clusters. This should not come as a surprise; others higher have observed the same effect. Second, volatility is non-directional. That, too, has been observed by others. I am comforted that my in-house work has supported those notions. However, I know there’s skew and have seen it in numbers, but in the case of this simple study described below I didn’t focus on the volatility of up-days versus the volatility of down-days.

Here’s what I did, and you can certainly replicate it. I took the difference of the day’s high and low and put it over the previous day’s close as a simple measurment of volatility. Call that variance. I then took the closing day-on-day change. Call that return. I did this back to 1962.

With that, I sorted the results in descending order of the daily high-low variance. I segmented the sort, with 20% of the highest variance days in one group and the other 80% in another. I resorted each group in chronological order. Then I indexed both to 100. I calculated the total return, and calaculated CAGR based on the number of days in both groups.

The result: the top 20.2% of the most volatile days accounted for 78.8% of the all the returns. Conversely, the 80% of the lesser volatile days resulted in just more than 20% of the returns.

Pareto in its beauty.

This silly, simple observation, however crude and elementary, has convinced me to reject practically everything Gaussian and Bachelier-based. Vilfredo Pareto gave us something more to observe than current academia, Wall Street houses and policy-makers focus on.

Keep pressing,
Chris Monoki