# Intraday Path Length, from Kim Zussman

December 14, 2007 |

The usual way to quantify intraday range is some comparison of high to low. But this misses another dimension - the length of the path traveled by price, which is related to speed of the market (since o-c time is constant, for the entire session  market speed = path length). For example there could be two days, between 930-415 ET (405 min), both with H-L = 20pt (ES). One goes steadily from low at open to high at close, a path length of 20 pt and rate 20pt/405m = 0.05pt/min. The other is a wild day, with a 20 pt gain followed by a 20 pt loss (net unchanged). The wild day path length is (simplifying) 40 pt, which is a rate of [20 + 20]/405 = 0.1pt/min.

Considering just the constant open-close daily period, market speed = path length (a potentially potent area of study is the reaction to market speed in short time intervals, but I will leave that for later). Exact path length would require summing tick data for each day, but for a reasonable estimate here I use 5 minute closing prices and estimate path length as sum { abs(5min moves) } for each day from 930-415. Here are the largest o-c path lengths since 1/07, along with the o-c return (ES points):

date     sum_abs oc
08/16/07 233.25  24.75
08/10/07 212.50    5
11/08/07 185.25  -7.75
08/01/07 185.25  12.25
11/20/07 176.50    9.5
07/26/07 175.75 -20.75
08/09/07 173.25 -20.75
11/02/07 161.50   -2.5
07/27/07 154.50  -31.5
08/17/07 151.00     -7
10/24/07 150.25   2.75
11/09/07 148.75  -3.25
08/15/07 148.25 -15.25
12/12/07 146.00    -22

Notice the big move yesterday is only 14th longest path length YTD. Since that path length is a form of volatility, I compared o-c return with contemporaneous path length and found the usual negative correlation:

Regression Analysis: oc versus sum abs

The regression equation is
oc = 4.49 - 0.0648 sum abs

Predictor      Coef  SE Coef   T      P
Constant     4.490   1.636   2.74  0.007
sum abs    -0.0648  0.019  -3.27  0.001

S = 11.7078   R-Sq = 4.3%   R-Sq(adj) = 3.9%

Do you consider in this calculation the distance from the previous day's close to the current period's open? If not, then a gap day's net price path sum won't include the overnight move in the path.

It is not just the range and such but which side is moving the market on that path. It is clear to me the gap from last night's close to today's opening is public activity, the path from today's open to the close much more professional activity; that's the key to the numbers as I see it.

## Jim Sogi remarks:

I agree with Larry, but for different reasons.  Rather than just pro/public, the night session is related to the global situation and large gaps seem to be a whole new area recently developing. Yet another new different unseen cycle.

## Paolo Pezzutti suggests:

There are at least two dimensions in play: one is speed, which is somehow associated with concepts such as range and volatility. Another is related to directionality. According to different combinations of these two dimensions you could build a matrix of market behavior. The areas would be:

1. volatile; directional
2. non-volatile; non-directional
3. volatile; non-directional
4. non volatile; directional

The problem is related to indicators to be used to efficiently define these areas. How you identify the borders/lines of contact between areas? This classification can be useful when trying to identify the proper tools and techniques to use in each area. What kind of indicator could one use to take into account speed? What can we use to identify directionality?

## Steve Ellison responds:

In his book "Trading and Exchanges", Larry Harris identifies two types of volatility. Fundamental volatility results from changes in fundamentals. Transitory volatility results from excesses of uninformed traders who move prices away from fundamental values. Price moves caused by transitory volatility are likely to reverse as informed traders take advantage of bargain prices to buy or rich prices to sell. Price moves caused by fundamental volatility are much less likely to reverse.

A hazard for a contrarian trader is falsely assuming volatility is transitory when it is in fact fundamental. Dealers and market makers protect themselves from this risk by widening spreads when the order book is one-sided.

I propose a 2×2 matrix of the actual type of volatility and the market's perception of the type of volatility:

.                     How most market participants
.                     perceive volatility
.                     Fundamental          Transitory
Actual
type of
volatility:
.                     Price quickly        Price trends
Fundamental           establishes a        as disbelievers
.                     new equilibrium      change their
.                                          minds one by
.                                          one
.
.                     Market reverses      Price quickly
Transitory            dramatically         reverts to
.                                          previous levels

For years, the trading literature was very heavily slanted toward trend following as the road to riches, which biased many traders toward assuming any volatility was fundamental. However, with much money having been yanked from trend following funds this year, the upper right quadrant is occurring with more frequency.

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