Mar

31

What is the relationship between range and return? Using SPY intraday 1/04-present, %range and %return defined as:

day range = ((H/L)-1)*100
return =((close/open)-1)*100

Then regressing return vs (same day) range:

The regression equation is day rt = 0.246 - 0.262 day range.

Predictor      Coef    SE Coef      T      P
Constant    0.24619  0.05315   4.63  0.000
day range  -0.26152  0.05195  -5.03  0.000

S = 0.605558   R-Sq = 3.0%   R-Sq(adj) = 2.9%

Wee! The bigger the range, the more the drop. Seems obvious in that large range implies large variance, and there is contemporaneous negative correlation between variance and return. Logically big range can accompany big gain, big drop, or little change, yet it turns out most often to drop.

Optics trivia: this scatter plot resembles geometric spot-diagram of off-axis star image for system exhibiting the aberration known as coma.

In other regressions, tomorrow's day return had little correlation with yesterday's range or return.

The association of big range with contemporaneous negative returns is also seen if plotting range vs. date since 2006, the broad and (so far) narrow peaks corresponding with summer 2006 and recently, respectfully. 

Bernd Dittmann adds:

To further Kim's findings, it would be interesting to note that the daily range (as defined above) is strongly partially auto-correlated with a maximum lag of 10 trading days for the sample period since Jan. 2004, whereas intraday returns do not exhibit such a degree of auto-correlation. This would be in sync with findings of volatility clusters.

Day of high volatility or high daily trading ranges are likely to be followed by days of similar wide trading ranges. If one were to expand the sample period back to 2000, the above returns vs. daily range equation no longer holds. Neither the intercept (0.041, p=0.41) nor range (-0.026, p=0.38) is significant. 


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