Using Quadratic Variation to Compare Trading-Range Variability

Summary

The document asks how to rank assets by variation in their daily trading ranges without relying on their average range. It proposes quadratic variation: take successive observations in the range series, calculate each change, square the changes, and sum them. This gives greater weight to large day-to-day shifts and is presented as a way to describe historical behavior rather than predict future moves.

For the supplied five-day examples, the calculation yields 1,075 for Asset A and 2 for Asset B, reflecting the much larger swings in A’s range values. The method measures variation in the sequence of reported ranges; it is not the same as calculating price-path quadratic variation from intraday or close-to-close returns. The answer offers no normalization for differences in units or scale, no statistical comparison across unequal sample lengths, and no guidance on choosing a window. Those choices matter if the measure is used to rank assets beyond the stated example.

Key ideas

• Quadratic variation can summarize changes in a sequence of daily range values.
• The measure sums the squared differences between consecutive observations.
• Squaring gives larger range changes greater influence on the total.
• In the example, Asset A’s calculated variation is much higher than Asset B’s.
• The answer describes a historical measure and does not claim predictive power.

Tags

# Variation of the trading range


# Variation of the trading range












Example: The trading range (in points) for each of the last 5 trading days for asset A is: 5,21,2,15,32 and for asset B is: 5,6,5,5,5. Is there an indicator that ranks assets based on variation of trading ranges over a certain time period? (I don’t mean average).

P.S: Not for predictive purposes, just to identify historical characteristics of certain assets.

## Answer by ASX Portfolio (score 0, accepted)

https://quant.stackexchange.com/a/68163

In this case, you could consider the quadratic variation of the asset price paths to indicate trading range. By quadratic variation, I make reference to the mathematics used in Stochastic Calculus, which is compute path-by-path (Steven E. Shreve, 2008).

$[M,M]_k=\sum^{k}_{j=1}{(M_j-M_{j-1})^2}$

Using your example above, Asset A variation is calculated as 1075 whereas Asset B variation is 2.

```
import numpy as np

# Quadratic Variation
quadratic_variation = lambda x: np.square(x[:-1]-x[1:]).sum()

asset_A = np.array([5,21,2,15,32])
asset_B = np.array([5,6,5,5,5])

variation_A = quadratic_variation(asset_A)
variation_B = quadratic_variation(asset_B)

print(variation_A,variation_B)
```

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.