Range-based volatility as a true-range construction

Volatility as a construction problem

Volatility can be defined as variation in the price of a tradable asset over a chosen interval and can be measured from either returns or ranges.

Return-based intervals use known event times. Range-based intervals generally record only the start and end of the window, not the exact time of the high or low.

Editorial: the interval is the yardstick. A scale that cannot see the opening gap, the travel inside the bar, or price drift will hand a distorted reading to any later regime view or position bound.

What the range must include

Parkinson's 1980 high-low estimator is more efficient than close-to-close standard deviation because it uses intraday movement, but it omits opening gaps and assumes no meaningful price drift.

A successful range-based volatility estimate should include both intraday and close-to-close prices, account for opening gaps, and remain usable when significant drift is present.

True range as the working scale

True range is the single-bar span from the higher of today's high or yesterday's close to the lower of today's low or yesterday's close. Wilder's true range already includes intraday prices and handles opening gaps.

Restating true range as a logarithmic ratio lets it be compared with later range-based estimators. Root-mean-square true range percent is that restatement combined as a root-mean-square and scaled to an annualized percentage.

Modified Rogers-Satchell uses high, low, open, and the prior close so both drift and opening gaps enter the estimate. On ten years of SPY data ending September 29, 2017, annualized modified Rogers-Satchell volatility and annualized root-mean-square true range percent showed a close correspondence.

Relative to the standard deviation of returns, true range captures intraday movement while still registering opening gaps and drift. True-range construction keeps the measured range larger than the same bar's drift, so directional travel cannot swallow the volatility reading.

One scale for regime and size

Historical volatility is a past-looking estimate of how much a market has moved, built from observed prices rather than from option prices. Implied volatility infers a forward-looking reading from option prices rather than from completed bars.

ATR position sizing is a way to scale a trade so that account risk stays within a pre-set bound once stop distance is measured in true-range units.

Editorial: the archive's workflow is the construction of the range. TradersWeek's interpretation is that the same true-range scale can describe the market regime and can bound how large a position may be, because both jobs use one yardstick that still sees gaps, intraday travel, and drift.