ATR Breakout Strategy: Mathematical Foundations of Adaptive Stop-Loss
The ATR Indicator True Range Conventional volatility measures based on the high-low range fail to account for gap openings. The True Range (TR), introduced by Wilder (1978), resolves this limitation by considering three sources of price movement: TRt=max{Ht−Lt∣Ht−Ct−1∣∣Lt−Ct−1∣ TR_t = \max \begin{cases} H_t - L_t \\ |H_t - C_{t-1}| \\ |L_t - C_{t-1}| \end{cases} where HtH_t denotes the current period high, LtL_t the current period low, and Ct−1C_{t-1} the previous period close. The three components of TR capture distinct volatility sources: intraday range (Ht−LtH_t - L_t), upward gaps (Ht−Ct−1H_t - C_{t-1}), and downward gaps (Lt−Ct−1L_t - C_{t-1}). By taking the maximum across these three values, TR ensures that gap-driven volatility is never understated, a property particularly important for instruments that frequently exhibit overnight jumps such as index futures and government bond futures. ...