Developer:J. Welles Wilder, Jr.: Directional Movement System. Concept: Trend-following trading strategy based on the Average Directional Index Rating (ADXR). Source: Wilder, J. W. (1978). New Concepts in Technical Trading Systems. Greensboro: Trend Research. Research Goal: Performance verification. Specification: Table 1. Results: Figure 1-2. Trade Entry: Table 1. Trade Exit: Table 1. Portfolio: 42 futures markets from four major market sectors (commodities, currencies, interest rates, and equity indexes). Data: 34 years since 1980. Testing Platform: MATLAB®.
II. Sensitivity Test
All 3-D charts are followed by 2-D contour charts for Profit Factor, Sharpe Ratio, Ulcer Performance Index, CAGR, Maximum Drawdown, Percent Profitable Trades, and Avg. Win / Avg. Loss Ratio. The final picture shows sensitivity of Equity Curve.
Tested Variables: ADXR_Look_Back & ADXR_Threshold (Definitions in Table 1):
Average Directional Index (ADX): Definition Average Directional Index Rating (ADXR): ARXR[i] = 0.5 * (ARX[i] + ARX[i − ADXR_Look_Back + 1]) Long/Short Trade Filter: Trade only when ADXR[i − 1] >= ADXR_Threshold. Index: i ~ Current Bar.
Stop Loss Exit: ATR(ATR_Length) is the Average True Range over a period of ATR_Length. ATR_Stop is a multiple of ATR(ATR_Length). Long Trades: A sell stop is placed at [Entry − ATR(ATR_Length) * ATR_Stop]. Short Trades: A buy stop is placed at [Entry + ATR(ATR_Length) * ATR_Stop]. Stop Loss Exit is used to normalize risk via position sizing. Directional Movement Exit: Long Trades: −DI (“Minus Directional Index”) crosses above +DI (“Plus Directional Index”). Short Trades: +DI (“Plus Directional Index”) crosses above −DI (“Minus Directional Index”). Index: i ~ Current Bar.
IV. Rating: Directional Movement | Trading Strategy
(i) The ADXR filter does not add value. When ADXR_Threshold > 0 (i.e. the filter is active), the strategy performance is reduced (Figure 2); (ii) The core momentum strategy based on the cross of Directional Index performs worse than the alternative momentum models.
CFTC RULE 4.41: HYPOTHETICAL OR SIMULATED PERFORMANCE RESULTS HAVE CERTAIN LIMITATIONS. UNLIKE AN ACTUAL PERFORMANCE RECORD, SIMULATED RESULTS DO NOT REPRESENT ACTUAL TRADING. ALSO, SINCE THE TRADES HAVE NOT BEEN EXECUTED, THE RESULTS MAY HAVE UNDER-OR-OVER COMPENSATED FOR THE IMPACT, IF ANY, OF CERTAIN MARKET FACTORS, SUCH AS LACK OF LIQUIDITY. SIMULATED TRADING PROGRAMS IN GENERAL ARE ALSO SUBJECT TO THE FACT THAT THEY ARE DESIGNED WITH THE BENEFIT OF HINDSIGHT. NO REPRESENTATION IS BEING MADE THAT ANY ACCOUNT WILL OR IS LIKELY TO ACHIEVE PROFIT OR LOSSES SIMILAR TO THOSE SHOWN.