Fractal Adaptive Moving Average  Trading Strategy (Setup)
I. Trading Strategy
Developer: John Ehlers. Source: Ehlers, J., FRAMA: Fractal Adaptive Moving Average. Concept: Trend following trading strategy based on adaptive price filters. Research Goal: To verify performance of the Fractal Adaptive Moving Average (FRAMA). Specification: Table 1. Results: Figure 12. Trade Setup: Long Trades: Close[i − 1] > Entry_Upper_Band[i − 1]. Short Trades: Close[i − 1] < Entry_Lower_Band[i − 1]. Index: i ~ Current Bar. Trade Entry: Long Trades: A buy at the open is placed after a bullish Setup. Short Trades: A sell at the open is placed after a bearish Setup. Portfolio: 42 futures markets from four major market sectors (commodities, currencies, interest rates, and equity indexes). Data: 36 years since 1980. Testing Platform: MATLAB®.
II. Sensitivity Test
All 3D charts are followed by 2D 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: FRAMA_Length, ATR_Band (Definitions: Table 1):
Figure 1  Portfolio Performance (Inputs: Table 1; Commission & Slippage: $0).
STRATEGY  SPECIFICATION  PARAMETERS 
Auxiliary Variables:  FRAMA(Price, FRAMA_Length) is the Fractal Adaptive Moving Average over a period of FRAMA_Length, where Price = (High + Low)/2. ATR(FRAMA_Length) is the Average True Range over a period of FRAMA_Length. ATR_Band is a number of ATRs to include in the envelope: Entry_Upper_Band[i] = FRAMA[i] + (ATR_Band * ATR[i]) Entry_Lower_Band[i] = FRAMA[i] − (ATR_Band * ATR[i]) Exit_Upper_Band[i] = FRAMA[i] + (0.5 * ATR_Band * ATR[i]) Exit_Lower_Band[i] = FRAMA[i] − (0.5 * ATR_Band * ATR[i]) Index: i ~ Current Bar. FRAMA Definition: Ehlers, J., FRAMA. 
FRAMA_Length = [10, 196], Step = 6; ATR_Band = [0.0, 6.0], Step = 0.2; 
Setup:  Long Trades: Close[i − 1] > Entry_Upper_Band[i − 1] Short Trades: Close[i − 1] < Entry_Lower_Band[i − 1] Index: i ~ Current Bar. 

Filter:  N/A  
Entry:  Long Trades: A buy at the open is placed after a bullish Setup. Short Trades: A sell at the open is placed after a bearish Setup. 

Exit:  Trend Exit: Long Trades: A sell at the open is placed if Close[i − 1] < Exit_Lower_Band[i − 1]. Short Trades: A buy at the open is placed if Close[i − 1] > Exit_Upper_Band[i − 1]. 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]. 
ATR_Length = 20; ATR_Stop = 6; 
Sensitivity Test:  FRAMA_Length = [10, 196], Step = 6 ATR_Band = [0.0, 6.0], Step = 0.2 

Position Sizing:  Initial_Capital = $1,000,000 Fixed_Fractional = 1% Portfolio = 42 US Futures ATR_Stop = 6 (ATR ~ Average True Range) ATR_Length = 20 

Data:  42 futures markets; 36 years (1980/01/01−2016/06/30) 
Table 1  Specification: Trading Strategy.
III. Sensitivity Test with Commission & Slippage
Tested Variables: FRAMA_Length, ATR_Band (Definitions: Table 1):
Figure 2  Portfolio Performance (Inputs: Table 1; Commission & Slippage: $100 Round Turn).
IV. Benchmarking
We benchmark the base case strategy against alternatives:
Case #1: ATR_Length = 60; ATR_Band = 3.
Case #2: ATR_Length = 80; ATR_Band = 3 (Base Case).
Case #3: ATR_Length = 100; ATR_Band = 3.
Case #4: ATR_Length = 120; ATR_Band = 3.
Fixed Fractional Sizing  Case #1  Case #2  Case #3  Case #4 
Net Profit ($)  61,547,224  77,609,025  120,731,962  122,322,363 
Sharpe Ratio  0.71  0.74  0.80  0.81 
Ulcer Performance Index (UPI)  0.80  0.80  1.02  1.08 
Profit Factor  1.15  1.17  1.16  1.24 
CAGR (%)  12.00  12.70  14.06  14.13 
Max. Drawdown (%)  (39.25)  (53.55)  (42.74)  (41.72) 
Percent Profitable Trades (%)  41.03  40.59  41.30  40.64 
Avg. Win / Avg. Loss Ratio  1.65  1.71  1.65  1.82 
Table 2  Inputs: Table 1; Fixed Fractional Sizing: 1%; Commission & Slippage: $100 Round Turn.
V. Rating: Fractal Adaptive Moving Average  Trading Strategy
A/B/C/D
VI. Summary
(i) The trading strategy based on the Fractal Adaptive Moving Average does not perform significantly better than alternative strategies; (ii) The Fractal Adaptive Moving Average is based on an approximation of the fractal dimension which is very inaccurate.
Related Entries: Zero Lag Moving Average Filter (Entry & Exit)  Simple Moving Average Filter (Entry & Exit)  Hull Moving Average Filter (Entry & Exit)
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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 UNDEROROVER 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.
RISK DISCLOSURE: U.S. GOVERNMENT REQUIRED DISCLAIMER  CFTC RULE 4.41
Codes: matlab/ehlers/FRAMA