R&D Blog
MACD: Part 1 | Trading Strategy (Entry)
I. Trading Strategy
Developer: Gerald Appel. Source: Appel, G. (2005). Technical Analysis. NJ: Pearson Education, Inc; Star, B., PhD (2016). Zero In On The MACD. Stocks & Commodities, May 2016. Concept: Trend following trading strategy based on the MACD (Moving Average Convergence Divergence) line. Research Goal: Performance verification of momentum signals. Specification: Table 1. Results: Figure 1-2. Trade Setup: Long Setup: MACD[i] > 0. Short Setup: MACD[i] < 0. Index: i ~ Current Bar. Trade Entry: Long Trade Entry: A buy at the open is placed after a long setup. Short Trade Entry: A sell at the open is placed after a short setup. Trade Exit: Table 1. Portfolio: 42 futures markets from four major market sectors (commodities, currencies, interest rates, and equity indexes). Data: 38 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: EMA#1_Look_Back & EMA#2_Index (Definitions: Table 1):
Figure 1 | Portfolio Performance (Inputs: Table 1; Commission & Slippage: $0).
| STRATEGY | SPECIFICATION | PARAMETERS |
| Auxiliary Variables: | Exponential Moving Average #1 (EMA#1): Alpha#1 = 2 / (EMA#1_Look_Back + 1); EMA#1[i] = Alpha#1 × Close[i] + (1 − Alpha#1) × EMA#1[i − 1]; Index: i ~ Current Bar. Exponential Moving Average #2 (EMA#2): Alpha#2 = 2 / (EMA#2_Look_Back + 1); EMA#2[i] = Alpha#2 × Close[i] + (1 − Alpha#2) × EMA#2[i − 1]; Index: i ~ Current Bar. MACD: MACD[i] = EMA#1[i] − EMA#2[i] Index: i ~ Current Bar. | EMA#1_Look_Back = [5, 40], Step = 1; EMA#2_Index = [2.0, 4.0], Step = 0.05; EMA#2_Look_Back = round(EMA#1_Look_Back × EMA#2_Index); |
| Setup: | Long Trades: MACD[i] > 0 Short Trades: MACD[i] < 0 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: | 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. | ATR_Length = 20; ATR_Stop = 6; |
| Sensitivity Test: | EMA#1_Look_Back = [5, 40], Step = 1 EMA#2_Index = [2.0, 4.0], Step = 0.05 | |
| 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; 38 years (1980/01/01−2018/3/31) |
Table 1 | Specification of Trading Strategy.
III. Sensitivity Test with Commission & Slippage
Tested Variables: EMA#1_Look_Back & EMA#2_Index (Definitions: Table 1):
Figure 2 | Portfolio Performance (Inputs: Table 1; Commission & Slippage: $100 Round Turn).
IV. Benchmarking
We benchmark the base case strategy against alternatives:
Case #1: EMA#1_Look_Back = 12; EMA#2_Look_Back = 26 (Base Case).
Case #2: EMA#1_Look_Back = 20; EMA#2_Look_Back = 40.
Case #3: EMA#1_Look_Back = 40; EMA#2_Look_Back = 80.
Case #4: EMA#1_Look_Back = 80; EMA#2_Look_Back = 160.
| Fixed Fractional Sizing | Case #1 | Case #2 | Case #3 | Case #4 |
| Net Profit ($) | 5,713,438 | 33,290,114 | 299,995,611 | 416,863,142 |
| Sharpe Ratio | 0.33 | 0.52 | 0.78 | 0.88 |
| Ulcer Performance Index (UPI) | 0.17 | 0.34 | 0.75 | 1.08 |
| Profit Factor | 1.02 | 1.04 | 1.14 | 1.33 |
| CAGR (%) | 5.10 | 9.68 | 16.09 | 17.09 |
| Max. Drawdown (%) | (84.08) | (76.69) | (58.96) | (49.37) |
| Percent Profitable Trades (%) | 29.27 | 30.14 | 32.03 | 33.50 |
| Avg. Win / Avg. Loss Ratio | 2.45 | 2.40 | 2.42 | 2.64 |
Table 2 | Inputs: Table 1; Fixed Fractional Sizing: 1%; Commission & Slippage: $100 Round Turn.
V. Basic Concepts
G. Appel, Technical Analysis (2005):
(1) MACD represents the difference of the short-term exponential moving average minus the long-term exponential average. (2) When market trends are improving, short-term averages will rise more quickly than long-term averages. MACD lines will turn up. (3) When market trends are losing strength, shorter-term averages will tend to flatten, ultimately falling below longer-term averages if declines continue. MACD lines will fall below 0.
What length moving averages should be employed for MACD? There are no hard and fast rules […]. As a general rule, the longer-term moving average will be two to three times the length of the shorter-term average.
VI. Rating: MACD (Part 1) | Trading Strategy
A/B/C/D
VII. Summary
(a) A trading strategy based on the MACD line crossing its zero line is an average momentum model; (b) The default parameters for the MACD should be avoided (i.e. EMA#1_Look_Back = 12 and EMA#2_Look_Back = 26).
Related Entries: MACD: Part 2 (Entry) | Fractal Adaptive Moving Average (Setup) | Zero Lag Moving Average (Entry & Exit) | Simple Moving Average Filter (Entry & Exit)
Related Topics: (Public) Trading Strategies
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