# R&D Blog

# Price Momentum Model | Trading Strategy (Benchmark)

## I. Trading Strategy

**Concept:** Trend-following trading strategy based on a simple price momentum. **Source:** Kaufman, P. J. (2013). *Trading Systems and Methods.* New Jersey: John Wiley & Sons, Inc. **Research Goal:** Performance verification of the simple price momentum model. **Specification:** Table 1. **Results:** Figure 1-2. **Portfolio:** 42 futures markets from four major market sectors (commodities, currencies, interest rates, and equity indexes). **Data:** 35 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: M1_Look_Back_Index & M2_Look_Back (Definitions in Table 1):

**Figure 1** | Portfolio Performance (Inputs: Table 1; Commission & Slippage: $0).

STRATEGY | SPECIFICATION | PARAMETERS |

Auxiliary Variables: | Momentum is defined as the change of price over some period of time. Sometimes this is called Rate of Change, but both names are incorrect. In physics, this is speed, and in mathematics it is the first difference.Fast Price Momentum (M1): M1[i] = Close[i] − Close[i − M1_Look_Back + 1] Slow Price Momentum (M2): M2[i] = Close[i] − Close[i − M2_Look_Back + 1] Index: i ~ Current Bar. | M1_Look_Back = M1_Look_Back_Index * M2_Look_Back; M1_Look_Back_Index = [0.25, 1.00], Step = 0.025; M2_Look_Back = [20, 200], Step = 5; |

Setup: | Long Trades: M1[i − 1] > 0 and M2[i − 1] > 0 Short Trades: M1[i − 1] < 0 and M2[i − 1] < 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: | Momentum Exit: Long Trades: A sell at the open is placed if M1[i − 1] < 0. Short Trades: A buy at the open is placed if M1[i − 1] > 0.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.Index: i ~ Current Bar. | ATR_Length = 20; ATR_Stop = 6; |

Sensitivity Test: | M1_Look_Back = M1_Look_Back_Index * M2_Look_Back M1_Look_Back_Index = [0.25, 1.00], Step = 0.025 M2_Look_Back = [20, 200], Step = 5 | |

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; 35 years (1980/01/01−2015/4/30). |

**Table 1** | Specification of Trading Strategy.

## III. Sensitivity Test with Commission & Slippage

Tested Variables: M1_Look_Back_Index & M2_Look_Back (Definitions in Table 1):

**Figure 2** | Portfolio Performance (Inputs: Table 1; Commission & Slippage: $100 Round Turn).

## IV. Rating: Price Momentum Model | Trading Strategy

A/B/**C**/D

## V. Summary

(i) The slow price momentum M2 performs better when M2_Look_Back > 80 days (Figure 1-2); (ii) The fast price momentum M1 is more robust when M1_Look_Back_Index > 0.5 (Figure 1-2); (iii) The trading strategy based on a simple price momentum can be further developed.

**Related Entries:** Normalized Linear Regression Slope (Entry) | J. Welles Wilder, Jr. – Volatility Breakout (Entry)

**Related Topics:** (Public) Trading Strategies

**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.

**RISK DISCLOSURE: **U.S. GOVERNMENT REQUIRED DISCLAIMER | CFTC RULE 4.41

Codes: matlab/kaufman/price-momentum/