Linear Regression Slope | Trading Strategy (Filter & Entry)
I. Trading Strategy
Concept: Trend-following strategy based on a linear regression slope. Source: Kaufman, P. J. (2005). New Trading Systems and Methods. New Jersey: John Wiley & Sons, Inc. Research Goal: Performance verification of the linear regression model applied over two time frames. Specification: Table 1. Results: Figure 1-2. Portfolio: 42 futures markets from four major market sectors (commodities, currencies, interest rates, and equity indexes). Data: 33 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.
Linear Regression Slope (LRS) is the slope (angle) of a straight line found using a least-squares regression: LRS = ∑[(Xi − AvgX)(Yi − AvgY)] / ∑(Xi − AvgX)2 where: Y is the price dimension (close prices), X is the time dimension, AvgX is the average value of Xi and AvgY is the average value of Yi. LRS_1: Linear Regression Slope over the Look_Back period used as a filter. LRS_2: Linear Regression Slope over the Look_Back × Look_Back_Index period used to generate signals.
Long Trades: Linear Regression Slope LRS_1[i – 1] > 0. Short Trades: Linear Regression Slope LRS_1[i – 1] < 0. Index: i ~ Current Bar.
Long Trades: A buy at the open is placed when LRS_1[i – 1] > 0 and LRS_2[i – 1] > 0. Short Trades: A sell at the open is placed when LRS_1[i – 1] < 0 and LRS_2[i – 1] < 0. 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].
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.