Quantitative Finance offers plethora of indicators and tools to predict future price movements of Stocks, commodities or any other traded instruments. Linear Regression is one of them through which price direction is speculated using statistical techniques. It has found it’s application in multiple proven trading systems used by hedge funds and large institutional investors. In this post, we will explore Linear regression trading system which is based on the principle of Mean reversion. We shall also understand the definition of linear regression and linear regression channel in simple terms.

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Linear Regression line and Linear Regression channel

Linear Regression line is the straight line drawn through the price points in a chart, which most effectively covers all the prices for a given period. It is a kind of ‘best fit’ line which shows the fair value of trading instrument. Any deviation from the linear regression line is considered to be the deviation of price from it’s supposed to be fair value. It is like a trend line and gives an idea of ongoing price trend in the chart.

Linear Regression channel contains two extra lines above and below the standard linear regression line. These extra lines are formed by calculating 1 or 2 standard deviations of linear regression line. If 1 standard deviation is used then linear regression channel covers 68% of prices for a given period, while if 2 standard deviations are used then it covers 95% of prices. Hence linear regression channel can effectively determine overbought and oversold areas, which makes it a perfect tool to develop mean reversion strategies.

Below is the simple illustration for Linear regression channel.

Linear Regression Trading System – AFL Overview

Parameter	Value
Preferred Time-frame	Hourly
Indicators Used	Linear Regression, Standard Deviation
Buy Condition	First candle closes below the lower band of linear regression channel. Second candle closes above the lower band. Third candle closes above the second candle.
Short Condition	First candle closes above the upper band of linear regression channel. Second candle closes below the upper band. Third candle closes below the second candle.
Sell Condition	Same as Short Stop Loss Hit Target met End of Trading day
Cover Condition	Same as Buy Stop Loss Hit Target met End of Trading day
Stop Loss	0.5%
Targets	0.5%
Position Size	100% of Equity
Initial Equity	200000
Brokerage	100 per order
Margin	10%

Linear Regression Trading System– AFL Code

This AFL code was originally published at Marketcalls.in. We have modified it to make it suitable for intraday trading and added various backtesting conditions.

Click here to download AFL code for this system.

AFL Screenshot

Also Read: Donchian Channel Trend following system

Linear Regression Trading System- Backtest Report

Linear Regression Trading system does not offer huge returns as it it based on mean reversion, but it is quite consistent owing to low drawdown value. It is suitable for intraday scalping.

Parameter	Value
	Nifty
Initial Capital	200000
Final Capital	736893.90
Scrip Name	NSE Nifty
Backtest Period	26-Feb-2008 to 30-Jun-2017
Timeframe	Hourly
Net Profit %	268.45%
Annual Return %	14.71%
Number of Trades	136
Winning Trade %	55.88%
Average holding Period	3.05 periods
Max consecutive losses	4
Max system % drawdown	-13.37%
Max Trade % drawdown	-13.86%

Download the detailed backtest report here.

Equity Curve

The equity curve is smooth and stable.

Profit Table

Additional Amibroker settings for backtesting

Goto Symbol–>Information, and specify the lot size and margin requirement. The below screenshot shows lot size of 75 and margin requirement of 10% for NSE Nifty:

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