Today I want to show how to use Volatility Position Sizing to improve strategy’s Risk Adjusted Performance. I will use the Average True Range (ATR) as a measure of Volatility and will increase allocation during low Volatility periods and will decrease allocation during high Volatility periods. Following are two good references that explain these strategy in detail:

• Position Sizing is Everything by Leigh Drogen
• Money Management – Position Sizing

First, let’s load prices for SPY and compute Buy & Hold performance using the Systematic Investor Toolbox:

###############################################################################
# Load Systematic Investor Toolbox (SIT)
# http://systematicinvestor.wordpress.com/systematic-investor-toolbox/
###############################################################################
con = gzcon(url('http://www.systematicportfolio.com/sit.gz', 'rb'))
    source(con)
close(con)

	#*****************************************************************
	# Load historical data
	#****************************************************************** 
	load.packages('quantmod')	
	tickers = spl('SPY')

	data <- new.env()
	getSymbols(tickers, src = 'yahoo', from = '1970-01-01', env = data, auto.assign = T)
		for(i in ls(data)) data[[i]] = adjustOHLC(data[[i]], use.Adjusted=T)			
	bt.prep(data, align='keep.all', dates='1970::')	
	
	#*****************************************************************
	# Code Strategies
	#****************************************************************** 
	prices = data$prices   
	nperiods = nrow(prices)
	
	models = list()
	
	#*****************************************************************
	# Buy & Hold
	#****************************************************************** 
	data$weight[] = 0
		data$weight[] = 1
	models$buy.hold = bt.run.share(data, clean.signal=T)

Next, let’s modify Buy & Hold strategy to vary it’s allocation according to the Average True Range (ATR).

	#*****************************************************************
	# Volatility Position Sizing - ATR
	#****************************************************************** 
	atr = bt.apply(data, function(x) ATR(HLC(x),20)[,'atr'])
		
	# position size in units = ((porfolio size * % of capital to risk)/(ATR*2)) 
	data$weight[] = NA
		capital = 100000
		
		# risk 2% of capital
		data$weight[] = (capital * 2/100) / (2 * atr)
		
		# make sure you are not committing more than 100%
		max.allocation = capital / prices
		data$weight[] = iif(data$weight > max.allocation, max.allocation,data$weight)
		
	models$buy.hold.2atr = bt.run(data, type='share', capital=capital)					
	
	#*****************************************************************
	# Create Report
	#****************************************************************** 	
	models = rev(models)
	
	plotbt.custom.report.part1(models)
	
	plotbt.custom.report.part2(models)

The Sharpe and DVR are both higher for new strategy and draw-downs are lower.

To view the complete source code for this example, please have a look at the bt.position.sizing.test() function in factor.model.test.r at github.