Cluster Risk Parity back-test

March 4, 2013
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In the Cluster Portfolio Allocation post, I have outlined the 3 steps to construct Cluster Risk Parity portfolio. At each rebalancing period:

  • Create Clusters
  • Allocate funds within each Cluster using Risk Parity
  • Allocate funds across all Clusters using Risk Parity

I created a helper function distribute.weights() function in strategy.r at github to automate these steps. It has 2 parameters:

  • Function to allocate funds. For example, risk.parity.portfolio, will use use risk parity to allocate funds both within and across clusters.
  • Function to create clusters. For example, cluster.group.kmeans.90, will create clusters using k-means algorithm

Here is the example how to put it all together. Let’s first load historical prices for the 10 major asset classes:

###############################################################################
# Load Systematic Investor Toolbox (SIT)
# http://systematicinvestor.wordpress.com/systematic-investor-toolbox/
###############################################################################
setInternet2(TRUE)
con = gzcon(url('http://www.systematicportfolio.com/sit.gz', 'rb'))
    source(con)
close(con)

	#*****************************************************************
	# Load historical data for ETFs
	#****************************************************************** 
	load.packages('quantmod')

	tickers = spl('GLD,UUP,SPY,QQQ,IWM,EEM,EFA,IYR,USO,TLT')

	data <- new.env()
	getSymbols(tickers, src = 'yahoo', from = '1900-01-01', env = data, auto.assign = T)
		for(i in ls(data)) data[[i]] = adjustOHLC(data[[i]], use.Adjusted=T)
		
	bt.prep(data, align='remove.na')

Next, let’s run the 2 versions of Cluster Portfolio Allocation using Equal Weight and Risk Parity algorithms to allocate funds:

	#*****************************************************************
	# Code Strategies
	#****************************************************************** 	
	periodicity = 'months'
	lookback.len = 250
	cluster.group = cluster.group.kmeans.90
	
	obj = portfolio.allocation.helper(data$prices, 
		periodicity = periodicity, lookback.len = lookback.len,
		min.risk.fns = list(
				EW=equal.weight.portfolio,
				RP=risk.parity.portfolio,
						
				C.EW = distribute.weights(equal.weight.portfolio, cluster.group),
				C.RP=distribute.weights(risk.parity.portfolio, cluster.group)
			)
	) 		
	
	models = create.strategies(obj, data)$models

Finally, let’s examine the results:

	#*****************************************************************
	# Create Report
	#****************************************************************** 	
	strategy.performance.snapshoot(models, T)

plot1.png.small

The Cluster Portfolio Allocation produce portfolios with better risk-adjusted returns and smaller drawdowns.

To view the complete source code for this example, please have a look at the bt.cluster.portfolio.allocation.test1() function in bt.test.r at github.

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