Today I want to share the test and implementation for the Fast Threshold Clustering Algorithm (FTCA) created by David Varadi. This implementation was developed and contributed by Pierre Chretien, I only made minor updates.

Let’s first replicate the results from the Fast Threshold Clustering Algorithm (FTCA) post:

###############################################################################
# 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('XLY,XLP,XLE,XLF,XLV,XLI,XLB,XLK,XLU')
	
	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='keep.all')

	#*****************************************************************
	# Helper function to compute portfolio allocation additional stats
	#****************************************************************** 
	portfolio.allocation.custom.stats.clusters <- function(x,ia) {
		return(list(
			clusters.FTCA = cluster.group.FTCA(0.5)(ia)			
		))
	}
	
	#*****************************************************************
	# Find clusters
	#****************************************************************** 		
	periodicity = 'months'
	lookback.len = 252
		
	obj = portfolio.allocation.helper(data$prices, 
		periodicity = periodicity, lookback.len = lookback.len,
		min.risk.fns = list(EW=equal.weight.portfolio),
		custom.stats.fn = portfolio.allocation.custom.stats.clusters
	) 			
	
	clusters = obj$clusters.FTCA$EW	
	clusters['2012:05::']

The clusters are stable and match David’s results

           XLB XLE XLF XLI XLK XLP XLU XLV XLY
2012-05-31   1   1   1   1   1   1   1   1   1
2012-06-29   1   1   1   1   1   1   1   1   1
2012-07-31   1   1   1   1   1   1   1   1   1
2012-08-31   1   1   1   1   1   1   1   1   1
2012-09-28   1   1   1   1   1   1   1   1   1
2012-10-31   1   1   1   1   1   1   1   1   1
2012-11-30   2   2   2   2   2   2   1   2   2
2012-12-31   2   2   2   2   2   2   1   2   2
2013-01-31   2   2   2   2   2   2   1   2   2
2013-02-28   1   1   1   1   1   1   1   1   1
2013-03-28   1   1   1   1   1   1   1   1   1
2013-04-30   1   1   1   1   1   1   1   1   1
2013-05-31   1   1   1   1   1   1   1   1   1
2013-06-28   1   1   1   1   1   1   1   1   1
2013-07-31   1   1   1   1   1   1   1   1   1
2013-08-30   1   1   1   1   1   1   1   1   1
2013-09-30   1   1   1   1   1   1   1   1   1
2013-10-31   1   1   1   1   1   1   1   1   1
2013-11-26   1   1   1   1   1   1   1   1   1

Next let’s compare the Cluster Portfolio Allocation Algorithm using K-means and FTCA:

	#*****************************************************************
	# Code Strategies
	#****************************************************************** 					
	obj = portfolio.allocation.helper(data$prices, 
		periodicity = periodicity, lookback.len = lookback.len, 
		min.risk.fns = list(
			C.EW.kmeans = distribute.weights(equal.weight.portfolio, cluster.group.kmeans.90),
			C.EW.FTCA = distribute.weights(equal.weight.portfolio, cluster.group.FTCA(0.5))			
		)
	)
	
	models = create.strategies(obj, data)$models
						
	#*****************************************************************
	# Create Report
	#******************************************************************    
	barplot.with.labels(sapply(models, compute.turnover, data), 'Average Annual Portfolio Turnover')

Both clustering algorithms produced very similar results. One noticeable difference is turnover. Since the Fast Threshold Clustering Algorithm (FTCA) produced more stable groups, it had smaller turnover.

The full source code and example for the cluster.group.FTCA() function is available in strategy.r at github.