Today I want to show how to use Factor Attribution to boost performance of the 1-Month Reversal Strategy. The Short-Term Residual Reversal by D. Blitz, J. Huij, S. Lansdorp, M. Verbeek (2011) paper presents the idea and discusses the results as applied to US stock market since 1929. To improve 1-Month Reversal Strategy performance authors investigate an alternative position ranking metric based on the residuals from the rolling Factor Attribution regression.

The base 1-Month Reversal Strategy forms portfolios each month by buying 20% of loosers and short selling 20% of winners from the S&P 500 index based on the prior 1-Month returns. The 1-Month Residual Reversal Strategy forms portfolios each month by buying 20% of loosers and short selling 20% of winners from the S&P 500 index based on the residuals from the rolling Factor Attribution regression. Following are the steps to form 1-Month Residual Reversal Strategy portfolio each month:

• 1. for each company in the S&P 500 index, run a rolling Factor Attribution regression on the prior 36 months and compute residuals: e.1, e.2, …, e.t, …, e.T for t in 1:36
• 2. alternative position ranking metric = e.T / standard deviation of (e)
• 3. form portfolios by buying 20% of loosers and short selling 20% of winners from the S&P 500 index based on the alternative position ranking metric

Let’s start by loading historical prices for all companies in the S&P 500 and create SPY and Equal Weight benchmarks using the Systematic Investor Toolbox:

###############################################################################
# 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
	#****************************************************************** 
	load.packages('quantmod')	
	tickers = sp500.components()$tickers
	
	data <- new.env()
	getSymbols(tickers, src = 'yahoo', from = '1970-01-01', env = data, auto.assign = T)
		# remove companies with less than 5 years of data
		rm.index = which( sapply(ls(data), function(x) nrow(data[[x]])) < 1000 )	
		rm(list=names(rm.index), envir=data)
		
		for(i in ls(data)) data[[i]] = adjustOHLC(data[[i]], use.Adjusted=T)		
	bt.prep(data, align='keep.all', dates='1994::')
		tickers = data$symbolnames
	
	
	data.spy <- new.env()
	getSymbols('SPY', src = 'yahoo', from = '1970-01-01', env = data.spy, auto.assign = T)
	bt.prep(data.spy, align='keep.all', dates='1994::')
	
	#*****************************************************************
	# Code Strategies
	#****************************************************************** 
	prices = data$prices
		n = ncol(prices)
					
	#*****************************************************************
	# Setup monthly periods
	#****************************************************************** 
	periodicity = 'months'
	
	period.ends = endpoints(data$prices, periodicity)
		period.ends = period.ends[period.ends > 0]
	
	prices = prices[period.ends, ]		
		
	#*****************************************************************
	# Create Benchmarks, omit results for the first 36 months - to be consistent with Factor Attribution
	#****************************************************************** 	
	models = list()
	
	# SPY
	data.spy$weight[] = NA
		data.spy$weight[] = 1
		data.spy$weight[1:period.ends[36],] = NA
	models$spy = bt.run(data.spy)
	
	# Equal Weight
	data$weight[] = NA
		data$weight[period.ends,] = ntop(prices, n)
		data$weight[1:period.ends[36],] = NA		
	models$equal.weight = bt.run(data)

Next let’s run Factor Attribution on each the stocks in the S&P 500 index to determine it’s alternative position ranking metric. I will save both e.T and e.T / standard deviation of (e) metrics.

# function to compute additional custom stats for factor.rolling.regression
factor.rolling.regression.custom.stats <- function(x,y,fit) {
	n = len(y)
	e = y - x %*% fit$coefficients
	se = sd(e)
	return(c(e[n], e[n]/se))
}

	#*****************************************************************
	# Load factors and align them with prices
	#****************************************************************** 	
	# load Fama/French factors
	factors = get.fama.french.data('F-F_Research_Data_Factors', periodicity = periodicity,download = T, clean = F)
	
	# align monthly dates
	map = match(format(index(factors$data), '%Y%m'), format(index(prices), '%Y%m'))
		dates = index(factors$data)
		dates[!is.na(map)] = index(prices)[na.omit(map)]
	index(factors$data) = as.Date(dates)
		
	
	# add factors and align
	data.fa <- new.env()
		for(i in tickers) data.fa[[i]] = data[[i]][period.ends, ]
		data.fa$factors = factors$data / 100
	bt.prep(data.fa, align='remove.na')

	
	index = match( index(data.fa$prices), index(data$prices) )
		prices = data$prices[index, ]
		
	#*****************************************************************
	# Compute Factor Attribution for each ticker
	#****************************************************************** 	

	temp = NA * prices
	factors	= list()
		factors$last.e = temp
		factors$last.e_s = temp
		factors$one.month = coredata(prices / mlag(prices))
	
	for(i in tickers) {
		cat(i, '\n')
		
		# Facto Loadings Regression
		obj = factor.rolling.regression(data.fa, i, 36, silent=T,
			factor.rolling.regression.custom.stats)

		for(j in 1:len(factors))		
			factors[[j]][,i] = obj$fl$custom[,j]
			
	}

Next let’s group stocks into Quantiles based on 1-Month Reversal factors and create reports.

	#*****************************************************************
	# Create Quantiles
	#****************************************************************** 
	quantiles = list()
	
	for(name in names(factors)) {
		cat(name, '\n')
		quantiles[[name]] = bt.make.quintiles(factors[[name]], data, index, start.t =  1+36, prefix=paste(name,'_',sep=''))
	}	

	#*****************************************************************
	# Create Report
	#****************************************************************** 					
	plotbt.custom.report.part1(quantiles$one.month$spread,quantiles$last.e$spread,quantiles$last.e_s$spread)
	
	plotbt.strategy.sidebyside(quantiles$one.month$spread,quantiles$last.e$spread,quantiles$last.e_s$spread)
		
	plotbt.custom.report.part1(quantiles$last.e_s)

The 1-Month Residual Reversal Strategy have done well over the last 10 years and handsomely outperformed the base 1-Month Reversal Strategy.

To view the complete source code for this example, please have a look at the bt.fa.one.month.test() function in bt.test.r at github.