Home > Backtesting, Factors, Portfolio Construction, R, Strategy, Trading Strategies > Factor Attribution to improve performance of the 1-Month Reversal Strategy

Factor Attribution to improve performance of the 1-Month Reversal Strategy

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
	
	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]
			
	}

	# add base strategy
	factors$one.month = coredata(prices / mlag(prices))

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.

About these ads
  1. Aeron
    July 17, 2012 at 5:24 pm

    Thank you soo much for sharing…Great post.

  2. Quant007
    July 18, 2012 at 2:01 pm

    I was wondering how you adjust for survival bias in your setup. Can you get S&P membership of stocks historically?

    • July 19, 2012 at 3:47 am

      I’m not aware of any public source for historical S&P constituents and historical prices for delisted companies.

  3. Paolo
    July 19, 2012 at 5:39 pm

    I went through some of the short-term reversal literature in the past and this post is very interesting.

    Several papers consider also 1. intra-industry effect (basically using sector neutral quantiles) and 2. trading cost/turnover (also testing smart rebalancing algorithms like rebalancing only those names going below a certain quantile threshold – De Groot2011 tests the 30/70, 40/60, 50/50, 60/40, 70/30 percentile thresholds).

    Can you expand your analysis by including them for testing robustness?

    Great post,

    Paolo

  4. John Mach
    July 20, 2012 at 12:54 pm

    Very interesting as always. I had a slight off the topic query

    regarding this line of code where you pick up components of an Index from Yahoo
    tickers = sp500.components()$tickers

    How do I change it for any other index say FTSE 100, where can I find the ticker names to use. I tried looking up on Yahoo and it didn’t help me much. Where did you see the actual syntax i.e. “sp500.components”

    Thanks for you attention.
    John

  1. July 27, 2012 at 2:07 am

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

Join 252 other followers

%d bloggers like this: