I want to share a brilliant idea and a great example from the You’re Looking at the Wrong Number post at the GestaltU blog. Today, I will focus on the section of this post that outlines simple steps to improve a typical 60/40 stock/bond portfolio by using risk allocation instead of dollar allocation, and targeting constant portfolio volatility.

I will use SPY (S&P 500) as a proxy for a stock allocation and TLT (20 Year Treasuries) as a proxy for a bond allocation. Let’s start by loading historical prices for SPY and a few fixed income ETF’s 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 = spl('SHY,IEF,TLT,SPY')

	data.all <- new.env()
	getSymbols(tickers, src = 'yahoo', from = '1990-01-01', env = data.all, auto.assign = T)	
	for(i in ls(data.all)) data.all[[i]] = adjustOHLC(data.all[[i]], use.Adjusted=T)		
	bt.prep(data.all, align='remove.na')
	
	prices = data.all$prices
		n = ncol(prices)
		nperiods = nrow(prices)

	# normalize all prices and plot them
	prices = prices/ matrix(first(prices), nr=nperiods, nc=n, byrow=T)
	plota.matplot(prices)

The fixed income ETFs are not as safe as you might have been expected. The SHY (Barclays 1-3 Year Treasury Bond Fund) is consistently up with out large draw-downs. However, both IEF (Barclays 7-10 Year Treasury Bond Fund) and TLT (Barclays 20 Year Treasury Bond Fund) do go through periods of loosing money.

Next let’s build a traditional dollar weighted 60/40 stock/bond portfolio and risk weighted version:

	#*****************************************************************
	# Load historical data
	#****************************************************************** 		
	data <- new.env()
		data$stock = data.all$SPY
		data$bond = data.all$TLT	
	bt.prep(data, align='remove.na')

	#*****************************************************************
	# Code Strategies
	#****************************************************************** 
	# all bonds began trading at 2002-07-31
	prices = data$prices
		n = ncol(prices)
		nperiods = nrow(prices)
	
	models = list()
	
	period.ends = endpoints(prices, 'months')
		period.ends = period.ends[period.ends > 0]
	
	#*****************************************************************
	# Traditional, Dollar Weighted 40% Bonds & 60% Stock
	#****************************************************************** 			
	weight.dollar = matrix(c(0.4, 0.6), nr=nperiods, nc=n, byrow=T)
	
	data$weight[] = NA
		data$weight[period.ends,] = weight.dollar[period.ends,]
	models$dollar.w.60.40 = bt.run.share(data, clean.signal=F)

	#*****************************************************************
	# Risk Weighted 40% Bonds & 60% Stock
	#****************************************************************** 				
	ret.log = bt.apply.matrix(prices, ROC, type='continuous')
	hist.vol = sqrt(252) * bt.apply.matrix(ret.log, runSD, n = 21)	
	weight.risk = weight.dollar / hist.vol
		weight.risk = weight.risk / rowSums(weight.risk)
		
	data$weight[] = NA
		data$weight[period.ends,] = weight.risk[period.ends,]
	models$risk.w.60.40 = bt.run.share(data, clean.signal=F)

Next let’s create a risk weighted portfolio with 6% volatility. I will adjust portfolio leverage up/down based on the one month historical volatility to target 6% annual volatility.

	#*****************************************************************
	# Helper function to adjust portfolio leverage to target given volatility
	#****************************************************************** 				
	target.vol.strategy <- function(model, weight, 
		target = 10/100, 
		lookback.len = 21,
		max.portfolio.leverage = 100/100) 
	{	
		ret.log.model = ROC(model$equity, type='continuous')
		hist.vol.model = sqrt(252) * runSD(ret.log.model, n = lookback.len)	
			hist.vol.model = as.vector(hist.vol.model)
		
		weight.target = weight * (target / hist.vol.model)
	
		# limit total leverage		
		rs = rowSums(abs(weight.target))
		weight.target = weight.target / iif(rs > max.portfolio.leverage, rs/max.portfolio.leverage, 1)		
		
		return(weight.target)	
	}
				
	#*****************************************************************
	# Scale Risk Weighted 40% Bonds & 60% Stock strategy to have 6% volatility
	#****************************************************************** 				
	data$weight[] = NA
		data$weight[period.ends,] = target.vol.strategy(models$risk.w.60.40,
						weight.risk, 6/100, 21, 100/100)[period.ends,]
	models$risk.w.60.40.target6 = bt.run.share(data, clean.signal=T)

In the last step, I want to invest portfolio cash position into short-term treasuries (SHY) to improve overall performance and create summary reports:

	#*****************************************************************
	# Same, plus invest cash into SHY
	#****************************************************************** 					
	weight = target.vol.strategy(models$risk.w.60.40, weight.risk, 6/100, 21, 100/100)
	data.all$weight[] = NA
		data.all$weight$SPY[period.ends,] = weight$stock[period.ends,]
		data.all$weight$TLT[period.ends,] = weight$bond[period.ends,]
		
		cash = 1-rowSums(weight)
		data.all$weight$SHY[period.ends,] = cash[period.ends]
	models$risk.w.60.40.target6.cash = bt.run.share(data.all, clean.signal=T)

	#*****************************************************************
	# Create Report
	#****************************************************************** 	
	plotbt.strategy.sidebyside(models)
	
	plotbt.custom.report.part1(models)
		
	plotbt.custom.report.part2(models$risk.w.60.40.target6)		
	plotbt.custom.report.part2(models$risk.w.60.40.target6.cash)		

I’m very happy with results: the returns went down a bit, but portfolio risk adjusted performance is up and draw-downs went down from 30% to 12%. The consistent returns are especially important for a retirement portfolio because it allows you to better plan how much money you can withdraw and sustain your fund for a longer term.

To view the complete source code for this example, please have a look at the bt.new.60.40.test() function in bt.test.r at github.