**Systematic Investor » R**, and kindly contributed to R-bloggers)

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.

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