Mode vs Mean in Tactical Allocation

August 25, 2011
By

(This article was first published on Timely Portfolio, and kindly contributed to R-bloggers)

Let’s take Modest Modeest for Moving Average one step further and use it in a basic tactical allocation system using Vanguard funds.  THIS IS NOT INVESTMENT ADVICE AND VERY EASILY MIGHT CAUSE LARGE LOSSES.  VANGUARD FUNDS IMPOSE EARLY REDEMPTION FEES THAT RENDER THIS NOT FEASIBLE.

If we use US Equities (vfinx for S&P 500), International Developed (vgstx), and Emerging (veiex) to fill the 60% equities slot in a portfolio and then add 40% US Bonds (vbmfx), we can fairly closely resemble a typical balanced allocation.  Instead of buy and hold, let’s only buy and hold when each is above its respective 10 month mode, but sell whenever it falls below that mode.  The result is fairly attractive especially in terms of drawdown reduction.

From TimelyPortfolio
From TimelyPortfolio
From TimelyPortfolio

Ultimately, to choose mode over mean, we should evaluate versus the Mebane Faber 10 month moving average system.  The results are far from conclusive, but both clearly beat the balanced benchmark in terms of drawdown.  Since I would think it is much easier to explain mean to clients, I would say that Mebane’s system wins in this very simple framework.  However, this is only start.  Please let me know any discoveries as you apply to a much more diverse set of allocation options.

From TimelyPortfolio

 

R code (click to download from Google Docs):

require(quantmod)
require(modeest)
require(PerformanceAnalytics)   start = "1990-12-31"
end = Sys.Date()   #use Vanguard funds as proxy for asset classes
#due to Vanguard fees for early redemption
#these funds not appropriate for Tactical system
tckrs <- c("VFINX","VEIEX","VGSTX","VBMFX")
getSymbols(tckrs, from=start, to=end, adjust=TRUE)
for (i in 1:length(tckrs)) {
assign(tckrs[i],to.monthly(get(tckrs[i]))[,4])
}   funds <- na.omit(merge(VFINX[,1],VEIEX[,1],VGSTX[,1],VBMFX[,1]))
#get dates to include day so format is YYYY-MM-DD
index(funds) <- as.Date(index(funds))
colnames(funds) <- tckrs   #get 1 month change
funds.roc <- ROC(funds,type="discrete",n=1)
#add a balanced benchmark
#20% of each equity fund for 60% total equities
#40% of US bonds
funds.roc <- merge(funds.roc,
0.2*funds.roc[,1]+0.2*funds.roc[,2]+0.2*funds.roc[,3]+0.4*funds.roc[,4])
funds.roc[1,5] <- 0
colnames(funds.roc) <- c(colnames(funds),"Balanced")   #combine all the funds into one xts
funds <- merge(funds,cumprod(1+funds.roc[,5]))
#charts.PerformanceSummary(funds.roc,
# main="Vanguard Funds for US, Emerging, Intl Stocks and US Bonds
# with a 60/40 Balanced Allocation")   #set width to be 10 months similar to Mebane Faber 10 month moving average
width = 10
#set up system.signal with same number of columns and rows as funds
system.signal <- funds
#loop through each column since I could not use apply with mode calculation
for (m in 1:NCOL(system.signal)) {
#another for loop to do the rolling mode since it also does not work with apply
for (n in width:NROW(system.signal[,m])) {
md <- mlv(funds[(n-width):n,m], method = "lientz", bw=0.4)
ifelse(n==width,
md.hist <- as.numeric(md[1]),
md.hist <- rbind(md.hist,as.numeric(md[1])))
}
#make into nice xts
md.xts <- as.xts(as.data.frame(md.hist),
order.by=index(system.signal[(width):NROW(system.signal)]))
#put rolling modes into system.signal
system.signal[(width):NROW(system.signal),m] <- md.hist
}   #jpeg(filename="mode chart.jpg",
# quality=100,width=6.25, height = 6.25, units="in",res=96)
plot.zoo(system.signal,main="Modes (lientz) of Funds",nc=1,
col=c("gray70","steelblue4","darkolivegreen4","goldenrod","purple"))
#dev.off()   #difficult way to get 1 for in and 0 for out
#but the ifelse gave me an index increasing order error
#will use apply instead
system.signal <- funds > system.signal
system.signal[,1:length(tckrs)] <- apply(system.signal[,1:length(tckrs)],MARGIN=2,FUN=as.numeric)
ret.signal <- lag(system.signal,k=1) * funds.roc[,1:5]
ret.compare <- merge(funds.roc[,4],
0.2*ret.signal[,1]+0.2*ret.signal[,2]+0.2*ret.signal[,3]+0.4*ret.signal[,4],
ret.signal[,5],
funds.roc[,5])
colnames(ret.compare) <- c("VBMFX.Bonds","ModeSystem","ModeOnBalanced","Balanced")   #jpeg(filename="signal chart.jpg",
# quality=100,width=6.25, height = 6.25, units="in",res=96)
plot.zoo(system.signal,main="Signals (hsm) of Funds",nc=1,
col=c("gray70","steelblue4","darkolivegreen4","goldenrod","purple"))
#dev.off()   #jpeg(filename="performance summary no average.jpg",
# quality=100,width=6.25, height = 6.25, units="in",res=96)
charts.PerformanceSummary(ret.compare,ylog=TRUE,
main="Performance of Tactical Approaches
with Balanced Benchmark"
,
colorset=c("gray70","steelblue4","darkolivegreen4","goldenrod","purple"),
cex.legend=1.2,lwd=2)
#dev.off()     #now let's compare to Mebane Faber 10-month moving average strategy
#will do in 1 line since there are multiple examples of how
#to implement this in R
ret.average <- lag(as.xts(apply(
funds > apply(funds[,1:5],MARGIN=2,FUN=runMean,10),MARGIN=2,as.numeric),order.by=index(funds)),k=1) * funds.roc
ret.compare <- merge(ret.compare,
0.2*ret.average[,1]+0.2*ret.average[,2]+0.2*ret.average[,3]+0.4*ret.average[,4])
colnames(ret.compare) <- c(colnames(ret.compare)[1:(NCOL(ret.compare)-1)],"Faber10moAvg")   #jpeg(filename="performance summary with Faber average.jpg",
# quality=100,width=6.25, height = 6.25, units="in",res=96)
charts.PerformanceSummary(ret.compare,ylog=TRUE,
main="Performance of Tactical Approaches
with Balanced Benchmark and Mebane Faber 10mo Mov Avg"
,
colorset=c("gray70","steelblue4","darkolivegreen4","goldenrod","purple"),
cex.legend=1.2,lwd=2)
#dev.off()

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