A few weeks back, after seeing my replication, one of the original authors of the Flexible Asset Allocation paper got in touch with me to tell me to make a slight adjustment to the code, in that rather than remove any negative-momentum securities before performing any ranking, to perform all ranking without taking absolute momentum into account, and only removing negative absolute momentum securities at the very end, after allocating weights.

Here’s the new code:

FAA <- function(prices, monthLookback = 4,
                weightMom = 1, weightVol = .5, weightCor = .5, 
                riskFreeName = NULL, bestN = 3,
                stepCorRank = FALSE, stepStartMethod = c("best", "default"),
                geometric = TRUE, ...) {
  stepStartMethod <- stepStartMethod[1]
  if(is.null(riskFreeName)) {
    prices$zeroes <- 0
    riskFreeName <- "zeroes"
    warning("No risk-free security specified. Recommended to use one of: quandClean('CHRIS/CME_US'), SHY, or VFISX. 
            Using vector of zeroes instead.")
  }
  returns <- Return.calculate(prices)
  monthlyEps <- endpoints(prices, on = "months")
  riskFreeCol <- grep(riskFreeName, colnames(prices))
  tmp <- list()
  dates <- list()
  
  for(i in 2:(length(monthlyEps) - monthLookback)) {
    #subset data
    priceData <- prices[monthlyEps[i]:monthlyEps[i+monthLookback],]
    returnsData <- returns[monthlyEps[i]:monthlyEps[i+monthLookback],]
    
    #perform computations
    momentum <- data.frame(t(t(priceData[nrow(priceData),])/t(priceData[1,]) - 1))
    momentum <- momentum[,!is.na(momentum)]
    #momentum[is.na(momentum)] <- -1 #set any NA momentum to negative 1 to keep R from crashing
    priceData <- priceData[,names(momentum)]
    returnsData <- returnsData[,names(momentum)]
    
    momRank <- rank(momentum)
    vols <- data.frame(StdDev(returnsData))
    volRank <- rank(-vols)
    cors <- cor(returnsData, use = "complete.obs")
    if (stepCorRank) {
      if(stepStartMethod=="best") {
        compositeMomVolRanks <- weightMom*momRank + weightVol*volRank
        maxRank <- compositeMomVolRanks[compositeMomVolRanks==max(compositeMomVolRanks)]
        corRank <- stepwiseCorRank(corMatrix=cors, startNames = names(maxRank), 
                                        bestHighestRank = TRUE, ...)
        
      } else {
        corRank <- stepwiseCorRank(corMatrix=cors, bestHighestRank=TRUE, ...)
      }
    } else {
      corRank <- rank(-rowSums(cors))
    }
    
    totalRank <- rank(weightMom*momRank + weightVol*volRank + weightCor*corRank)
    
    upper <- length(names(returnsData))
    lower <- max(upper-bestN+1, 1)
    topNvals <- sort(totalRank, partial=seq(from=upper, to=lower))[c language="(upper:lower)"][/c]
    
    #compute weights
    longs <- totalRank %in% topNvals #invest in ranks length - bestN or higher (in R, rank 1 is lowest)
    longs[momentum < 0] <- 0 #in previous algorithm, removed momentums < 0, this time, we zero them out at the end.
    longs <- longs/sum(longs) #equal weight all candidates
    longs[longs > 1/bestN] <- 1/bestN #in the event that we have fewer than top N invested into, lower weights to 1/top N
    names(longs) <- names(totalRank)
    
    
    #append removed names (those with momentum < 0)
    removedZeroes <- rep(0, ncol(returns)-length(longs))
    names(removedZeroes) <- names(returns)[!names(returns) %in% names(longs)]
    longs <- c(longs, removedZeroes)
    
    #reorder to be in the same column order as original returns/prices
    longs <- data.frame(t(longs))
    longs <- longs[, names(returns)]
    
    #append lists
    tmp[[i]] <- longs
    dates[[i]] <- index(returnsData)[nrow(returnsData)]
  }
  
  weights <- do.call(rbind, tmp)
  dates <- do.call(c, dates)
  weights <- xts(weights, order.by=as.Date(dates)) 
  weights[, riskFreeCol] <- weights[, riskFreeCol] + 1-rowSums(weights)
  strategyReturns <- Return.rebalancing(R = returns, weights = weights, geometric = geometric)
  colnames(strategyReturns) <- paste(monthLookback, weightMom, weightVol, weightCor, sep="_")
  return(strategyReturns)
}

And here are the new results, both with the original configuration, and using the stepwise correlation ranking algorithm introduced by David Varadi:

mutualFunds <- c("VTSMX", #Vanguard Total Stock Market Index
                 "FDIVX", #Fidelity Diversified International Fund
                 "VEIEX", #Vanguard Emerging Markets Stock Index Fund
                 "VFISX", #Vanguard Short-Term Treasury Fund
                 "VBMFX", #Vanguard Total Bond Market Index Fund
                 "QRAAX", #Oppenheimer Commodity Strategy Total Return 
                 "VGSIX" #Vanguard REIT Index Fund
)

#mid 1997 to end of 2012
getSymbols(mutualFunds, from="1997-06-30", to="2014-10-30")
tmp <- list()
for(fund in mutualFunds) {
  tmp[[fund]] <- Ad(get(fund))
}

#always use a list hwne intending to cbind/rbind large quantities of objects
adPrices <- do.call(cbind, args = tmp)
colnames(adPrices) <- gsub(".Adjusted", "", colnames(adPrices))

original <- FAA(adPrices, riskFreeName="VFISX")
swc <- FAA(adPrices, riskFreeName="VFISX", stepCorRank = TRUE)
originalOld <- FAAreturns(adPrices, riskFreeName="VFISX")
swcOld <- FAAreturns(adPrices, riskFreeName="VFISX", stepCorRank=TRUE)
all4 <- cbind(original, swc, originalOld, swcOld)
names(all4) <- c("original", "swc", "origOld", "swcOld")
charts.PerformanceSummary(all4)


> rbind(Return.annualized(all4)*100,
+       maxDrawdown(all4)*100,
+       SharpeRatio.annualized(all4))
                                 original       swc   origOld    swcOld
Annualized Return               12.795205 14.135997 13.221775 14.037137
Worst Drawdown                  11.361801 11.361801 13.082294 13.082294
Annualized Sharpe Ratio (Rf=0%)  1.455302  1.472924  1.377914  1.390025

And the resulting equity curve comparison

Overall, it seems filtering on absolute momentum after applying all weightings using only relative momentum to rank actually improves downside risk profiles ever so slightly compared to removing negative momentum securities ahead of time. In any case, FAAreturns will be the function that removes negative momentum securities ahead of time, and FAA will be the ones that removes them after all else is said and done.

I’ll return to the standard volatility trading agenda soon.

Thanks for reading.

Note: I am a freelance consultant in quantitative analysis on topics related to this blog. If you have contract or full time roles available for proprietary research that could benefit from my skills, please contact me through my LinkedIn here.