This post will demonstrate a downside to rankings-based strategies, particularly when using data of a questionable quality (which, unless one pays multiple thousands of dollars per month for data, most likely is of questionable quality). Essentially, by making one small change to the way the strategy filters, it introduces a massive performance drop in terms of drawdown. This exercise effectively demonstrates a different possible way of throwing a curve-ball at ranking strategies to test for robustness.

Recently, a discussion came up between myself, Terry Doherty, Cliff Smith, and some others on Seeking Alpha regarding what happened when I substituted the 63-day SMA for the three month SMA in Cliff Smith’s QTS strategy (quarterly tactical strategy…strategy).

Essentially, by simply substituting a 63-day SMA (that is, using daily data instead of monthly) for a 3-month SMA, the results were drastically affected.

Here’s the new QTS code, now in a function.

qts <- function(prices, nShort = 20, nLong = 105, nMonthSMA = 3, nDaySMA = 63, wRankShort=1, wRankLong=1.01, 
                movAvgType = c("monthly", "daily"), cashAsset="VUSTX", returnNames = FALSE) {
  cashCol <- grep(cashAsset, colnames(prices))
  
  #start our data off on the security with the least data (VGSIX in this case)
  prices <- prices[!is.na(prices[,7]),] 
  
  #cash is not a formal asset in our ranking
  cashPrices <- prices[, cashCol]
  prices <- prices[, -cashCol]
  
  #compute momentums
  rocShort <- prices/lag(prices, nShort) - 1
  rocLong <- prices/lag(prices, nLong) - 1
  
  #take the endpoints of quarter start/end
  quarterlyEps <- endpoints(prices, on="quarters")
  monthlyEps <- endpoints(prices, on = "months")
  
  #take the prices at quarterly endpoints
  quarterlyPrices <- prices[quarterlyEps,]
  
  #short momentum at quarterly endpoints (20 day)
  rocShortQtrs <- rocShort[quarterlyEps,]
  
  #long momentum at quarterly endpoints (105 day)
  rocLongQtrs <- rocLong[quarterlyEps,]
  
  #rank short momentum, best highest rank
  rocSrank <- t(apply(rocShortQtrs, 1, rank))
  
  #rank long momentum, best highest rank
  rocLrank <- t(apply(rocLongQtrs, 1, rank))
  
  #total rank, long slightly higher than short, sum them
  totalRank <- wRankLong * rocLrank + wRankShort * rocSrank 
  
  #function that takes 100% position in highest ranked security
  maxRank <- function(rankRow) {
    return(rankRow==max(rankRow))
  }
  
  #apply above function to our quarterly ranks every quarter
  rankPos <- t(apply(totalRank, 1, maxRank))
  
  #SMA of securities, only use monthly endpoints
  #subset to quarters
  #then filter
  movAvgType = movAvgType[1]
  if(movAvgType=="monthly") {
    monthlyPrices <- prices[monthlyEps,]
    monthlySMAs <- xts(apply(monthlyPrices, 2, SMA, n=nMonthSMA), order.by=index(monthlyPrices))
    quarterlySMAs <- monthlySMAs[index(quarterlyPrices),]
    smaFilter <- quarterlyPrices > quarterlySMAs
  } else if (movAvgType=="daily") {
    smas <- xts(apply(prices, 2, SMA, n=nDaySMA), order.by=index(prices))
    quarterlySMAs <- smas[index(quarterlyPrices),]
    smaFilter <- quarterlyPrices > quarterlySMAs
  } else {
    stop("invalid moving average type")
  }
  
  finalPos <- rankPos*smaFilter
  finalPos <- finalPos[!is.na(rocLongQtrs[,1]),]
  cash <- xts(1-rowSums(finalPos), order.by=index(finalPos))
  finalPos <- merge(finalPos, cash, join='inner')
  
  prices <- merge(prices, cashPrices, join='inner')
  returns <- Return.calculate(prices)
  stratRets <- Return.portfolio(returns, finalPos)
  
  if(returnNames) {
    findNames <- function(pos) {
      return(names(pos[pos==1]))
    }
    tmp <- apply(finalPos, 1, findNames)
    assetNames <- xts(tmp, order.by=as.Date(names(tmp)))
    return(list(assetNames, stratRets))
  }
  return(stratRets)
}

The one change I made is this:

  movAvgType = movAvgType[1]
  if(movAvgType=="monthly") {
    monthlyPrices <- prices[monthlyEps,]
    monthlySMAs <- xts(apply(monthlyPrices, 2, SMA, n=nMonthSMA), order.by=index(monthlyPrices))
    quarterlySMAs <- monthlySMAs[index(quarterlyPrices),]
    smaFilter <- quarterlyPrices > quarterlySMAs
  } else if (movAvgType=="daily") {
    smas <- xts(apply(prices, 2, SMA, n=nDaySMA), order.by=index(prices))
    quarterlySMAs <- smas[index(quarterlyPrices),]
    smaFilter <- quarterlyPrices > quarterlySMAs
  } else {
    stop("invalid moving average type")
  }

In essence, it allows the function to use either a monthly-calculated moving average, or a daily, which is then subset to the quarterly frequency of the rest of the data.

(I also allow the function to return the names of the selected securities.)

So now we can do two tests:

1) The initial parameter settings (20-day short-term momentum, 105-day long-term momentum, equal weigh their ranks (tiebreaker to the long-term), and use a 3-month SMA to filter)
2) The same exact parameter settings, except a 63-day SMA for the filter.

Here’s the code to do that.

#get our data from yahoo, use adjusted prices
symbols <- c("NAESX", #small cap
             "PREMX", #emerging bond
             "VEIEX", #emerging markets
             "VFICX", #intermediate investment grade
             "VFIIX", #GNMA mortgage
             "VFINX", #S&P 500 index
             "VGSIX", #MSCI REIT
             "VGTSX", #total intl stock idx
             "VUSTX") #long term treasury (cash)

getSymbols(symbols, from="1990-01-01")
prices <- list()
for(i in 1:length(symbols)) {
  prices[[i]] <- Ad(get(symbols[i]))  
}
prices <- do.call(cbind, prices)
colnames(prices) <- gsub("\\.[A-z]*", "", colnames(prices))

monthlySMAqts <- qts(prices, returnNames=TRUE)
dailySMAqts <- qts(prices, wRankShort=.95, wRankLong=1.05, movAvgType = "daily", returnNames=TRUE)

retsComparison <- cbind(monthlySMAqts[[2]], dailySMAqts[[2]])
colnames(retsComparison) <- c("monthly SMA qts", "daily SMA qts")
retsComparison <- retsComparison["2003::"]
charts.PerformanceSummary(retsComparison["2003::"])
rbind(table.AnnualizedReturns(retsComparison["2003::"]), maxDrawdown(retsComparison["2003::"]))

And here are the results:

Statistics:

                          monthly SMA qts daily SMA qts
Annualized Return               0.2745000     0.2114000
Annualized Std Dev              0.1725000     0.1914000
Annualized Sharpe (Rf=0%)       1.5915000     1.1043000
Worst Drawdown                  0.1911616     0.3328411

With the corresponding equity curves:

Here are the several instances in which the selections do not match thanks to the filters:

selectedNames <- cbind(monthlySMAqts[[1]], dailySMAqts[[1]])
colnames(selectedNames) <- c("Monthly SMA Filter", "Daily SMA Filter")
differentSelections <- selectedNames[selectedNames[,1]!=selectedNames[,2],]

With the results:

           Monthly SMA Filter Daily SMA Filter
1997-03-31 "VGSIX"            "cash"          
2007-12-31 "cash"             "PREMX"         
2008-06-30 "cash"             "VFIIX"         
2008-12-31 "cash"             "NAESX"         
2011-06-30 "cash"             "NAESX"  

Now, of course, many can make the arguments that Yahoo’s data is junk, my backtest doesn’t reflect reality, etc., which would essentially miss the point: this data here, while not a perfect realization of the reality of Planet Earth, may as well have been valid (you know, like all the academics, who use various simulation techniques to synthesize more data or explore other scenarios?). All I did here was change the filter to something logically comparable (that is, computing the moving average filter on a different time-scale, which does not in any way change the investment logic). From 2003 onward, this change only affected the strategy in four places. However, those instances were enough to create some noticeable changes (for the worse) in the strategy’s performance. Essentially, the downside of rankings-based strategies are when the overall number of selected instruments (in this case, ONE!) is small, a few small changes in parameters, data, etc. can lead to drastically different results.

As I write this, Cliff Smith already has ideas as to how to counteract this phenomenon. However, unto my experience, once a strategy starts getting into “how do we smooth out that one bump on the equity curve” territory, I think it’s time to go back and re-examine the strategy altogether. In my opinion, while the idea of momentum is of course, sound, with a great deal of literature devoted to it, the idea of selecting just one instrument at a time as the be-all-end-all strategy does not sit well with me. However, to me, QTS nevertheless presents an interesting framework for analyzing small subgroups of securities, and using it as one layer of an overarching strategy framework, such that the return streams are sub-strategies, instead of raw instruments.

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.

This post introduces the Quarterly Tactical Strategy, introduced by Cliff Smith on a Seeking Alpha article. It presents a variation on the typical dual-momentum strategy that only trades over once a quarter, yet delivers a seemingly solid risk/return profile. The article leaves off a protracted period of unimpressive performance at the turn of the millennium, however.

First off, due to the imprecision of the English language, I received some help from TrendXplorer in implementing this strategy. Those who are fans of Amibroker are highly encouraged to visit his blog.

In any case, this strategy is fairly simple:

Take a group of securities (in this case, 8 mutual funds), and do the following:

Rank a long momentum (105 days) and a short momentum (20 days), and invest in the security with the highest composite rank, with ties going to the long momentum (that is, .501*longRank + .499*shortRank, for instance). If the security with the highest composite rank is greater than its three month SMA, invest in that security, otherwise, hold cash.

There are two critical points that must be made here:

1) The three-month SMA is *not* a 63-day SMA. It is precisely a three-point SMA up to that point on the monthly endpoints of that security.
2) Unlike in flexible asset allocation or elastic asset allocation, the cash asset is not treated as a formal asset.

Let’s look at the code. Here’s the data–which are adjusted-data mutual fund data (although with a quarterly turnover, the frequent trading constraint of not trading out of the security is satisfied, though I’m not sure how dividends are treated–that is, whether a retail investor would actually realize these returns less a hopefully tiny transaction cost through their brokers–aka hopefully not too much more than $1 per transaction):

require(quantmod)
require(PerformanceAnalytics)
require(TTR)

#get our data from yahoo, use adjusted prices
symbols <- c("NAESX", #small cap
             "PREMX", #emerging bond
             "VEIEX", #emerging markets
             "VFICX", #intermediate investment grade
             "VFIIX", #GNMA mortgage
             "VFINX", #S&P 500 index
             "VGSIX", #MSCI REIT
             "VGTSX", #total intl stock idx
             "VUSTX") #long term treasury (cash)

getSymbols(symbols, from="1990-01-01")
prices <- list()
for(i in 1:length(symbols)) {
  prices[[i]] <- Ad(get(symbols[i]))  
}
prices <- do.call(cbind, prices)
colnames(prices) <- gsub("\\.[A-z]*", "", colnames(prices))

#define our cash asset and keep track of which column it is
cashAsset <- "VUSTX"
cashCol <- grep(cashAsset, colnames(prices))

#start our data off on the security with the least data (VGSIX in this case)
prices <- prices[!is.na(prices[,7]),] 

#cash is not a formal asset in our ranking
cashPrices <- prices[, cashCol]
prices <- prices[, -cashCol]

Nothing anybody hasn’t seen before up to this point. Get data, start it off at most recent inception mutual fund, separate the cash prices, moving along.

What follows is a rather rough implementation of QTS, not wrapped up in any sort of function that others can plug and play with (though I hope I made the code readable enough for others to tinker with).

Let’s define parameters and compute momentum.

#define our parameters
nShort <- 20
nLong <- 105
nMonthSMA <- 3

#compute momentums
rocShort <- prices/lag(prices, nShort) - 1
rocLong <- prices/lag(prices, nLong) - 1

Now comes some endpoints functionality (or, more colloquially, magic) that the xts library provides. It’s what allows people to get work done in R much faster than in other programming languages.

#take the endpoints of quarter start/end
quarterlyEps <- endpoints(prices, on="quarters")
monthlyEps <- endpoints(prices, on = "months")

#take the prices at quarterly endpoints
quarterlyPrices <- prices[quarterlyEps,]

#short momentum at quarterly endpoints (20 day)
rocShortQtrs <- rocShort[quarterlyEps,]

#long momentum at quarterly endpoints (105 day)
rocLongQtrs <- rocLong[quarterlyEps,]

In short, get the quarterly endpoints (and monthly, we need those for the monthly SMA which you’ll see shortly) and subset our momentum computations on those quarterly endpoints. Now let’s get the total rank for those subset-on-quarters momentum computations.

#rank short momentum, best highest rank
rocSrank <- t(apply(rocShortQtrs, 1, rank))

#rank long momentum, best highest rank
rocLrank <- t(apply(rocLongQtrs, 1, rank))

#total rank, long slightly higher than short, sum them
totalRank <- 1.01*rocLrank + rocSrank 

#function that takes 100% position in highest ranked security
maxRank <- function(rankRow) {
  return(rankRow==max(rankRow))
}

#apply above function to our quarterly ranks every quarter
rankPos <- t(apply(totalRank, 1, maxRank))

So as you can see, I rank the momentum computations by row, take a weighted sum (in slight favor of the long momentum), and then simply take the security with the highest rank at every period, giving me one 1 in every row and 0s otherwise.

Now let’s do the other end of what determines position, which is the SMA filter. In this case, we need monthly data points for our three-month SMA, and then subset it to quarters to be on the same timescale as the quarterly ranks.

#SMA of securities, only use monthly endpoints
#subset to quarters
#then filter
monthlyPrices <- prices[monthlyEps,]
monthlySMAs <- xts(apply(monthlyPrices, 2, SMA, n=nMonthSMA), order.by=index(monthlyPrices))
quarterlySMAs <- monthlySMAs[index(quarterlyPrices),]
smaFilter <- quarterlyPrices > quarterlySMAs

Now let’s put it together to get our final positions. Our cash position is simply one if we don’t have a single investment in the time period, zero else.

finalPos <- rankPos*smaFilter
finalPos <- finalPos[!is.na(rocLongQtrs[,1]),]
cash <- xts(1-rowSums(finalPos), order.by=index(finalPos))
finalPos <- merge(finalPos, cash, join='inner')

Now we can finally compute our strategy returns.

prices <- merge(prices, cashPrices, join='inner')
returns <- Return.calculate(prices)
stratRets <- Return.portfolio(returns, finalPos)
table.AnnualizedReturns(stratRets)
maxDrawdown(stratRets)
charts.PerformanceSummary(stratRets)
plot(log(cumprod(1+stratRets)))

So what do things look like?

Like this:

> table.AnnualizedReturns(stratRets)
                          portfolio.returns
Annualized Return                    0.1899
Annualized Std Dev                   0.1619
Annualized Sharpe (Rf=0%)            1.1730
> maxDrawdown(stratRets)
[1] 0.1927991

And since the first equity curve doesn’t give much of an indication in the early years, I’ll take Tony Cooper’s (of Double Digit Numerics) advice and show the log equity curve as well.

In short, from 1997 through 2002, this strategy seemed to be going nowhere, and then took off. As I was able to get this backtest going back to 1997, it makes me wonder why it was only started in 2003 for the SeekingAlpha article, since even with 1997-2002 thrown in, this strategy’s risk/reward profile still looks fairly solid. CAR about 1 (slightly less, but that’s okay, for something that turns over so infrequently, and in so few securities!), and a Sharpe higher than 1. Certainly better than what the market itself offered over the same period of time for retail investors. Perhaps Cliff Smith himself could chime in regarding his choice of time frame.

In any case, Cliff Smith marketed the strategy as having a higher than 28% CAGR, and his article was published on August 15, 2014, and started from 2003. Let’s see if we can replicate those results.

stratRets <- stratRets["2002-12-31::2014-08-15"]
table.AnnualizedReturns(stratRets)
maxDrawdown(stratRets)
charts.PerformanceSummary(stratRets)
plot(log(cumprod(1+stratRets)))

Which results in this:

> table.AnnualizedReturns(stratRets)
                          portfolio.returns
Annualized Return                    0.2862
Annualized Std Dev                   0.1734
Annualized Sharpe (Rf=0%)            1.6499
> maxDrawdown(stratRets)
[1] 0.1911616

A far improved risk/return profile without 1997-2002 (or the out-of-sample period after Cliff Smith’s publishing date). Here are the two equity curves in-sample.

In short, the results look better, and the SeekingAlpha article’s results are validated.

Now, let’s look at the out-of-sample periods on their own.

stratRets <- Return.portfolio(returns, finalPos)
earlyOOS <- stratRets["::2002-12-31"]
table.AnnualizedReturn(earlyOOS)
maxDrawdown(earlyOOS)
charts.PerformanceSummary(earlyOOS)

Here are the results:

> table.AnnualizedReturns(earlyOOS)
                          portfolio.returns
Annualized Return                    0.0321
Annualized Std Dev                   0.1378
Annualized Sharpe (Rf=0%)            0.2327
> maxDrawdown(earlyOOS)
[1] 0.1927991

And with the corresponding equity curve (which does not need a log-scale this time).

In short, it basically did nothing for an entire five years. That’s rough, and I definitely don’t like the fact that it was left off of the SeekingAlpha article, as anytime I can extend a backtest further back than a strategy’s original author and then find skeletons in the closet (as happened for each and every one of Harry Long’s strategies), it sets off red flags on this end, so I’m hoping that there’s some good explanation for leaving off 1997-2002 that I’m simply failing to mention.

Lastly, let’s look at the out-of-sample performance.

lateOOS <- stratRets["2014-08-15::"]
charts.PerformanceSummary(lateOOS)
table.AnnualizedReturns(lateOOS)
maxDrawdown(lateOOS)

With the following results:

> table.AnnualizedReturns(lateOOS)
                          portfolio.returns
Annualized Return                    0.0752
Annualized Std Dev                   0.1426
Annualized Sharpe (Rf=0%)            0.5277
> maxDrawdown(lateOOS)
[1] 0.1381713

And the following equity curve:

Basically, while it’s ugly, it made new equity highs over only two more transactions (and in such a small sample size, anything can happen), so I’ll put this one down as a small, ugly win, but a win nevertheless.

If anyone has any questions or comments about this strategy, I’d love to see them, as this is basically a first-pass replica. To Mr. Cliff Smith’s credit, the results check out, and when the worst thing one can say about a strategy is that it had a period of a flat performance (aka when the market crested at the end of the Clinton administration right before the dot-com burst), well, that’s not the worst thing in the world.

More replications (including one requested by several readers) will be upcoming.

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.