Since I’ve hit a rut in trend following (how do you quantify rising/falling/flat? What even defines those three terms in precise, machine definition? How do you avoid buying tops while not getting chopped by whipsaws?), I decided to look the other way, with oscillators. Certainly, I’m not ready to give up on Dr. Ehlers just yet. So, in this post, I’ll introduce a recent innovation of the RSI by Dr. John Ehlers.

The indicator is Dr. Ehlers’s modified RSI from Chapter 7 of Cycle Analytics for Traders.

For starters, here’s how the Ehlers RSI is different than the usual ones: it gets filtered with a high-pass filter and then smoothed with a supersmoother filter. While Michael Kapler also touched on this topic a while back, I suppose it can’t hurt if I attempted to touch on it myself.

Here is the high pass filter and the super smoother, from the utility.R file in DSTrading. They’re not exported since as of the moment, they’re simply components of other indicators.

highPassFilter <- function(x) {
  alpha1 <- (cos(.707*2*pi/48)+sin(.707*2*pi/48)-1)/cos(.707*2*pi/48)
  HP <- (1-alpha1/2)*(1-alpha1/2)*(x-2*lag(x)+lag(x,2))
  HP <- HP[-c(1,2)]
  HP <- filter(HP, c(2*(1-alpha1), -1*(1-alpha1)*(1-alpha1)), method="recursive")
  HP <- c(NA, NA, HP)
  HP <- xts(HP, order.by=index(x))
  return(HP)
}

superSmoother <- function(x) {
  a1 <- exp(-1.414*pi/10)
  b1 <- 2*a1*cos(1.414*pi/10)
  c2 <- b1
  c3 <- -a1*a1
  c1 <- 1-c2-c3
  filt <- c1*(x+lag(x))/2
  leadNAs <- sum(is.na(filt))
  filt <- filt[-c(1:leadNAs)]
  filt <- filter(filt, c(c2, c3), method="recursive")
  filt <- c(rep(NA,leadNAs), filt)
  filt <- xts(filt, order.by=index(x))
}

In a nutshell, both of these functions serve to do an exponential smoothing on the data using some statically computed trigonometric quantities, the rationale of which I will simply defer to Dr. Ehlers’s book (link here).

Here’s the modified ehlers RSI, which I call CycleRSI, from the book in which it’s defined:

"CycleRSI" <- function(x, n=20) {
  filt <- superSmoother(highPassFilter(x))
  diffFilt <- diff(filt)
  posDiff <- negDiff <- diffFilt
  posDiff[posDiff < 0] <- 0
  negDiff[negDiff > 0] <- 0
  negDiff <- negDiff*-1
  posSum <- runSum(posDiff, n)
  negSum <- runSum(negDiff, n)
  denom <- posSum+negSum
  rsi <- posSum/denom
  rsi <- superSmoother(rsi)*100
  colnames(rsi) <- "CycleRSI"
  return(rsi)
}

Here’s a picture comparing four separate RSIs.

The first is the RSI featured in this post (cycle RSI) in blue. The next is the basic RSI(2) in red. The one after that is Larry Connors’s Connors RSI , which may be touched on in the future, and the last one, in purple, is the generalized Laguerre RSI, which is yet another Dr. Ehlers creation (which I’ll have to test sometime in the future).

To start things off with the Cycle RSI, I decided to throw a simple strategy around it:

Buy when the CycleRSI(2) crosses under 10 when the close is above the SMA200, which is in the vein of a Larry Connors trading strategy from “Short Term ETF Trading Strategies That Work” (whether they work or not remains debatable), and sell when the CycleRSI(2) crosses above 70, or when the close falls below the SMA200 so that the strategy doesn’t get caught in a runaway downtrend.

Since the strategy comes from an ETF Trading book, I decided to use my old ETF data set, from 2003 through 2010.

Here’s the strategy code, as usual:

require(DSTrading)
require(IKTrading)
require(quantstrat)
require(PerformanceAnalytics)

initDate="1990-01-01"
from="2003-01-01"
to="2010-12-31"
options(width=70)
verbose=TRUE

source("demoData.R")

#trade sizing and initial equity settings
tradeSize <- 100000
initEq <- tradeSize*length(symbols)

strategy.st <- portfolio.st <- account.st <- "Cycle_RSI_I"
rm.strat(portfolio.st)
rm.strat(strategy.st)
initPortf(portfolio.st, symbols=symbols, initDate=initDate, currency='USD')
initAcct(account.st, portfolios=portfolio.st, initDate=initDate, currency='USD',initEq=initEq)
initOrders(portfolio.st, initDate=initDate)
strategy(strategy.st, store=TRUE)

#parameters
nRSI=2
RSIentry=10
RSIexit=70

nSMA=200

period=10
pctATR=.04

#indicators
add.indicator(strategy.st, name="lagATR", 
              arguments=list(HLC=quote(HLC(mktdata)), n=period), 
              label="atrX")
add.indicator(strategy.st, name="SMA",
              arguments=list(x=quote(Cl(mktdata)), n=nSMA),
              label="SMA")
add.indicator(strategy.st, name="CycleRSI",
              arguments=list(x=quote(Cl(mktdata)), n=nRSI),
              label="RSI")

#signals
add.signal(strategy.st, name="sigComparison",
           arguments=list(columns=c("Close", "SMA"), relationship="gt"),
           label="ClGtSMA")

add.signal(strategy.st, name="sigThreshold",
           arguments=list(column="CycleRSI.RSI", threshold=RSIentry, 
                          relationship="lt", cross=FALSE),
           label="RSIltEntryThresh")

add.signal(strategy.st, name="sigAND",
           arguments=list(columns=c("ClGtSMA", "RSIltEntryThresh"), 
                          cross=TRUE),
           label="longEntry")

add.signal(strategy.st, name="sigCrossover",
           arguments=list(columns=c("Close", "SMA"), relationship="lt"),
           label="exitSMA")

add.signal(strategy.st, name="sigThreshold",
           arguments=list(column="CycleRSI.RSI", threshold=RSIexit,
                          relationship="gt", cross=TRUE),
           label="longExit")

#rules
#rules
add.rule(strategy.st, name="ruleSignal", 
         arguments=list(sigcol="longEntry", sigval=TRUE, 
                        ordertype="market", 
                        orderside="long", replace=FALSE, 
                        prefer="Open", osFUN=osDollarATR,
                        tradeSize=tradeSize, pctATR=pctATR, 
                        atrMod="X"), 
         type="enter", path.dep=TRUE)

add.rule(strategy.st, name="ruleSignal", 
         arguments=list(sigcol="longExit", sigval=TRUE, 
                        orderqty="all", ordertype="market", 
                        orderside="long", replace=FALSE, 
                        prefer="Open"), 
         type="exit", path.dep=TRUE)

add.rule(strategy.st, name="ruleSignal", 
         arguments=list(sigcol="exitSMA", sigval=TRUE, 
                        orderqty="all", ordertype="market", 
                        orderside="long", replace=FALSE, 
                        prefer="Open"), 
         type="exit", path.dep=TRUE)

#apply strategy
t1 <- Sys.time()
out <- applyStrategy(strategy=strategy.st,portfolios=portfolio.st)
t2 <- Sys.time()
print(t2-t1)

#set up analytics
updatePortf(portfolio.st)
dateRange <- time(getPortfolio(portfolio.st)$summary)[-1]
updateAcct(portfolio.st,dateRange)
updateEndEq(account.st)

And here are the results:

> (aggPF <- sum(tStats$Gross.Profits)/-sum(tStats$Gross.Losses))
[1] 1.846124
> (aggCorrect <- mean(tStats$Percent.Positive))
[1] 65.071
> (numTrades <- sum(tStats$Num.Trades))
[1] 2048
> (meanAvgWLR <- mean(tStats$Avg.WinLoss.Ratio[tStats$Avg.WinLoss.Ratio < Inf], na.rm=TRUE))
[1] 1.028333

> print(t(durStats))
      [,1]
Min      1
Q1       6
Med      9
Mean    11
Q3      14
Max     43
WMin     1
WQ1      7
WMed     9
WMean   11
WQ3     13
WMax    40
LMin     1
LQ1      6
LMed    11
LMean   12
LQ3     15
LMax    43

> print(mean(as.numeric(as.character(mktExposure$MktExposure))))
[1] 0.2806

> mean(corMeans)
[1] 0.2763

> SharpeRatio.annualized(portfRets)
                                    [,1]
Annualized Sharpe Ratio (Rf=0%) 1.215391
> Return.annualized(portfRets)
                       [,1]
Annualized Return 0.1634448
> maxDrawdown(portfRets)
[1] 0.1694307

Overall, the statistics don’t look bad. However, the 1:1 annualized returns to max drawdown isn’t particularly pleasing, as it means that this strategy can’t be leveraged effectively to continue getting outsized returns in this state. Quite irritating. Here’s the equity curve.

In short, as with other mean reverters, when drawdowns happen, they happen relatively quickly and brutally.

Here’s an individual instrument position chart.

By the looks of things, the strategy does best in a market that grinds upwards, rather than a completely choppy sideways market.

Finally, here’s some code for charting all of the different trades.

agg.chart.ME <- function(Portfolio, Symbols, type=c("MAE", "MFE"), scale=c("cash", "percent", "tick")) {
  type=type[1]
  scale=scale[1]
  trades <- list()
  length(trades) <- length(Symbols)
  for(Symbol in Symbols) {
    trades[[Symbol]] <- pts <- perTradeStats(Portfolio=Portfolio, Symbol=Symbol, includeOpenTrade=FALSE)
  }
  trades <- do.call(rbind, trades)
  trades$Pct.Net.Trading.PL <- 100 * trades$Pct.Net.Trading.PL
  trades$Pct.MAE <- 100 * trades$Pct.MAE
  trades$Pct.MFE <- 100 * trades$Pct.MFE
  profitable <- (trades$Net.Trading.PL > 0)
  switch(scale, cash = {
    .ylab <- "Profit/Loss (cash)"
    if (type == "MAE") {
      .cols <- c("MAE", "Net.Trading.PL")
      .xlab <- "Drawdown (cash)"
      .main <- "Maximum Adverse Excursion (MAE)"
    } else {
      .cols <- c("MFE", "Net.Trading.PL")
      .xlab <- "Run Up (cash)"
      .main <- "Maximum Favourable Excursion (MFE)"
    }
  }, percent = {
    .ylab <- "Profit/Loss (%)"
    if (type == "MAE") {
      .cols <- c("Pct.MAE", "Pct.Net.Trading.PL")
      .xlab <- "Drawdown (%)"
      .main <- "Maximum Adverse Excursion (MAE)"
    } else {
      .cols <- c("Pct.MFE", "Pct.Net.Trading.PL")
      .xlab <- "Run Up (%)"
      .main <- "Maximum Favourable Excursion (MFE)"
    }
  }, tick = {
    .ylab <- "Profit/Loss (ticks)"
    if (type == "MAE") {
      .cols <- c("tick.MAE", "tick.Net.Trading.PL")
      .xlab <- "Drawdown (ticks)"
      .main <- "Maximum Adverse Excursion (MAE)"
    } else {
      .cols <- c("tick.MFE", "tick.Net.Trading.PL")
      .xlab <- "Run Up (ticks)"
      .main <- "Maximum Favourable Excursion (MFE)"
    }
  })
  .main <- paste("All trades", .main)
  plot(abs(trades[, .cols]), type = "n", xlab = .xlab, ylab = .ylab, 
       main = .main)
  grid()
  points(abs(trades[profitable, .cols]), pch = 24, col = "green", 
         bg = "green", cex = 0.6)
  points(abs(trades[!profitable, .cols]), pch = 25, col = "red", 
         bg = "red", cex = 0.6)
  abline(a = 0, b = 1, lty = "dashed", col = "darkgrey")
  legend(x = "bottomright", inset = 0.1, legend = c("Profitable Trade", 
                                                    "Losing Trade"), pch = c(24, 25), col = c("green", "red"), 
         pt.bg = c("green", "red"))
}

And the resulting plot:

One last thing to note…that $50,000 trade in the upper left hand corner? That was a yahoo data issue and is a false print. Beyond that, once again, this seems like standard fare for a mean reverter–when trades go bad, they’re *really* bad, but the puzzle of where to put a stop is a completely separate issue, as it usually means locking in plenty of losses that decrease in magnitude, along with possibly turning winners into losers. On the flip side, here’s the maximum favorable excursion plot.

In short, there are definitely trades that could have been stopped for a profit that turned into losers.

In conclusion, while the initial trading system seems to be a good start, it’s far from complete.

Thanks for reading.

So, it is possible to create a trading system that can correctly isolate severe and protracted downturns, without taking (too many) false signals.

Here are the rules:

126 day FRAMA, FC=4, SC=300 (we’re still modifying the original ETFHQ strategy).
A running median (somewhere between 150 days and 252 days–seemingly, all these configurations work).

Both the FRAMA and the confirmatory median must be moving in the same direction (up for a long trade, down for a short trade–the median rising is the new rule here), and the price must cross the FRAMA in that direction to enter into a trade, while exiting when the price crosses below the FRAMA. Presented as a set of quantstrat rules, it gets rather lengthy, since a rule needs to specify the three setup conditions, a rule to bind them together, and an exit rule (5 rules each side).

The strategy works on both long and short ends, though the short version seems more of an insurance strategy than anything else. Here’s the equity curve for a 150 day median:

Basically, it makes money in terrible periods, but gives some of it back during just about any other time. It’s there just to put it out there as something that can finally try and isolate the truly despicable conditions and give you a pop in those times. Other than that? Using it would depend on how often someone believes those sorts of drawdown conditions would occur–that is, a descending adaptive indicator, a descending 7-12 month median.

Here are the trade and portfolio statistics:

> (aggPF <- sum(tStats$Gross.Profits)/-sum(tStats$Gross.Losses))
[1] 1.169916
> (aggCorrect <- mean(tStats$Percent.Positive))
[1] 33.475
> (numTrades <- sum(tStats$Num.Trades))
[1] 667
> (meanAvgWLR <- mean(tStats$Avg.WinLoss.Ratio[tStats$Avg.WinLoss.Ratio < Inf], na.rm=TRUE))
[1] 2.631724

                                      [,1]
Annualized Sharpe Ratio (Rf=0%) 0.07606299
> Return.annualized(portfRets)
                         [,1]
Annualized Return 0.004247807
> maxDrawdown(portfRets)
[1] 0.09845553

In other words, it’s absolutely not a standalone strategy, but more of a little something to give a long-only strategy a boost during bad times. It’s certainly not as spectacular as it gets. For instance, here’s the equity curve for XLK in late 2008-2009. Mainly, the problem with the ETFHQ strategy (I’m still on that, yes) is that it does not at all take into account the magnitude of the direction of the indicator. This means that in a reverting market, this strategy has a potential to lose a great deal of money unnecessarily.

Basically, this strategy is highly conservative, meaning that it has a tendency to miss good trades, take unnecessary ones, and is generally flawed because it has no way of really estimating the slope of the FRAMA.

As the possible solution to this involves a strategy by John Ehlers, I think I’ll leave this strategy here for now.

So, to send off this original ETFHQ price cross strategy off, I’ll test it out of sample using a 200-day median, using both long and short sides (from 2010-03-01 to get the 200 day median burned in, to the current date as of the time of this writing, 2014-06-20).

Here are the trade stats and portfolio stats:

> (aggPF <- sum(tStats$Gross.Profits)/-sum(tStats$Gross.Losses))
[1] 1.195693
> (aggCorrect <- mean(tStats$Percent.Positive))
[1] 36.20733
> (numTrades <- sum(tStats$Num.Trades))
[1] 1407
> (meanAvgWLR <- mean(tStats$Avg.WinLoss.Ratio[tStats$Avg.WinLoss.Ratio < Inf], na.rm=TRUE))
[1] 2.263333

> SharpeRatio.annualized(portfRets)
                                     [,1]
Annualized Sharpe Ratio (Rf=0%) 0.3290298
> Return.annualized(portfRets)
                        [,1]
Annualized Return 0.02467234
> maxDrawdown(portfRets)
[1] 0.1354166

With the corresponding equity curve:

In short, definitely not good. Why?

Here’s a good symptom as to why:

This is the out-of-sample equity curve of SHY–that is, the ETF of short term bonds. The trend had ended, but the trading system didn’t pick up on that.

In this case, you can see that the magnitude of the trend makes no difference to the strategy–which is a major problem. Although the counter-trend trading was eliminated, forcing action was not, and trying to remain loyal to the price crossing the indicator strategy while sticking to more conventional methods (a confirming indicator) turns out to be flawed. Here is another side symptom of a flawed system:

In this instance, using such a conservative confirmatory indicator for the short trade and simply using that same indicator for the long side indicates that there may very well have been overfitting on the system. On a more general note, however, this picture makes one wonder whether a confirmatory indicator was even necessary. For instance, there were certainly protracted periods during which there was a long trend that were cut off due to the running median being slightly negative. There were both long and short opportunities missed.

In my opinion, I think this puts the kibosh on something as ham-handed as a long-running confirmatory indicator. Why? Because I think that it over-corrects for a flawed order logic system that doesn’t take into account the magnitude of the slope of the indicator. Obviously, trading in a countertrend (descending indicator) is a terrible idea. But what about a slight change of directional sign as part of a greater counter-trend? Suddenly, a robust, deliberately lagging confirmatory indicator no longer seems like such a bad idea. However, as you can see, the downside of a lagging indicator is that it may very well lag your primary indicator in a good portion of cases. And it does nothing to eliminate sideways trading.

Surely, a more elegant solution exists that attempts to quantify the fact that sometimes, the smooth-yet-adaptive FRAMA can trend rapidly (and such trades should be taken posthaste), and can also go flat. Ultimately, I think that while the indicator settings from ETFHQ have some merit, the simplistic order logic on its own can certainly hurt–and coupled with an order-sizing function that downsizes orders in times of trending while magnifying them in times of calm (a side-effect of ATR, which was created to equalize risk across instruments, but with the unintended consequence of very much not equalizing risk across market conditions) can cause problems.

The next strategy will attempt to rectify these issues.

Thanks for reading.

This post examines an n-day median filter for two desirable properties: robustness to outliers and an inherent trend-confirming lag. While this is an incomplete filter (or maybe even inferior), it offers some key insights into improving the trading system.

The strategy will be thus:

First and foremost, this will be a short-only strategy, due to the long bias within the sample period, so the stress-test of the system will be to attempt to capture the non-dominant trend (and only when appropriate).

Here’s the strategy: we will continue to use the same 126 day FRAMA with the fast constant set at 4, and a slow constant at 300 (that is, it can oscillate anywhere between an EMA4 and EMA300). We will only enter into a short position when this indicator is descending, below the 126-day median of the price action, and when the price action is lower than this indicator (usually this means a cross, not in all cases though). We will exit when the price action rises back above the indicator.

Here’s the strategy in R code:

require(DSTrading)
require(IKTrading)
require(quantstrat)
require(PerformanceAnalytics)

initDate="1990-01-01"
from="2003-01-01"
to="2010-12-31"
options(width=70)

#to rerun the strategy, rerun everything below this line
source("demoData.R") #contains all of the data-related boilerplate.

#trade sizing and initial equity settings
tradeSize <- 10000
initEq <- tradeSize*length(symbols)

strategy.st <- portfolio.st <- account.st <- "FRAMA_III"
rm.strat(portfolio.st)
rm.strat(strategy.st)
initPortf(portfolio.st, symbols=symbols, initDate=initDate, currency='USD')
initAcct(account.st, portfolios=portfolio.st, initDate=initDate, currency='USD',initEq=initEq)
initOrders(portfolio.st, initDate=initDate)
strategy(strategy.st, store=TRUE)

#parameters

FC=4
SC=300
n=126
triggerLag=1

period=10
pctATR=.02

#indicators 

add.indicator(strategy.st, name="FRAMA",
              arguments=list(HLC=quote(HLC(mktdata)), n=n, 
                             SC=SC, FC=FC, triggerLag=triggerLag),
              label="primary")

add.indicator(strategy.st, name="runMedian",
              arguments=list(x=quote(Cl(mktdata)), n=n),
              label="confirmatory")

add.indicator(strategy.st, name="lagATR", 
              arguments=list(HLC=quote(HLC(mktdata)), n=period), 
              label="atrX")

# #long signals
# 
# add.signal(strategy.st, name="sigComparison",
#            arguments=list(columns=c("FRAMA.primary", "X1.confirmatory"), 
#                           relationship="gte"),
#            label="FRAMAgteMedian")
# 
# add.signal(strategy.st, name="sigComparison",
#            arguments=list(columns=c("FRAMA.primary", "trigger.primary"), 
#                           relationship="gte"),
#            label="FRAMArising")
# 
# add.signal(strategy.st, name="sigComparison",
#            arguments=list(columns=c("Close", "FRAMA.primary"), 
#                           relationship="gte"),
#            label="ClGtFRAMA")
# 
# add.signal(strategy.st, name="sigAND",
#            arguments=list(columns=c("FRAMAgteMedian", 
#                                     "FRAMArising", "ClGtFRAMA"), 
#                           cross=TRUE),
#            label="longEntry")
# 
# add.signal(strategy.st, name="sigCrossover",
#            arguments=list(columns=c("Close", "FRAMA.primary"), 
#                           relationship="lt"),
#            label="longExit")
# 
# #long rules
# 
# add.rule(strategy.st, name="ruleSignal", 
#          arguments=list(sigcol="longEntry", sigval=TRUE, ordertype="market", 
#                         orderside="long", replace=FALSE, prefer="Open", osFUN=osDollarATR,
#                         tradeSize=tradeSize, pctATR=pctATR, atrMod="X"), 
#          type="enter", path.dep=TRUE)
# 
# add.rule(strategy.st, name="ruleSignal", 
#          arguments=list(sigcol="longExit", sigval=TRUE, orderqty="all", ordertype="market", 
#                         orderside="long", replace=FALSE, prefer="Open"), 
#          type="exit", path.dep=TRUE)

#short signals

add.signal(strategy.st, name="sigComparison",
           arguments=list(columns=c("FRAMA.primary", "X1.confirmatory"), 
                          relationship="lt"),
           label="FRAMAltMedian")

add.signal(strategy.st, name="sigComparison",
           arguments=list(columns=c("FRAMA.primary", "trigger.primary"), 
                          relationship="lt"),
           label="FRAMAfalling")

add.signal(strategy.st, name="sigComparison",
           arguments=list(columns=c("Close", "FRAMA.primary"), 
                          relationship="lt"),
           label="ClLtFRAMA")

add.signal(strategy.st, name="sigAND",
           arguments=list(columns=c("FRAMAltMedian", 
                                    "FRAMAfalling", "ClLtFRAMA"), 
                          cross=TRUE),
           label="shortEntry")

add.signal(strategy.st, name="sigCrossover",
           arguments=list(columns=c("Close", "FRAMA.primary"), 
                          relationship="gt"),
           label="shortExit")

#short rules

add.rule(strategy.st, name="ruleSignal", 
         arguments=list(sigcol="shortEntry", sigval=TRUE, ordertype="market", 
                        orderside="short", replace=FALSE, prefer="Open", osFUN=osDollarATR,
                        tradeSize=-tradeSize, pctATR=pctATR, atrMod="X"), 
         type="enter", path.dep=TRUE)

add.rule(strategy.st, name="ruleSignal", 
         arguments=list(sigcol="shortExit", sigval=TRUE, orderqty="all", ordertype="market", 
                        orderside="short", replace=FALSE, prefer="Open"), 
         type="exit", path.dep=TRUE)



#apply strategy
t1 <- Sys.time()
out <- applyStrategy(strategy=strategy.st,portfolios=portfolio.st)
t2 <- Sys.time()
print(t2-t1)


#set up analytics
updatePortf(portfolio.st)
dateRange <- time(getPortfolio(portfolio.st)$summary)[-1]
updateAcct(portfolio.st,dateRange)
updateEndEq(account.st)

The results aren’t pretty, meaning that the filter is still incomplete. Here are the trade stats:

                        EFA      EPP      EWA      EWC      EWG
Num.Txns              90.00    68.00    85.00    66.00    90.00
Num.Trades            44.00    34.00    41.00    33.00    45.00
Net.Trading.PL     -2030.68   -25.54 -1485.82 -2283.03  -356.83
Avg.Trade.PL         -46.15    -0.75   -36.24   -69.18    -7.93
Med.Trade.PL        -103.99   -44.95   -77.27  -100.40   -69.91
Largest.Winner      1238.56  1656.56  1106.59  2195.51  3197.29
Largest.Loser       -661.04  -786.27  -548.06  -823.55  -783.65
Gross.Profits       4336.92  4455.45  3246.48  3566.35  5948.76
Gross.Losses       -6367.61 -4480.99 -4732.30 -5849.38 -6305.59
Std.Dev.Trade.PL     364.75   419.42   288.36   487.05   557.98
Percent.Positive      29.55    32.35    43.90    24.24    37.78
Percent.Negative      70.45    67.65    56.10    75.76    62.22
Profit.Factor          0.68     0.99     0.69     0.61     0.94
Avg.Win.Trade        333.61   405.04   180.36   445.79   349.93
Med.Win.Trade         57.09   238.60    66.34   124.31   101.88
Avg.Losing.Trade    -205.41  -194.83  -205.75  -233.98  -225.20
Med.Losing.Trade    -156.80  -122.45  -170.49  -166.84  -184.70
Avg.Daily.PL         -46.15    -0.75   -36.24   -69.18    -7.93
Med.Daily.PL        -103.99   -44.95   -77.27  -100.40   -69.91
Std.Dev.Daily.PL     364.75   419.42   288.36   487.05   557.98
Ann.Sharpe            -2.01    -0.03    -2.00    -2.25    -0.23
Max.Drawdown       -5089.55 -3095.58 -3609.64 -4915.76 -4222.60
Profit.To.Max.Draw    -0.40    -0.01    -0.41    -0.46    -0.08
Avg.WinLoss.Ratio      1.62     2.08     0.88     1.91     1.55
Med.WinLoss.Ratio      0.36     1.95     0.39     0.75     0.55
Max.Equity           146.74  1473.19   834.54    78.43  1467.12
Min.Equity         -4942.81 -2562.72 -2775.10 -4837.32 -3960.49
End.Equity         -2030.68   -25.54 -1485.82 -2283.03  -356.83

                        EWH      EWJ      EWS      EWT      EWU
Num.Txns              74.00   102.00    72.00    66.00    72.00
Num.Trades            36.00    51.00    35.00    33.00    36.00
Net.Trading.PL       596.16 -1493.76   982.93  1354.40   439.00
Avg.Trade.PL          16.56   -29.29    28.08    41.04    12.19
Med.Trade.PL         -54.45   -89.63   -52.85   -40.22   -56.50
Largest.Winner      3436.43  1076.25  1165.10  1980.68  1680.33
Largest.Loser       -544.78  -781.15  -429.64  -441.47  -468.28
Gross.Profits       4519.53  5681.81  4763.28  4317.26  5105.73
Gross.Losses       -3923.37 -7175.57 -3780.35 -2962.87 -4666.73
Std.Dev.Trade.PL     610.29   368.61   353.59   408.77   415.23
Percent.Positive      38.89    37.25    37.14    42.42    33.33
Percent.Negative      61.11    62.75    62.86    57.58    66.67
Profit.Factor          1.15     0.79     1.26     1.46     1.09
Avg.Win.Trade        322.82   299.04   366.41   308.38   425.48
Med.Win.Trade         79.88    99.19   267.75   115.47   399.34
Avg.Losing.Trade    -178.33  -224.24  -171.83  -155.94  -194.45
Med.Losing.Trade    -137.71  -175.69  -141.06   -95.88  -180.13
Avg.Daily.PL          16.56   -29.29    28.08    41.04    12.19
Med.Daily.PL         -54.45   -89.63   -52.85   -40.22   -56.50
Std.Dev.Daily.PL     610.29   368.61   353.59   408.77   415.23
Ann.Sharpe             0.43    -1.26     1.26     1.59     0.47
Max.Drawdown       -2390.89 -2994.16 -1689.63 -2113.93 -3192.52
Profit.To.Max.Draw     0.25    -0.50     0.58     0.64     0.14
Avg.WinLoss.Ratio      1.81     1.33     2.13     1.98     2.19
Med.WinLoss.Ratio      0.58     0.56     1.90     1.20     2.22
Max.Equity          2534.61  1380.90  1938.04  2065.70  1845.45
Min.Equity         -2131.17 -2540.03 -1265.23 -1501.15 -3192.52
End.Equity           596.16 -1493.76   982.93  1354.40   439.00

                        EWY      EWZ      EZU      IEF      IGE
Num.Txns              68.00    80.00    96.00    63.00    56.00
Num.Trades            34.00    40.00    48.00    32.00    28.00
Net.Trading.PL      1359.59 -2763.77  -178.24 -5286.17  -588.44
Avg.Trade.PL          39.99   -69.09    -3.71  -165.19   -21.02
Med.Trade.PL          19.52  -103.71   -73.53  -253.57   -87.68
Largest.Winner      1799.34  2495.03  1423.73   908.54  2146.42
Largest.Loser       -467.07  -496.73  -847.67  -758.78  -466.57
Gross.Profits       4729.27  2790.33  5960.68  2309.18  2757.36
Gross.Losses       -3369.68 -5554.10 -6138.92 -7595.36 -3345.80
Std.Dev.Trade.PL     414.55   440.16   402.00   349.52   456.89
Percent.Positive      55.88    15.00    33.33    25.00    25.00
Percent.Negative      44.12    85.00    66.67    75.00    75.00
Profit.Factor          1.40     0.50     0.97     0.30     0.82
Avg.Win.Trade        248.91   465.05   372.54   288.65   393.91
Med.Win.Trade         58.75    43.02    67.59   156.68    43.03
Avg.Losing.Trade    -224.65  -163.36  -191.84  -316.47  -159.32
Med.Losing.Trade    -217.23  -110.98  -139.29  -284.87  -115.98
Avg.Daily.PL          39.99   -69.09    -3.71  -192.64   -21.02
Med.Daily.PL          19.52  -103.71   -73.53  -260.53   -87.68
Std.Dev.Daily.PL     414.55   440.16   402.00   318.33   456.89
Ann.Sharpe             1.53    -2.49    -0.15    -9.61    -0.73
Max.Drawdown       -2237.74 -3903.71 -3510.08 -6682.82 -2836.80
Profit.To.Max.Draw     0.61    -0.71    -0.05    -0.79    -0.21
Avg.WinLoss.Ratio      1.11     2.85     1.94     0.91     2.47
Med.WinLoss.Ratio      0.27     0.39     0.49     0.55     0.37
Max.Equity          3532.28   836.88  1270.40   669.24   709.44
Min.Equity          -790.83 -3066.84 -3222.22 -6013.57 -2127.36
End.Equity          1359.59 -2763.77  -178.24 -5286.17  -588.44

                        IYR      IYZ      LQD      RWR      SHY
Num.Txns              96.00   108.00    63.00    98.00    51.00
Num.Trades            48.00    54.00    31.00    49.00    25.00
Net.Trading.PL     -3444.89 -2032.70  1532.27 -3740.29 -4049.16
Avg.Trade.PL         -71.77   -37.64    49.43   -76.33  -161.97
Med.Trade.PL        -129.99   -83.00   -84.44  -114.84  -141.20
Largest.Winner      1714.13  2673.04  2693.04  1455.78    86.02
Largest.Loser       -745.50  -463.08  -480.73  -578.29  -644.17
Gross.Profits       4652.33  4978.26  5114.62  3534.95   365.46
Gross.Losses       -8097.22 -7010.97 -3582.35 -7275.24 -4414.63
Std.Dev.Trade.PL     405.93   479.46   604.30   341.37   195.72
Percent.Positive      22.92    22.22    35.48    16.33    28.00
Percent.Negative      77.08    77.78    64.52    83.67    72.00
Profit.Factor          0.57     0.71     1.43     0.49     0.08
Avg.Win.Trade        422.94   414.86   464.97   441.87    52.21
Med.Win.Trade        110.81    29.28   139.76   188.82    44.33
Avg.Losing.Trade    -218.84  -166.93  -179.12  -177.44  -245.26
Med.Losing.Trade    -182.73  -134.02  -129.79  -138.78  -232.61
Avg.Daily.PL         -71.77   -37.64    45.47   -76.33  -162.83
Med.Daily.PL        -129.99   -83.00   -86.18  -114.84  -144.12
Std.Dev.Daily.PL     405.93   479.46   614.22   341.37   199.88
Ann.Sharpe            -2.81    -1.25     1.18    -3.55   -12.93
Max.Drawdown       -3857.85 -5575.45 -2876.51 -4695.60 -4049.16
Profit.To.Max.Draw    -0.89    -0.36     0.53    -0.80    -1.00
Avg.WinLoss.Ratio      1.93     2.49     2.60     2.49     0.21
Med.WinLoss.Ratio      0.61     0.22     1.08     1.36     0.19
Max.Equity           260.07   118.92  3375.06   302.96     0.00
Min.Equity         -3597.77 -5456.52 -2138.62 -4392.65 -4049.16
End.Equity         -3444.89 -2032.70  1532.27 -3740.29 -4049.16

                        TLT      XLB      XLE      XLF      XLI
Num.Txns              85.00   104.00    50.00   120.00    92.00
Num.Trades            43.00    51.00    25.00    60.00    46.00
Net.Trading.PL     -4037.97 -5591.16  -308.15 -3036.79 -2136.85
Avg.Trade.PL         -93.91  -109.63   -12.33   -50.61   -46.45
Med.Trade.PL        -133.03  -138.47   -96.47   -79.48  -108.98
Largest.Winner      1425.91  1831.45  1828.51  1058.03  1218.87
Largest.Loser       -543.28  -707.20  -430.13  -711.69  -632.77
Gross.Profits       3355.40  3130.31  2472.08  5282.27  4597.82
Gross.Losses       -7393.37 -8721.48 -2780.24 -8319.05 -6734.68
Std.Dev.Trade.PL     338.88   345.20   420.71   309.84   342.80
Percent.Positive      25.58    25.49    20.00    30.00    23.91
Percent.Negative      74.42    74.51    80.00    70.00    76.09
Profit.Factor          0.45     0.36     0.89     0.63     0.68
Avg.Win.Trade        305.04   240.79   494.42   293.46   417.98
Med.Win.Trade        168.50    83.98    33.87   135.46   294.74
Avg.Losing.Trade    -231.04  -229.51  -139.01  -198.07  -192.42
Med.Losing.Trade    -197.38  -207.82  -120.99  -171.67  -149.06
Avg.Daily.PL        -101.44  -109.63   -12.33   -50.61   -46.45
Med.Daily.PL        -140.48  -138.47   -96.47   -79.48  -108.98
Std.Dev.Daily.PL     339.33   345.20   420.71   309.84   342.80
Ann.Sharpe            -4.75    -5.04    -0.47    -2.59    -2.15
Max.Drawdown       -4926.34 -6711.79 -1938.05 -3451.10 -4068.90
Profit.To.Max.Draw    -0.82    -0.83    -0.16    -0.88    -0.53
Avg.WinLoss.Ratio      1.32     1.05     3.56     1.48     2.17
Med.WinLoss.Ratio      0.85     0.40     0.28     0.79     1.98
Max.Equity           459.78     0.00  1298.51   414.31     0.00
Min.Equity         -4466.56 -6711.79 -1329.01 -3036.79 -4068.90
End.Equity         -4037.97 -5591.16  -308.15 -3036.79 -2136.85

                        XLK      XLP      XLU      XLV      XLY
Num.Txns              86.00    92.00    82.00    94.00    82.00
Num.Trades            43.00    45.00    40.00    47.00    40.00
Net.Trading.PL     -1205.62 -4427.34 -3490.76 -4291.56  -230.80
Avg.Trade.PL         -28.04   -98.39   -87.27   -91.31    -5.77
Med.Trade.PL        -101.30  -153.01   -93.87   -98.69  -140.01
Largest.Winner      2403.16  1008.09  1805.03   842.35  2090.68
Largest.Loser       -806.29  -460.10  -462.68  -554.57  -698.45
Gross.Profits       4984.72  2839.42  2493.63  2959.31  6253.33
Gross.Losses       -6190.34 -7266.76 -5984.39 -7250.87 -6484.14
Std.Dev.Trade.PL     464.22   294.41   350.37   280.87   495.21
Percent.Positive      30.23    15.56    20.00    19.15    30.00
Percent.Negative      69.77    84.44    80.00    80.85    70.00
Profit.Factor          0.81     0.39     0.42     0.41     0.96
Avg.Win.Trade        383.44   405.63   311.70   328.81   521.11
Med.Win.Trade        191.31   116.12    61.87   266.16   307.13
Avg.Losing.Trade    -206.34  -191.23  -187.01  -190.81  -231.58
Med.Losing.Trade    -188.49  -191.04  -156.33  -161.51  -171.21
Avg.Daily.PL         -28.04   -98.39   -87.27   -91.31    -5.77
Med.Daily.PL        -101.30  -153.01   -93.87   -98.69  -140.01
Std.Dev.Daily.PL     464.22   294.41   350.37   280.87   495.21
Ann.Sharpe            -0.96    -5.30    -3.95    -5.16    -0.18
Max.Drawdown       -3448.99 -5384.93 -3540.13 -5186.60 -3964.07
Profit.To.Max.Draw    -0.35    -0.82    -0.99    -0.83    -0.06
Avg.WinLoss.Ratio      1.86     2.12     1.67     1.72     2.25
Med.WinLoss.Ratio      1.01     0.61     0.40     1.65     1.79
Max.Equity           646.11   651.59     0.00   895.04  2960.96
Min.Equity         -3003.57 -4733.34 -3540.13 -4291.56 -1003.11
End.Equity         -1205.62 -4427.34 -3490.76 -4291.56  -230.80

At this point, for the sake of brevity, I’ll leave off the equity curves and portfolio statistics (they’ll obviously be bad). However, let’s look at some images of what exactly is going on with individual trades.

Here is the full-backtest equity curve and corresponding indicators for XLP. The FRAMA is in purple, with the 126-day median in orange, along with the 10-day ATR (lagged by a day) on the bottom.

And here we can immediately see certain properties:

1) ATR order-sizing is not a be-all, end-all type of order. It was created for one purpose, which is to equalize risk across instruments (the original idea of which, I defer to Andreas Clenow’s article). However, that is only a base from which to begin, using other scaled order-sizing procedures which can attempt to quantify the confidence in any particular trade. As it currently stands, for short strategies in equities, the best opportunities happen in the depths of rapid falling price action, during which ATR will rise. One may consider augmenting the ATR order sizing function in order to accomplish this task (or merely apply leverage at the proper time, through modifying the pctATR parameter).

2) While the running median certainly has value as a filter to keep out obviously brainless trades (E.G. in the middle of an uptrend), once the FRAMA crosses the median, anything can happen, as the only logic is that the current FRAMA is just slightly lower than the previous day’s. This may mean that the running median itself is still rising, or that the FRAMA is effectively flat, and what is being traded on is purely noise. And furthermore, with ATR order sizing amplifying the consequences of that noise, this edge case can have disastrous consequences on an equity curve.

Here’s a zoom in on 2005, where we see a pretty severe drawdown (chart time series recolored for clarity).

As can be seen, even though the FRAMA seems to be slightly rising, a price crossing when the FRAMA is lower than the previous day by even an invisibly small amount (compare the purple–the FRAMA, to the red–the same quantity lagged a day) is enough to trigger a trade that will buy a sizable number of shares, even when the volatility is too small to justify such a trade. Essentially, most of the losses in this trading system arise as a result of trading during these flat periods during which the system attempts to force action.

This pattern repeats itself. Here is the equity curve for XLB.

Again, aside from maybe a bad trade in the end thanks to any trade being taken once all three conditions line up (decreasing FRAMA, FRAMA lower than median, price lower than FRAMA) too late due to a flat FRAMA/median relationship, most of the losers seem to be trades made during very flat and calm market action, even when the running median may be going in the opposite direction of the FRAMA, during which the ATR order-sizing function tried to force action. A second filter that serves to catch these edge-case situations (or maybe a filter that replaces the running median entirely) will be investigated in the future.

So, to recap this post:

The running median filter is an intrinsically lagging but robust indicator, chosen deliberately for these two properties. It is able to filter out trades that obviously go against the trend. However, due to some edge cases, there were still a great deal of losses that were incurred, which drown out the one good shorting opportunity over this sample period. This is an issue that needs addressing.

Thanks for reading.