FRAMA Part II: Replicating A Simple Strategy
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This post will begin the investigation into FRAMA strategies, with the aim of ultimately finding a FRAMA trading strategy with less market exposure, fewer whipsaw trades, and fewer counter-trend trades. This post will also introduce new analytics regarding trade duration.
To begin the investigation into developing strategies based on the previously-introduced FRAMA, I’m going to replicate the simple strategy from ETFHQ — use a 126 day FRAMA with a fast constant of 4 (that is, an EMA that goes as fast as a 4-day EMA), and all the way up to a slow constant of 300. For my ATR order-sizing, which, once again, was inspired by Andreas Clenow in the post on leverage being pointless, I’m going to use 2 percent of notional capital, with a 10 day ATR for my order sizing (ATR 20 and 30 display slightly weaker results, but nevertheless, are very close in performance).
Once again, let’s start by looking at the strategy, using our same 30 instruments as with our TVI demos (I thought about testing on mutual funds, but due to the obnoxious fees that mutual funds charge for trying to trade with them, I feel that I’d have to employ too much magical thinking to neglect their obscene trading transaction costs):
require(DSTrading)
require(IKTrading)
require(quantstrat)
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_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
FC=4
SC=300
n=126
triggerLag=1
pctATR=.02
period=10
#indicators
add.indicator(strategy.st, name="FRAMA",
arguments=list(HLC=quote(HLC(mktdata)),n=n,
FC=FC, SC=SC, triggerLag=triggerLag),
label="frama")
add.indicator(strategy.st, name="lagATR",
arguments=list(HLC=quote(HLC(mktdata)), n=period),
label="atrX")
#signals
add.signal(strategy.st, name="sigCrossover",
arguments=list(columns=c("Close", "FRAMA.frama"), relationship="gte"),
label="longEntry")
add.signal(strategy.st, name="sigCrossover",
arguments=list(columns=c("Close", "FRAMA.frama"), relationship="lt"),
label="longExit")
#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)
#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)
It’s a fairly simple strategy–buy the next day’s open when the price crosses above the indicator, and vice versa. In other words, it’s about as simple a strategy as you can get as its sole purpose was to demonstrate the effectiveness of the indicator. And while someone interested can peruse through ETFHQ to find all of the indicator relative tests, the general gist is that adaptive moving averages work very well, and the FRAMA (the fractal adaptive moving average) works slightly better than the rest. Ultimately though, if one believes ETFHQ’s analysis (and I do), then even one good trend-following indicator will be sufficient.
Here are the trade statistics:
EFA EPP EWA EWC EWG
Num.Txns 289.00 245.00 281.00 219.00 248.00
Num.Trades 145.00 123.00 140.00 109.00 121.00
Net.Trading.PL 9233.11 17020.32 14917.84 14298.85 13603.78
Avg.Trade.PL 63.68 138.38 106.56 131.18 112.43
Med.Trade.PL -46.29 -26.79 -24.81 -21.06 -28.14
Largest.Winner 2454.58 4499.10 3301.82 4031.95 3582.43
Largest.Loser -523.15 -847.71 -607.41 -613.76 -531.39
Gross.Profits 23874.49 29202.05 28060.29 23541.10 24820.41
Gross.Losses -14641.38 -12181.73 -13142.45 -9242.26 -11216.63
Std.Dev.Trade.PL 420.81 624.11 518.71 565.75 565.31
Percent.Positive 42.07 46.34 46.43 46.79 46.28
Percent.Negative 57.93 53.66 53.57 53.21 53.72
Profit.Factor 1.63 2.40 2.14 2.55 2.21
Avg.Win.Trade 391.39 512.32 431.70 461.59 443.22
Med.Win.Trade 199.18 238.18 220.98 236.81 179.68
Avg.Losing.Trade -174.30 -184.57 -175.23 -159.35 -172.56
Med.Losing.Trade -152.31 -121.13 -159.74 -133.38 -128.70
Avg.Daily.PL 63.07 137.42 105.72 128.59 112.43
Med.Daily.PL -49.26 -29.12 -27.68 -22.15 -28.14
Std.Dev.Daily.PL 422.22 626.59 520.49 567.74 565.31
Ann.Sharpe 2.37 3.48 3.22 3.60 3.16
Max.Drawdown -2338.49 -1945.85 -3026.93 -2001.41 -2047.83
Profit.To.Max.Draw 3.95 8.75 4.93 7.14 6.64
Avg.WinLoss.Ratio 2.25 2.78 2.46 2.90 2.57
Med.WinLoss.Ratio 1.31 1.97 1.38 1.78 1.40
Max.Equity 9902.70 17058.92 14996.93 14298.85 14604.43
Min.Equity -136.30 -189.12 -159.59 -233.07 -315.54
End.Equity 9233.11 17020.32 14917.84 14298.85 13603.78
EWH EWJ EWS EWT EWU
Num.Txns 271.00 243.00 275.00 199.00 227.00
Num.Trades 135.00 119.00 133.00 96.00 111.00
Net.Trading.PL 11548.79 5965.14 12676.51 12221.36 12044.63
Avg.Trade.PL 85.55 50.13 95.31 127.31 108.51
Med.Trade.PL -27.05 -26.14 -12.78 14.04 -7.08
Largest.Winner 2668.92 1872.67 2773.40 2749.00 2521.64
Largest.Loser -572.88 -521.96 -593.95 -537.06 -603.96
Gross.Profits 23173.00 17577.09 23801.66 19413.97 21927.72
Gross.Losses -11624.21 -11611.96 -11125.16 -7192.61 -9883.09
Std.Dev.Trade.PL 501.77 395.06 470.11 506.25 512.20
Percent.Positive 44.44 43.70 46.62 53.12 49.55
Percent.Negative 55.56 56.30 53.38 46.88 50.45
Profit.Factor 1.99 1.51 2.14 2.70 2.22
Avg.Win.Trade 386.22 338.02 383.90 380.67 398.69
Med.Win.Trade 125.17 140.16 212.49 172.84 195.04
Avg.Losing.Trade -154.99 -173.31 -156.69 -159.84 -176.48
Med.Losing.Trade -111.58 -146.64 -115.28 -138.75 -158.23
Avg.Daily.PL 86.78 38.81 94.45 108.42 108.20
Med.Daily.PL -25.57 -32.55 -17.73 12.24 -7.80
Std.Dev.Daily.PL 503.45 376.87 471.79 473.73 514.53
Ann.Sharpe 2.74 1.63 3.18 3.63 3.34
Max.Drawdown -2298.32 -3445.56 -2017.06 -2764.34 -2071.61
Profit.To.Max.Draw 5.02 1.73 6.28 4.42 5.81
Avg.WinLoss.Ratio 2.49 1.95 2.45 2.38 2.26
Med.WinLoss.Ratio 1.12 0.96 1.84 1.25 1.23
Max.Equity 12708.66 6336.41 13177.76 12221.36 12640.57
Min.Equity -272.68 -307.36 -331.04 0.00 -57.47
End.Equity 11548.79 5965.14 12676.51 12221.36 12044.63
EWY EWZ EZU IEF IGE
Num.Txns 261.00 265.00 270.00 216.00 249.00
Num.Trades 130.00 133.00 134.00 107.00 125.00
Net.Trading.PL 10513.27 14496.80 11233.90 13370.63 12428.65
Avg.Trade.PL 80.87 109.00 83.84 124.96 99.43
Med.Trade.PL 21.32 -42.35 -34.59 -41.49 -93.07
Largest.Winner 1550.67 2633.38 3163.76 2799.11 3710.24
Largest.Loser -614.98 -682.75 -553.54 -542.02 -576.53
Gross.Profits 23615.06 28466.25 25227.96 22877.10 26829.04
Gross.Losses -13101.78 -13969.45 -13994.06 -9506.47 -14400.39
Std.Dev.Trade.PL 417.96 548.34 538.74 546.44 660.65
Percent.Positive 50.77 43.61 42.54 42.06 32.80
Percent.Negative 49.23 56.39 57.46 57.94 67.20
Profit.Factor 1.80 2.04 1.80 2.41 1.86
Avg.Win.Trade 357.80 490.80 442.60 508.38 654.37
Med.Win.Trade 207.28 210.90 194.52 221.16 367.42
Avg.Losing.Trade -204.72 -186.26 -181.74 -153.33 -171.43
Med.Losing.Trade -187.43 -163.60 -144.77 -129.05 -154.06
Avg.Daily.PL 77.86 105.49 83.84 124.96 77.08
Med.Daily.PL 19.08 -44.57 -34.59 -41.49 -93.37
Std.Dev.Daily.PL 418.17 548.93 538.74 546.44 614.05
Ann.Sharpe 2.96 3.05 2.47 3.63 1.99
Max.Drawdown -2462.61 -2188.41 -2310.88 -2650.59 -3045.12
Profit.To.Max.Draw 4.27 6.62 4.86 5.04 4.08
Avg.WinLoss.Ratio 1.75 2.64 2.44 3.32 3.82
Med.WinLoss.Ratio 1.11 1.29 1.34 1.71 2.38
Max.Equity 10513.27 14760.11 12629.07 14339.37 12428.65
Min.Equity -339.01 -214.04 -203.63 -278.08 -268.60
End.Equity 10513.27 14496.80 11233.90 13370.63 12428.65
IYR IYZ LQD RWR SHY
Num.Txns 253.00 257.00 222.00 267.00 300.00
Num.Trades 125.00 127.00 108.00 133.00 143.00
Net.Trading.PL 9702.92 8599.09 13277.24 12090.68 15021.96
Avg.Trade.PL 77.62 67.71 122.94 90.91 105.05
Med.Trade.PL -60.97 -47.00 -17.31 -63.38 -41.73
Largest.Winner 2602.17 2511.55 2526.23 2810.42 1987.06
Largest.Loser -864.63 -619.97 -339.49 -758.94 -971.00
Gross.Profits 22264.43 20356.47 20777.57 25087.09 30006.10
Gross.Losses -12561.51 -11757.38 -7500.32 -12996.41 -14984.14
Std.Dev.Trade.PL 488.33 426.35 486.90 528.23 499.11
Percent.Positive 36.80 43.31 46.30 39.10 44.06
Percent.Negative 63.20 56.69 53.70 60.90 55.94
Profit.Factor 1.77 1.73 2.77 1.93 2.00
Avg.Win.Trade 484.01 370.12 415.55 482.44 476.29
Med.Win.Trade 313.81 182.80 139.12 228.24 229.73
Avg.Losing.Trade -159.01 -163.30 -129.32 -160.45 -187.30
Med.Losing.Trade -126.56 -112.84 -103.66 -147.59 -145.26
Avg.Daily.PL 75.21 66.83 122.94 88.59 105.05
Med.Daily.PL -61.69 -50.50 -17.31 -65.60 -41.73
Std.Dev.Daily.PL 489.56 427.93 486.90 529.57 499.11
Ann.Sharpe 2.44 2.48 4.01 2.66 3.34
Max.Drawdown -5488.96 -2253.39 -1261.10 -5062.88 -2852.91
Profit.To.Max.Draw 1.77 3.82 10.53 2.39 5.27
Avg.WinLoss.Ratio 3.04 2.27 3.21 3.01 2.54
Med.WinLoss.Ratio 2.48 1.62 1.34 1.55 1.58
Max.Equity 13313.44 9225.39 14084.98 15192.88 16570.24
Min.Equity -152.91 -522.27 -347.48 -394.76 -1036.81
End.Equity 9702.92 8599.09 13277.24 12090.68 15021.96
TLT XLB XLE XLF XLI
Num.Txns 238.00 247.00 229.00 245.00 261.00
Num.Trades 118.00 122.00 115.00 121.00 130.00
Net.Trading.PL 7117.62 6227.48 10335.40 -8.45 6351.34
Avg.Trade.PL 60.32 51.04 89.87 -0.07 48.86
Med.Trade.PL -71.33 -62.80 -65.87 -56.76 -45.18
Largest.Winner 2548.77 2083.24 2407.81 1895.31 1571.81
Largest.Loser -509.75 -544.43 -484.90 -626.99 -465.20
Gross.Profits 20099.36 19500.08 21827.84 12869.00 17364.07
Gross.Losses -12981.73 -13272.60 -11492.44 -12877.45 -11012.73
Std.Dev.Trade.PL 506.64 421.98 566.48 345.43 379.26
Percent.Positive 31.36 36.89 34.78 35.54 41.54
Percent.Negative 68.64 63.11 65.22 64.46 58.46
Profit.Factor 1.55 1.47 1.90 1.00 1.58
Avg.Win.Trade 543.23 433.34 545.70 299.28 321.56
Med.Win.Trade 230.04 248.59 241.31 153.68 129.61
Avg.Losing.Trade -160.27 -172.37 -153.23 -165.10 -144.90
Med.Losing.Trade -130.27 -159.19 -148.44 -134.74 -131.29
Avg.Daily.PL 60.32 47.96 68.35 -8.00 34.56
Med.Daily.PL -71.33 -65.49 -66.25 -58.07 -46.28
Std.Dev.Daily.PL 506.64 422.35 519.59 335.64 343.76
Ann.Sharpe 1.89 1.80 2.09 -0.38 1.60
Max.Drawdown -4938.54 -3692.51 -2780.65 -5704.14 -3013.95
Profit.To.Max.Draw 1.44 1.69 3.72 0.00 2.11
Avg.WinLoss.Ratio 3.39 2.51 3.56 1.81 2.22
Med.WinLoss.Ratio 1.77 1.56 1.63 1.14 0.99
Max.Equity 9318.18 6780.72 10335.40 4191.68 6357.94
Min.Equity -693.51 -213.25 -557.67 -1512.46 -795.23
End.Equity 7117.62 6227.48 10335.40 -8.45 6351.34
XLK XLP XLU XLV XLY
Num.Txns 254.00 280.00 241.00 218.00 220.00
Num.Trades 127.00 137.00 121.00 107.00 109.00
Net.Trading.PL 2940.29 2543.61 7904.42 3189.25 6727.03
Avg.Trade.PL 23.15 18.57 65.33 29.81 61.72
Med.Trade.PL -72.35 -85.92 -38.84 -88.65 -71.80
Largest.Winner 2050.23 1782.84 1240.83 1927.28 2667.81
Largest.Loser -749.16 -679.39 -598.65 -662.12 -559.61
Gross.Profits 16321.02 17361.88 18269.97 14178.93 18237.47
Gross.Losses -13380.73 -14818.27 -10365.55 -10989.67 -11510.44
Std.Dev.Trade.PL 389.23 363.63 363.21 418.10 525.74
Percent.Positive 35.43 32.12 43.80 28.97 39.45
Percent.Negative 64.57 67.88 56.20 71.03 60.55
Profit.Factor 1.22 1.17 1.76 1.29 1.58
Avg.Win.Trade 362.69 394.59 344.72 457.38 424.13
Med.Win.Trade 158.36 236.63 180.99 238.62 159.38
Avg.Losing.Trade -163.18 -159.34 -152.43 -144.60 -174.40
Med.Losing.Trade -135.65 -131.38 -124.59 -122.90 -146.41
Avg.Daily.PL 23.15 18.57 63.70 29.81 61.72
Med.Daily.PL -72.35 -85.92 -41.32 -88.65 -71.80
Std.Dev.Daily.PL 389.23 363.63 364.29 418.10 525.74
Ann.Sharpe 0.94 0.81 2.78 1.13 1.86
Max.Drawdown -3074.10 -4531.59 -2545.84 -4623.78 -4041.34
Profit.To.Max.Draw 0.96 0.56 3.10 0.69 1.66
Avg.WinLoss.Ratio 2.22 2.48 2.26 3.16 2.43
Med.WinLoss.Ratio 1.17 1.80 1.45 1.94 1.09
Max.Equity 2981.10 2993.23 8632.88 3902.68 6838.89
Min.Equity -1716.68 -1538.36 -165.00 -1213.50 -310.63
End.Equity 2940.29 2543.61 7904.42 3189.25 6727.03
And the aggregate trade statistics:
> (aggPF <- sum(tStats$Gross.Profits)/-sum(tStats$Gross.Losses)) [1] 1.828178 > (aggCorrect <- mean(tStats$Percent.Positive)) [1] 41.55233 > (numTrades <- sum(tStats$Num.Trades)) [1] 3704 > (meanAvgWLR <- mean(tStats$Avg.WinLoss.Ratio)) [1] 2.619
Far from spectacular. Less than 50% hit rate, the profit factor definitely indicates that there is massive room for improvement as well.
Here are the daily statistics:
EFA EPP EWA EWC EWG
Total.Net.Profit 9233.11 17020.32 14917.84 14298.85 13603.78
Total.Days 1280.00 1330.00 1330.00 1296.00 1264.00
Winning.Days 690.00 729.00 725.00 719.00 702.00
Losing.Days 590.00 601.00 605.00 577.00 562.00
Avg.Day.PL 7.21 12.80 11.22 11.03 10.76
Med.Day.PL 12.85 16.84 17.06 18.59 21.33
Largest.Winner 725.53 521.47 428.25 648.73 510.14
Largest.Loser -973.81 -1162.04 -722.38 -505.11 -841.33
Gross.Profits 72427.12 85143.30 80490.48 70817.88 75036.35
Gross.Losses -63194.01 -68122.98 -65572.64 -56519.03 -61432.57
Std.Dev.Daily.PL 139.51 153.35 140.28 125.46 141.11
Percent.Positive 53.91 54.81 54.51 55.48 55.54
Percent.Negative 46.09 45.19 45.49 44.52 44.46
Profit.Factor 1.15 1.25 1.23 1.25 1.22
Avg.Win.Day 104.97 116.79 111.02 98.49 106.89
Med.Win.Day 83.48 95.05 90.88 83.65 84.31
Avg.Losing.Day -107.11 -113.35 -108.38 -97.95 -109.31
Med.Losing.Day -81.61 -83.94 -84.18 -72.76 -84.31
Avg.Daily.PL 7.21 12.80 11.22 11.03 10.76
Med.Daily.PL 12.85 16.84 17.06 18.59 21.33
Std.Dev.Daily.PL.1 139.51 153.35 140.28 125.46 141.11
Ann.Sharpe 0.82 1.32 1.27 1.40 1.21
Max.Drawdown -2338.49 -1945.85 -3026.93 -2001.41 -2047.83
Profit.To.Max.Draw 3.95 8.75 4.93 7.14 6.64
Avg.WinLoss.Ratio 0.98 1.03 1.02 1.01 0.98
Med.WinLoss.Ratio 1.02 1.13 1.08 1.15 1.00
Max.Equity 9902.70 17058.92 14996.93 14298.85 14604.43
Min.Equity -136.30 -189.12 -159.59 -233.07 -315.54
End.Equity 9233.11 17020.32 14917.84 14298.85 13603.78
EWH EWJ EWS EWT EWU
Total.Net.Profit 11548.79 5965.14 12676.51 12221.36 12044.63
Total.Days 1221.00 1130.00 1300.00 1138.00 1252.00
Winning.Days 644.00 588.00 712.00 610.00 689.00
Losing.Days 577.00 542.00 588.00 528.00 563.00
Avg.Day.PL 9.46 5.28 9.75 10.74 9.62
Med.Day.PL 11.07 13.74 17.01 18.92 18.71
Largest.Winner 456.34 640.14 578.24 780.22 596.56
Largest.Loser -495.32 -496.23 -1058.32 -835.42 -812.47
Gross.Profits 71689.04 67809.75 70413.47 71565.95 71295.50
Gross.Losses -60140.25 -61844.61 -57736.96 -59344.59 -59250.87
Std.Dev.Daily.PL 138.92 148.13 130.19 150.04 132.82
Percent.Positive 52.74 52.04 54.77 53.60 55.03
Percent.Negative 47.26 47.96 45.23 46.40 44.97
Profit.Factor 1.19 1.10 1.22 1.21 1.20
Avg.Win.Day 111.32 115.32 98.90 117.32 103.48
Med.Win.Day 89.52 94.38 79.32 95.13 87.31
Avg.Losing.Day -104.23 -114.10 -98.19 -112.40 -105.24
Med.Losing.Day -81.34 -92.34 -75.96 -85.69 -82.84
Avg.Daily.PL 9.46 5.28 9.75 10.74 9.62
Med.Daily.PL 11.07 13.74 17.01 18.92 18.71
Std.Dev.Daily.PL.1 138.92 148.13 130.19 150.04 132.82
Ann.Sharpe 1.08 0.57 1.19 1.14 1.15
Max.Drawdown -2298.32 -3445.56 -2017.06 -2764.34 -2071.61
Profit.To.Max.Draw 5.02 1.73 6.28 4.42 5.81
Avg.WinLoss.Ratio 1.07 1.01 1.01 1.04 0.98
Med.WinLoss.Ratio 1.10 1.02 1.04 1.11 1.05
Max.Equity 12708.66 6336.41 13177.76 12221.36 12640.57
Min.Equity -272.68 -307.36 -331.04 0.00 -57.47
End.Equity 11548.79 5965.14 12676.51 12221.36 12044.63
EWY EWZ EZU IEF IGE
Total.Net.Profit 10513.27 14496.80 11233.90 13370.63 12428.65
Total.Days 1297.00 1351.00 1282.00 1186.00 1362.00
Winning.Days 714.00 743.00 705.00 628.00 730.00
Losing.Days 583.00 608.00 577.00 558.00 632.00
Avg.Day.PL 8.11 10.73 8.76 11.27 9.13
Med.Day.PL 15.39 16.83 16.09 13.04 12.81
Largest.Winner 461.13 661.59 726.99 660.63 666.40
Largest.Loser -819.21 -837.40 -1254.82 -555.37 -643.72
Gross.Profits 77069.26 77329.78 74286.39 79557.53 81524.20
Gross.Losses -66555.99 -62832.98 -63052.49 -66186.90 -69095.55
Std.Dev.Daily.PL 146.05 135.63 142.76 158.58 142.55
Percent.Positive 55.05 55.00 54.99 52.95 53.60
Percent.Negative 44.95 45.00 45.01 47.05 46.40
Profit.Factor 1.16 1.23 1.18 1.20 1.18
Avg.Win.Day 107.94 104.08 105.37 126.68 111.68
Med.Win.Day 88.89 81.86 84.23 99.02 92.92
Avg.Losing.Day -114.16 -103.34 -109.28 -118.61 -109.33
Med.Losing.Day -80.09 -78.39 -82.94 -94.81 -90.22
Avg.Daily.PL 8.11 10.73 8.76 11.27 9.13
Med.Daily.PL 15.39 16.83 16.09 13.04 12.81
Std.Dev.Daily.PL.1 146.05 135.63 142.76 158.58 142.55
Ann.Sharpe 0.88 1.26 0.97 1.13 1.02
Max.Drawdown -2462.61 -2188.41 -2310.88 -2650.59 -3045.12
Profit.To.Max.Draw 4.27 6.62 4.86 5.04 4.08
Avg.WinLoss.Ratio 0.95 1.01 0.96 1.07 1.02
Med.WinLoss.Ratio 1.11 1.04 1.02 1.04 1.03
Max.Equity 10513.27 14760.11 12629.07 14339.37 12428.65
Min.Equity -339.01 -214.04 -203.63 -278.08 -268.60
End.Equity 10513.27 14496.80 11233.90 13370.63 12428.65
IYR IYZ LQD RWR SHY
Total.Net.Profit 9702.92 8599.09 13277.24 12090.68 15021.96
Total.Days 1272.00 1232.00 1231.00 1306.00 1350.00
Winning.Days 689.00 656.00 687.00 708.00 738.00
Losing.Days 583.00 576.00 544.00 598.00 612.00
Avg.Day.PL 7.63 6.98 10.79 9.26 11.13
Med.Day.PL 12.50 11.72 14.81 11.46 20.75
Largest.Winner 550.83 601.69 1475.28 648.22 591.25
Largest.Loser -749.58 -803.69 -724.79 -960.12 -988.98
Gross.Profits 68544.80 62158.11 60933.53 74573.82 80464.45
Gross.Losses -58841.88 -53559.03 -47656.28 -62483.14 -65442.49
Std.Dev.Daily.PL 131.85 123.46 119.48 139.10 140.36
Percent.Positive 54.17 53.25 55.81 54.21 54.67
Percent.Negative 45.83 46.75 44.19 45.79 45.33
Profit.Factor 1.16 1.16 1.28 1.19 1.23
Avg.Win.Day 99.48 94.75 88.70 105.33 109.03
Med.Win.Day 82.65 72.40 70.23 83.85 88.76
Avg.Losing.Day -100.93 -92.98 -87.60 -104.49 -106.93
Med.Losing.Day -72.35 -70.97 -69.84 -78.11 -88.06
Avg.Daily.PL 7.63 6.98 10.79 9.26 11.13
Med.Daily.PL 12.50 11.72 14.81 11.46 20.75
Std.Dev.Daily.PL.1 131.85 123.46 119.48 139.10 140.36
Ann.Sharpe 0.92 0.90 1.43 1.06 1.26
Max.Drawdown -5488.96 -2253.39 -1261.10 -5062.88 -2852.91
Profit.To.Max.Draw 1.77 3.82 10.53 2.39 5.27
Avg.WinLoss.Ratio 0.99 1.02 1.01 1.01 1.02
Med.WinLoss.Ratio 1.14 1.02 1.01 1.07 1.01
Max.Equity 13313.44 9225.39 14084.98 15192.88 16570.24
Min.Equity -152.91 -522.27 -347.48 -394.76 -1036.81
End.Equity 9702.92 8599.09 13277.24 12090.68 15021.96
TLT XLB XLE XLF XLI
Total.Net.Profit 7117.62 6227.48 10335.40 -8.45 6351.34
Total.Days 1126.00 1252.00 1336.00 1208.00 1291.00
Winning.Days 576.00 679.00 732.00 626.00 694.00
Losing.Days 550.00 573.00 604.00 582.00 597.00
Avg.Day.PL 6.32 4.97 7.74 -0.01 4.92
Med.Day.PL 7.01 12.34 15.29 6.50 11.06
Largest.Winner 706.10 586.14 525.30 425.95 479.01
Largest.Loser -609.88 -815.74 -501.16 -446.61 -384.75
Gross.Profits 70845.43 64778.65 73739.30 55919.96 61941.72
Gross.Losses -63727.80 -58551.17 -63403.90 -55928.41 -55590.37
Std.Dev.Daily.PL 158.57 130.49 131.97 122.51 116.99
Percent.Positive 51.15 54.23 54.79 51.82 53.76
Percent.Negative 48.85 45.77 45.21 48.18 46.24
Profit.Factor 1.11 1.11 1.16 1.00 1.11
Avg.Win.Day 123.00 95.40 100.74 89.33 89.25
Med.Win.Day 93.07 72.97 79.85 66.21 73.41
Avg.Losing.Day -115.87 -102.18 -104.97 -96.10 -93.12
Med.Losing.Day -89.17 -77.13 -79.13 -69.41 -72.87
Avg.Daily.PL 6.32 4.97 7.74 -0.01 4.92
Med.Daily.PL 7.01 12.34 15.29 6.50 11.06
Std.Dev.Daily.PL.1 158.57 130.49 131.97 122.51 116.99
Ann.Sharpe 0.63 0.61 0.93 0.00 0.67
Max.Drawdown -4938.54 -3692.51 -2780.65 -5704.14 -3013.95
Profit.To.Max.Draw 1.44 1.69 3.72 0.00 2.11
Avg.WinLoss.Ratio 1.06 0.93 0.96 0.93 0.96
Med.WinLoss.Ratio 1.04 0.95 1.01 0.95 1.01
Max.Equity 9318.18 6780.72 10335.40 4191.68 6357.94
Min.Equity -693.51 -213.25 -557.67 -1512.46 -795.23
End.Equity 7117.62 6227.48 10335.40 -8.45 6351.34
XLK XLP XLU XLV XLY
Total.Net.Profit 2940.29 2543.61 7904.42 3189.25 6727.03
Total.Days 1210.00 1326.00 1322.00 1153.00 1179.00
Winning.Days 664.00 704.00 710.00 593.00 611.00
Losing.Days 546.00 622.00 612.00 560.00 568.00
Avg.Day.PL 2.43 1.92 5.98 2.77 5.71
Med.Day.PL 14.64 11.03 12.12 5.31 8.48
Largest.Winner 437.09 537.52 546.32 453.96 450.42
Largest.Loser -765.80 -750.98 -855.10 -726.49 -447.69
Gross.Profits 57610.32 62334.98 61795.49 53165.92 58852.52
Gross.Losses -54670.02 -59791.38 -53891.07 -49976.67 -52125.49
Std.Dev.Daily.PL 122.10 118.49 115.44 117.37 120.29
Percent.Positive 54.88 53.09 53.71 51.43 51.82
Percent.Negative 45.12 46.91 46.29 48.57 48.18
Profit.Factor 1.05 1.04 1.15 1.06 1.13
Avg.Win.Day 86.76 88.54 87.04 89.66 96.32
Med.Win.Day 71.15 73.84 70.10 72.61 78.75
Avg.Losing.Day -100.13 -96.13 -88.06 -89.24 -91.77
Med.Losing.Day -72.57 -74.82 -65.52 -71.56 -70.88
Avg.Daily.PL 2.43 1.92 5.98 2.77 5.71
Med.Daily.PL 14.64 11.03 12.12 5.31 8.48
Std.Dev.Daily.PL.1 122.10 118.49 115.44 117.37 120.29
Ann.Sharpe 0.32 0.26 0.82 0.37 0.75
Max.Drawdown -3074.10 -4531.59 -2545.84 -4623.78 -4041.34
Profit.To.Max.Draw 0.96 0.56 3.10 0.69 1.66
Avg.WinLoss.Ratio 0.87 0.92 0.99 1.00 1.05
Med.WinLoss.Ratio 0.98 0.99 1.07 1.01 1.11
Max.Equity 2981.10 2993.23 8632.88 3902.68 6838.89
Min.Equity -1716.68 -1538.36 -165.00 -1213.50 -310.63
End.Equity 2940.29 2543.61 7904.42 3189.25 6727.03
Now, I’d like to introduce some new analytics found in my IKTrading package–namely, trade duration statistics. This is a simple little function that breaks down the trades by duration, in aggregate, winners, and losers, using the usual five-number summary and the mean time. It’s programmed under the assumption that the units are days. Once you start drilling into more frequent trading, one would likely need a bit more refined analysis. However, as most freely available data occurs at the daily frequency, this function should be sufficient for most analyses.
Here is the input and output for this strategy:
durStats <- durationStatistics(Portfolio=portfolio.st, Symbols=sort(symbols))
print(t(durStats))
EFA EPP EWA EWC EWG EWH EWJ EWS EWT EWU EWY EWZ EZU IEF IGE IYR
Min 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Q1 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 3
Med 6 6 5 7 6 4 5 6 6 6 6 6 6 4 6 6
Mean 12 14 13 16 14 12 12 13 16 15 13 13 12 15 14 13
Q3 14 15 14 17 13 12 11 14 18 14 15 14 13 17 14 12
Max 119 132 135 122 126 185 130 139 106 132 105 95 131 144 125 128
WMin 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1
WQ1 9 7 3 8 3 2 2 6 3 6 5 7 5 6 9 7
WMed 14 14 14 18 12 11 8 13 14 14 13 14 13 17 19 15
WMean 22 25 22 28 24 21 20 23 24 27 21 24 23 28 30 28
WQ3 20 28 26 34 25 20 25 23 38 28 27 37 22 38 42 33
WMax 119 132 135 122 126 185 130 139 106 132 105 95 131 144 125 128
LMin 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
LQ1 1 1 1 2 1 2 2 1 1 1 1 1 1 1 1 2
LMed 3 4 3 4 3 3 3 3 3 3 3 3 3 3 3 4
LMean 4 5 5 6 5 5 6 5 7 4 5 5 5 5 6 5
LQ3 5 7 6 7 7 6 8 6 6 6 6 6 6 5 6 6
LMax 30 22 22 34 28 30 25 41 64 17 28 43 22 40 62 40
IYZ LQD RWR SHY TLT XLB XLE XLF XLI XLK XLP XLU XLV XLY
Min 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Q1 3 1 2 2 2 3 2 2 2 2 2 3 2 3
Med 6 4 5 6 5 7 6 5 7 6 4 7 5 8
Mean 13 15 13 12 12 14 15 13 12 13 13 15 14 15
Q3 13 14 12 14 12 15 16 15 13 13 13 14 13 14
Max 115 151 128 109 90 105 113 130 99 116 117 121 132 123
WMin 1 1 1 1 1 6 1 1 1 1 1 1 1 1
WQ1 6 3 7 6 9 12 9 9 6 6 5 7 9 11
WMed 13 13 14 14 21 16 19 17 12 14 17 16 15 14
WMean 23 27 27 22 29 28 31 27 21 27 29 27 35 28
WQ3 34 28 27 28 43 34 48 32 20 38 45 40 44 28
WMax 115 151 128 109 90 105 113 130 99 116 117 121 132 123
LMin 1 1 1 1 1 1 1 1 1 1 1 1 1 1
LQ1 2 1 1 2 1 1 1 2 1 1 1 1 1 2
LMed 4 2 3 4 3 3 3 3 4 4 4 4 4 4
LMean 5 5 4 5 5 6 6 6 7 5 6 5 6 6
LQ3 6 5 6 6 6 7 7 7 8 7 7 7 7 8
LMax 33 25 32 42 31 36 38 41 36 19 41 39 69 35
From top to bottom in this transposed table (or left to right in the original), we have aggregate trade duration statistics, the same statistics on winners, and finally, losers. This paints a picture of this current strategy as having a profile of a classic trend follower: let your winners run, and cut your losses. Or, to set it to a higher standard, the occasional winner at the price of plenty of small whipsaws, with the occasional long-duration loser. Note that this loser may not have been a loser the entire time–it could very well have been a trade that was going sideways for a long time and finally sunk into negative territory near the end, but it seems that every instrument has had at least one somewhat long-running trade that wound up losing at least a penny.
On the winning side of the trade, the winning trades stay in the market for long berths, with the best ones riding waves that last for around half a year. Ultimately, this is the appeal of trend following–the idea of just getting in once, and just having the market pay you. The goal of investigating the FRAMA (and potentially other trend indicators), is to try and locate those long profit waves while avoiding the whipsaws, countertrends, and so on.
One other interesting piece of analytics I’m incorporating into this demo is the idea of market exposure–or what percentage of the time that the strategy is actually *in* the market. Here is the code and the results:
#market exposure
tmp <- list()
length(tmp) <- length(symbols)
for(i in 1:nrow(dStats)) {
totalDays <- nrow(get(rownames(dStats)[i]))
mktExposure <- dStats$Total.Days[i]/totalDays
tmp[[i]] <- c(rownames(dStats)[i], round(mktExposure, 3))
}
mktExposure <- data.frame(do.call(rbind, tmp))
colnames(mktExposure) <- c("Symbol","MktExposure")
print(mktExposure)
Essentially, this little piece of code takes advantage of the daily statistics output to compute market exposure. Here’s the output:
Symbol MktExposure 1 EFA 0.635 2 EPP 0.66 3 EWA 0.66 4 EWC 0.643 5 EWG 0.627 6 EWH 0.606 7 EWJ 0.561 8 EWS 0.645 9 EWT 0.565 10 EWU 0.621 11 EWY 0.644 12 EWZ 0.67 13 EZU 0.636 14 IEF 0.589 15 IGE 0.676 16 IYR 0.631 17 IYZ 0.611 18 LQD 0.611 19 RWR 0.648 20 SHY 0.67 21 TLT 0.559 22 XLB 0.621 23 XLE 0.663 24 XLF 0.6 25 XLI 0.641 26 XLK 0.6 27 XLP 0.658 28 XLU 0.656 29 XLV 0.572 30 XLY 0.585
So basically, around 60-66% of the time spent in the market, most of which are short, sporadic, losing trades, with the occasional long winner.
Here’s what the equity curve looks like:
As can be seen during the crisis, this baseline strategy is taking lots of trades…for no reason at all.
And here are the three aggregate portfolio statistics:
> SharpeRatio.annualized(portfRets)
[,1]
Annualized Sharpe Ratio (Rf=0%) 1.334861
> Return.annualized(portfRets)
[,1]
Annualized Return 0.1288973
> maxDrawdown(portfRets)
[1] 0.1562275
The largest drawdown occurs during the crisis, but beyond that, the annualized returns are solid. What I find most impressive is that the annualized Sharpe Ratio over the course of this backtest, even with what seems to be a period of drawdowns that can be removed with what seems to be relative ease (most market timing trend-followers seem to do a decent job of avoiding most of the brunt of the crisis).
And finally, to demonstrate the indicator and investigate areas for improvement, here’s the equity curve of XLF (not XLB this time), since XLF lost eight dollars over the course of the backtest.
One advantage that I think the FRAMA has over the Trend Vigor is that as it is an indicator that’s superimposed directly on the price action, it’s easier to understand visually. (Also, the math is definitely more intuitive.) As we can see from the XLF equity curve, the base strategy presented by ETFHQ could certainly use a confirmatory, slower-moving indicator to keep out counter-trend trading. After all, while the tiny little whipsaw trades are undoubtedly a nuisance, correcting counter-trend trading is a lower-hanging fruit, and would seem to be more profitable in addressing.
Thanks for reading.
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