The last post gave a cursory overview of implementing a basic quantstrat strategy, and an introduction to Dr. Ehlers’s Trend Vigor indicator, with a less than intelligent exit. This post will delve further into this indicator, and how it can be made to act as a long-term trend follower to a short-term momentum trader, to probably anything in between, with a parameter called delta. Dr. Ehlers’s indicators often use some trigonometric math, the rationale of which is based on signal processing theory, and often times, that math uses a user-input parameter denoted by a Greek letter, such as alpha, gamma, delta, and so forth.
Rather than leave these esoteric parameters completely unexplored, out of sheer curiosity, I decided to alter the delta parameter. By tuning the delta parameter, it’s possible to tune how fast Trend Vigor oscillates, and thereby, how fast it judges that newer observations are part of a new trend (but at the same time, how much longer the indicator classifies a trend as ongoing). This would allow a user to tune the Trend Vigor indicator in a similar fashion as other trend following indicators to capture different sorts of market phenomena, such as long term trend-following/filtering, to shorter-term phenomena. On the *downside*, this means that as a user tunes the period and the delta, that he or she could easily overfit.
Furthermore, this blog post is going to make the portfolio analysis portion of the analytics make far more sense than a roughly-sketched, price-weighted equity curve. The results were that the benefits of diversification were…certainly less than expected. This backtest is going to implement an equal-weight asset allocation scheme, which will also showcase that quantstrat can implement custom order-sizing functions. Equal-weight asset allocation schemes can be improved upon, but that’s a discussion for a future time.
The strategy for this blog post is slightly different, as well. In this case, the strategy will use a more intelligent exit, by selling when the indicator crosses under its one-day lagged trigger, and buying not only when the indicator crosses above 1, but also if it should cross over its one-day lagged computation, but still be above 1. This is so that the strategy would stay in what it perceives as a trend, rather than sell and not come back until the computation dipped back below 1 (an arbitrary value, to be sure) and came back up again. The idea for the exit came from one of Dr. Ehlers’s presentations, in which he presented several more trend-following smoothers, some of which are already in the DSTrading package (FRAMA, KAMA, VIDYA which I call VIDA, and the Ehlers filters), and which I’ll visit in the future. The link to the presentation can be found here:
http://www.mesasoftware.com/Seminars/TradeStation%20World%2005.pdf
One last detail to mind is that between the last blog post and this one, I changed the Trend Vigor indicator to backfill any leading NAs as zero, since this is an indicator centered around zero. This will allow the strategy to instantly jump into the middle of a trend, if one was under way the moment the first true value of the indicator was computed.
My custom order-sizing function is found in my IKTrading package, which is my own personal collection of non-Ehlers indicators, miscellaneous tools, custom order-sizing functions, and generally serves as a catch-all for trading ideas I come across that don’t have enough content behind them to warrant a package of their own.
Let’s look at the code of the updated indicator.
First, the updated Trend Vigor indicator:
"TVI" <- function(x, period=20, delta=.2, triggerLag=1, ...) {
if(period!=0) { #static, length-1 period
beta <- cos(2*pi/period)
gamma <- 1/cos(4*pi*delta/period)
alpha <- gamma - sqrt(gamma*gamma-1)
BP <- .5*(1-alpha)*(x-lag(x,2))
BP[1] <- BP[2] <- 0
BP <- filter(BP, c(beta*(1+alpha),-1*alpha),method="recursive")
BP <- xts(BP, order.by=index(x))
signal <- BP - lag(BP, round(period/2))
lead <- 1.4*(BP-lag(BP, round(period/4)))
BP2 <- BP*BP
LBP2 <- lag(BP2, round(period/4))
power <- runSum(BP2, period)+runSum(LBP2, period)
RMS <- sqrt(power/period)
PtoP <- 2*sqrt(2)*RMS
a1 <- exp(-sqrt(2)*pi/period)
b1 <- 2*a1*cos(sqrt(2)*pi/period)
coef2 <- b1
coef3 <- -a1*a1
coef1 <- 1-coef2-coef3
trend <- coef1*(x-lag(x, period))
trend[is.na(trend)] <- 0
trend <- filter(trend, c(coef2, coef3), method="recursive")
trend <- xts(trend, order.by=index(x))
vigor <- trend/PtoP
vigor[vigor > 2] <- 2
vigor[vigor < -2] <- -2
vigor[is.na(vigor)] <- 0
trigger <- lag(vigor, triggerLag)
out <- cbind(vigor, signal, lead, trigger)
colnames(out) <- c("vigor", "signal", "lead", "trigger")
return(out)
} else {
stop("Dynamic period computation not implemented yet.")
#TODO -- DYNAMIC PERIOD TREND VIGOR
}
}
Delta is a parameter involved in an involved trigonometric calculation, lending to the idea that there may be some sort of circular relationship with delta, rather than simply a “trend sensitivity” as I described. That stated, considering that the default value that Dr. Ehlers used was .2, it implies that the parameter should probably be held between 0 and 1. Once beyond that, there’s no guarantee that the algorithm even runs (at some point, it will just make later computations come out as NaNs).
Next, I’d like to introduce a couple of functions from my IKTrading package.
sigAND <- function(label, data=mktdata, columns, cross = FALSE) {
ret_sig = NULL
colNums <- rep(0, length(columns))
for(i in 1:length(columns)) {
colNums[i] <- match.names(columns[i], colnames(data))
}
ret_sig <- data[, colNums[1]]
for(i in 2:length(colNums)) {
ret_sig <- ret_sig & data[, colNums[i]]
}
ret_sig <- ret_sig*1
if (isTRUE(cross))
ret_sig <- diff(ret_sig) == 1
colnames(ret_sig) <- label
return(ret_sig)
}
osMaxDollar <- function(data, timestamp, orderqty, ordertype, orderside,
portfolio, symbol, prefer="Open", tradeSize,
maxSize, integerQty=TRUE,
...) {
pos <- getPosQty(portfolio, symbol, timestamp)
if(prefer=="Close") {
price <- as.numeric(Cl(mktdata[timestamp,]))
} else {
price <- as.numeric(Op(mktdata[timestamp,]))
}
posVal <- pos*price
if (orderside=="short") {
dollarsToTransact <- max(tradeSize, maxSize-posVal)
#If our position is profitable, we don't want to cover needlessly.
if(dollarsToTransact > 0) {dollarsToTransact=0}
} else {
dollarsToTransact <- min(tradeSize, maxSize-posVal)
#If our position is profitable, we don't want to sell needlessly.
if(dollarsToTransact < 0) {dollarsToTransact=0}
}
qty <- dollarsToTransact/price
if(integerQty) {
qty <- trunc(qty)
}
return(qty)
}
The first function is a basic AND operator for signals in quantstrat. While quantstrat itself has a signal function called sigFormula, I myself am not exactly a fan of it. The second function, however, is a bit more innovative, in that it allows a strategy to control positions by their total current dollar value. What it doesn’t do, however, is remember the initial dollar value of a position. That is, if you invested $10,000, with a limit of $20,000 in a position, and your initial position went to $11,000, this function would only allow up to another $9,000 worth of the instrument to be ordered. Negative quantities should be used for shorting. That is, if the goal is to short a security, rather than input 20000 as the maxSize and 10000 as the tradeSize, the parameters should be -20000 and -10000, respectively.
Again, the order sizing function takes into account the value of the position at the time of a new order, not the original value of the transaction. That is, the function does not do this: “You have an existing position that you entered into at some previous date, and your position then was $10,000, but now it’s $15,000, but I’ll order another $10,000 anyway”. The function currently does this: “You have a position with a current market value of $15,000. You want to add $10,000 to your position, but have a limit of $20,000. I’ll order the nearest integer quantity to the difference ($5,000).”
Moving on, here’s the modified strategy.
require(DSTrading)
require(IKTrading)
require(quantstrat)
#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 <- "TVI_TF_2"
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 (trigger lag unchanged, defaulted at 1)
delta=.2
period=100
#indicators
add.indicator(strategy.st, name="TVI", arguments=list(x=quote(Cl(mktdata)),
period=period, delta=delta), label="TVI")
#signals
add.signal(strategy.st, name="sigThreshold",
arguments=list(threshold=1, column="vigor.TVI",
relationship="gte", cross=FALSE),
label="TVIgtThresh")
add.signal(strategy.st, name="sigComparison",
arguments=list(columns=c("vigor.TVI","trigger.TVI"),
relationship="gt"),
label="TVIgtLag")
add.signal(strategy.st, name="sigAND",
arguments=list(columns=c("TVIgtThresh","TVIgtLag"),
cross=TRUE),
label="longEntry")
add.signal(strategy.st, name="sigCrossover",
arguments=list(columns=c("vigor.TVI","trigger.TVI"),
relationship="lt"),
label="longExit")
#rules
add.rule(strategy.st, name="ruleSignal",
arguments=list(sigcol="longEntry", sigval=TRUE, orderqty=100,
ordertype="market", orderside="long",
replace=FALSE, prefer="Open", osFUN=osMaxDollar,
tradeSize=10000, maxSize=10000),
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)
For the moment, we’re going to go with the previous settings of delta = .2, and period = 100, but this time, using an order size of the nearest integer quantity that $10,000 can buy of that particular security. Also, we’re going to exit when the indicator shifts from moving up or flat (if it’s at 2), to downward, and buying whenever it shifts from moving downward to moving upward (but still has a value above 1). Also, note that now, there is an initial equity allocation, which will allow for the computation of portfolio returns.
Here are the results.
Trade Stats:
#tradeStats tStats <- tradeStats(Portfolios = portfolio.st, use="trades", inclZeroDays=FALSE) tStats[,4:ncol(tStats)] <- round(tStats[,4:ncol(tStats)], 2) print(data.frame(t(tStats[,-c(1,2)])))
EFA EPP EWA EWC EWG
Num.Txns 21.00 15.00 27.00 37.00 17.00
Num.Trades 11.00 8.00 14.00 19.00 9.00
Net.Trading.PL 3389.91 6323.15 6933.26 2213.97 4983.35
Avg.Trade.PL 308.17 790.39 495.23 116.52 553.71
Med.Trade.PL 298.45 549.42 107.35 110.98 206.57
Largest.Winner 869.60 2507.07 3410.61 1607.61 2600.90
Largest.Loser -297.25 -675.35 -452.79 -1191.14 -343.19
Gross.Profits 4073.17 7327.60 8446.23 5734.53 5847.80
Gross.Losses -683.26 -1004.45 -1512.97 -3520.55 -864.45
Std.Dev.Trade.PL 425.12 1189.75 1118.82 648.91 957.64
Percent.Positive 72.73 62.50 57.14 63.16 66.67
Percent.Negative 27.27 37.50 42.86 36.84 33.33
Profit.Factor 5.96 7.30 5.58 1.63 6.76
Avg.Win.Trade 509.15 1465.52 1055.78 477.88 974.63
Med.Win.Trade 485.27 1680.62 448.04 313.63 747.17
Avg.Losing.Trade -227.75 -334.82 -252.16 -502.94 -288.15
Med.Losing.Trade -266.17 -184.29 -220.96 -440.34 -274.72
Avg.Daily.PL 323.18 923.99 490.48 82.59 657.26
Med.Daily.PL 305.15 1057.21 54.49 100.34 465.90
Std.Dev.Daily.PL 445.03 1218.54 1164.36 650.14 968.40
Ann.Sharpe 11.53 12.04 6.69 2.02 10.77
Max.Drawdown -1730.57 -2428.18 -2827.76 -3214.22 -2070.43
Profit.To.Max.Draw 1.96 2.60 2.45 0.69 2.41
Avg.WinLoss.Ratio 2.24 4.38 4.19 0.95 3.38
Med.WinLoss.Ratio 1.82 9.12 2.03 0.71 2.72
Max.Equity 3785.99 8030.74 7734.21 4215.37 5775.50
Min.Equity -4.60 -186.62 -399.56 -272.20 -97.78
End.Equity 3389.91 6323.15 6933.26 2213.97 4983.35
EWH EWJ EWS EWT EWU
Num.Txns 17.00 19.00 21.00 23.00 24.00
Num.Trades 9.00 10.00 11.00 12.00 12.00
Net.Trading.PL 6281.71 1861.09 8115.03 1920.39 1113.36
Avg.Trade.PL 697.97 186.11 737.73 160.03 92.78
Med.Trade.PL 760.09 18.58 312.10 -180.82 -0.03
Largest.Winner 2223.08 2555.03 2736.35 3078.42 1243.53
Largest.Loser -496.03 -1392.37 -531.77 -1219.88 -1009.85
Gross.Profits 7214.77 4666.47 9381.95 6413.88 3747.87
Gross.Losses -933.06 -2805.38 -1266.92 -4493.49 -2634.51
Std.Dev.Trade.PL 959.96 1123.51 1178.37 1280.43 695.45
Percent.Positive 66.67 60.00 63.64 33.33 50.00
Percent.Negative 33.33 40.00 36.36 66.67 50.00
Profit.Factor 7.73 1.66 7.41 1.43 1.42
Avg.Win.Trade 1202.46 777.75 1340.28 1603.47 624.64
Med.Win.Trade 1046.89 314.63 1388.79 1505.03 541.51
Avg.Losing.Trade -311.02 -701.35 -316.73 -561.69 -439.08
Med.Losing.Trade -434.34 -591.09 -287.07 -478.14 -358.87
Avg.Daily.PL 785.55 142.07 780.29 69.58 92.78
Med.Daily.PL 857.90 6.87 291.84 -320.95 -0.03
Std.Dev.Daily.PL 987.05 1182.47 1233.16 1302.09 695.45
Ann.Sharpe 12.63 1.91 10.04 0.85 2.12
Max.Drawdown -2240.59 -3140.49 -2181.89 -4191.97 -2682.76
Profit.To.Max.Draw 2.80 0.59 3.72 0.46 0.42
Avg.WinLoss.Ratio 3.87 1.11 4.23 2.85 1.42
Med.WinLoss.Ratio 2.41 0.53 4.84 3.15 1.51
Max.Equity 7033.54 3474.11 8268.38 3740.33 3093.03
Min.Equity -101.98 -7.71 -715.49 -451.64 -298.31
End.Equity 6281.71 1861.09 8115.03 1920.39 1113.36
EWY EWZ EZU IEF IGE
Num.Txns 23.00 30.00 18.00 24.00 31.00
Num.Trades 12.00 15.00 9.00 12.00 16.00
Net.Trading.PL 11094.89 11017.62 3581.04 558.64 1425.90
Avg.Trade.PL 924.57 734.51 397.89 46.55 89.12
Med.Trade.PL 517.60 474.34 334.80 -21.76 -12.94
Largest.Winner 3654.10 3907.76 1415.98 544.99 2085.48
Largest.Loser -497.47 -1034.75 -442.68 -286.86 -1357.10
Gross.Profits 12382.75 14795.36 4311.30 1551.73 5886.15
Gross.Losses -1287.86 -3777.74 -730.26 -993.09 -4460.25
Std.Dev.Trade.PL 1396.50 1528.15 616.20 276.42 860.95
Percent.Positive 66.67 60.00 66.67 50.00 50.00
Percent.Negative 33.33 40.00 33.33 50.00 50.00
Profit.Factor 9.61 3.92 5.90 1.56 1.32
Avg.Win.Trade 1547.84 1643.93 718.55 258.62 735.77
Med.Win.Trade 1239.91 1050.52 707.66 245.34 614.69
Avg.Losing.Trade -321.97 -629.62 -243.42 -165.52 -557.53
Med.Losing.Trade -312.32 -654.53 -144.05 -161.22 -478.79
Avg.Daily.PL 946.10 734.51 397.89 46.55 29.55
Med.Daily.PL 347.37 474.34 334.80 -21.76 -95.89
Std.Dev.Daily.PL 1462.58 1528.15 616.20 276.42 856.36
Ann.Sharpe 10.27 7.63 10.25 2.67 0.55
Max.Drawdown -3706.83 -4468.28 -1746.39 -1033.18 -4134.77
Profit.To.Max.Draw 2.99 2.47 2.05 0.54 0.34
Avg.WinLoss.Ratio 4.81 2.61 2.95 1.56 1.32
Med.WinLoss.Ratio 3.97 1.60 4.91 1.52 1.28
Max.Equity 11151.40 14325.48 4132.73 1324.33 3847.27
Min.Equity -512.94 -669.31 -127.83 -496.42 -360.99
End.Equity 11094.89 11017.62 3581.04 558.64 1425.90
IYR IYZ LQD RWR SHY
Num.Txns 20.00 21.00 26.00 18.00 20.00
Num.Trades 10.00 10.00 13.00 9.00 10.00
Net.Trading.PL 3551.70 565.56 278.51 3846.21 1431.72
Avg.Trade.PL 355.17 56.56 21.42 427.36 143.17
Med.Trade.PL 285.85 -171.99 17.47 340.07 28.08
Largest.Winner 1457.62 1789.36 435.59 1465.93 1298.58
Largest.Loser -397.79 -832.16 -516.47 -611.82 -79.25
Gross.Profits 4524.52 2743.13 1145.51 4698.97 1605.02
Gross.Losses -972.82 -2177.58 -867.00 -852.76 -173.30
Std.Dev.Trade.PL 623.44 729.51 238.26 665.66 410.76
Percent.Positive 70.00 30.00 69.23 77.78 60.00
Percent.Negative 30.00 70.00 30.77 22.22 40.00
Profit.Factor 4.65 1.26 1.32 5.51 9.26
Avg.Win.Trade 646.36 914.38 127.28 671.28 267.50
Med.Win.Trade 497.94 737.25 32.03 531.59 55.68
Avg.Losing.Trade -324.27 -311.08 -216.75 -426.38 -43.32
Med.Losing.Trade -298.46 -242.80 -165.48 -426.38 -34.23
Avg.Daily.PL 355.17 -19.08 21.42 427.36 143.17
Med.Daily.PL 285.85 -211.89 17.47 340.07 28.08
Std.Dev.Daily.PL 623.44 730.99 238.26 665.66 410.76
Ann.Sharpe 9.04 -0.41 1.43 10.19 5.53
Max.Drawdown -2117.09 -2239.16 -853.57 -2500.81 -206.62
Profit.To.Max.Draw 1.68 0.25 0.33 1.54 6.93
Avg.WinLoss.Ratio 1.99 2.94 0.59 1.57 6.17
Med.WinLoss.Ratio 1.67 3.04 0.19 1.25 1.63
Max.Equity 4939.41 1994.72 729.12 5125.30 1496.21
Min.Equity 0.00 -803.23 -815.95 0.00 -178.23
End.Equity 3551.70 565.56 278.51 3846.21 1431.72
TLT XLB XLE XLF XLI
Num.Txns 24.00 23.00 35.00 22.00 25.00
Num.Trades 12.00 12.00 18.00 11.00 13.00
Net.Trading.PL 1685.94 6026.21 -721.62 1073.90 3270.62
Avg.Trade.PL 140.49 502.18 -40.09 97.63 251.59
Med.Trade.PL 43.43 511.49 -148.36 53.82 -3.41
Largest.Winner 1244.42 2158.21 2243.05 1390.72 1358.00
Largest.Loser -595.88 -750.40 -1151.80 -659.29 -378.11
Gross.Profits 2725.69 7456.59 4402.78 2346.46 4152.62
Gross.Losses -1039.76 -1430.38 -5124.39 -1272.56 -882.00
Std.Dev.Trade.PL 468.08 819.50 771.46 512.62 512.44
Percent.Positive 58.33 66.67 22.22 63.64 46.15
Percent.Negative 41.67 33.33 77.78 36.36 53.85
Profit.Factor 2.62 5.21 0.86 1.84 4.71
Avg.Win.Trade 389.38 932.07 1100.69 335.21 692.10
Med.Win.Trade 195.01 997.33 857.45 226.90 589.41
Avg.Losing.Trade -207.95 -357.59 -366.03 -318.14 -126.00
Med.Losing.Trade -100.91 -301.05 -193.50 -239.29 -59.12
Avg.Daily.PL 140.49 499.71 -97.77 97.63 241.51
Med.Daily.PL 43.43 511.49 -152.39 53.82 -18.57
Std.Dev.Daily.PL 468.08 887.28 754.14 512.62 533.87
Ann.Sharpe 4.76 8.94 -2.06 3.02 7.18
Max.Drawdown -2020.60 -2343.85 -5364.07 -1497.18 -1480.30
Profit.To.Max.Draw 0.83 2.57 -0.13 0.72 2.21
Avg.WinLoss.Ratio 1.87 2.61 3.01 1.05 5.49
Med.WinLoss.Ratio 1.93 3.31 4.43 0.95 9.97
Max.Equity 3278.94 6034.85 3638.56 2209.75 4344.89
Min.Equity -1033.35 -234.71 -1725.52 -353.34 0.00
End.Equity 1685.94 6026.21 -721.62 1073.90 3270.62
XLK XLP XLU XLV XLY
Num.Txns 25.00 25.00 16.00 21.00 21.00
Num.Trades 13.00 12.00 8.00 11.00 11.00
Net.Trading.PL 2786.08 1691.84 2071.68 329.36 1596.47
Avg.Trade.PL 214.31 140.99 258.96 29.94 145.13
Med.Trade.PL 19.79 27.51 -175.95 -152.51 42.65
Largest.Winner 2153.72 1339.05 2416.22 1492.98 914.92
Largest.Loser -586.52 -1482.72 -1180.81 -511.62 -228.81
Gross.Profits 4276.67 3888.90 4456.67 2179.92 1974.22
Gross.Losses -1490.59 -2197.06 -2385.00 -1850.56 -377.75
Std.Dev.Trade.PL 687.96 747.73 1254.25 552.25 310.09
Percent.Positive 53.85 50.00 37.50 36.36 63.64
Percent.Negative 46.15 50.00 62.50 63.64 36.36
Profit.Factor 2.87 1.77 1.87 1.18 5.23
Avg.Win.Trade 610.95 648.15 1485.56 544.98 282.03
Med.Win.Trade 437.51 594.68 1966.92 301.18 180.59
Avg.Losing.Trade -248.43 -366.18 -477.00 -264.37 -94.44
Med.Losing.Trade -220.94 -132.84 -397.83 -238.91 -73.86
Avg.Daily.PL 195.71 125.23 258.96 10.26 149.62
Med.Daily.PL -14.41 -24.11 -175.95 -187.75 39.16
Std.Dev.Daily.PL 715.13 782.14 1254.25 578.04 326.49
Ann.Sharpe 4.34 2.54 3.28 0.28 7.28
Max.Drawdown -1984.37 -2106.40 -2360.48 -1327.16 -1540.71
Profit.To.Max.Draw 1.40 0.80 0.88 0.25 1.04
Avg.WinLoss.Ratio 2.46 1.77 3.11 2.06 2.99
Med.WinLoss.Ratio 1.98 4.48 4.94 1.26 2.45
Max.Equity 2883.68 2116.10 4325.65 653.11 2920.67
Min.Equity -739.92 -49.59 -1004.33 -1293.46 -393.05
End.Equity 2786.08 1691.84 2071.68 329.36 1596.47
Already, we can see that the equal dollar weighting scheme may not have been the greatest. For instance, the gross profits (that is, total dollars gained, not net profit) vary wildly. For instance, the command:
summary(tStats$Gross.Profit)
Gives the output:
Min. 1st Qu. Median Mean 3rd Qu. Max. 1146 2994 4430 5145 6282 14800
Which means that either a few instruments were just fortunate, or more likely, that $10,000 in different instruments buys different levels of risk. Ideally, with trend following (or any investment strategy, for that matter), order sizing should be done with some measure of volatility in mind. Jeff Swanson of System Trader Success uses position sizing scaled with ATR, for instance.
Moving on, here are the daily stats.
#dailyStats
dStats <- dailyStats(Portfolios = portfolio.st, use="Equity")
rownames(dStats) <- gsub(".DailyEndEq","", rownames(dStats))
print(data.frame(t(dStats)))
EFA EPP EWA EWC EWG
Total.Net.Profit 3389.91 6323.15 6933.26 2213.97 4983.35
Total.Days 715.00 860.00 814.00 720.00 606.00
Winning.Days 397.00 472.00 457.00 394.00 337.00
Losing.Days 318.00 388.00 357.00 326.00 269.00
Avg.Day.PL 4.74 7.35 8.52 3.07 8.22
Med.Day.PL 11.05 13.86 24.93 16.08 17.82
Largest.Winner 349.71 520.81 651.16 383.73 430.91
Largest.Loser -441.39 -658.33 -737.68 -533.75 -511.74
Gross.Profits 29341.17 51407.19 56127.72 35108.16 35014.78
Gross.Losses -25951.26 -45084.04 -49194.46 -32894.18 -30031.43
Std.Dev.Daily.PL 101.85 151.01 173.50 121.89 138.19
Percent.Positive 55.52 54.88 56.14 54.72 55.61
Percent.Negative 44.48 45.12 43.86 45.28 44.39
Profit.Factor 1.13 1.14 1.14 1.07 1.17
Avg.Win.Day 73.91 108.91 122.82 89.11 103.90
Med.Win.Day 62.74 87.40 100.18 76.90 86.18
Avg.Losing.Day -81.61 -116.20 -137.80 -100.90 -111.64
Med.Losing.Day -60.59 -76.11 -98.03 -70.68 -84.29
Avg.Daily.PL 4.74 7.35 8.52 3.07 8.22
Med.Daily.PL 11.05 13.86 24.93 16.08 17.82
Std.Dev.Daily.PL.1 101.85 151.01 173.50 121.89 138.19
Ann.Sharpe 0.74 0.77 0.78 0.40 0.94
Max.Drawdown -1730.57 -2428.18 -2827.76 -3214.22 -2070.43
Profit.To.Max.Draw 1.96 2.60 2.45 0.69 2.41
Avg.WinLoss.Ratio 0.91 0.94 0.89 0.88 0.93
Med.WinLoss.Ratio 1.04 1.15 1.02 1.09 1.02
Max.Equity 3785.99 8030.74 7734.21 4215.37 5775.50
Min.Equity -4.60 -186.62 -399.56 -272.20 -97.78
End.Equity 3389.91 6323.15 6933.26 2213.97 4983.35
EWH EWJ EWS EWT EWU
Total.Net.Profit 6281.71 1861.09 8115.03 1920.39 1113.36
Total.Days 694.00 499.00 853.00 554.00 639.00
Winning.Days 365.00 264.00 469.00 282.00 336.00
Losing.Days 329.00 235.00 384.00 272.00 303.00
Avg.Day.PL 9.05 3.73 9.51 3.47 1.74
Med.Day.PL 13.35 13.75 19.75 8.49 9.84
Largest.Winner 793.54 550.75 760.20 603.79 393.65
Largest.Loser -821.31 -560.56 -967.53 -606.81 -500.81
Gross.Profits 49928.51 29574.53 56989.19 36177.69 28874.40
Gross.Losses -43646.80 -27713.44 -48874.16 -34257.30 -27761.04
Std.Dev.Daily.PL 184.78 146.73 167.87 164.58 114.57
Percent.Positive 52.59 52.91 54.98 50.90 52.58
Percent.Negative 47.41 47.09 45.02 49.10 47.42
Profit.Factor 1.14 1.07 1.17 1.06 1.04
Avg.Win.Day 136.79 112.02 121.51 128.29 85.94
Med.Win.Day 103.78 94.05 89.94 110.89 72.42
Avg.Losing.Day -132.67 -117.93 -127.28 -125.95 -91.62
Med.Losing.Day -93.35 -86.26 -98.90 -88.80 -69.88
Avg.Daily.PL 9.05 3.73 9.51 3.47 1.74
Med.Daily.PL 13.35 13.75 19.75 8.49 9.84
Std.Dev.Daily.PL.1 184.78 146.73 167.87 164.58 114.57
Ann.Sharpe 0.78 0.40 0.90 0.33 0.24
Max.Drawdown -2240.59 -3140.49 -2181.89 -4191.97 -2682.76
Profit.To.Max.Draw 2.80 0.59 3.72 0.46 0.42
Avg.WinLoss.Ratio 1.03 0.95 0.95 1.02 0.94
Med.WinLoss.Ratio 1.11 1.09 0.91 1.25 1.04
Max.Equity 7033.54 3474.11 8268.38 3740.33 3093.03
Min.Equity -101.98 -7.71 -715.49 -451.64 -298.31
End.Equity 6281.71 1861.09 8115.03 1920.39 1113.36
EWY EWZ EZU IEF IGE
Total.Net.Profit 11094.89 11017.62 3581.04 558.64 1425.90
Total.Days 819.00 938.00 625.00 559.00 636.00
Winning.Days 457.00 521.00 348.00 282.00 347.00
Losing.Days 362.00 417.00 277.00 277.00 289.00
Avg.Day.PL 13.55 11.75 5.73 1.00 2.24
Med.Day.PL 28.70 27.38 14.64 1.17 17.39
Largest.Winner 802.78 921.65 339.49 203.78 400.87
Largest.Loser -713.20 -983.67 -593.68 -193.81 -486.10
Gross.Profits 70050.73 98473.12 30606.55 11313.46 36042.39
Gross.Losses -58955.83 -87455.50 -27025.51 -10754.82 -34616.50
Std.Dev.Daily.PL 206.98 261.11 121.98 52.18 138.92
Percent.Positive 55.80 55.54 55.68 50.45 54.56
Percent.Negative 44.20 44.46 44.32 49.55 45.44
Profit.Factor 1.19 1.13 1.13 1.05 1.04
Avg.Win.Day 153.28 189.01 87.95 40.12 103.87
Med.Win.Day 124.00 151.02 70.52 33.60 90.45
Avg.Losing.Day -162.86 -209.73 -97.57 -38.83 -119.78
Med.Losing.Day -112.49 -157.93 -69.01 -28.87 -100.54
Avg.Daily.PL 13.55 11.75 5.73 1.00 2.24
Med.Daily.PL 28.70 27.38 14.64 1.17 17.39
Std.Dev.Daily.PL.1 206.98 261.11 121.98 52.18 138.92
Ann.Sharpe 1.04 0.71 0.75 0.30 0.26
Max.Drawdown -3706.83 -4468.28 -1746.39 -1033.18 -4134.77
Profit.To.Max.Draw 2.99 2.47 2.05 0.54 0.34
Avg.WinLoss.Ratio 0.94 0.90 0.90 1.03 0.87
Med.WinLoss.Ratio 1.10 0.96 1.02 1.16 0.90
Max.Equity 11151.40 14325.48 4132.73 1324.33 3847.27
Min.Equity -512.94 -669.31 -127.83 -496.42 -360.99
End.Equity 11094.89 11017.62 3581.04 558.64 1425.90
IYR IYZ LQD RWR SHY
Total.Net.Profit 3551.70 565.56 278.51 3846.21 1431.72
Total.Days 734.00 573.00 652.00 739.00 1113.00
Winning.Days 403.00 294.00 346.00 400.00 621.00
Losing.Days 331.00 279.00 306.00 339.00 492.00
Avg.Day.PL 4.84 0.99 0.43 5.20 1.29
Med.Day.PL 14.36 3.93 3.56 12.15 1.30
Largest.Winner 670.92 284.62 121.85 697.50 47.06
Largest.Loser -589.08 -417.80 -158.88 -604.38 -56.73
Gross.Profits 38230.24 20613.93 9963.95 39597.03 5662.04
Gross.Losses -34678.54 -20048.37 -9685.44 -35750.82 -4230.32
Std.Dev.Daily.PL 137.96 93.19 39.22 142.32 11.76
Percent.Positive 54.90 51.31 53.07 54.13 55.80
Percent.Negative 45.10 48.69 46.93 45.87 44.20
Profit.Factor 1.10 1.03 1.03 1.11 1.34
Avg.Win.Day 94.86 70.12 28.80 98.99 9.12
Med.Win.Day 78.84 57.86 23.58 76.99 7.16
Avg.Losing.Day -104.77 -71.86 -31.65 -105.46 -8.60
Med.Losing.Day -71.21 -51.15 -23.52 -73.72 -6.71
Avg.Daily.PL 4.84 0.99 0.43 5.20 1.29
Med.Daily.PL 14.36 3.93 3.56 12.15 1.30
Std.Dev.Daily.PL.1 137.96 93.19 39.22 142.32 11.76
Ann.Sharpe 0.56 0.17 0.17 0.58 1.74
Max.Drawdown -2117.09 -2239.16 -853.57 -2500.81 -206.62
Profit.To.Max.Draw 1.68 0.25 0.33 1.54 6.93
Avg.WinLoss.Ratio 0.91 0.98 0.91 0.94 1.06
Med.WinLoss.Ratio 1.11 1.13 1.00 1.04 1.07
Max.Equity 4939.41 1994.72 729.12 5125.30 1496.21
Min.Equity 0.00 -803.23 -815.95 0.00 -178.23
End.Equity 3551.70 565.56 278.51 3846.21 1431.72
TLT XLB XLE XLF XLI
Total.Net.Profit 1685.94 6026.21 -721.62 1073.90 3270.62
Total.Days 561.00 696.00 577.00 413.00 646.00
Winning.Days 291.00 389.00 305.00 211.00 355.00
Losing.Days 270.00 307.00 272.00 202.00 291.00
Avg.Day.PL 3.01 8.66 -1.25 2.60 5.06
Med.Day.PL 7.24 18.15 11.98 3.59 9.82
Largest.Winner 532.71 409.39 497.44 532.50 576.04
Largest.Loser -377.39 -446.88 -494.46 -631.42 -442.08
Gross.Profits 21279.66 36728.98 33683.15 16124.85 26384.16
Gross.Losses -19593.73 -30702.77 -34404.77 -15050.95 -23113.53
Std.Dev.Daily.PL 100.15 125.48 149.29 112.73 102.81
Percent.Positive 51.87 55.89 52.86 51.09 54.95
Percent.Negative 48.13 44.11 47.14 48.91 45.05
Profit.Factor 1.09 1.20 0.98 1.07 1.14
Avg.Win.Day 73.13 94.42 110.44 76.42 74.32
Med.Win.Day 50.91 80.16 93.17 50.84 64.46
Avg.Losing.Day -72.57 -100.01 -126.49 -74.51 -79.43
Med.Losing.Day -57.64 -71.25 -96.00 -47.78 -55.28
Avg.Daily.PL 3.01 8.66 -1.25 2.60 5.06
Med.Daily.PL 7.24 18.15 11.98 3.59 9.82
Std.Dev.Daily.PL.1 100.15 125.48 149.29 112.73 102.81
Ann.Sharpe 0.48 1.10 -0.13 0.37 0.78
Max.Drawdown -2020.60 -2343.85 -5364.07 -1497.18 -1480.30
Profit.To.Max.Draw 0.83 2.57 -0.13 0.72 2.21
Avg.WinLoss.Ratio 1.01 0.94 0.87 1.03 0.94
Med.WinLoss.Ratio 0.88 1.13 0.97 1.06 1.17
Max.Equity 3278.94 6034.85 3638.56 2209.75 4344.89
Min.Equity -1033.35 -234.71 -1725.52 -353.34 0.00
End.Equity 1685.94 6026.21 -721.62 1073.90 3270.62
XLK XLP XLU XLV XLY
Total.Net.Profit 2786.08 1691.84 2071.68 329.36 1596.47
Total.Days 608.00 693.00 745.00 430.00 538.00
Winning.Days 339.00 378.00 407.00 214.00 283.00
Losing.Days 269.00 315.00 338.00 216.00 255.00
Avg.Day.PL 4.58 2.44 2.78 0.77 2.97
Med.Day.PL 14.76 8.42 11.72 -3.08 9.24
Largest.Winner 370.61 231.60 314.64 274.83 542.64
Largest.Loser -434.61 -664.12 -425.69 -281.88 -410.21
Gross.Profits 27166.46 18243.42 29482.80 12726.07 21293.42
Gross.Losses -24380.38 -16551.58 -27411.12 -12396.71 -19696.96
Std.Dev.Daily.PL 111.27 67.51 101.03 75.55 103.78
Percent.Positive 55.76 54.55 54.63 49.77 52.60
Percent.Negative 44.24 45.45 45.37 50.23 47.40
Profit.Factor 1.11 1.10 1.08 1.03 1.08
Avg.Win.Day 80.14 48.26 72.44 59.47 75.24
Med.Win.Day 59.85 41.83 59.86 46.78 59.84
Avg.Losing.Day -90.63 -52.54 -81.10 -57.39 -77.24
Med.Losing.Day -64.53 -40.45 -55.63 -45.04 -50.75
Avg.Daily.PL 4.58 2.44 2.78 0.77 2.97
Med.Daily.PL 14.76 8.42 11.72 -3.08 9.24
Std.Dev.Daily.PL.1 111.27 67.51 101.03 75.55 103.78
Ann.Sharpe 0.65 0.57 0.44 0.16 0.45
Max.Drawdown -1984.37 -2106.40 -2360.48 -1327.16 -1540.71
Profit.To.Max.Draw 1.40 0.80 0.88 0.25 1.04
Avg.WinLoss.Ratio 0.88 0.92 0.89 1.04 0.97
Med.WinLoss.Ratio 0.93 1.03 1.08 1.04 1.18
Max.Equity 2883.68 2116.10 4325.65 653.11 2920.67
Min.Equity -739.92 -49.59 -1004.33 -1293.46 -393.05
End.Equity 2786.08 1691.84 2071.68 329.36 1596.47
This leads to the following cash Sharpe ratio:
#portfolio cash PL portPL <- .blotter$portfolio.TVI_TF_2$summary$Net.Trading.PL #Cash Sharpe (SharpeRatio.annualized(portPL, geometric=FALSE))
Net.Trading.PL
Annualized Sharpe Ratio (Rf=0%) 0.611745
This is the resulting equity curve, compared to SPY.
instRets <- PortfReturns(account.st)
portfRets <- xts(rowMeans(instRets)*ncol(instRets), order.by=index(instRets))
cumPortfRets <- cumprod(1+portfRets)-1
firstNonZeroDay <- index(portfRets)[min(which(portfRets!=0))]
getSymbols("SPY", from=firstNonZeroDay, to="2010-12-31")
SPYrets <- diff(log(Cl(SPY)))[-1]
cumSPYrets <- cumprod(1+SPYrets)-1
comparison <- cbind(cumPortfRets, cumSPYrets)
colnames(comparison) <- c("strategy", "SPY")
chart.TimeSeries(comparison, legend.loc = "topleft",
main=paste0("Period=", period, ", Delta=",delta))
Here are the Sharpe based on returns, annualized returns, and max drawdown.
> SharpeRatio.annualized(portfRets)
[,1]
Annualized Sharpe Ratio (Rf=0%) 0.5891719
> Return.annualized(portfRets)
[,1]
Annualized Return 0.04025855
> maxDrawdown(portfRets)
[1] 0.0979138
Essentially, 4% annualized return for a max drawdown of nearly 10%, with a Sharpe Ratio nowhere close to 1. Definitely not the greatest strategy, but nevertheless, compared to SPY, far less volatile, when comparing equity curves. Once again, however, keep in mind that currently, the Trend Vigor is being used as a market mode indicator, rather than a dedicated trend follower. Keep that in the back of your mind as you look at the value of the actual indicator over time.
chart.Posn(portfolio.st, "XLB") tmp <- TVI(Cl(XLB), period=period, delta=delta, triggerLag=30) add_TA(tmp$vigor) add_TA(tmp$trigger, on=5, col="red")
To note, this is *not* the actual indicator I am using. The indicator for the strategy has triggerLag at 1–that is, the same computation, lagged a day. So I buy when the black line goes from heading downward to heading upward, and sell vice versa. This lags the indicator by 30 days (the red line) just to illustrate the concept for human visibility at that scale.
So, that’s a walkthrough of the default settings strategy.
Now, it’s time to explore the interaction of delta and the period setting.
First, I’m going to try setting delta to .05. In the demo, this is one of the earlier lines, and one of the earlier lines in the blog post (scroll up to see the exact code). Here are the trade and daily statistics after running the demo.
#Trade Statistics
EFA EPP EWA EWC EWG
Num.Txns 15.00 15.00 15.00 17.00 15.00
Num.Trades 8.00 8.00 8.00 9.00 8.00
Net.Trading.PL 8227.33 11063.30 13924.03 10733.98 9025.04
Avg.Trade.PL 1028.42 1382.91 1740.50 1192.66 1128.13
Med.Trade.PL 1019.15 887.77 1708.82 1057.51 589.32
Largest.Winner 2882.94 3910.23 4012.78 2849.73 4583.32
Largest.Loser -595.29 0.00 0.00 -700.52 -1555.36
Gross.Profits 9030.96 11063.30 13924.03 11563.24 10730.64
Gross.Losses -803.63 0.00 0.00 -829.26 -1705.60
Std.Dev.Trade.PL 1225.82 1230.98 1445.19 1273.92 1960.06
Percent.Positive 75.00 100.00 100.00 77.78 75.00
Percent.Negative 25.00 0.00 0.00 22.22 25.00
Profit.Factor 11.24 Inf Inf 13.94 6.29
Avg.Win.Trade 1505.16 1382.91 1740.50 1651.89 1788.44
Med.Win.Trade 1468.87 887.77 1708.82 1865.24 1383.92
Avg.Losing.Trade -401.82 NaN NaN -414.63 -852.80
Med.Losing.Trade -401.82 NA NA -414.63 -852.80
Avg.Daily.PL 1151.85 1511.09 1940.12 1274.24 1283.89
Med.Daily.PL 1300.39 1077.08 2230.28 1461.37 861.35
Std.Dev.Daily.PL 1269.20 1270.64 1436.92 1336.51 2062.93
Ann.Sharpe 14.41 18.88 21.43 15.13 9.88
Max.Drawdown -1973.63 -3221.65 -2703.01 -3330.82 -2252.59
Profit.To.Max.Draw 4.17 3.43 5.15 3.22 4.01
Avg.WinLoss.Ratio 3.75 NaN NaN 3.98 2.10
Med.WinLoss.Ratio 3.66 NA NA 4.50 1.62
Max.Equity 8783.50 11706.29 15425.82 10733.98 9377.84
Min.Equity -165.27 -186.62 -399.56 -272.20 -16.66
End.Equity 8227.33 11063.30 13924.03 10733.98 9025.04
EWH EWJ EWS EWT EWU
Num.Txns 17.00 15.00 17.00 23.00 15.00
Num.Trades 9.00 8.00 9.00 12.00 8.00
Net.Trading.PL 8607.81 3989.12 12749.63 1198.79 8737.48
Avg.Trade.PL 956.42 498.64 1416.63 99.90 1092.18
Med.Trade.PL 603.38 145.35 803.77 -126.44 717.13
Largest.Winner 2737.89 3119.88 4604.52 1186.44 3266.73
Largest.Loser 0.00 -897.44 -548.92 -1112.23 -683.09
Gross.Profits 8610.51 5284.21 13298.55 4610.06 9945.34
Gross.Losses -2.70 -1295.09 -548.92 -3411.26 -1207.86
Std.Dev.Trade.PL 1041.04 1245.20 1659.47 855.59 1509.68
Percent.Positive 88.89 62.50 88.89 41.67 75.00
Percent.Negative 11.11 37.50 11.11 58.33 25.00
Profit.Factor 3192.83 4.08 24.23 1.35 8.23
Avg.Win.Trade 1076.31 1056.84 1662.32 922.01 1657.56
Med.Win.Trade 625.45 519.93 1353.14 1032.56 1475.05
Avg.Losing.Trade -2.70 -431.70 -548.92 -487.32 -603.93
Med.Losing.Trade -2.70 -342.50 -548.92 -366.82 -603.93
Avg.Daily.PL 1076.31 495.60 1493.23 -30.81 1205.85
Med.Daily.PL 625.45 7.05 1163.55 -244.67 1005.50
Std.Dev.Daily.PL 1044.39 1344.93 1756.95 761.39 1593.25
Ann.Sharpe 16.36 5.85 13.49 -0.64 12.01
Max.Drawdown -3209.01 -2930.01 -2495.29 -5536.64 -1932.03
Profit.To.Max.Draw 2.68 1.36 5.11 0.22 4.52
Avg.WinLoss.Ratio 399.10 2.45 3.03 1.89 2.74
Med.WinLoss.Ratio 231.92 1.52 2.47 2.81 2.44
Max.Equity 9206.16 6227.40 12909.67 3431.84 9432.62
Min.Equity 0.00 -542.64 -412.24 -2104.80 -253.67
End.Equity 8607.81 3989.12 12749.63 1198.79 8737.48
EWY EWZ EZU IEF IGE
Num.Txns 21.00 12.00 20.00 19.00 29.00
Num.Trades 11.00 6.00 10.00 10.00 15.00
Net.Trading.PL 8265.64 24932.44 6119.14 585.45 9010.26
Avg.Trade.PL 751.42 4155.41 611.91 58.55 600.68
Med.Trade.PL 590.63 3411.21 281.39 56.80 17.71
Largest.Winner 3444.27 11178.58 2767.56 578.57 4768.77
Largest.Loser -1639.42 -1956.40 -1612.20 -452.40 -1044.03
Gross.Profits 11590.14 27007.07 9032.54 1631.70 13257.71
Gross.Losses -3324.50 -2074.63 -2913.40 -1046.25 -4247.45
Std.Dev.Trade.PL 1635.85 5142.41 1467.12 334.39 1601.62
Percent.Positive 54.55 66.67 50.00 50.00 53.33
Percent.Negative 45.45 33.33 50.00 50.00 46.67
Profit.Factor 3.49 13.02 3.10 1.56 3.12
Avg.Win.Trade 1931.69 6751.77 1806.51 326.34 1657.21
Med.Win.Trade 1663.75 6783.34 2240.25 283.77 1170.69
Avg.Losing.Trade -664.90 -1037.32 -582.68 -209.25 -606.78
Med.Losing.Trade -548.58 -1037.32 -380.50 -229.98 -496.26
Avg.Daily.PL 719.50 4155.41 611.91 43.81 582.55
Med.Daily.PL 207.44 3411.21 281.39 -11.57 -18.62
Std.Dev.Daily.PL 1720.73 5142.41 1467.12 351.22 1660.48
Ann.Sharpe 6.64 12.83 6.62 1.98 5.57
Max.Drawdown -4430.88 -8099.04 -2376.14 -1042.38 -3292.00
Profit.To.Max.Draw 1.87 3.08 2.58 0.56 2.74
Avg.WinLoss.Ratio 2.91 6.51 3.10 1.56 2.73
Med.WinLoss.Ratio 3.03 6.54 5.89 1.23 2.36
Max.Equity 9939.98 27860.83 6964.49 1297.25 10608.96
Min.Equity -275.58 -699.79 -119.44 -977.06 -360.99
End.Equity 8265.64 24932.44 6119.14 585.45 9010.26
IYR IYZ LQD RWR SHY
Num.Txns 18.00 23.00 20.00 18.00 17.00
Num.Trades 9.00 12.00 10.00 9.00 9.00
Net.Trading.PL 5152.30 1708.37 130.39 6718.45 1745.26
Avg.Trade.PL 572.48 142.36 13.04 746.49 193.92
Med.Trade.PL 563.22 -120.54 75.65 526.70 23.61
Largest.Winner 2918.00 3024.24 405.72 3621.48 1408.27
Largest.Loser -866.08 -719.83 -437.61 -525.69 -38.96
Gross.Profits 6578.80 4526.67 1234.36 7766.42 1838.06
Gross.Losses -1426.50 -2818.30 -1103.97 -1047.98 -92.81
Std.Dev.Trade.PL 1116.84 1009.69 279.74 1259.65 461.97
Percent.Positive 55.56 33.33 60.00 66.67 66.67
Percent.Negative 44.44 66.67 40.00 33.33 33.33
Profit.Factor 4.61 1.61 1.12 7.41 19.81
Avg.Win.Trade 1315.76 1131.67 205.73 1294.40 306.34
Med.Win.Trade 1065.80 607.86 193.42 935.99 94.33
Avg.Losing.Trade -356.62 -352.29 -275.99 -349.33 -30.94
Med.Losing.Trade -207.69 -356.49 -272.49 -422.60 -37.39
Avg.Daily.PL 572.48 83.84 13.04 746.49 206.09
Med.Daily.PL 563.22 -193.76 75.65 526.70 19.61
Std.Dev.Daily.PL 1116.84 1037.40 279.74 1259.65 492.32
Ann.Sharpe 8.14 1.28 0.74 9.41 6.65
Max.Drawdown -2630.67 -1861.72 -936.63 -2352.97 -256.48
Profit.To.Max.Draw 1.96 0.92 0.14 2.86 6.80
Avg.WinLoss.Ratio 3.69 3.21 0.75 3.71 9.90
Med.WinLoss.Ratio 5.13 1.71 0.71 2.21 2.52
Max.Equity 6254.05 2468.70 536.06 7751.61 1786.95
Min.Equity 0.00 -1795.37 -899.01 0.00 -89.54
End.Equity 5152.30 1708.37 130.39 6718.45 1745.26
TLT XLB XLE XLF XLI
Num.Txns 24.00 21.00 27.00 16.00 15.00
Num.Trades 12.00 11.00 14.00 8.00 8.00
Net.Trading.PL 2066.64 4949.22 12832.20 3832.14 4152.85
Avg.Trade.PL 172.22 449.93 916.59 479.02 519.11
Med.Trade.PL 64.51 299.25 29.49 177.45 432.70
Largest.Winner 1516.76 2465.37 10722.60 2492.20 2076.85
Largest.Loser -799.95 -1213.35 -1470.10 -1011.16 -780.27
Gross.Profits 3385.01 8451.54 16601.75 5130.47 5213.68
Gross.Losses -1318.37 -3502.32 -3769.55 -1298.33 -1060.84
Std.Dev.Trade.PL 571.70 1338.56 3059.14 1099.30 908.57
Percent.Positive 58.33 63.64 57.14 62.50 75.00
Percent.Negative 41.67 36.36 42.86 37.50 25.00
Profit.Factor 2.57 2.41 4.40 3.95 4.91
Avg.Win.Trade 483.57 1207.36 2075.22 1026.09 868.95
Med.Win.Trade 353.25 696.82 520.06 745.78 635.27
Avg.Losing.Trade -263.67 -875.58 -628.26 -432.78 -530.42
Med.Losing.Trade -127.47 -965.22 -502.49 -243.40 -530.42
Avg.Daily.PL 172.22 425.24 897.10 479.02 483.63
Med.Daily.PL 64.51 172.27 25.82 177.45 362.26
Std.Dev.Daily.PL 571.70 1408.32 3183.15 1099.30 975.37
Ann.Sharpe 4.78 4.79 4.47 6.92 7.87
Max.Drawdown -2230.38 -3263.67 -3550.72 -2353.27 -1876.74
Profit.To.Max.Draw 0.93 1.52 3.61 1.63 2.21
Avg.WinLoss.Ratio 1.83 1.38 3.30 2.37 1.64
Med.WinLoss.Ratio 2.77 0.72 1.03 3.06 1.20
Max.Equity 3450.04 6216.57 13284.80 5838.21 5031.19
Min.Equity -1261.84 -116.14 -468.28 -106.64 -134.79
End.Equity 2066.64 4949.22 12832.20 3832.14 4152.85
XLK XLP XLU XLV XLY
Num.Txns 19.00 13.00 15.00 21.00 15.00
Num.Trades 10.00 7.00 8.00 11.00 8.00
Net.Trading.PL 5676.09 3673.84 4611.03 -318.04 5316.38
Avg.Trade.PL 567.61 524.83 576.38 -28.91 664.55
Med.Trade.PL 437.57 170.61 273.18 12.47 254.12
Largest.Winner 3770.88 1614.82 3011.64 619.76 3835.14
Largest.Loser -698.78 -248.32 -966.49 -679.66 -601.28
Gross.Profits 7910.97 3943.62 5906.06 1676.74 6737.00
Gross.Losses -2234.88 -269.78 -1295.04 -1994.78 -1420.62
Std.Dev.Trade.PL 1370.91 704.46 1281.22 417.22 1496.94
Percent.Positive 60.00 71.43 75.00 54.55 62.50
Percent.Negative 40.00 28.57 25.00 45.45 37.50
Profit.Factor 3.54 14.62 4.56 0.84 4.74
Avg.Win.Trade 1318.49 788.72 984.34 279.46 1347.40
Med.Win.Trade 787.39 1043.70 426.32 208.37 600.59
Avg.Losing.Trade -558.72 -134.89 -647.52 -398.96 -473.54
Med.Losing.Trade -581.97 -134.89 -647.52 -424.36 -497.16
Avg.Daily.PL 600.09 583.87 596.95 -48.94 692.34
Med.Daily.PL 599.90 551.34 126.12 -65.24 38.23
Std.Dev.Daily.PL 1449.98 752.49 1382.45 434.18 1614.65
Ann.Sharpe 6.57 12.32 6.85 -1.79 6.81
Max.Drawdown -2163.21 -945.00 -2389.00 -1574.99 -2265.49
Profit.To.Max.Draw 2.62 3.89 1.93 -0.20 2.35
Avg.WinLoss.Ratio 2.36 5.85 1.52 0.70 2.85
Med.WinLoss.Ratio 1.35 7.74 0.66 0.49 1.21
Max.Equity 6522.36 3705.07 5776.84 731.12 7076.43
Min.Equity -206.72 -315.77 -772.21 -1189.32 -55.79
End.Equity 5676.09 3673.84 4611.03 -318.04 5316.38
#Daily Statistics
EFA EPP EWA EWC EWG
Total.Net.Profit 8227.33 11063.30 13924.03 10733.98 9025.04
Total.Days 1007.00 1161.00 1171.00 1131.00 1006.00
Winning.Days 554.00 639.00 661.00 635.00 558.00
Losing.Days 453.00 522.00 510.00 496.00 448.00
Avg.Day.PL 8.17 9.53 11.89 9.49 8.97
Med.Day.PL 12.93 13.50 21.99 24.36 19.33
Largest.Winner 408.21 705.97 644.19 517.86 510.65
Largest.Loser -446.90 -653.65 -726.30 -640.19 -578.28
Gross.Profits 48673.31 74367.84 84153.20 67767.25 62690.85
Gross.Losses -40445.98 -63304.54 -70229.17 -57033.27 -53665.80
Std.Dev.Daily.PL 116.11 164.25 178.88 143.87 150.39
Percent.Positive 55.01 55.04 56.45 56.15 55.47
Percent.Negative 44.99 44.96 43.55 43.85 44.53
Profit.Factor 1.20 1.17 1.20 1.19 1.17
Avg.Win.Day 87.86 116.38 127.31 106.72 112.35
Med.Win.Day 72.86 87.42 100.11 86.51 89.18
Avg.Losing.Day -89.28 -121.27 -137.70 -114.99 -119.79
Med.Losing.Day -66.22 -80.24 -95.53 -82.40 -89.92
Avg.Daily.PL 8.17 9.53 11.89 9.49 8.97
Med.Daily.PL 12.93 13.50 21.99 24.36 19.33
Std.Dev.Daily.PL.1 116.11 164.25 178.88 143.87 150.39
Ann.Sharpe 1.12 0.92 1.06 1.05 0.95
Max.Drawdown -1973.63 -3221.65 -2703.01 -3330.82 -2252.59
Profit.To.Max.Draw 4.17 3.43 5.15 3.22 4.01
Avg.WinLoss.Ratio 0.98 0.96 0.92 0.93 0.94
Med.WinLoss.Ratio 1.10 1.09 1.05 1.05 0.99
Max.Equity 8783.50 11706.29 15425.82 10733.98 9377.84
Min.Equity -165.27 -186.62 -399.56 -272.20 -16.66
End.Equity 8227.33 11063.30 13924.03 10733.98 9025.04
EWH EWJ EWS EWT EWU
Total.Net.Profit 8607.81 3989.12 12749.63 1198.79 8737.48
Total.Days 1012.00 726.00 1146.00 851.00 1014.00
Winning.Days 531.00 379.00 639.00 438.00 554.00
Losing.Days 481.00 347.00 507.00 413.00 460.00
Avg.Day.PL 8.51 5.49 11.13 1.41 8.62
Med.Day.PL 12.53 13.79 21.28 8.92 15.16
Largest.Winner 753.74 517.40 785.37 880.75 462.83
Largest.Loser -902.02 -782.59 -974.26 -1417.30 -590.98
Gross.Profits 72436.39 43880.76 82366.04 58541.90 54123.90
Gross.Losses -63828.58 -39891.64 -69616.41 -57343.10 -45386.42
Std.Dev.Daily.PL 182.08 149.18 181.55 183.18 128.25
Percent.Positive 52.47 52.20 55.76 51.47 54.64
Percent.Negative 47.53 47.80 44.24 48.53 45.36
Profit.Factor 1.13 1.10 1.18 1.02 1.19
Avg.Win.Day 136.42 115.78 128.90 133.66 97.70
Med.Win.Day 104.08 94.55 91.27 108.07 80.81
Avg.Losing.Day -132.70 -114.96 -137.31 -138.85 -98.67
Med.Losing.Day -95.34 -85.90 -104.28 -99.70 -72.84
Avg.Daily.PL 8.51 5.49 11.13 1.41 8.62
Med.Daily.PL 12.53 13.79 21.28 8.92 15.16
Std.Dev.Daily.PL.1 182.08 149.18 181.55 183.18 128.25
Ann.Sharpe 0.74 0.58 0.97 0.12 1.07
Max.Drawdown -3209.01 -2930.01 -2495.29 -5536.64 -1932.03
Profit.To.Max.Draw 2.68 1.36 5.11 0.22 4.52
Avg.WinLoss.Ratio 1.03 1.01 0.94 0.96 0.99
Med.WinLoss.Ratio 1.09 1.10 0.88 1.08 1.11
Max.Equity 9206.16 6227.40 12909.67 3431.84 9432.62
Min.Equity 0.00 -542.64 -412.24 -2104.80 -253.67
End.Equity 8607.81 3989.12 12749.63 1198.79 8737.48
EWY EWZ EZU IEF IGE
Total.Net.Profit 8265.64 24932.44 6119.14 585.45 9010.26
Total.Days 1115.00 1271.00 980.00 874.00 1212.00
Winning.Days 599.00 709.00 539.00 438.00 670.00
Losing.Days 516.00 562.00 441.00 436.00 542.00
Avg.Day.PL 7.41 19.62 6.24 0.67 7.43
Med.Day.PL 18.37 37.21 14.74 0.78 20.63
Largest.Winner 833.96 1516.20 511.25 359.14 456.89
Largest.Loser -757.96 -1676.65 -743.07 -195.28 -600.22
Gross.Profits 96772.35 173737.17 52301.23 17413.21 79833.45
Gross.Losses -88506.71 -148804.74 -46182.09 -16827.76 -70823.19
Std.Dev.Daily.PL 218.24 347.76 134.07 52.43 159.01
Percent.Positive 53.72 55.78 55.00 50.11 55.28
Percent.Negative 46.28 44.22 45.00 49.89 44.72
Profit.Factor 1.09 1.17 1.13 1.03 1.13
Avg.Win.Day 161.56 245.05 97.03 39.76 119.15
Med.Win.Day 131.89 190.69 76.26 32.13 100.58
Avg.Losing.Day -171.52 -264.78 -104.72 -38.60 -130.67
Med.Losing.Day -118.99 -181.70 -73.90 -29.23 -103.79
Avg.Daily.PL 7.41 19.62 6.24 0.67 7.43
Med.Daily.PL 18.37 37.21 14.74 0.78 20.63
Std.Dev.Daily.PL.1 218.24 347.76 134.07 52.43 159.01
Ann.Sharpe 0.54 0.90 0.74 0.20 0.74
Max.Drawdown -4430.88 -8099.04 -2376.14 -1042.38 -3292.00
Profit.To.Max.Draw 1.87 3.08 2.58 0.56 2.74
Avg.WinLoss.Ratio 0.94 0.93 0.93 1.03 0.91
Med.WinLoss.Ratio 1.11 1.05 1.03 1.10 0.97
Max.Equity 9939.98 27860.83 6964.49 1297.25 10608.96
Min.Equity -275.58 -699.79 -119.44 -977.06 -360.99
End.Equity 8265.64 24932.44 6119.14 585.45 9010.26
IYR IYZ LQD RWR SHY
Total.Net.Profit 5152.30 1708.37 130.39 6718.45 1745.26
Total.Days 981.00 948.00 770.00 992.00 1345.00
Winning.Days 536.00 480.00 408.00 538.00 753.00
Losing.Days 445.00 468.00 362.00 454.00 592.00
Avg.Day.PL 5.25 1.80 0.17 6.77 1.30
Med.Day.PL 14.23 3.87 3.36 16.33 1.31
Largest.Winner 670.92 455.49 211.30 697.50 47.38
Largest.Loser -589.08 -439.41 -274.58 -604.38 -57.51
Gross.Profits 53330.41 36851.16 12914.84 56782.80 6920.89
Gross.Losses -48178.11 -35142.78 -12784.45 -50064.35 -5175.63
Std.Dev.Daily.PL 139.95 100.60 44.38 146.67 11.97
Percent.Positive 54.64 50.63 52.99 54.23 55.99
Percent.Negative 45.36 49.37 47.01 45.77 44.01
Profit.Factor 1.11 1.05 1.01 1.13 1.34
Avg.Win.Day 99.50 76.77 31.65 105.54 9.19
Med.Win.Day 81.52 60.01 24.89 84.35 7.19
Avg.Losing.Day -108.27 -75.09 -35.32 -110.27 -8.74
Med.Losing.Day -76.06 -53.60 -27.51 -81.40 -6.81
Avg.Daily.PL 5.25 1.80 0.17 6.77 1.30
Med.Daily.PL 14.23 3.87 3.36 16.33 1.31
Std.Dev.Daily.PL.1 139.95 100.60 44.38 146.67 11.97
Ann.Sharpe 0.60 0.28 0.06 0.73 1.72
Max.Drawdown -2630.67 -1861.72 -936.63 -2352.97 -256.48
Profit.To.Max.Draw 1.96 0.92 0.14 2.86 6.80
Avg.WinLoss.Ratio 0.92 1.02 0.90 0.96 1.05
Med.WinLoss.Ratio 1.07 1.12 0.90 1.04 1.06
Max.Equity 6254.05 2468.70 536.06 7751.61 1786.95
Min.Equity 0.00 -1795.37 -899.01 0.00 -89.54
End.Equity 5152.30 1708.37 130.39 6718.45 1745.26
TLT XLB XLE XLF XLI
Total.Net.Profit 2066.64 4949.22 12832.20 3832.14 4152.85
Total.Days 755.00 1039.00 1154.00 738.00 1001.00
Winning.Days 390.00 569.00 630.00 386.00 544.00
Losing.Days 365.00 470.00 524.00 352.00 457.00
Avg.Day.PL 2.74 4.76 11.12 5.19 4.15
Med.Day.PL 4.68 16.84 23.19 6.77 9.43
Largest.Winner 546.86 543.49 649.18 521.32 567.57
Largest.Loser -387.41 -561.19 -898.57 -695.88 -461.98
Gross.Profits 29206.43 60629.30 91312.60 34177.43 41796.72
Gross.Losses -27139.79 -55680.08 -78480.40 -30345.29 -37643.87
Std.Dev.Daily.PL 102.19 145.68 196.01 128.37 105.23
Percent.Positive 51.66 54.76 54.59 52.30 54.35
Percent.Negative 48.34 45.24 45.41 47.70 45.65
Profit.Factor 1.08 1.09 1.16 1.13 1.11
Avg.Win.Day 74.89 106.55 144.94 88.54 76.83
Med.Win.Day 52.20 90.91 112.15 61.85 62.90
Avg.Losing.Day -74.36 -118.47 -149.77 -86.21 -82.37
Med.Losing.Day -59.22 -87.40 -108.63 -54.35 -59.78
Avg.Daily.PL 2.74 4.76 11.12 5.19 4.15
Med.Daily.PL 4.68 16.84 23.19 6.77 9.43
Std.Dev.Daily.PL.1 102.19 145.68 196.01 128.37 105.23
Ann.Sharpe 0.43 0.52 0.90 0.64 0.63
Max.Drawdown -2230.38 -3263.67 -3550.72 -2353.27 -1876.74
Profit.To.Max.Draw 0.93 1.52 3.61 1.63 2.21
Avg.WinLoss.Ratio 1.01 0.90 0.97 1.03 0.93
Med.WinLoss.Ratio 0.88 1.04 1.03 1.14 1.05
Max.Equity 3450.04 6216.57 13284.80 5838.21 5031.19
Min.Equity -1261.84 -116.14 -468.28 -106.64 -134.79
End.Equity 2066.64 4949.22 12832.20 3832.14 4152.85
XLK XLP XLU XLV XLY
Total.Net.Profit 5676.09 3673.84 4611.03 -318.04 5316.38
Total.Days 964.00 999.00 1024.00 892.00 795.00
Winning.Days 536.00 549.00 562.00 449.00 422.00
Losing.Days 428.00 450.00 462.00 443.00 373.00
Avg.Day.PL 5.89 3.68 4.50 -0.36 6.69
Med.Day.PL 13.65 8.52 11.94 3.04 8.89
Largest.Winner 431.35 298.68 359.25 291.48 741.77
Largest.Loser -462.31 -261.14 -429.41 -319.27 -560.75
Gross.Profits 45283.91 28445.54 41231.21 27231.30 37590.36
Gross.Losses -39607.82 -24771.70 -36620.18 -27549.33 -32273.98
Std.Dev.Daily.PL 117.38 67.41 101.36 79.97 123.15
Percent.Positive 55.60 54.95 54.88 50.34 53.08
Percent.Negative 44.40 45.05 45.12 49.66 46.92
Profit.Factor 1.14 1.15 1.13 0.99 1.16
Avg.Win.Day 84.48 51.81 73.37 60.65 89.08
Med.Win.Day 60.65 42.81 59.91 50.84 67.06
Avg.Losing.Day -92.54 -55.05 -79.26 -62.19 -86.53
Med.Losing.Day -64.97 -44.88 -54.05 -49.00 -56.79
Avg.Daily.PL 5.89 3.68 4.50 -0.36 6.69
Med.Daily.PL 13.65 8.52 11.94 3.04 8.89
Std.Dev.Daily.PL.1 117.38 67.41 101.36 79.97 123.15
Ann.Sharpe 0.80 0.87 0.71 -0.07 0.86
Max.Drawdown -2163.21 -945.00 -2389.00 -1574.99 -2265.49
Profit.To.Max.Draw 2.62 3.89 1.93 -0.20 2.35
Avg.WinLoss.Ratio 0.91 0.94 0.93 0.98 1.03
Med.WinLoss.Ratio 0.93 0.95 1.11 1.04 1.18
Max.Equity 6522.36 3705.07 5776.84 731.12 7076.43
Min.Equity -206.72 -315.77 -772.21 -1189.32 -55.79
End.Equity 5676.09 3673.84 4611.03 -318.04 5316.38
The equity curve (vs. SPY)
This time, while you take on more risk, your returns are definitely better–essentially keeping pace with SPY in its bullish phases while missing the financial crisis (as any decent trend-follower does). That stated, the drawdowns between this strategy and SPY happen at similar times, meaning that given that there are more equity indices than the SPY (as well as bond indices), that position sizing for the strategy can be improved for diversification.
Here are the three portfolio statistics:
> SharpeRatio.annualized(portfRets)
[,1]
Annualized Sharpe Ratio (Rf=0%) 0.7914488
> Return.annualized(portfRets)
[,1]
Annualized Return 0.08098812
> maxDrawdown(portfRets)
[1] 0.1283513
Finally, here’s the new indicator plot, this time with the true lagged indicator plotted.
Notice that the indicator stays at more extreme values more often.
Let’s take this to the limit and set delta to zero.
Here are the trade stats:
EFA EPP EWA EWC EWG
Num.Txns 11.00 9.00 11.00 11.00 11.00
Num.Trades 6.00 5.00 6.00 6.00 6.00
Net.Trading.PL 9095.11 12779.16 14602.67 12673.96 11222.15
Avg.Trade.PL 1515.85 2555.83 2433.78 2112.33 1870.36
Med.Trade.PL 1820.06 2623.33 2709.23 2305.23 1861.94
Largest.Winner 3631.16 4615.15 5833.88 6144.25 3159.37
Largest.Loser -933.65 0.00 -590.11 -1792.36 0.00
Gross.Profits 10028.75 12779.16 15192.78 14466.32 11222.15
Gross.Losses -933.65 0.00 -590.11 -1792.36 0.00
Std.Dev.Trade.PL 1684.91 1513.27 2196.84 2607.66 1142.29
Percent.Positive 83.33 100.00 83.33 83.33 100.00
Percent.Negative 16.67 0.00 16.67 16.67 0.00
Profit.Factor 10.74 Inf 25.75 8.07 Inf
Avg.Win.Trade 2005.75 2555.83 3038.56 2893.26 1870.36
Med.Win.Trade 2479.23 2623.33 2780.49 2762.52 1861.94
Avg.Losing.Trade -933.65 NaN -590.11 -1792.36 NaN
Med.Losing.Trade -933.65 NA -590.11 -1792.36 NA
Avg.Daily.PL 1772.55 3065.78 2764.58 2357.14 2203.82
Med.Daily.PL 2479.23 2874.02 2780.49 2762.52 2359.07
Std.Dev.Daily.PL 1747.70 1148.77 2282.97 2837.32 892.78
Ann.Sharpe 16.10 42.37 19.22 13.19 39.19
Max.Drawdown -2804.25 -3977.43 -4487.98 -4446.67 -3101.41
Profit.To.Max.Draw 3.24 3.21 3.25 2.85 3.62
Avg.WinLoss.Ratio 2.15 NaN 5.15 1.61 NaN
Med.WinLoss.Ratio 2.66 NA 4.71 1.54 NA
Max.Equity 10373.87 14886.32 16959.46 12828.77 12321.51
Min.Equity -165.27 -186.62 -399.56 -272.20 -16.66
End.Equity 9095.11 12779.16 14602.67 12673.96 11222.15
EWH EWJ EWS EWT EWU
Num.Txns 7.00 13.00 9.00 15.00 11.00
Num.Trades 4.00 7.00 5.00 8.00 6.00
Net.Trading.PL 15840.82 5176.40 18882.47 3321.05 8340.94
Avg.Trade.PL 3960.20 739.49 3776.49 415.13 1390.16
Med.Trade.PL 3129.89 641.19 2657.46 125.19 1255.15
Largest.Winner 7545.70 3116.82 11080.06 3111.65 3892.96
Largest.Loser 0.00 -1200.32 -1012.71 -2126.89 -1020.86
Gross.Profits 15840.82 6376.72 19895.19 6644.85 9361.80
Gross.Losses 0.00 -1200.32 -1012.71 -3323.80 -1020.86
Std.Dev.Trade.PL 2449.69 1342.88 4478.92 1657.15 1717.55
Percent.Positive 100.00 85.71 80.00 62.50 83.33
Percent.Negative 0.00 14.29 20.00 37.50 16.67
Profit.Factor Inf 5.31 19.65 2.00 9.17
Avg.Win.Trade 3960.20 1062.79 4973.80 1328.97 1872.36
Med.Win.Trade 3129.89 738.02 3334.30 1366.22 1290.27
Avg.Losing.Trade NaN -1200.32 -1012.71 -1107.93 -1020.86
Med.Losing.Trade NA -1200.32 -1012.71 -811.78 -1020.86
Avg.Daily.PL 4601.83 723.59 4183.99 200.63 1601.16
Med.Daily.PL 3307.58 391.69 3334.30 33.08 1290.27
Std.Dev.Daily.PL 2555.65 1470.34 5063.65 1665.66 1831.27
Ann.Sharpe 28.58 7.81 13.12 1.91 13.88
Max.Drawdown -6279.36 -3186.71 -6357.43 -5074.58 -2806.72
Profit.To.Max.Draw 2.52 1.62 2.97 0.65 2.97
Avg.WinLoss.Ratio NaN 0.89 4.91 1.20 1.83
Med.WinLoss.Ratio NA 0.61 3.29 1.68 1.26
Max.Equity 16555.02 6833.58 19063.41 3473.68 9627.51
Min.Equity -117.59 -396.06 -412.24 -1842.71 -253.67
End.Equity 15840.82 5176.40 18882.47 3321.05 8340.94
EWY EWZ EZU IEF IGE
Num.Txns 11.00 9.00 9.00 17.00 9.00
Num.Trades 6.00 5.00 5.00 9.00 5.00
Net.Trading.PL 16345.10 29677.36 9371.42 835.02 14116.64
Avg.Trade.PL 2724.18 5935.47 1874.28 92.78 2823.33
Med.Trade.PL 1151.79 7224.58 1259.50 -13.70 1578.21
Largest.Winner 7324.66 11173.16 4689.91 934.88 11236.40
Largest.Loser -59.53 0.00 0.00 -243.00 -2370.85
Gross.Profits 16404.63 29677.36 9552.12 1538.80 16487.49
Gross.Losses -59.53 0.00 -180.70 -703.78 -2370.85
Std.Dev.Trade.PL 3043.54 4291.41 1838.25 365.25 5039.93
Percent.Positive 83.33 100.00 80.00 44.44 80.00
Percent.Negative 16.67 0.00 20.00 55.56 20.00
Profit.Factor 275.58 Inf 52.86 2.19 6.95
Avg.Win.Trade 3280.93 5935.47 2388.03 384.70 4121.87
Med.Win.Trade 1208.67 7224.58 1879.94 210.16 1915.33
Avg.Losing.Trade -59.53 NaN -180.70 -140.76 -2370.85
Med.Losing.Trade -59.53 NA -180.70 -206.60 -2370.85
Avg.Daily.PL 3072.41 7399.70 2388.03 81.43 3134.61
Med.Daily.PL 1208.67 7532.93 1879.94 -20.44 1836.44
Std.Dev.Daily.PL 3266.42 3203.41 1657.09 388.77 5763.85
Ann.Sharpe 14.93 36.67 22.88 3.32 8.63
Max.Drawdown -4656.74 -8660.23 -3353.89 -1345.79 -4492.64
Profit.To.Max.Draw 3.51 3.43 2.79 0.62 3.14
Avg.WinLoss.Ratio 55.12 NaN 13.22 2.73 1.74
Med.WinLoss.Ratio 20.30 NA 10.40 1.02 0.81
Max.Equity 16548.01 31682.83 11221.49 1756.16 14420.81
Min.Equity 0.00 -699.79 -119.44 -714.17 -360.99
End.Equity 16345.10 29677.36 9371.42 835.02 14116.64
IYR IYZ LQD RWR SHY
Num.Txns 11.00 13.00 15.00 9.00 9.00
Num.Trades 6.00 7.00 8.00 5.00 5.00
Net.Trading.PL 12860.27 5906.68 2177.09 15725.34 2126.96
Avg.Trade.PL 2143.38 843.81 272.14 3145.07 425.39
Med.Trade.PL 1549.35 -4.31 -9.55 1933.28 265.78
Largest.Winner 2494.86 2704.21 239.07 3664.07 1544.02
Largest.Loser -1003.00 -789.18 -176.30 -664.12 -28.09
Gross.Profits 13863.26 7533.20 2468.60 16389.46 2155.05
Gross.Losses -1003.00 -1626.52 -291.51 -664.12 -28.09
Std.Dev.Trade.PL 2977.41 2061.62 767.56 3956.03 639.74
Percent.Positive 83.33 42.86 37.50 80.00 80.00
Percent.Negative 16.67 57.14 62.50 20.00 20.00
Profit.Factor 13.82 4.63 8.47 24.68 76.71
Avg.Win.Trade 2772.65 2511.07 822.87 4097.37 538.76
Med.Win.Trade 1859.25 2704.21 239.07 2798.67 277.14
Avg.Losing.Trade -1003.00 -406.63 -58.30 -664.12 -28.09
Med.Losing.Trade -1003.00 -416.51 -36.93 -664.12 -28.09
Avg.Daily.PL 1031.33 200.00 4.06 1518.44 459.61
Med.Daily.PL 1239.44 -143.55 -15.28 1536.90 161.27
Std.Dev.Daily.PL 1344.03 1272.26 128.95 1796.50 733.41
Ann.Sharpe 12.18 2.50 0.50 13.42 9.95
Max.Drawdown -4545.72 -3655.24 -1126.20 -4720.58 -258.24
Profit.To.Max.Draw 2.83 1.62 1.93 3.33 8.24
Avg.WinLoss.Ratio 2.76 6.18 14.11 6.17 19.18
Med.WinLoss.Ratio 1.85 6.49 6.47 4.21 9.86
Max.Equity 13193.50 5906.68 2600.28 16148.05 2169.34
Min.Equity 0.00 -1458.57 -750.84 0.00 -62.71
End.Equity 12860.27 5906.68 2177.09 15725.34 2126.96
TLT XLB XLE XLF XLI
Num.Txns 16.00 13.00 9.00 11.00 13.00
Num.Trades 8.00 7.00 5.00 6.00 7.00
Net.Trading.PL -1042.28 8143.08 16350.23 6938.82 8270.94
Avg.Trade.PL -130.28 1163.30 3270.05 1156.47 1181.56
Med.Trade.PL -190.63 1181.00 1463.69 1327.34 915.45
Largest.Winner 442.59 2651.96 12793.77 2912.28 3541.70
Largest.Loser -816.24 -920.78 -2248.45 -681.58 -1047.09
Gross.Profits 1090.18 9063.85 18598.68 7620.40 9318.03
Gross.Losses -2132.46 -920.78 -2248.45 -681.58 -1047.09
Std.Dev.Trade.PL 463.66 1253.96 5680.01 1285.82 1537.81
Percent.Positive 37.50 85.71 80.00 83.33 85.71
Percent.Negative 62.50 14.29 20.00 16.67 14.29
Profit.Factor 0.51 9.84 8.27 11.18 8.90
Avg.Win.Trade 363.39 1510.64 4649.67 1524.08 1553.00
Med.Win.Trade 326.19 1375.19 2343.25 1551.96 1241.86
Avg.Losing.Trade -426.49 -920.78 -2248.45 -681.58 -1047.09
Med.Losing.Trade -297.11 -920.78 -2248.45 -681.58 -1047.09
Avg.Daily.PL -130.28 1160.35 3721.63 1167.22 1225.92
Med.Daily.PL -190.63 1106.96 2170.61 1551.96 1032.03
Std.Dev.Daily.PL 463.66 1373.62 6454.23 1437.28 1679.67
Ann.Sharpe -4.46 13.41 9.15 12.89 11.59
Max.Drawdown -3334.35 -2518.13 -4156.71 -2212.82 -2700.70
Profit.To.Max.Draw -0.31 3.23 3.93 3.14 3.06
Avg.WinLoss.Ratio 0.85 1.64 2.07 2.24 1.48
Med.WinLoss.Ratio 1.10 1.49 1.04 2.28 1.19
Max.Equity 1995.24 9004.95 17110.53 7130.66 9488.70
Min.Equity -1736.55 -116.14 -468.28 -106.64 -134.79
End.Equity -1042.28 8143.08 16350.23 6938.82 8270.94
XLK XLP XLU XLV XLY
Num.Txns 13.00 13.00 11.00 17.00 15.00
Num.Trades 7.00 7.00 6.00 9.00 8.00
Net.Trading.PL 3773.49 5237.29 7443.30 -2400.55 2813.65
Avg.Trade.PL 539.07 748.18 1240.55 -266.73 351.71
Med.Trade.PL 11.43 320.54 164.75 -237.80 -130.81
Largest.Winner 3116.75 2419.39 6111.02 933.17 2821.36
Largest.Loser -871.76 -965.46 -1390.74 -2162.93 -572.05
Gross.Profits 5172.39 6202.75 9530.05 1757.14 4713.91
Gross.Losses -1398.90 -965.46 -2086.75 -4157.69 -1900.26
Std.Dev.Trade.PL 1392.56 1220.14 2826.50 889.12 1191.92
Percent.Positive 57.14 85.71 50.00 44.44 37.50
Percent.Negative 42.86 14.29 50.00 55.56 62.50
Profit.Factor 3.70 6.42 4.57 0.42 2.48
Avg.Win.Trade 1293.10 1033.79 3176.68 439.28 1571.30
Med.Win.Trade 1022.11 725.83 3054.43 341.19 1288.17
Avg.Losing.Trade -466.30 -965.46 -695.58 -831.54 -380.05
Med.Losing.Trade -475.97 -965.46 -660.91 -565.29 -508.62
Avg.Daily.PL 568.92 819.46 1415.74 -317.77 315.61
Med.Daily.PL -19.87 616.89 -35.09 -319.04 -225.91
Std.Dev.Daily.PL 1523.02 1320.53 3123.49 936.31 1282.69
Ann.Sharpe 5.93 9.85 7.20 -5.39 3.91
Max.Drawdown -3680.30 -2095.40 -3243.95 -3650.41 -3721.65
Profit.To.Max.Draw 1.03 2.50 2.29 -0.66 0.76
Avg.WinLoss.Ratio 2.77 1.07 4.57 0.53 4.13
Med.WinLoss.Ratio 2.15 0.75 4.62 0.60 2.53
Max.Equity 4245.23 5269.06 10132.95 318.90 4439.62
Min.Equity -776.77 -244.67 -772.21 -3331.51 -1497.63
End.Equity 3773.49 5237.29 7443.30 -2400.55 2813.65
At this point, profit factors become obscene, and even the aggregate profit factor (sum of all gross profits divided by the negative sum of all gross losses) clocks in above 9, with the average percentage correct being above 70% (mean of the percent positive). In reality, this turns Trend Vigor into an up-or-down classifier (to use some machine-learning terminology), with no-in betweens, as you’ll see in a moment.
Here are the daily stats.
EFA EPP EWA EWC EWG
Total.Net.Profit 9095.11 12779.16 14602.67 12673.96 11222.15
Total.Days 1322.00 1414.00 1412.00 1492.00 1252.00
Winning.Days 725.00 773.00 784.00 829.00 697.00
Losing.Days 597.00 641.00 628.00 663.00 555.00
Avg.Day.PL 6.88 9.04 10.34 8.49 8.96
Med.Day.PL 13.62 14.90 21.27 20.66 19.16
Largest.Winner 568.38 880.27 1041.16 567.09 528.85
Largest.Loser -576.56 -862.67 -975.68 -631.38 -864.63
Gross.Profits 71000.29 97398.68 111477.67 96460.68 80358.74
Gross.Losses -61905.18 -84619.52 -96875.01 -83786.73 -69136.60
Std.Dev.Daily.PL 134.58 178.50 201.37 157.55 158.11
Percent.Positive 54.84 54.67 55.52 55.56 55.67
Percent.Negative 45.16 45.33 44.48 44.44 44.33
Profit.Factor 1.15 1.15 1.15 1.15 1.16
Avg.Win.Day 97.93 126.00 142.19 116.36 115.29
Med.Win.Day 79.54 95.29 109.27 93.87 91.68
Avg.Losing.Day -103.69 -132.01 -154.26 -126.38 -124.57
Med.Losing.Day -72.20 -84.37 -109.70 -93.87 -91.16
Avg.Daily.PL 6.88 9.04 10.34 8.49 8.96
Med.Daily.PL 13.62 14.90 21.27 20.66 19.16
Std.Dev.Daily.PL.1 134.58 178.50 201.37 157.55 158.11
Ann.Sharpe 0.81 0.80 0.82 0.86 0.90
Max.Drawdown -2804.25 -3977.43 -4487.98 -4446.67 -3101.41
Profit.To.Max.Draw 3.24 3.21 3.25 2.85 3.62
Avg.WinLoss.Ratio 0.94 0.95 0.92 0.92 0.93
Med.WinLoss.Ratio 1.10 1.13 1.00 1.00 1.01
Max.Equity 10373.87 14886.32 16959.46 12828.77 12321.51
Min.Equity -165.27 -186.62 -399.56 -272.20 -16.66
End.Equity 9095.11 12779.16 14602.67 12673.96 11222.15
EWH EWJ EWS EWT
Total.Net.Profit 15840.82 5176.40 18882.47 3321.05
Total.Days 1447.00 1100.00 1510.00 1250.00
Winning.Days 762.00 578.00 835.00 639.00
Losing.Days 685.00 522.00 675.00 611.00
Avg.Day.PL 10.95 4.71 12.50 2.66
Med.Day.PL 13.07 14.51 26.15 8.46
Largest.Winner 1319.35 559.95 1304.43 1170.33
Largest.Loser -1338.75 -846.93 -1618.16 -1445.34
Gross.Profits 123714.47 65127.12 133821.56 93059.51
Gross.Losses -107873.66 -59950.72 -114939.08 -89738.46
Std.Dev.Daily.PL 235.97 147.88 241.58 198.13
Percent.Positive 52.66 52.55 55.30 51.12
Percent.Negative 47.34 47.45 44.70 48.88
Profit.Factor 1.15 1.09 1.16 1.04
Avg.Win.Day 162.35 112.68 160.27 145.63
Med.Win.Day 111.04 94.31 112.39 114.48
Avg.Losing.Day -157.48 -114.85 -170.28 -146.87
Med.Losing.Day -101.79 -85.77 -113.32 -109.38
Avg.Daily.PL 10.95 4.71 12.50 2.66
Med.Daily.PL 13.07 14.51 26.15 8.46
Std.Dev.Daily.PL.1 235.97 147.88 241.58 198.13
Ann.Sharpe 0.74 0.51 0.82 0.21
Max.Drawdown -6279.36 -3186.71 -6357.43 -5074.58
Profit.To.Max.Draw 2.52 1.62 2.97 0.65
Avg.WinLoss.Ratio 1.03 0.98 0.94 0.99
Med.WinLoss.Ratio 1.09 1.10 0.99 1.05
Max.Equity 16555.02 6833.58 19063.41 3473.68
Min.Equity -117.59 -396.06 -412.24 -1842.71
End.Equity 15840.82 5176.40 18882.47 3321.05
EWU EWY EWZ EZU
Total.Net.Profit 8340.94 16345.10 29677.36 9371.42
Total.Days 1327.00 1329.00 1456.00 1282.00
Winning.Days 718.00 726.00 809.00 703.00
Losing.Days 609.00 603.00 647.00 579.00
Avg.Day.PL 6.29 12.30 20.38 7.31
Med.Day.PL 15.37 26.80 38.84 15.88
Largest.Winner 591.81 930.95 1552.63 653.02
Largest.Loser -626.26 -921.64 -1664.19 -837.62
Gross.Profits 73312.40 131699.63 211601.85 78062.97
Gross.Losses -64971.45 -115354.53 -181924.49 -68691.55
Std.Dev.Daily.PL 139.76 245.04 368.97 155.45
Percent.Positive 54.11 54.63 55.56 54.84
Percent.Negative 45.89 45.37 44.44 45.16
Profit.Factor 1.13 1.14 1.16 1.14
Avg.Win.Day 102.11 181.40 261.56 111.04
Med.Win.Day 80.81 149.33 208.05 84.24
Avg.Losing.Day -106.69 -191.30 -281.18 -118.64
Med.Losing.Day -74.99 -134.62 -203.45 -78.91
Avg.Daily.PL 6.29 12.30 20.38 7.31
Med.Daily.PL 15.37 26.80 38.84 15.88
Std.Dev.Daily.PL.1 139.76 245.04 368.97 155.45
Ann.Sharpe 0.71 0.80 0.88 0.75
Max.Drawdown -2806.72 -4656.74 -8660.23 -3353.89
Profit.To.Max.Draw 2.97 3.51 3.43 2.79
Avg.WinLoss.Ratio 0.96 0.95 0.93 0.94
Med.WinLoss.Ratio 1.08 1.11 1.02 1.07
Max.Equity 9627.51 16548.01 31682.83 11221.49
Min.Equity -253.67 0.00 -699.79 -119.44
End.Equity 8340.94 16345.10 29677.36 9371.42
IEF IGE IYR IYZ LQD
Total.Net.Profit 835.02 14116.64 12860.27 5906.68 2177.09
Total.Days 1300.00 1557.00 1358.00 1352.00 1353.00
Winning.Days 658.00 847.00 738.00 701.00 724.00
Losing.Days 642.00 710.00 620.00 651.00 629.00
Avg.Day.PL 0.64 9.07 9.47 4.37 1.61
Med.Day.PL 1.17 22.95 13.29 6.22 4.38
Largest.Winner 365.18 848.16 1014.33 478.75 200.55
Largest.Loser -199.68 -1047.33 -840.63 -560.06 -260.62
Gross.Profits 24532.29 132479.70 90821.52 62514.78 23695.57
Gross.Losses -23697.27 -118363.07 -77961.26 -56608.11 -21518.48
Std.Dev.Daily.PL 49.69 213.61 175.83 118.94 44.01
Percent.Positive 50.62 54.40 54.34 51.85 53.51
Percent.Negative 49.38 45.60 45.66 48.15 46.49
Profit.Factor 1.04 1.12 1.16 1.10 1.10
Avg.Win.Day 37.28 156.41 123.06 89.18 32.73
Med.Win.Day 28.82 124.52 88.98 69.57 26.67
Avg.Losing.Day -36.91 -166.71 -125.74 -86.96 -34.21
Med.Losing.Day -28.18 -125.16 -84.29 -62.95 -26.77
Avg.Daily.PL 0.64 9.07 9.47 4.37 1.61
Med.Daily.PL 1.17 22.95 13.29 6.22 4.38
Std.Dev.Daily.PL.1 49.69 213.61 175.83 118.94 44.01
Ann.Sharpe 0.21 0.67 0.85 0.58 0.58
Max.Drawdown -1345.79 -4492.64 -4545.72 -3655.24 -1126.20
Profit.To.Max.Draw 0.62 3.14 2.83 1.62 1.93
Avg.WinLoss.Ratio 1.01 0.94 0.98 1.03 0.96
Med.WinLoss.Ratio 1.02 0.99 1.06 1.11 1.00
Max.Equity 1756.16 14420.81 13193.50 5906.68 2600.28
Min.Equity -714.17 -360.99 0.00 -1458.57 -750.84
End.Equity 835.02 14116.64 12860.27 5906.68 2177.09
RWR SHY TLT XLB XLE
Total.Net.Profit 15725.34 2126.96 -1042.28 8143.08 16350.23
Total.Days 1373.00 1617.00 1152.00 1324.00 1551.00
Winning.Days 744.00 904.00 569.00 720.00 852.00
Losing.Days 629.00 713.00 583.00 604.00 699.00
Avg.Day.PL 11.45 1.32 -0.90 6.15 10.54
Med.Day.PL 14.97 1.31 -1.15 15.83 24.94
Largest.Winner 1126.73 57.15 532.71 715.64 1037.19
Largest.Loser -976.30 -67.00 -377.39 -582.22 -1019.83
Gross.Profits 100846.82 8420.38 38752.96 84332.47 147238.93
Gross.Losses -85121.48 -6293.43 -39795.24 -76189.40 -130888.71
Std.Dev.Daily.PL 193.61 12.14 92.65 159.83 242.37
Percent.Positive 54.19 55.91 49.39 54.38 54.93
Percent.Negative 45.81 44.09 50.61 45.62 45.07
Profit.Factor 1.18 1.34 0.97 1.11 1.12
Avg.Win.Day 135.55 9.31 68.11 117.13 172.82
Med.Win.Day 95.73 7.26 50.05 99.01 132.61
Avg.Losing.Day -135.33 -8.83 -68.26 -126.14 -187.25
Med.Losing.Day -91.57 -6.86 -50.02 -90.01 -132.46
Avg.Daily.PL 11.45 1.32 -0.90 6.15 10.54
Med.Daily.PL 14.97 1.31 -1.15 15.83 24.94
Std.Dev.Daily.PL.1 193.61 12.14 92.65 159.83 242.37
Ann.Sharpe 0.94 1.72 -0.16 0.61 0.69
Max.Drawdown -4720.58 -258.24 -3334.35 -2518.13 -4156.71
Profit.To.Max.Draw 3.33 8.24 -0.31 3.23 3.93
Avg.WinLoss.Ratio 1.00 1.06 1.00 0.93 0.92
Med.WinLoss.Ratio 1.05 1.06 1.00 1.10 1.00
Max.Equity 16148.05 2169.34 1995.24 9004.95 17110.53
Min.Equity 0.00 -62.71 -1736.55 -116.14 -468.28
End.Equity 15725.34 2126.96 -1042.28 8143.08 16350.23
XLF XLI XLK XLP XLU
Total.Net.Profit 6938.82 8270.94 3773.49 5237.29 7443.30
Total.Days 1168.00 1320.00 1227.00 1429.00 1459.00
Winning.Days 623.00 722.00 670.00 780.00 805.00
Losing.Days 545.00 598.00 557.00 649.00 654.00
Avg.Day.PL 5.94 6.27 3.08 3.67 5.10
Med.Day.PL 10.20 11.53 13.24 8.69 13.99
Largest.Winner 584.93 747.16 691.12 415.09 393.51
Largest.Loser -650.83 -608.16 -526.35 -566.03 -475.47
Gross.Profits 57073.77 64421.38 60132.26 46969.42 62856.16
Gross.Losses -50134.96 -56150.44 -56358.77 -41732.13 -55412.87
Std.Dev.Daily.PL 129.53 123.59 127.43 83.31 108.03
Percent.Positive 53.34 54.70 54.60 54.58 55.17
Percent.Negative 46.66 45.30 45.40 45.42 44.83
Profit.Factor 1.14 1.15 1.07 1.13 1.13
Avg.Win.Day 91.61 89.23 89.75 60.22 78.08
Med.Win.Day 64.79 72.02 65.43 47.42 63.25
Avg.Losing.Day -91.99 -93.90 -101.18 -64.30 -84.73
Med.Losing.Day -59.41 -67.06 -71.16 -47.83 -59.11
Avg.Daily.PL 5.94 6.27 3.08 3.67 5.10
Med.Daily.PL 10.20 11.53 13.24 8.69 13.99
Std.Dev.Daily.PL.1 129.53 123.59 127.43 83.31 108.03
Ann.Sharpe 0.73 0.80 0.38 0.70 0.75
Max.Drawdown -2212.82 -2700.70 -3680.30 -2095.40 -3243.95
Profit.To.Max.Draw 3.14 3.06 1.03 2.50 2.29
Avg.WinLoss.Ratio 1.00 0.95 0.89 0.94 0.92
Med.WinLoss.Ratio 1.09 1.07 0.92 0.99 1.07
Max.Equity 7130.66 9488.70 4245.23 5269.06 10132.95
Min.Equity -106.64 -134.79 -776.77 -244.67 -772.21
End.Equity 6938.82 8270.94 3773.49 5237.29 7443.30
XLV XLY
Total.Net.Profit -2400.55 2813.65
Total.Days 1114.00 1123.00
Winning.Days 560.00 588.00
Losing.Days 554.00 535.00
Avg.Day.PL -2.15 2.51
Med.Day.PL 3.02 8.24
Largest.Winner 883.88 693.65
Largest.Loser -820.10 -524.37
Gross.Profits 35341.85 50246.96
Gross.Losses -37742.40 -47433.31
Std.Dev.Daily.PL 93.29 119.81
Percent.Positive 50.27 52.36
Percent.Negative 49.73 47.64
Profit.Factor 0.94 1.06
Avg.Win.Day 63.11 85.45
Med.Win.Day 51.38 63.20
Avg.Losing.Day -68.13 -88.66
Med.Losing.Day -49.88 -65.09
Avg.Daily.PL -2.15 2.51
Med.Daily.PL 3.02 8.24
Std.Dev.Daily.PL.1 93.29 119.81
Ann.Sharpe -0.37 0.33
Max.Drawdown -3650.41 -3721.65
Profit.To.Max.Draw -0.66 0.76
Avg.WinLoss.Ratio 0.93 0.96
Med.WinLoss.Ratio 1.03 0.97
Max.Equity 318.90 4439.62
Min.Equity -3331.51 -1497.63
End.Equity -2400.55 2813.65
Once again, portfolio comparisons:
Basically, this variant seemingly maximizes market exposure. Here are the three relevant statistics:
> SharpeRatio.annualized(portfRets)
[,1]
Annualized Sharpe Ratio (Rf=0%) 0.7911671
> Return.annualized(portfRets)
[,1]
Annualized Return 0.1111565
> maxDrawdown(portfRets)
[1] 0.2038124
And finally, an equity curve demonstrating the indicator at its reasonable limit (that is, zero–at the other end of the spectrum, when I used a delta of .4, there was only one trade on one of the instruments, and it was a bad trade, so that’s definitely not an interesting case).
As you can see, as the delta parameter becomes smaller and smaller, the sensitivity to a trend increases. At the limit, it essentially becomes akin to an either-or classifier. So basically, for those with the statistics backgrounds (and if you’ve understood everything thus far, you have one), then the confusion matrix becomes “go long in a trend”, “go long without a trend”, “don’t go long but miss a trend”, “stay out of the market in which there’s no trend”, and this variant essentially leans towards the idea of “I have a slight hunch there’s a trend. Oh well. That’s enough! Time to buy!” And so long as so much as even a hunch persists, the strategy will stay long.
Interestingly enough, as judging by the percentage correct and the trade statistics, the ability of the Trend Vigor indicator to correctly predict seems to be served by the statistics. That, or it could just be that in quite a few seemingly separate cases, I got lucky with my parameters (always a possibility).
One *last* variant to look at, with this evidence in hand, is whether the Trend Vigor, with its tendency to buy (or not buy) at a whim, yet getting these correct, is whether or not it would work on a shorter time-frame.
Let’s set the period from 100 to, say, 20. That is, a period of 20, and a delta of 0.
As you may guess, this changes the characteristics of the strategy in terms of what trade statistics considerably. It sacrifices the win-over-the-long-haul philosophy in favor of a style more akin to spray-and-pray, rat-ta-tat-tat, or twitch trading.
Here are the trade stats:
EFA EPP EWA EWC EWG
Num.Txns 63.00 63.00 57.00 67.00 59.00
Num.Trades 32.00 32.00 29.00 34.00 30.00
Net.Trading.PL 10328.66 11706.48 14951.72 10930.59 11660.57
Avg.Trade.PL 322.77 365.83 515.58 321.49 388.69
Med.Trade.PL 105.46 118.05 228.71 1.33 -12.68
Largest.Winner 2279.85 2396.63 3471.56 2690.74 2758.24
Largest.Loser -1263.24 -988.61 -924.28 -983.47 -1871.14
Gross.Profits 14668.25 15556.53 19711.78 17893.46 17887.77
Gross.Losses -4339.59 -3850.04 -4760.05 -6962.87 -6227.20
Std.Dev.Trade.PL 777.48 845.22 1144.47 958.73 1098.44
Percent.Positive 65.62 59.38 58.62 50.00 43.33
Percent.Negative 34.38 40.62 41.38 50.00 56.67
Profit.Factor 3.38 4.04 4.14 2.57 2.87
Avg.Win.Trade 698.49 818.76 1159.52 1052.56 1375.98
Med.Win.Trade 537.00 477.74 406.41 1147.88 1344.79
Avg.Losing.Trade -394.51 -296.16 -396.67 -409.58 -366.31
Med.Losing.Trade -344.54 -156.95 -443.07 -348.37 -298.35
Avg.Daily.PL 328.05 372.03 521.65 289.41 403.80
Med.Daily.PL 101.91 110.59 226.95 -41.34 -11.20
Std.Dev.Daily.PL 789.75 858.45 1165.00 954.88 1114.71
Ann.Sharpe 6.59 6.88 7.11 4.81 5.75
Max.Drawdown -3211.45 -2427.49 -2405.94 -3523.79 -4453.04
Profit.To.Max.Draw 3.22 4.82 6.21 3.10 2.62
Avg.WinLoss.Ratio 1.77 2.76 2.92 2.57 3.76
Med.WinLoss.Ratio 1.56 3.04 0.92 3.29 4.51
Max.Equity 10842.33 13002.93 16586.93 12975.13 12865.77
Min.Equity -16.31 -109.20 0.00 -403.80 -163.53
End.Equity 10328.66 11706.48 14951.72 10930.59 11660.57
EWH EWJ EWS EWT EWU
Num.Txns 57.00 69.00 53.00 61.00 55.00
Num.Trades 29.00 34.00 27.00 31.00 27.00
Net.Trading.PL 12897.27 4660.14 14727.03 7944.62 7348.04
Avg.Trade.PL 444.73 137.06 545.45 256.28 272.15
Med.Trade.PL 181.76 -25.35 448.00 -65.56 73.74
Largest.Winner 3627.23 1400.58 3929.35 2827.61 2861.20
Largest.Loser -985.69 -785.43 -959.90 -1435.07 -1208.44
Gross.Profits 16866.14 9250.53 18536.96 15689.70 12192.51
Gross.Losses -3968.87 -4590.39 -3809.93 -7745.07 -4844.48
Std.Dev.Trade.PL 1017.17 550.76 1137.96 1044.37 915.22
Percent.Positive 68.97 47.06 70.37 48.39 59.26
Percent.Negative 31.03 52.94 29.63 51.61 40.74
Profit.Factor 4.25 2.02 4.87 2.03 2.52
Avg.Win.Trade 843.31 578.16 975.63 1045.98 762.03
Med.Win.Trade 492.64 405.30 531.92 707.58 373.84
Avg.Losing.Trade -440.99 -255.02 -476.24 -484.07 -440.41
Med.Losing.Trade -498.05 -188.85 -566.37 -367.15 -355.87
Avg.Daily.PL 462.31 104.67 560.53 191.39 279.48
Med.Daily.PL 186.54 -28.59 459.00 -70.68 50.79
Std.Dev.Daily.PL 1031.33 525.38 1157.74 996.64 932.54
Ann.Sharpe 7.12 3.16 7.69 3.05 4.76
Max.Drawdown -3217.65 -4387.88 -3405.18 -4227.76 -2937.97
Profit.To.Max.Draw 4.01 1.06 4.32 1.88 2.50
Avg.WinLoss.Ratio 1.91 2.27 2.05 2.16 1.73
Med.WinLoss.Ratio 0.99 2.15 0.94 1.93 1.05
Max.Equity 13521.46 6000.56 15436.93 9038.22 8680.76
Min.Equity -42.01 -224.21 -1025.47 -1277.92 -464.92
End.Equity 12897.27 4660.14 14727.03 7944.62 7348.04
EWY EWZ EZU IEF IGE
Num.Txns 63.00 65.00 57.00 62.00 67.00
Num.Trades 32.00 33.00 29.00 31.00 34.00
Net.Trading.PL 12546.44 24852.10 11517.70 4753.61 9332.27
Avg.Trade.PL 392.08 753.09 397.16 153.34 274.48
Med.Trade.PL 65.75 462.80 62.94 97.07 25.89
Largest.Winner 3227.55 4129.19 2673.10 938.96 1874.11
Largest.Loser -1138.25 -1397.89 -1504.99 -349.00 -939.08
Gross.Profits 19138.92 32892.49 16773.02 5715.50 14964.70
Gross.Losses -6592.48 -8040.39 -5255.32 -961.89 -5632.43
Std.Dev.Trade.PL 1139.40 1521.21 1012.85 273.84 787.90
Percent.Positive 53.12 57.58 55.17 70.97 52.94
Percent.Negative 46.88 42.42 44.83 29.03 47.06
Profit.Factor 2.90 4.09 3.19 5.94 2.66
Avg.Win.Trade 1125.82 1731.18 1048.31 259.80 831.37
Med.Win.Trade 665.93 1333.10 835.84 190.61 821.62
Avg.Losing.Trade -439.50 -574.31 -404.26 -106.88 -352.03
Med.Losing.Trade -303.33 -562.67 -296.63 -80.24 -264.51
Avg.Daily.PL 388.31 762.17 408.36 153.34 206.26
Med.Daily.PL 13.15 470.00 62.27 97.07 24.11
Std.Dev.Daily.PL 1158.03 1544.64 1029.61 273.84 690.66
Ann.Sharpe 5.32 7.83 6.30 8.89 4.74
Max.Drawdown -4645.24 -3257.05 -3413.71 -578.24 -2724.91
Profit.To.Max.Draw 2.70 7.63 3.37 8.22 3.42
Avg.WinLoss.Ratio 2.56 3.01 2.59 2.43 2.36
Med.WinLoss.Ratio 2.20 2.37 2.82 2.38 3.11
Max.Equity 12546.44 26158.50 13292.18 4906.20 9504.76
Min.Equity -682.05 0.00 0.00 -33.44 -422.88
End.Equity 12546.44 24852.10 11517.70 4753.61 9332.27
IYR IYZ LQD RWR SHY
Num.Txns 57.00 67.00 60.00 57.00 54.00
Num.Trades 29.00 34.00 30.00 29.00 25.00
Net.Trading.PL 11784.87 3862.91 5120.54 12724.61 2122.23
Avg.Trade.PL 406.37 113.62 170.68 438.78 84.89
Med.Trade.PL 185.62 -57.11 39.73 125.87 16.55
Largest.Winner 3974.51 1380.22 1515.52 3092.87 808.92
Largest.Loser -785.87 -1172.77 -737.21 -849.73 -70.04
Gross.Profits 16606.09 10171.73 6591.01 17523.83 2332.06
Gross.Losses -4821.22 -6308.82 -1470.47 -4799.22 -209.83
Std.Dev.Trade.PL 1145.72 616.42 417.69 1022.20 183.23
Percent.Positive 62.07 44.12 66.67 55.17 64.00
Percent.Negative 37.93 55.88 33.33 44.83 36.00
Profit.Factor 3.44 1.61 4.48 3.65 11.11
Avg.Win.Trade 922.56 678.12 329.55 1095.24 145.75
Med.Win.Trade 297.43 652.59 134.84 906.46 75.00
Avg.Losing.Trade -438.29 -332.04 -147.05 -369.17 -23.31
Med.Losing.Trade -349.87 -275.45 -82.17 -355.79 -21.51
Avg.Daily.PL 410.73 81.37 170.68 443.64 84.89
Med.Daily.PL 171.77 -57.61 39.73 106.12 16.55
Std.Dev.Daily.PL 1166.50 596.14 417.69 1040.62 183.23
Ann.Sharpe 5.59 2.17 6.49 6.77 7.35
Max.Drawdown -3274.47 -3375.87 -1372.68 -2818.87 -155.30
Profit.To.Max.Draw 3.60 1.14 3.73 4.51 13.67
Avg.WinLoss.Ratio 2.10 2.04 2.24 2.97 6.25
Med.WinLoss.Ratio 0.85 2.37 1.64 2.55 3.49
Max.Equity 14392.21 5329.35 5186.13 14807.38 2164.16
Min.Equity -279.58 -317.86 -49.93 -157.88 -4.04
End.Equity 11784.87 3862.91 5120.54 12724.61 2122.23
TLT XLB XLE XLF XLI
Num.Txns 66.00 69.00 75.00 67.00 61.00
Num.Trades 33.00 35.00 38.00 34.00 31.00
Net.Trading.PL 3413.99 5977.21 6441.87 5609.93 8660.57
Avg.Trade.PL 103.45 170.78 169.52 165.00 279.37
Med.Trade.PL -3.63 -83.75 -9.57 -51.46 153.63
Largest.Winner 1565.81 1617.61 1866.44 2722.10 1877.40
Largest.Loser -557.57 -609.79 -1481.92 -1198.56 -665.85
Gross.Profits 7060.83 12273.84 14304.04 11466.12 12686.72
Gross.Losses -3646.84 -6296.63 -7862.18 -5856.19 -4026.15
Std.Dev.Trade.PL 460.12 672.56 815.91 776.04 679.43
Percent.Positive 48.48 45.71 47.37 47.06 54.84
Percent.Negative 51.52 54.29 52.63 52.94 45.16
Profit.Factor 1.94 1.95 1.82 1.96 3.15
Avg.Win.Trade 441.30 767.11 794.67 716.63 746.28
Med.Win.Trade 334.21 774.71 567.38 389.75 531.89
Avg.Losing.Trade -214.52 -331.40 -393.11 -325.34 -287.58
Med.Losing.Trade -251.27 -334.69 -362.33 -215.27 -286.47
Avg.Daily.PL 103.45 119.78 103.25 166.56 237.50
Med.Daily.PL -3.63 -96.78 -14.83 -59.69 130.21
Std.Dev.Daily.PL 460.12 610.13 716.01 788.01 649.09
Ann.Sharpe 3.57 3.12 2.29 3.36 5.81
Max.Drawdown -2817.81 -2503.48 -4987.44 -4930.20 -1956.37
Profit.To.Max.Draw 1.21 2.39 1.29 1.14 4.43
Avg.WinLoss.Ratio 2.06 2.31 2.02 2.20 2.60
Med.WinLoss.Ratio 1.33 2.31 1.57 1.81 1.86
Max.Equity 5371.15 6455.14 8728.55 7579.35 8667.19
Min.Equity -158.45 -490.54 -246.66 -531.75 -420.93
End.Equity 3413.99 5977.21 6441.87 5609.93 8660.57
XLK XLP XLU XLV XLY
Num.Txns 65.00 73.00 57.00 71.00 59.00
Num.Trades 33.00 37.00 28.00 36.00 30.00
Net.Trading.PL 4961.98 4662.87 10652.74 2240.98 10791.01
Avg.Trade.PL 150.36 126.02 380.45 62.25 359.70
Med.Trade.PL 27.70 -3.74 239.19 20.12 47.17
Largest.Winner 1665.69 1210.01 2127.10 1071.64 2201.18
Largest.Loser -848.60 -375.31 -1027.85 -1019.87 -526.48
Gross.Profits 10911.42 7698.10 13356.14 6743.69 14198.58
Gross.Losses -5949.44 -3035.22 -2703.40 -4502.72 -3407.57
Std.Dev.Trade.PL 644.75 385.79 697.17 424.35 812.76
Percent.Positive 51.52 45.95 75.00 55.56 53.33
Percent.Negative 48.48 54.05 25.00 44.44 46.67
Profit.Factor 1.83 2.54 4.94 1.50 4.17
Avg.Win.Trade 641.85 452.83 636.01 337.18 887.41
Med.Win.Trade 596.95 439.53 567.87 268.84 769.48
Avg.Losing.Trade -371.84 -151.76 -386.20 -281.42 -243.40
Med.Losing.Trade -332.32 -132.19 -351.24 -198.33 -201.01
Avg.Daily.PL 153.44 126.43 392.89 63.18 318.03
Med.Daily.PL -4.08 -3.95 244.66 15.94 16.97
Std.Dev.Daily.PL 654.82 391.25 707.28 430.50 793.86
Ann.Sharpe 3.72 5.13 8.82 2.33 6.36
Max.Drawdown -3122.38 -1207.25 -1975.52 -1692.71 -2096.56
Profit.To.Max.Draw 1.59 3.86 5.39 1.32 5.15
Avg.WinLoss.Ratio 1.73 2.98 1.65 1.20 3.65
Med.WinLoss.Ratio 1.80 3.33 1.62 1.36 3.83
Max.Equity 5806.42 4786.14 10838.46 3229.36 10908.43
Min.Equity -744.34 -230.94 0.00 -26.15 -187.64
End.Equity 4961.98 4662.87 10652.74 2240.98 10791.01
Some aggregate trade stats (that I implemented as I was writing this post, so forgive the fact that they weren’t in previous outputs):
> mean(tStats$Percent.Positive) [1] 55.921 > (aggPF <- sum(tStats$Gross.Profits)/-sum(tStats$Gross.Losses)) [1] 2.889328 > (aggCorrect <- mean(tStats$Percent.Positive)) [1] 55.921 > (numTrades <- sum(tStats$Num.Trades)) [1] 946 > (meanAvgWLR <- mean(tStats$Avg.WinLoss.Ratio)) [1] 2.495
In other words, over nearly a thousand relatively short-term momentum trades (can you say “whipsaw”?), the strategy still gets it right more than half the time, and the trades it *does* get right, on average, it gets them right by a ratio of 2.5 to 1. Of course, this backtest doesn’t take transaction costs into account, and when dealing with these shorter-term strategies, if you’re a retail investor out to try and rub two pennies together and you’re getting taken for a ride on the order of $10 per buy or sell order from ETrade, you’ll have to look at the average trade P&L. (Also, if you’re a retail investor, your bigger obstacle would be the $3,000,000 to be able to even trade something like this.)
Again, the daily statistics:
EFA EPP EWA EWC EWG
Total.Net.Profit 10328.66 11706.48 14951.72 10930.59 11660.57
Total.Days 1316.00 1323.00 1303.00 1297.00 1281.00
Winning.Days 713.00 722.00 730.00 729.00 719.00
Losing.Days 603.00 601.00 573.00 568.00 562.00
Avg.Day.PL 7.85 8.85 11.47 8.43 9.10
Med.Day.PL 10.61 12.80 17.88 19.87 19.80
Largest.Winner 496.25 718.51 694.25 563.65 582.80
Largest.Loser -479.06 -702.36 -817.83 -738.35 -582.80
Gross.Profits 62165.44 75323.28 85846.23 74892.07 77119.80
Gross.Losses -51836.78 -63616.80 -70894.51 -63961.48 -65459.22
Std.Dev.Daily.PL 116.04 145.52 164.08 144.76 147.76
Percent.Positive 54.18 54.57 56.02 56.21 56.13
Percent.Negative 45.82 45.43 43.98 43.79 43.87
Profit.Factor 1.20 1.18 1.21 1.17 1.18
Avg.Win.Day 87.19 104.33 117.60 102.73 107.26
Med.Win.Day 69.61 82.93 96.06 83.06 87.10
Avg.Losing.Day -85.96 -105.85 -123.73 -112.61 -116.48
Med.Losing.Day -64.01 -70.20 -88.59 -77.41 -80.38
Avg.Daily.PL 7.85 8.85 11.47 8.43 9.10
Med.Daily.PL 10.61 12.80 17.88 19.87 19.80
Std.Dev.Daily.PL.1 116.04 145.52 164.08 144.76 147.76
Ann.Sharpe 1.07 0.97 1.11 0.92 0.98
Max.Drawdown -3211.45 -2427.49 -2405.94 -3523.79 -4453.04
Profit.To.Max.Draw 3.22 4.82 6.21 3.10 2.62
Avg.WinLoss.Ratio 1.01 0.99 0.95 0.91 0.92
Med.WinLoss.Ratio 1.09 1.18 1.08 1.07 1.08
Max.Equity 10842.33 13002.93 16586.93 12975.13 12865.77
Min.Equity -16.31 -109.20 0.00 -403.80 -163.53
End.Equity 10328.66 11706.48 14951.72 10930.59 11660.57
EWH EWJ EWS EWT EWU
Total.Net.Profit 12897.27 4660.14 14727.03 7944.62 7348.04
Total.Days 1246.00 1108.00 1302.00 1173.00 1250.00
Winning.Days 667.00 568.00 726.00 608.00 670.00
Losing.Days 579.00 540.00 576.00 565.00 580.00
Avg.Day.PL 10.35 4.21 11.31 6.77 5.88
Med.Day.PL 14.00 9.37 22.80 8.93 12.28
Largest.Winner 780.02 553.05 1036.49 1451.05 536.21
Largest.Loser -927.10 -562.11 -1149.10 -1250.21 -573.84
Gross.Profits 79332.19 58476.51 86625.31 84432.94 64333.36
Gross.Losses -66434.93 -53816.37 -71898.28 -76488.32 -56985.33
Std.Dev.Daily.PL 160.07 132.14 166.55 190.61 131.32
Percent.Positive 53.53 51.26 55.76 51.83 53.60
Percent.Negative 46.47 48.74 44.24 48.17 46.40
Profit.Factor 1.19 1.09 1.20 1.10 1.13
Avg.Win.Day 118.94 102.95 119.32 138.87 96.02
Med.Win.Day 90.55 81.48 91.21 106.86 72.21
Avg.Losing.Day -114.74 -99.66 -124.82 -135.38 -98.25
Med.Losing.Day -82.06 -78.95 -93.30 -98.23 -69.18
Avg.Daily.PL 10.35 4.21 11.31 6.77 5.88
Med.Daily.PL 14.00 9.37 22.80 8.93 12.28
Std.Dev.Daily.PL.1 160.07 132.14 166.55 190.61 131.32
Ann.Sharpe 1.03 0.51 1.08 0.56 0.71
Max.Drawdown -3217.65 -4387.88 -3405.18 -4227.76 -2937.97
Profit.To.Max.Draw 4.01 1.06 4.32 1.88 2.50
Avg.WinLoss.Ratio 1.04 1.03 0.96 1.03 0.98
Med.WinLoss.Ratio 1.10 1.03 0.98 1.09 1.04
Max.Equity 13521.46 6000.56 15436.93 9038.22 8680.76
Min.Equity -42.01 -224.21 -1025.47 -1277.92 -464.92
End.Equity 12897.27 4660.14 14727.03 7944.62 7348.04
EWY EWZ EZU IEF IGE
Total.Net.Profit 12546.44 24852.10 11517.70 4753.61 9332.27
Total.Days 1245.00 1368.00 1288.00 1220.00 1288.00
Winning.Days 687.00 770.00 702.00 647.00 710.00
Losing.Days 558.00 598.00 586.00 573.00 578.00
Avg.Day.PL 10.08 18.17 8.94 3.90 7.25
Med.Day.PL 21.94 37.02 16.02 3.66 18.41
Largest.Winner 738.74 1037.10 599.94 341.03 559.04
Largest.Loser -808.23 -1146.86 -609.07 -193.92 -623.74
Gross.Profits 97414.83 136096.17 71253.39 24136.54 81842.78
Gross.Losses -84868.38 -111244.08 -59735.69 -19382.93 -72510.51
Std.Dev.Daily.PL 195.32 238.67 138.16 47.45 157.77
Percent.Positive 55.18 56.29 54.50 53.03 55.12
Percent.Negative 44.82 43.71 45.50 46.97 44.88
Profit.Factor 1.15 1.22 1.19 1.25 1.13
Avg.Win.Day 141.80 176.75 101.50 37.31 115.27
Med.Win.Day 110.49 141.00 79.01 29.85 94.60
Avg.Losing.Day -152.09 -186.03 -101.94 -33.83 -125.45
Med.Losing.Day -109.42 -134.77 -70.49 -26.24 -95.78
Avg.Daily.PL 10.08 18.17 8.94 3.90 7.25
Med.Daily.PL 21.94 37.02 16.02 3.66 18.41
Std.Dev.Daily.PL.1 195.32 238.67 138.16 47.45 157.77
Ann.Sharpe 0.82 1.21 1.03 1.30 0.73
Max.Drawdown -4645.24 -3257.05 -3413.71 -578.24 -2724.91
Profit.To.Max.Draw 2.70 7.63 3.37 8.22 3.42
Avg.WinLoss.Ratio 0.93 0.95 1.00 1.10 0.92
Med.WinLoss.Ratio 1.01 1.05 1.12 1.14 0.99
Max.Equity 12546.44 26158.50 13292.18 4906.20 9504.76
Min.Equity -682.05 0.00 0.00 -33.44 -422.88
End.Equity 12546.44 24852.10 11517.70 4753.61 9332.27
IYR IYZ LQD RWR SHY
Total.Net.Profit 11784.87 3862.91 5120.54 12724.61 2122.23
Total.Days 1312.00 1213.00 1290.00 1324.00 1403.00
Winning.Days 711.00 641.00 720.00 713.00 796.00
Losing.Days 601.00 572.00 570.00 611.00 607.00
Avg.Day.PL 8.98 3.18 3.97 9.61 1.51
Med.Day.PL 13.12 8.69 4.71 9.40 2.15
Largest.Winner 1266.62 499.01 267.59 1410.02 71.37
Largest.Loser -1344.56 -517.73 -623.17 -1305.30 -65.40
Gross.Profits 85524.01 52701.88 23905.68 89163.11 7220.54
Gross.Losses -73739.14 -48838.97 -18785.14 -76438.50 -5098.31
Std.Dev.Daily.PL 187.62 114.92 47.09 196.38 11.86
Percent.Positive 54.19 52.84 55.81 53.85 56.74
Percent.Negative 45.81 47.16 44.19 46.15 43.26
Profit.Factor 1.16 1.08 1.27 1.17 1.42
Avg.Win.Day 120.29 82.22 33.20 125.05 9.07
Med.Win.Day 83.38 57.42 25.92 83.55 6.47
Avg.Losing.Day -122.69 -85.38 -32.96 -125.10 -8.40
Med.Losing.Day -75.71 -60.20 -23.53 -77.73 -6.33
Avg.Daily.PL 8.98 3.18 3.97 9.61 1.51
Med.Daily.PL 13.12 8.69 4.71 9.40 2.15
Std.Dev.Daily.PL.1 187.62 114.92 47.09 196.38 11.86
Ann.Sharpe 0.76 0.44 1.34 0.78 2.02
Max.Drawdown -3274.47 -3375.87 -1372.68 -2818.87 -155.30
Profit.To.Max.Draw 3.60 1.14 3.73 4.51 13.67
Avg.WinLoss.Ratio 0.98 0.96 1.01 1.00 1.08
Med.WinLoss.Ratio 1.10 0.95 1.10 1.07 1.02
Max.Equity 14392.21 5329.35 5186.13 14807.38 2164.16
Min.Equity -279.58 -317.86 -49.93 -157.88 -4.04
End.Equity 11784.87 3862.91 5120.54 12724.61 2122.23
TLT XLB XLE XLF XLI
Total.Net.Profit 3413.99 5977.21 6441.87 5609.93 8660.57
Total.Days 1177.00 1262.00 1306.00 1153.00 1285.00
Winning.Days 613.00 680.00 702.00 607.00 711.00
Losing.Days 564.00 582.00 604.00 546.00 574.00
Avg.Day.PL 2.90 4.74 4.93 4.87 6.74
Med.Day.PL 5.66 11.89 12.61 8.42 10.49
Largest.Winner 528.00 669.10 951.16 1615.41 609.93
Largest.Loser -331.64 -696.80 -1194.78 -1400.78 -478.61
Gross.Profits 37930.87 69474.84 85294.45 66345.27 57592.48
Gross.Losses -34516.87 -63497.63 -78852.59 -60735.35 -48931.91
Std.Dev.Daily.PL 84.71 141.74 170.38 182.33 116.56
Percent.Positive 52.08 53.88 53.75 52.65 55.33
Percent.Negative 47.92 46.12 46.25 47.35 44.67
Profit.Factor 1.10 1.09 1.08 1.09 1.18
Avg.Win.Day 61.88 102.17 121.50 109.30 81.00
Med.Win.Day 46.15 84.21 97.96 67.92 59.72
Avg.Losing.Day -61.20 -109.10 -130.55 -111.24 -85.25
Med.Losing.Day -43.92 -78.65 -101.67 -64.90 -59.16
Avg.Daily.PL 2.90 4.74 4.93 4.87 6.74
Med.Daily.PL 5.66 11.89 12.61 8.42 10.49
Std.Dev.Daily.PL.1 84.71 141.74 170.38 182.33 116.56
Ann.Sharpe 0.54 0.53 0.46 0.42 0.92
Max.Drawdown -2817.81 -2503.48 -4987.44 -4930.20 -1956.37
Profit.To.Max.Draw 1.21 2.39 1.29 1.14 4.43
Avg.WinLoss.Ratio 1.01 0.94 0.93 0.98 0.95
Med.WinLoss.Ratio 1.05 1.07 0.96 1.05 1.01
Max.Equity 5371.15 6455.14 8728.55 7579.35 8667.19
Min.Equity -158.45 -490.54 -246.66 -531.75 -420.93
End.Equity 3413.99 5977.21 6441.87 5609.93 8660.57
XLK XLP XLU XLV XLY
Total.Net.Profit 4961.98 4662.87 10652.74 2240.98 10791.01
Total.Days 1216.00 1284.00 1388.00 1178.00 1234.00
Winning.Days 674.00 705.00 770.00 617.00 653.00
Losing.Days 542.00 579.00 618.00 561.00 581.00
Avg.Day.PL 4.08 3.63 7.67 1.90 8.74
Med.Day.PL 15.35 8.51 13.15 3.87 9.07
Largest.Winner 443.80 642.73 945.06 339.99 1098.25
Largest.Loser -440.72 -380.30 -721.42 -479.49 -477.11
Gross.Profits 56694.07 38477.60 57865.62 39848.98 61218.76
Gross.Losses -51732.09 -33814.73 -47212.88 -37608.01 -50427.75
Std.Dev.Daily.PL 119.48 74.90 104.74 87.22 130.20
Percent.Positive 55.43 54.91 55.48 52.38 52.92
Percent.Negative 44.57 45.09 44.52 47.62 47.08
Profit.Factor 1.10 1.14 1.23 1.06 1.21
Avg.Win.Day 84.12 54.58 75.15 64.59 93.75
Med.Win.Day 62.97 42.12 61.26 51.22 67.20
Avg.Losing.Day -95.45 -58.40 -76.40 -67.04 -86.79
Med.Losing.Day -65.34 -45.63 -53.32 -49.44 -59.22
Avg.Daily.PL 4.08 3.63 7.67 1.90 8.74
Med.Daily.PL 15.35 8.51 13.15 3.87 9.07
Std.Dev.Daily.PL.1 119.48 74.90 104.74 87.22 130.20
Ann.Sharpe 0.54 0.77 1.16 0.35 1.07
Max.Drawdown -3122.38 -1207.25 -1975.52 -1692.71 -2096.56
Profit.To.Max.Draw 1.59 3.86 5.39 1.32 5.15
Avg.WinLoss.Ratio 0.88 0.93 0.98 0.96 1.08
Med.WinLoss.Ratio 0.96 0.92 1.15 1.04 1.13
Max.Equity 5806.42 4786.14 10838.46 3229.36 10908.43
Min.Equity -744.34 -230.94 0.00 -26.15 -187.64
End.Equity 4961.98 4662.87 10652.74 2240.98 10791.01
A lot of the cash Sharpe ratios (now in the *daily* statistics, not the trade statistics) are nearing 1. Not exactly spectacular, by any stretch of the imagination, when considering a short-term trading strategy before commissions/slippage, but definitely nothing to scoff at. Something I notice just by eyeballing the statistics is that there definitely seems to be an edge in the percentage of days positive. Of course, I won’t rule out the fact that all of this may simply be the fact that many of these securities are equity indices, and thus, may have a slightly inherent long bias in them.
Let’s move onto the portfolio equity curve.
Looking at this equity curve, the first thing to note is that it’s strikingly similar to the SPY equity curve up until the crisis, and the drawdowns happen at about the same exact times. Maybe this means that all of my global equity ETFs that I chose for the data were correlated because at the end of the day, aside from the few fixed income ETFs available before 2003, that they’re still separate slices of the equities asset class, or that my volatility (and returns?) are mainly driven by the 9 XL sectors. What’s also worth noting is that the strategy attempted to go “dumpster diving”, to put it kindly–that is, still try to find those positive-momentum trades in the depths of the financial crisis. While it certainly seemed to try, in this case, the best move would have been to do nothing at all. However, when the market rebounded, the strategy quickly made up its losses (and then some).
For the final time in this post, the three portfolio statistics:
> SharpeRatio.annualized(portfRets)
[,1]
Annualized Sharpe Ratio (Rf=0%) 0.9692246
> Return.annualized(portfRets)
[,1]
Annualized Return 0.1113647
> maxDrawdown(portfRets)
[1] 0.1801516
In other words, an 11% return, at a maximum drawdown of 18%. I am of course, still not pleased with the last two numbers, since a maximum drawdown larger than the annualized return means that it’s quite possible to simply have a down year. However, the idea of an 18% drawdown while seemingly keeping pace with an S&P 500 (with a simplistic asset allocation and order-sizing strategy, no less) in its good years is nothing to scoff at. (In my last job, I was responsible for developing the analytics package in terms of portfolio management. Suffice to say that there are a lot more ways to slice up performance.)
Finally, just for fun, here’s the equity curve and the indicator of XLB for this two-parameter (three if you count trigger lag, and four if you count the threshold setting) configuration:
In other words, for those that prefer the “lots and lots of little ones” to the “long-term trend-following” alternative, there you go.
Interesting to note, comparing the few portfolio equity curves I’ve shown in this post, overall, the performances look somewhat similar regardless of the philosophy–whether a very long-term trend-following approach, or a more short-term orientation. The difference shows up in the trade statistics, but as they say about roads leading to Rome…in my opinion, this probably counts as a vote for the robustness of the strategy.
Now, to conclude this exploration, here are some things I can take away from it:
By adjusting the period and delta parameters, it’s possible to take what was originally a market mode filter and:
A) keep it as a double-purpose trend follower and market mode indicator
B) turn it into a long-term trend indicator
C) turn it into a short(er) term momentum trader.
Paradoxically (at least according to the basic risk/reward blabber found in typical academic finance), it seems that by lowering delta and having a willingness to take on “more” risk in the form of greater market exposure, one actually achieves a better annualized Sharpe Ratio than with the default, more risk-averse, setting.
Next time, I’ll look at more intelligent risk-weighting schemes.
Thanks for reading.
QuantStrat TradeR 