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To continue the investigation of Trend Vigor (see part 1 here, and part 2 here), let’s examine the importance of position sizing. Also, this post will show the way to obtain this equity curve:
Before starting this post, I would like to defer to an authority in terms of the importance of position sizing. That would be one Andreas Clenow, author of an extremely highly-rated book about trend-following. Here’s his post: Why Leverage Is Pointless
Now before starting the main thrust of this post, I’d like to make a quick comparison regarding the 30 ETFs I selected for this demo–namely, their inter-instrument correlations.
tmp <- list()
length(tmp) <- length(symbols)
for (i in 1:length(symbols)) {
tmp[[i]] <-Cl(get(symbols[i]))
}
tmp <- do.call(cbind, tmp)
baseCors <- cor(tmp)
diag(baseCors) <- NA
instrumentAverageBaseCors <- rowMeans(baseCors, na.rm=TRUE)
names(instrumentAverageBaseCors) <- gsub(".Close", "", names(instrumentAverageBaseCors))
instrumentAverageBaseCors
(grandMeanBaseCors <- mean(instrumentAverageBaseCors))
> instrumentAverageBaseCors
XLB XLE XLF XLP XLI XLU XLV
0.8208166 0.7872692 0.2157401 0.7618719 0.7882733 0.8049700 0.7487639
XLK XLY RWR EWJ EWG EWU EWC
0.7785739 0.5912142 0.7055041 0.6665144 0.8112501 0.7735207 0.8159072
EWY EWA EWH EWS IYZ EZU IYR
0.8231610 0.8234274 0.8022086 0.7971305 0.6875318 0.7669643 0.6894201
EWT EWZ EFA IGE EPP LQD SHY
0.7746172 0.7227011 0.8047205 0.8034852 0.8274662 0.5552580 0.4339562
IEF TLT
0.3954464 0.3863955
> (grandMeanBaseCors <- mean(instrumentAverageBaseCors))
[1] 0.7054693
In other words, pretty ugly. All sorts of ugly, but I suppose this is what happens when limiting the choices to ETFs in inception since 2003. So remember that number. A correlation north of .70 on average among all the instruments.
Now, onto the main thrust of the topic of this post:
In the previous post, we saw that some highly successful instruments, when analyzed at their own scale, such as SHY (the short term bonds ETF), had spectacular performances. However, in the grand scheme of things, due to identical notional risk allocation, the fact that SHY itself just didn’t move as much as, say, the SPDR sector ETFs meant that its performance could not make as much of an impact in the portfolio performance. This implication meant that despite having 30 instruments in the portfolio, not only were the base instruments highly correlated (quandl futures data algorithm coming sometime in the future!), but beyond that, the performance was dominated by the most volatile among them. This is clearly undesirable, and with most trading information in the public domain looking at a “trading system” as just a set of indicators, signals, and rules on one instrument at a time, there is very little emphasis placed on relative position sizing, with the occasional thoughtful writer saying “my order size is based on dividing some notional amount by some ATR”, and leaving it at that.
How important is that one little detail? As Andreas Clenow has pointed out in his post, it is extremely important, and in many cases, far more important than a couple of simplistic rules.
The approach I take is rooted in futures trading. In futures trading, due to the discontinuous nature of contracts, in order to formulate a backtest, quants/engineers/traders/whoever have to create a continuous contract, going back in time, and have to find some way to smooth over those price discontinuities between the two contracts they roll between at any point in time. More often than not, these changes add up quickly, and so, any computation that was sensitive to the addition of a scalar quantity was instantly off the table (this means that anything depending on percentage changes in price? Gone). One solution to this is the Average True Range, which not only succeeds in this regard, but also isn’t penalized by directional volatility, like standard deviation in a trend (consider a monotonically rising price–a moving average across that time period would constantly lag the current quantity, and a standard deviation would consistently punish that divergence). Furthermore, if I have not yet stated it already, the ATR has a very important interpretation for position sizing:
It’s a measure of the actual dollar movement of the security.
What does this mean? It means that rather that rather than ordering a notional quantity of the security, the trading system can instead order a specific level of *risk*, regardless of the notional price. This allows a trading system simulation to *force* equal risk contributions from all securities involved in the system. My implementation of this idea (found in my IKTrading package, see my about page for my github link) grew into a little bit of a Swiss army knife to include maximum position sizing, and a rebalancing feature.
Here’s the function, along with a necessary sister function:
"lagATR" <- function(HLC, n=14, maType, lag=1, ...) {
ATR <- ATR(HLC, n=n, maType=maType, ...)
ATR <- lag(ATR, lag)
out <- ATR$atr
colnames(out) <- "atr"
return(out)
}
"osDollarATR" <- function(orderside, tradeSize, pctATR, maxPctATR=pctATR, data, timestamp, symbol,
prefer="Open", portfolio, integerQty=TRUE, atrMod="", rebal=FALSE, ...) {
if(tradeSize > 0 & orderside == "short"){
tradeSize <- tradeSize*-1
}
pos <- getPosQty(portfolio, symbol, timestamp)
atrString <- paste0("atr",atrMod)
atrCol <- grep(atrString, colnames(mktdata))
if(length(atrCol)==0) {
stop(paste("Term", atrString, "not found in mktdata column names."))
}
atrTimeStamp <- mktdata[timestamp, atrCol]
if(is.na(atrTimeStamp) | atrTimeStamp==0) {
stop(paste("ATR corresponding to",atrString,"is invalid at this point in time.
Add a logical operator to account for this."))
}
dollarATR <- pos*atrTimeStamp
desiredDollarATR <- pctATR*tradeSize
remainingRiskCapacity <- tradeSize*maxPctATR-dollarATR
if(orderside == "long"){
qty <- min(tradeSize*pctATR/atrTimeStamp, remainingRiskCapacity/atrTimeStamp)
} else {
qty <- max(tradeSize*pctATR/atrTimeStamp, remainingRiskCapacity/atrTimeStamp)
}
if(integerQty) {
qty <- trunc(qty)
}
if(!rebal) {
if(orderside == "long" & qty < 0) {
qty <- 0
}
if(orderside == "short" & qty > 0) {
qty <- 0
}
}
if(rebal) {
if(pos == 0) {
qty <- 0
}
}
return(qty)
}
To get it out of the way, the lagATR function exists to, as its name says, lag the ATR computation, in order to prevent look-ahead bias. After all, you cannot buy the open using an ATR value computed at the close of that same day.
Now, moving onto the actual osDollarATR function, the way it works is like this: it has the user specify a notional trade size (tradeSize), that is, a notional dollar amount, and then the risk level the user would like on that notional dollar amount (pctATR). And here’s where it gets fun–by multiplying the notional dollar amount by the percentage ATR, it allows the strategy to basically buy units of ATR. Beyond this, for strategies that scale in, pyramid, dollar-cost-average, or otherwise stack up positions, there is functionality to cap the risk, along with a feature that would check if the maximum risk level had been breached, and to pare down (not featured in this demonstration). Essentially, inherent in this conversion from dollars to ATR is an implicit variable leverage factor. That is, consider a security A that had an ATR for a given period of $2, that was priced for $50. Now consider another security B that was priced at $100 with an ATR for the same period of $1. If you wished to risk a notional 2% of $10,000 (that is, $200 worth of ATR), you’d only need 100 units of security A, essentially staying 50% in cash for that transaction, while for security B, you’d actually leverage 2:1 in order to purchase 200 units, even if you “lack” the notional capital. Obviously, since this is a computer, the function is assuming that you can actually *obtain* the proper leverage to properly position-size. But beyond that, this function inherently embodies the idea of showing “why leverage is pointless”.
The strategy is identical to the previous post’s, using the same TVI(20,0) indicator (or if you want, (20,0,1), if you take into account the triggerLag parameter), with one key difference: rather than using the equal dollar weight order-sizing function, I will instead use this new ATR order sizing function.
Here’s the code:
require(DSTrading)
require(IKTrading)
require(quantstrat)
initDate="1990-01-01"
from="2003-01-01"
to="2010-12-31"
#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_osATR"
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=0
period=20
pctATR=.02 #control risk with this parameter
#indicators
add.indicator(strategy.st, name="TVI", arguments=list(x=quote(Cl(mktdata)), period=period, delta=delta), label="TVI")
add.indicator(strategy.st, name="lagATR", arguments=list(HLC=quote(HLC(mktdata)), n=period), label="atrX")
#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, 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)
Notice the addition of the new indicator (using an ATR period tied to the TVI period of 20), and the modified entry rule. Also, a small detail is the atrMod string modifier. This modifies the string “atr”, by appending the modifier to the end of it. While it looks superfluous at first, the reason for this addition is in case the user wishes to make use of multiple atr indicators, and thereby allowing the order sizing function to locate the appropriate column. Also note that the label on the indicator has to be the term “atr” and then the modifier. If this seems slightly kludge-y, I’m open for any suggestions.
One other thing to note–the computation for the ATR order stream should have valid values before the first order signal fires, or it will not work. That is, consider a system that, for argument’s sake, has a 20-day period to compute its indicator (such as TVI(20,0)), but a 100-day ATR computation. At the beginning of the data, it could very well be the case that there is not yet a valid value for the ATR computation, and therefore, a valid order quantity cannot be returned.
So, those two notes about using this function dealt with, let’s move onto the results.
Here are the 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)])))
(aggPF <- sum(tStats$Gross.Profits)/-sum(tStats$Gross.Losses))
(aggCorrect <- mean(tStats$Percent.Positive))
(numTrades <- sum(tStats$Num.Trades))
(meanAvgWLR <- mean(tStats$Avg.WinLoss.Ratio))
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 15389.57 15578.88 16204.18 11846.58 12646.07
Avg.Trade.PL 480.92 486.84 558.76 348.43 421.54
Med.Trade.PL 185.67 179.37 275.26 -13.31 -15.89
Largest.Winner 2440.60 3542.54 3609.82 3040.75 2875.15
Largest.Loser -840.30 -1190.45 -937.03 -1199.78 -912.56
Gross.Profits 20142.82 20037.94 20434.89 19120.45 18349.74
Gross.Losses -4753.25 -4459.05 -4230.71 -7273.88 -5703.66
Std.Dev.Trade.PL 953.83 1055.36 1191.82 1022.49 1097.44
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 4.24 4.49 4.83 2.63 3.22
Avg.Win.Trade 959.18 1054.63 1202.05 1124.73 1411.52
Med.Win.Trade 902.74 722.86 592.03 1075.71 1042.79
Avg.Losing.Trade -432.11 -343.00 -352.56 -427.88 -335.51
Med.Losing.Trade -450.96 -231.60 -284.15 -377.76 -346.90
Avg.Daily.PL 489.72 495.27 565.90 314.01 438.00
Med.Daily.PL 163.09 133.15 243.61 -56.13 -14.28
Std.Dev.Daily.PL 968.28 1071.71 1213.06 1018.14 1113.09
Ann.Sharpe 8.03 7.34 7.41 4.90 6.25
Max.Drawdown -2338.43 -2430.09 -2168.66 -2982.50 -2904.73
Profit.To.Max.Draw 6.58 6.41 7.47 3.97 4.35
Avg.WinLoss.Ratio 2.22 3.07 3.41 2.63 4.21
Med.WinLoss.Ratio 2.00 3.12 2.08 2.85 3.01
Max.Equity 15968.41 16789.50 17435.72 13048.24 13773.99
Min.Equity -17.93 -188.46 0.00 -393.45 -100.42
End.Equity 15389.57 15578.88 16204.18 11846.58 12646.07
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 12085.74 7457.81 13356.23 6906.24 7492.71
Avg.Trade.PL 416.75 219.35 494.68 222.78 277.51
Med.Trade.PL 192.70 -34.71 425.41 -52.39 87.70
Largest.Winner 2924.25 2586.20 3268.76 1965.93 2715.28
Largest.Loser -1552.50 -854.08 -631.60 -1052.89 -999.50
Gross.Profits 16111.39 12289.56 15881.04 13110.95 12459.02
Gross.Losses -4025.66 -4831.75 -2524.81 -6204.71 -4966.31
Std.Dev.Trade.PL 925.26 736.30 848.37 883.21 872.02
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 4.00 2.54 6.29 2.11 2.51
Avg.Win.Trade 805.57 768.10 835.84 874.06 778.69
Med.Win.Trade 465.57 571.09 576.83 517.53 542.01
Avg.Losing.Trade -447.30 -268.43 -315.60 -387.79 -451.48
Med.Losing.Trade -413.37 -206.93 -338.84 -322.41 -433.08
Avg.Daily.PL 434.15 169.87 504.61 129.14 284.11
Med.Daily.PL 201.67 -36.02 430.95 -54.67 72.31
Std.Dev.Daily.PL 937.40 687.94 863.57 725.09 888.60
Ann.Sharpe 7.35 3.92 9.28 2.83 5.08
Max.Drawdown -2229.93 -4036.69 -2021.12 -3147.85 -2599.57
Profit.To.Max.Draw 5.42 1.85 6.61 2.19 2.88
Avg.WinLoss.Ratio 1.80 2.86 2.65 2.25 1.72
Med.WinLoss.Ratio 1.13 2.76 1.70 1.61 1.25
Max.Equity 13043.23 8395.92 14415.11 6906.24 9160.15
Min.Equity -33.87 -274.69 -699.37 -788.28 -327.38
End.Equity 12085.74 7457.81 13356.23 6906.24 7492.71
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 9736.49 16814.33 13135.27 17932.39 13435.41
Avg.Trade.PL 304.27 509.53 452.94 578.46 395.16
Med.Trade.PL 61.08 295.06 94.54 362.74 32.80
Largest.Winner 2278.76 2821.49 2805.66 4412.27 2955.08
Largest.Loser -915.90 -1170.96 -1222.74 -836.09 -763.29
Gross.Profits 14597.54 22199.95 18539.53 21651.92 18691.32
Gross.Losses -4861.05 -5385.61 -5404.25 -3719.52 -5255.91
Std.Dev.Trade.PL 815.28 1006.45 1097.26 1097.78 984.69
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 3.00 4.12 3.43 5.82 3.56
Avg.Win.Trade 858.68 1168.42 1158.72 984.18 1038.41
Med.Win.Trade 617.31 1071.08 1068.20 552.55 708.61
Avg.Losing.Trade -324.07 -384.69 -415.71 -413.28 -328.49
Med.Losing.Trade -293.26 -391.20 -339.56 -420.83 -303.28
Avg.Daily.PL 296.04 510.77 465.74 578.46 324.22
Med.Daily.PL 8.30 249.20 89.51 362.74 17.63
Std.Dev.Daily.PL 827.41 1022.53 1115.19 1097.78 907.45
Ann.Sharpe 5.68 7.93 6.63 8.36 5.67
Max.Drawdown -2689.16 -2599.61 -2764.56 -1475.57 -2439.52
Profit.To.Max.Draw 3.62 6.47 4.75 12.15 5.51
Avg.WinLoss.Ratio 2.65 3.04 2.79 2.38 3.16
Med.WinLoss.Ratio 2.10 2.74 3.15 1.31 2.34
Max.Equity 9736.49 17637.00 14909.94 18695.22 13435.41
Min.Equity -392.89 0.00 0.00 -127.86 -654.86
End.Equity 9736.49 16814.33 13135.27 17932.39 13435.41
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 13555.67 7434.57 12091.15 13301.24 31955.85
Avg.Trade.PL 467.44 218.66 403.04 458.66 1278.23
Med.Trade.PL 137.55 -65.13 133.08 142.52 261.88
Largest.Winner 6726.10 1967.48 2512.92 2396.20 13432.83
Largest.Loser -511.83 -931.17 -1902.27 -664.22 -887.59
Gross.Profits 17122.17 13327.47 16376.88 17323.42 34748.07
Gross.Losses -3566.50 -5892.89 -4285.72 -4022.18 -2792.21
Std.Dev.Trade.PL 1379.47 754.07 947.51 914.56 2874.15
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 4.80 2.26 3.82 4.31 12.44
Avg.Win.Trade 951.23 888.50 818.84 1082.71 2171.75
Med.Win.Trade 338.57 542.36 623.46 929.54 1104.65
Avg.Losing.Trade -324.23 -310.15 -428.57 -309.40 -310.25
Med.Losing.Trade -377.80 -289.92 -311.99 -232.44 -336.51
Avg.Daily.PL 471.34 177.85 403.04 461.77 1278.23
Med.Daily.PL 129.71 -70.50 133.08 127.80 261.88
Std.Dev.Daily.PL 1404.62 726.63 947.51 931.19 2874.15
Ann.Sharpe 5.33 3.89 6.75 7.87 7.06
Max.Drawdown -2623.12 -2791.39 -3237.00 -2463.55 -1756.33
Profit.To.Max.Draw 5.17 2.66 3.74 5.40 18.19
Avg.WinLoss.Ratio 2.93 2.86 1.91 3.50 7.00
Med.WinLoss.Ratio 0.90 1.87 2.00 4.00 3.28
Max.Equity 15608.04 8133.92 12349.90 14777.73 32781.60
Min.Equity -473.13 -520.47 -146.25 -314.85 -63.98
End.Equity 13555.67 7434.57 12091.15 13301.24 31955.85
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 9170.38 6286.92 9724.35 6689.67 9474.51
Avg.Trade.PL 277.89 179.63 255.90 196.76 305.63
Med.Trade.PL -9.84 -92.05 -2.16 -65.18 165.99
Largest.Winner 2658.27 1727.45 2624.41 1948.36 1610.51
Largest.Loser -797.00 -821.66 -686.89 -470.70 -762.56
Gross.Profits 15454.01 12787.87 15637.04 10744.46 13894.65
Gross.Losses -6283.62 -6500.94 -5912.69 -4054.78 -4420.15
Std.Dev.Trade.PL 902.92 707.04 857.84 599.09 700.96
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 2.46 1.97 2.64 2.65 3.14
Avg.Win.Trade 965.88 799.24 868.72 671.53 817.33
Med.Win.Trade 721.04 790.04 632.93 515.21 885.41
Avg.Losing.Trade -369.62 -342.15 -295.63 -225.27 -315.72
Med.Losing.Trade -417.82 -309.84 -236.16 -188.27 -301.85
Avg.Daily.PL 277.89 126.90 186.61 198.53 262.31
Med.Daily.PL -9.84 -97.36 -3.15 -95.20 147.54
Std.Dev.Daily.PL 902.92 644.05 754.17 608.29 669.41
Ann.Sharpe 4.89 3.13 3.93 5.18 6.22
Max.Drawdown -4200.46 -2545.47 -3708.60 -2393.02 -2159.46
Profit.To.Max.Draw 2.18 2.47 2.62 2.80 4.39
Avg.WinLoss.Ratio 2.61 2.34 2.94 2.98 2.59
Med.WinLoss.Ratio 1.73 2.55 2.68 2.74 2.93
Max.Equity 11046.45 6319.32 10527.81 8171.61 9481.43
Min.Equity -367.76 -489.76 -301.10 -458.76 -348.23
End.Equity 9170.38 6286.92 9724.35 6689.67 9474.51
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 6074.82 6211.79 14167.62 2959.63 10416.38
Avg.Trade.PL 184.09 167.89 505.99 82.21 347.21
Med.Trade.PL 45.54 -6.88 218.93 35.12 54.36
Largest.Winner 2118.84 1518.72 2715.03 1515.40 2324.63
Largest.Loser -800.36 -710.82 -595.12 -1025.77 -814.78
Gross.Profits 12263.07 12061.50 16821.17 9472.62 14850.49
Gross.Losses -6188.26 -5849.72 -2653.56 -6512.99 -4434.12
Std.Dev.Trade.PL 714.36 617.33 862.82 582.88 861.18
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 1.98 2.06 6.34 1.45 3.35
Avg.Win.Trade 721.36 709.50 801.01 473.63 928.16
Med.Win.Trade 653.80 760.76 782.21 301.14 746.86
Avg.Losing.Trade -386.77 -292.49 -379.08 -407.06 -316.72
Med.Losing.Trade -300.13 -203.01 -491.90 -310.13 -267.52
Avg.Daily.PL 187.13 164.72 521.39 82.91 302.83
Med.Daily.PL 4.72 -7.27 249.47 33.66 23.93
Std.Dev.Daily.PL 725.58 625.78 875.33 591.37 840.78
Ann.Sharpe 4.09 4.18 9.46 2.23 5.72
Max.Drawdown -2615.33 -2565.79 -1696.88 -2604.95 -2431.47
Profit.To.Max.Draw 2.32 2.42 8.35 1.14 4.28
Avg.WinLoss.Ratio 1.87 2.43 2.11 1.16 2.93
Med.WinLoss.Ratio 2.18 3.75 1.59 0.97 2.79
Max.Equity 6786.94 6374.13 14371.31 4236.64 10538.74
Min.Equity -523.50 -269.87 0.00 -205.49 -154.97
End.Equity 6074.82 6211.79 14167.62 2959.63 10416.38
And aggregate daily stats:
> (aggPF <- sum(tStats$Gross.Profits)/-sum(tStats$Gross.Losses)) [1] 3.37825 > (aggCorrect <- mean(tStats$Percent.Positive)) [1] 55.921 > (numTrades <- sum(tStats$Num.Trades)) [1] 946 > (meanAvgWLR <- mean(tStats$Avg.WinLoss.Ratio)) [1] 2.766667
If you scroll down to the end of the , you can see that the aggregate profit factor broke above 3 per trade (that is, when you aggregate all the trades on their own merit, you take away more than $3 for every $1 that the market claims, and even the standalone average per-instrument win to loss ratio improved (you’ll see why in a moment).
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 15389.57 15578.88 16204.18 11846.58 12646.07
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 11.69 11.78 12.44 9.13 9.87
Med.Day.PL 16.38 16.83 21.71 21.41 20.15
Largest.Winner 677.61 663.11 1056.94 449.52 525.11
Largest.Loser -951.74 -1054.27 -1049.55 -576.75 -880.58
Gross.Profits 82528.83 93453.33 86183.11 74841.31 78603.60
Gross.Losses -67139.26 -77874.45 -69978.93 -62994.74 -65957.53
Std.Dev.Daily.PL 147.33 171.22 159.08 134.32 147.41
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 1.23 1.20 1.23 1.19 1.19
Avg.Win.Day 115.75 129.44 118.06 102.66 109.32
Med.Win.Day 96.00 104.99 98.53 88.60 88.28
Avg.Losing.Day -111.34 -129.57 -122.13 -110.91 -117.36
Med.Losing.Day -86.50 -92.48 -89.56 -82.30 -87.95
Avg.Daily.PL 11.69 11.78 12.44 9.13 9.87
Med.Daily.PL 16.38 16.83 21.71 21.41 20.15
Std.Dev.Daily.PL.1 147.33 171.22 159.08 134.32 147.41
Ann.Sharpe 1.26 1.09 1.24 1.08 1.06
Max.Drawdown -2338.43 -2430.09 -2168.66 -2982.50 -2904.73
Profit.To.Max.Draw 6.58 6.41 7.47 3.97 4.35
Avg.WinLoss.Ratio 1.04 1.00 0.97 0.93 0.93
Med.WinLoss.Ratio 1.11 1.14 1.10 1.08 1.00
Max.Equity 15968.41 16789.50 17435.72 13048.24 13773.99
Min.Equity -17.93 -188.46 0.00 -393.45 -100.42
End.Equity 15389.57 15578.88 16204.18 11846.58 12646.07
EWH EWJ EWS EWT EWU
Total.Net.Profit 12085.74 7457.81 13356.23 6906.24 7492.71
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 9.70 6.73 10.26 5.89 5.99
Med.Day.PL 12.96 11.70 20.48 8.74 15.91
Largest.Winner 518.58 677.56 659.34 716.23 557.67
Largest.Loser -977.28 -498.25 -1032.26 -1114.68 -922.23
Gross.Profits 76296.60 72956.55 76089.41 69500.58 71225.98
Gross.Losses -64210.86 -65498.74 -62733.18 -62594.34 -63733.27
Std.Dev.Daily.PL 148.85 163.57 140.94 149.35 139.57
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 1.11 1.21 1.11 1.12
Avg.Win.Day 114.39 128.44 104.81 114.31 106.31
Med.Win.Day 89.18 99.48 82.86 92.69 91.01
Avg.Losing.Day -110.90 -121.29 -108.91 -110.79 -109.88
Med.Losing.Day -82.75 -92.33 -86.52 -80.77 -82.34
Avg.Daily.PL 9.70 6.73 10.26 5.89 5.99
Med.Daily.PL 12.96 11.70 20.48 8.74 15.91
Std.Dev.Daily.PL.1 148.85 163.57 140.94 149.35 139.57
Ann.Sharpe 1.03 0.65 1.16 0.63 0.68
Max.Drawdown -2229.93 -4036.69 -2021.12 -3147.85 -2599.57
Profit.To.Max.Draw 5.42 1.85 6.61 2.19 2.88
Avg.WinLoss.Ratio 1.03 1.06 0.96 1.03 0.97
Med.WinLoss.Ratio 1.08 1.08 0.96 1.15 1.11
Max.Equity 13043.23 8395.92 14415.11 6906.24 9160.15
Min.Equity -33.87 -274.69 -699.37 -788.28 -327.38
End.Equity 12085.74 7457.81 13356.23 6906.24 7492.71
EWY EWZ EZU IEF IGE
Total.Net.Profit 9736.49 16814.33 13135.27 17932.39 13435.41
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 7.82 12.29 10.20 14.70 10.43
Med.Day.PL 19.58 24.81 18.68 15.24 22.02
Largest.Winner 551.45 638.31 641.61 718.28 641.62
Largest.Loser -850.59 -873.96 -1149.58 -629.94 -585.35
Gross.Profits 78146.89 91623.76 78313.24 89399.23 87064.44
Gross.Losses -68410.40 -74809.43 -65177.97 -71466.84 -73629.04
Std.Dev.Daily.PL 155.20 158.93 147.61 169.04 160.78
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 1.14 1.22 1.20 1.25 1.18
Avg.Win.Day 113.75 118.99 111.56 138.18 122.63
Med.Win.Day 92.47 99.96 89.60 111.01 100.82
Avg.Losing.Day -122.60 -125.10 -111.23 -124.72 -127.39
Med.Losing.Day -87.06 -96.89 -82.02 -100.19 -101.57
Avg.Daily.PL 7.82 12.29 10.20 14.70 10.43
Med.Daily.PL 19.58 24.81 18.68 15.24 22.02
Std.Dev.Daily.PL.1 155.20 158.93 147.61 169.04 160.78
Ann.Sharpe 0.80 1.23 1.10 1.38 1.03
Max.Drawdown -2689.16 -2599.61 -2764.56 -1475.57 -2439.52
Profit.To.Max.Draw 3.62 6.47 4.75 12.15 5.51
Avg.WinLoss.Ratio 0.93 0.95 1.00 1.11 0.96
Med.WinLoss.Ratio 1.06 1.03 1.09 1.11 0.99
Max.Equity 9736.49 17637.00 14909.94 18695.22 13435.41
Min.Equity -392.89 0.00 0.00 -127.86 -654.86
End.Equity 9736.49 16814.33 13135.27 17932.39 13435.41
IYR IYZ LQD RWR SHY
Total.Net.Profit 13555.67 7434.57 12091.15 13301.24 31955.85
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 10.33 6.13 9.37 10.05 22.78
Med.Day.PL 13.97 11.30 13.65 14.07 23.56
Largest.Winner 690.00 539.17 414.09 701.08 743.43
Largest.Loser -995.13 -747.09 -1607.99 -999.24 -896.22
Gross.Profits 80483.61 60768.48 65938.33 81751.44 104570.57
Gross.Losses -66927.95 -53333.91 -53847.18 -68450.20 -72614.72
Std.Dev.Daily.PL 150.96 123.03 125.94 153.36 167.92
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 1.20 1.14 1.22 1.19 1.44
Avg.Win.Day 113.20 94.80 91.58 114.66 131.37
Med.Win.Day 95.20 70.59 74.82 94.50 95.01
Avg.Losing.Day -111.36 -93.24 -94.47 -112.03 -119.63
Med.Losing.Day -79.94 -70.65 -73.01 -78.78 -95.52
Avg.Daily.PL 10.33 6.13 9.37 10.05 22.78
Med.Daily.PL 13.97 11.30 13.65 14.07 23.56
Std.Dev.Daily.PL.1 150.96 123.03 125.94 153.36 167.92
Ann.Sharpe 1.09 0.79 1.18 1.04 2.15
Max.Drawdown -2623.12 -2791.39 -3237.00 -2463.55 -1756.33
Profit.To.Max.Draw 5.17 2.66 3.74 5.40 18.19
Avg.WinLoss.Ratio 1.02 1.02 0.97 1.02 1.10
Med.WinLoss.Ratio 1.19 1.00 1.02 1.20 0.99
Max.Equity 15608.04 8133.92 12349.90 14777.73 32781.60
Min.Equity -473.13 -520.47 -146.25 -314.85 -63.98
End.Equity 13555.67 7434.57 12091.15 13301.24 31955.85
TLT XLB XLE XLF XLI
Total.Net.Profit 9170.38 6286.92 9724.35 6689.67 9474.51
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 7.79 4.98 7.45 5.80 7.37
Med.Day.PL 14.24 13.77 12.90 11.39 12.93
Largest.Winner 779.53 558.63 506.82 417.23 725.14
Largest.Loser -626.74 -760.41 -498.32 -870.83 -603.54
Gross.Profits 80421.50 70434.95 78663.61 58593.75 63680.92
Gross.Losses -71251.12 -64148.03 -68939.26 -51904.08 -54206.41
Std.Dev.Daily.PL 169.42 137.85 145.10 126.64 121.34
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 1.13 1.10 1.14 1.13 1.17
Avg.Win.Day 131.19 103.58 112.06 96.53 89.57
Med.Win.Day 100.56 87.71 92.88 73.21 70.48
Avg.Losing.Day -126.33 -110.22 -114.14 -95.06 -94.44
Med.Losing.Day -96.87 -84.01 -92.03 -68.77 -74.02
Avg.Daily.PL 7.79 4.98 7.45 5.80 7.37
Med.Daily.PL 14.24 13.77 12.90 11.39 12.93
Std.Dev.Daily.PL.1 169.42 137.85 145.10 126.64 121.34
Ann.Sharpe 0.73 0.57 0.81 0.73 0.96
Max.Drawdown -4200.46 -2545.47 -3708.60 -2393.02 -2159.46
Profit.To.Max.Draw 2.18 2.47 2.62 2.80 4.39
Avg.WinLoss.Ratio 1.04 0.94 0.98 1.02 0.95
Med.WinLoss.Ratio 1.04 1.04 1.01 1.06 0.95
Max.Equity 11046.45 6319.32 10527.81 8171.61 9481.43
Min.Equity -367.76 -489.76 -301.10 -458.76 -348.23
End.Equity 9170.38 6286.92 9724.35 6689.67 9474.51
XLK XLP XLU XLV XLY
Total.Net.Profit 6074.82 6211.79 14167.62 2959.63 10416.38
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 5.00 4.84 10.21 2.51 8.44
Med.Day.PL 17.93 15.90 16.14 6.56 12.17
Largest.Winner 574.72 900.15 556.47 473.90 769.98
Largest.Loser -724.67 -556.91 -838.97 -710.57 -629.37
Gross.Profits 61490.68 61791.76 69063.01 54247.40 64353.02
Gross.Losses -55415.86 -55579.98 -54895.40 -51287.76 -53936.65
Std.Dev.Daily.PL 125.72 118.81 118.48 117.04 126.47
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 1.11 1.11 1.26 1.06 1.19
Avg.Win.Day 91.23 87.65 89.69 87.92 98.55
Med.Win.Day 73.60 71.94 71.86 72.65 77.55
Avg.Losing.Day -102.24 -95.99 -88.83 -91.42 -92.83
Med.Losing.Day -74.44 -75.68 -64.76 -73.67 -74.04
Avg.Daily.PL 5.00 4.84 10.21 2.51 8.44
Med.Daily.PL 17.93 15.90 16.14 6.56 12.17
Std.Dev.Daily.PL.1 125.72 118.81 118.48 117.04 126.47
Ann.Sharpe 0.63 0.65 1.37 0.34 1.06
Max.Drawdown -2615.33 -2565.79 -1696.88 -2604.95 -2431.47
Profit.To.Max.Draw 2.32 2.42 8.35 1.14 4.28
Avg.WinLoss.Ratio 0.89 0.91 1.01 0.96 1.06
Med.WinLoss.Ratio 0.99 0.95 1.11 0.99 1.05
Max.Equity 6786.94 6374.13 14371.31 4236.64 10538.74
Min.Equity -523.50 -269.87 0.00 -205.49 -154.97
End.Equity 6074.82 6211.79 14167.62 2959.63 10416.38
#portfolio cash PL
portPL <- .blotter$portfolio.TVI_osATR$summary$Net.Trading.PL
#Cash Sharpe
(SharpeRatio.annualized(portPL, geometric=FALSE))
> (SharpeRatio.annualized(portPL, geometric=FALSE))
Net.Trading.PL
Annualized Sharpe Ratio (Rf=0%) 1.383361
So a cash Sharpe (a conservative estimate) a healthy amount higher than 1. Now let’s look at something interesting. Remember those base instrument correlations at the beginning of this post?
#Portfolio comparisons to SPY
instRets <- PortfReturns(account.st)
#Correlations
instCors <- cor(instRets)
diag(instRets) <- NA
corMeans <- rowMeans(instCors, na.rm=TRUE)
names(corMeans) <- gsub(".DailyEndEq", "", names(corMeans))
print(round(corMeans,3))
mean(corMeans)
> print(round(corMeans,3))
EFA EPP EWA EWC EWG EWH EWJ EWS EWT EWU
0.503 0.456 0.406 0.392 0.457 0.392 0.354 0.417 0.355 0.452
EWY EWZ EZU IEF IGE IYR IYZ LQD RWR SHY
0.399 0.387 0.471 -0.001 0.384 0.322 0.375 0.078 0.313 -0.013
TLT XLB XLE XLF XLI XLK XLP XLU XLV XLY
0.009 0.447 0.362 0.407 0.434 0.407 0.333 0.314 0.336 0.412
> mean(corMeans)
[1] 0.3452772
With this (somewhat) simplistic market timer, the correlations of some dangerously correlated instruments have been, on aggregate, sliced by more than 50%. Pretty impressive, no?
Let’s look at equity curve comparisons.
cumPortfRets <- cumprod(1+portfRets)
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)
comparison <- cbind(cumPortfRets, cumSPYrets)
colnames(comparison) <- c("strategy", "SPY")
chart.TimeSeries(comparison, legend.loc = "topleft",
main=paste0("Period=", period, ", Delta=",delta), colors=c("green","red"))
To compare, here is the equity curve with all three strategies–buy and hold the SPY, and the two TVI strategies–the ATR in green and the equal dollar weight in black.
Notice how, with better order sizing, that the recession barely even scratched the equity curve?
Here are the aggregate portfolio statistics:
#Sharpe, Returns, max DD
SharpeRatio.annualized(portfRets)
Return.annualized(portfRets)
maxDrawdown(portfRets)
> SharpeRatio.annualized(portfRets)
[,1]
Annualized Sharpe Ratio (Rf=0%) 1.428448
> Return.annualized(portfRets)
[,1]
Annualized Return 0.1504228
> maxDrawdown(portfRets)
[1] 0.1103311
First off: annualized Sharpe Ratio above 1.4. Daily returns. Next, something that personally impresses me: annualized return higher than maximum drawdown. My interpretation of this is that while you *may* have the occasional down year, on average, even in the absolute worst case scenario, it takes you less than a year to recover from your absolute worst drawdown.
And keep in mind, this is with 30 instruments, most of them highly correlated!
Lastly, let’s look at an individual instrument’s equity curve and how the position-sizing algorithm helps out.
#Individual instrument equity curve chart.Posn(portfolio.st, "XLB") #The triggerLag is NOT 30 for the strategy, just amplified in this case to illustrate exit logic. #The actual trigger lag is defaulted at 1. tmp <- TVI(Cl(XLB), period=period, delta=delta, triggerLag=1) add_TA(tmp$vigor, lwd=3) add_TA(tmp$trigger, on=5, col="red", lwd=1.5) tmp2 <- lagATR(HLC=HLC(XLB), n=period) add_TA(tmp2$atr, col="blue", lwd=2)
Remember how even the average win to loss ratios went up? This is why. Notice the height of the blue rectangles (position sizes up, duration of trade across), in relation to the ATR (the blue line across the bottom). In the depths of the financial crisis, even though the actual strategy wasn’t intelligent enough to know to keep out, through the use of ATR position sizing, it reduced trade sizes considerably. The result was a failsafe that prevented a great deal of damage to a system that had no idea it was trading against a massive longer time horizon trend going in the opposite direction.
Of course, this does not mean that ATR order sizing on entry is a complete catch-all for everything that can go wrong. At longer time frames, an entry signal’s calculation may have little relevance to the actual risk of the position currently. On this strategy, because I was using a 20-day period, I felt that the issue of rebalancing wouldn’t be a major factor, because old positions were exited, and new positions were entered at a good pace (about 1,000 trades in 7 years is 142 trades per year on average, over 30 instruments, that’s around 4 trades per year per instrument, which puts each trade at a couple of months on average, and considering that rebalancing can happen monthly to quarterly, rebalancing isn’t an issue at this frequency). However, this does not apply to longer time frames.
For instance, if the period (both for the Trend Vigor and for the ATR computation) were changed to 60 days, these are the results:
trade stats:
EFA EPP EWA EWC EWG
Num.Txns 21.00 19.00 17.00 15.00 21.00
Num.Trades 11.00 10.00 9.00 8.00 11.00
Net.Trading.PL 10208.50 17160.90 16467.19 16571.75 10873.05
Avg.Trade.PL 928.05 1716.09 1829.69 2071.47 988.46
Med.Trade.PL 1139.43 1599.47 2284.16 2714.11 1024.49
Largest.Winner 3958.71 6239.36 4809.68 4067.28 5039.72
Largest.Loser -2055.34 -1680.48 -1293.99 -552.08 -1506.05
Gross.Profits 14866.20 20617.57 19559.85 17387.68 14996.28
Gross.Losses -4657.70 -3456.67 -3092.66 -815.93 -4123.23
Std.Dev.Trade.PL 1986.71 2532.82 2298.49 1699.23 2040.81
Percent.Positive 63.64 70.00 66.67 75.00 63.64
Percent.Negative 36.36 30.00 33.33 25.00 36.36
Profit.Factor 3.19 5.96 6.32 21.31 3.64
Avg.Win.Trade 2123.74 2945.37 3259.97 2897.95 2142.33
Med.Win.Trade 1635.86 2404.87 3413.33 2931.19 1490.68
Avg.Losing.Trade -1164.43 -1152.22 -1030.89 -407.97 -1030.81
Med.Losing.Trade -1165.87 -1088.41 -954.82 -407.97 -1038.36
Avg.Daily.PL 857.26 1696.47 2070.98 2155.75 940.86
Med.Daily.PL 822.59 1306.31 2284.16 2874.79 668.54
Std.Dev.Daily.PL 2079.51 2685.65 3206.53 1817.23 2144.75
Ann.Sharpe 6.54 10.03 10.25 18.83 6.96
Max.Drawdown -5394.64 -3799.80 -3919.36 -3229.19 -5185.89
Profit.To.Max.Draw 1.89 4.52 4.20 5.13 2.10
Avg.WinLoss.Ratio 1.82 2.56 3.16 7.10 2.08
Med.WinLoss.Ratio 1.40 2.21 3.57 7.18 1.44
Max.Equity 13816.60 18136.21 17072.51 16571.75 14015.59
Min.Equity 0.00 -135.30 0.00 -132.86 -75.34
End.Equity 10208.50 17160.90 16467.19 16571.75 10873.05
EWH EWJ EWS EWT EWU
Num.Txns 19.00 25.00 19.00 21.00 25.00
Num.Trades 10.00 13.00 9.00 11.00 13.00
Net.Trading.PL 12558.12 8228.69 15686.23 4112.81 6421.97
Avg.Trade.PL 1255.81 632.98 1742.91 373.89 494.00
Med.Trade.PL 1286.07 38.30 1543.49 131.24 1188.66
Largest.Winner 5381.90 5983.06 6090.42 2292.56 2041.08
Largest.Loser -1189.78 -1476.27 -787.18 -1439.03 -1987.03
Gross.Profits 14737.19 12329.23 17166.54 8550.62 10961.68
Gross.Losses -2179.07 -4100.54 -1480.31 -4437.82 -4539.71
Std.Dev.Trade.PL 1962.01 2047.60 2255.20 1461.94 1278.47
Percent.Positive 70.00 53.85 77.78 63.64 61.54
Percent.Negative 30.00 46.15 22.22 36.36 38.46
Profit.Factor 6.76 3.01 11.60 1.93 2.41
Avg.Win.Trade 2105.31 1761.32 2452.36 1221.52 1370.21
Med.Win.Trade 1722.40 454.78 1586.46 1018.02 1478.14
Avg.Losing.Trade -726.36 -683.42 -740.16 -1109.45 -907.94
Med.Losing.Trade -908.19 -673.37 -740.16 -1169.46 -877.51
Avg.Daily.PL 1161.34 543.61 1762.47 113.24 434.83
Med.Daily.PL 1051.12 -79.18 1250.27 73.92 768.38
Std.Dev.Daily.PL 2056.75 2112.00 2410.10 1242.73 1316.60
Ann.Sharpe 8.96 4.09 11.61 1.45 5.24
Max.Drawdown -4368.83 -6749.29 -3010.28 -4204.52 -4997.13
Profit.To.Max.Draw 2.87 1.22 5.21 0.98 1.29
Avg.WinLoss.Ratio 2.90 2.58 3.31 1.10 1.51
Med.WinLoss.Ratio 1.90 0.68 2.14 0.87 1.68
Max.Equity 13935.41 13216.89 15878.52 4375.25 9759.45
Min.Equity -281.46 0.00 0.00 -22.49 0.00
End.Equity 12558.12 8228.69 15686.23 4112.81 6421.97
EWY EWZ EZU IEF IGE
Num.Txns 15.00 15.00 19.00 22.00 25.00
Num.Trades 8.00 8.00 10.00 11.00 13.00
Net.Trading.PL 13779.39 23013.79 7849.71 10099.65 14095.94
Avg.Trade.PL 1722.42 2876.72 784.97 918.15 1084.30
Med.Trade.PL 1977.00 2866.24 1019.40 395.20 45.68
Largest.Winner 3889.04 6791.13 2859.00 4103.15 5685.82
Largest.Loser -1312.72 -1003.77 -1640.20 -1292.50 -1069.15
Gross.Profits 15092.11 24017.56 10979.15 12939.41 17823.91
Gross.Losses -1312.72 -1003.77 -3129.45 -2839.76 -3727.97
Std.Dev.Trade.PL 1594.21 2830.98 1540.22 1747.80 2125.97
Percent.Positive 87.50 87.50 70.00 63.64 53.85
Percent.Negative 12.50 12.50 30.00 36.36 46.15
Profit.Factor 11.50 23.93 3.51 4.56 4.78
Avg.Win.Trade 2156.02 3431.08 1568.45 1848.49 2546.27
Med.Win.Trade 2339.69 3735.41 1562.23 1595.67 2222.50
Avg.Losing.Trade -1312.72 -1003.77 -1043.15 -709.94 -621.33
Med.Losing.Trade -1312.72 -1003.77 -1205.35 -726.74 -543.04
Avg.Daily.PL 1633.02 3143.63 786.64 918.15 989.45
Med.Daily.PL 1614.30 3735.41 1268.81 395.20 -134.88
Std.Dev.Daily.PL 1700.14 2947.08 1633.64 1747.80 2191.58
Ann.Sharpe 15.25 16.93 7.64 8.34 7.17
Max.Drawdown -4564.52 -4072.32 -5298.53 -4019.55 -3449.65
Profit.To.Max.Draw 3.02 5.65 1.48 2.51 4.09
Avg.WinLoss.Ratio 1.64 3.42 1.50 2.60 4.10
Med.WinLoss.Ratio 1.78 3.72 1.30 2.20 4.09
Max.Equity 13779.39 23910.96 10592.36 12909.83 14200.07
Min.Equity 0.00 0.00 -165.41 -1675.30 -88.76
End.Equity 13779.39 23013.79 7849.71 10099.65 14095.94
IYR IYZ LQD RWR SHY
Num.Txns 17.00 21.00 20.00 19.00 14.00
Num.Trades 9.00 11.00 10.00 10.00 7.00
Net.Trading.PL 12982.75 9649.19 4756.41 11097.68 30866.81
Avg.Trade.PL 1442.53 877.20 475.64 1109.77 4409.54
Med.Trade.PL 1332.53 846.90 172.62 1280.34 449.49
Largest.Winner 3712.91 5017.76 3474.77 4332.24 24644.48
Largest.Loser -515.27 -977.05 -891.57 -993.55 -259.33
Gross.Profits 13790.04 11967.93 7704.54 13487.26 31126.14
Gross.Losses -807.29 -2318.75 -2948.14 -2389.57 -259.33
Std.Dev.Trade.PL 1542.81 1654.02 1388.08 1710.13 9013.08
Percent.Positive 77.78 72.73 50.00 70.00 85.71
Percent.Negative 22.22 27.27 50.00 30.00 14.29
Profit.Factor 17.08 5.16 2.61 5.64 120.03
Avg.Win.Trade 1970.01 1495.99 1540.91 1926.75 5187.69
Med.Win.Trade 1596.75 1104.29 1437.80 1685.60 1540.67
Avg.Losing.Trade -403.65 -772.92 -589.63 -796.52 -259.33
Med.Losing.Trade -403.65 -916.94 -725.42 -886.53 -259.33
Avg.Daily.PL 1480.73 770.38 475.64 1130.97 4409.54
Med.Daily.PL 1464.64 617.43 172.62 1641.75 449.49
Std.Dev.Daily.PL 1644.78 1703.02 1388.08 1812.47 9013.08
Ann.Sharpe 14.29 7.18 5.44 9.91 7.77
Max.Drawdown -4095.25 -2939.04 -3263.55 -4582.43 -3537.22
Profit.To.Max.Draw 3.17 3.28 1.46 2.42 8.73
Avg.WinLoss.Ratio 4.88 1.94 2.61 2.42 20.00
Med.WinLoss.Ratio 3.96 1.20 1.98 1.90 5.94
Max.Equity 13142.58 9649.19 5704.58 12750.19 31638.96
Min.Equity -257.82 -18.03 -876.30 -336.91 -401.25
End.Equity 12982.75 9649.19 4756.41 11097.68 30866.81
TLT XLB XLE XLF XLI
Num.Txns 20.00 23.00 27.00 17.00 17.00
Num.Trades 10.00 12.00 14.00 9.00 9.00
Net.Trading.PL 7984.42 10276.48 15328.84 2931.55 11452.17
Avg.Trade.PL 798.44 856.37 1094.92 325.73 1272.46
Med.Trade.PL 635.82 553.43 298.85 353.89 1530.29
Largest.Winner 4084.20 3877.14 10982.05 1552.10 3382.70
Largest.Loser -1295.01 -1514.24 -1066.86 -1658.50 -1082.79
Gross.Profits 11035.29 13539.19 18826.91 5044.64 13147.30
Gross.Losses -3050.87 -3262.71 -3498.08 -2113.09 -1695.13
Std.Dev.Trade.PL 1656.89 1654.32 3020.85 1003.42 1538.10
Percent.Positive 60.00 58.33 50.00 77.78 66.67
Percent.Negative 40.00 41.67 50.00 22.22 33.33
Profit.Factor 3.62 4.15 5.38 2.39 7.76
Avg.Win.Trade 1839.22 1934.17 2689.56 720.66 2191.22
Med.Win.Trade 1779.55 1758.72 1297.88 602.56 1887.54
Avg.Losing.Trade -762.72 -652.54 -499.73 -1056.55 -565.04
Med.Losing.Trade -616.18 -444.05 -502.26 -1056.55 -482.61
Avg.Daily.PL 798.44 733.48 993.83 248.29 1246.61
Med.Daily.PL 635.82 175.80 -75.82 215.38 1598.19
Std.Dev.Daily.PL 1656.89 1676.63 3119.46 1043.56 1642.21
Ann.Sharpe 7.65 6.94 5.06 3.78 12.05
Max.Drawdown -4815.13 -3002.83 -3697.94 -3305.04 -2288.62
Profit.To.Max.Draw 1.66 3.42 4.15 0.89 5.00
Avg.WinLoss.Ratio 2.41 2.96 5.38 0.68 3.88
Med.WinLoss.Ratio 2.89 3.96 2.58 0.57 3.91
Max.Equity 11680.33 10377.57 16209.04 4685.40 11458.63
Min.Equity -1228.87 -87.21 -130.15 -225.91 0.00
End.Equity 7984.42 10276.48 15328.84 2931.55 11452.17
XLK XLP XLU XLV XLY
Num.Txns 23.00 17.00 21.00 21.00 19.00
Num.Trades 12.00 9.00 11.00 11.00 10.00
Net.Trading.PL 5168.06 7233.14 9654.01 1295.79 4546.69
Avg.Trade.PL 430.67 803.68 877.64 117.80 454.67
Med.Trade.PL 28.36 167.20 412.15 332.08 418.47
Largest.Winner 2489.14 4607.82 6094.87 1824.31 2341.47
Largest.Loser -886.51 -2168.49 -1121.59 -1818.18 -1633.72
Gross.Profits 8101.55 10272.30 12840.30 6498.45 8842.45
Gross.Losses -2933.49 -3039.15 -3186.30 -5202.66 -4295.76
Std.Dev.Trade.PL 1117.36 1954.14 2261.27 1240.89 1461.48
Percent.Positive 50.00 55.56 54.55 54.55 50.00
Percent.Negative 50.00 44.44 45.45 45.45 50.00
Profit.Factor 2.76 3.38 4.03 1.25 2.06
Avg.Win.Trade 1350.26 2054.46 2140.05 1083.08 1768.49
Med.Win.Trade 1432.23 1902.15 790.75 978.13 1744.68
Avg.Losing.Trade -488.91 -759.79 -637.26 -1040.53 -859.15
Med.Losing.Trade -456.93 -335.80 -779.63 -820.91 -668.55
Avg.Daily.PL 336.75 666.37 912.78 47.83 367.23
Med.Daily.PL -184.80 -15.93 129.41 -121.08 -404.63
Std.Dev.Daily.PL 1121.11 2042.13 2380.42 1284.94 1522.13
Ann.Sharpe 4.77 5.18 6.09 0.59 3.83
Max.Drawdown -3136.49 -4108.70 -3440.49 -6294.99 -3508.84
Profit.To.Max.Draw 1.65 1.76 2.81 0.21 1.30
Avg.WinLoss.Ratio 2.76 2.70 3.36 1.04 2.06
Med.WinLoss.Ratio 3.13 5.66 1.01 1.19 2.61
Max.Equity 5216.66 7583.26 11588.28 4179.18 4986.43
Min.Equity -88.40 0.00 -144.19 -2115.81 0.00
End.Equity 5168.06 7233.14 9654.01 1295.79 4546.69
> (aggPF <- sum(tStats$Gross.Profits)/-sum(tStats$Gross.Losses))
[1] 4.86916
> (aggCorrect <- mean(tStats$Percent.Positive))
[1] 65.397
> (numTrades <- sum(tStats$Num.Trades))
[1] 309
> (meanAvgWLR <- mean(tStats$Avg.WinLoss.Ratio))
[1] 3.348667
The trade stats look better mainly because of the strength of the indicator to identify periods of good entries. However, the advantages end there.
Here are the daily stats:
EFA EPP EWA EWC EWG
Total.Net.Profit 10208.50 17160.90 16467.19 16571.75 10873.05
Total.Days 1315.00 1374.00 1413.00 1462.00 1225.00
Winning.Days 717.00 753.00 792.00 815.00 678.00
Losing.Days 598.00 621.00 621.00 647.00 547.00
Avg.Day.PL 7.76 12.49 11.65 11.33 8.88
Med.Day.PL 16.17 18.89 24.11 21.70 18.39
Largest.Winner 854.72 818.41 902.53 735.67 651.33
Largest.Loser -891.71 -1089.41 -1022.44 -691.88 -870.92
Gross.Profits 88275.97 110279.44 104118.90 97654.12 81458.62
Gross.Losses -78067.47 -93118.55 -87651.72 -81082.37 -70585.57
Std.Dev.Daily.PL 169.32 200.83 183.57 157.83 165.30
Percent.Positive 54.52 54.80 56.05 55.75 55.35
Percent.Negative 45.48 45.20 43.95 44.25 44.65
Profit.Factor 1.13 1.18 1.19 1.20 1.15
Avg.Win.Day 123.12 146.45 131.46 119.82 120.15
Med.Win.Day 96.83 118.04 108.51 102.89 94.74
Avg.Losing.Day -130.55 -149.95 -141.15 -125.32 -129.04
Med.Losing.Day -96.63 -102.98 -96.38 -91.98 -93.83
Avg.Daily.PL 7.76 12.49 11.65 11.33 8.88
Med.Daily.PL 16.17 18.89 24.11 21.70 18.39
Std.Dev.Daily.PL.1 169.32 200.83 183.57 157.83 165.30
Ann.Sharpe 0.73 0.99 1.01 1.14 0.85
Max.Drawdown -5394.64 -3799.80 -3919.36 -3229.19 -5185.89
Profit.To.Max.Draw 1.89 4.52 4.20 5.13 2.10
Avg.WinLoss.Ratio 0.94 0.98 0.93 0.96 0.93
Med.WinLoss.Ratio 1.00 1.15 1.13 1.12 1.01
Max.Equity 13816.60 18136.21 17072.51 16571.75 14015.59
Min.Equity 0.00 -135.30 0.00 -132.86 -75.34
End.Equity 10208.50 17160.90 16467.19 16571.75 10873.05
EWH EWJ EWS EWT EWU
Total.Net.Profit 12558.12 8228.69 15686.23 4112.81 6421.97
Total.Days 1334.00 1112.00 1337.00 1232.00 1294.00
Winning.Days 706.00 583.00 745.00 630.00 699.00
Losing.Days 628.00 529.00 592.00 602.00 595.00
Avg.Day.PL 9.41 7.40 11.73 3.34 4.96
Med.Day.PL 12.37 16.23 22.24 7.50 17.61
Largest.Winner 1132.42 747.36 1048.83 714.29 855.70
Largest.Loser -1149.08 -1130.40 -1334.88 -1051.58 -761.51
Gross.Profits 98567.49 88747.53 93204.72 77892.68 79104.53
Gross.Losses -86009.37 -80518.84 -77518.49 -73779.88 -72682.57
Std.Dev.Daily.PL 201.14 204.93 177.78 167.18 155.18
Percent.Positive 52.92 52.43 55.72 51.14 54.02
Percent.Negative 47.08 47.57 44.28 48.86 45.98
Profit.Factor 1.15 1.10 1.20 1.06 1.09
Avg.Win.Day 139.61 152.23 125.11 123.64 113.17
Med.Win.Day 98.81 110.77 95.35 96.74 94.35
Avg.Losing.Day -136.96 -152.21 -130.94 -122.56 -122.16
Med.Losing.Day -94.53 -109.95 -97.43 -91.36 -93.62
Avg.Daily.PL 9.41 7.40 11.73 3.34 4.96
Med.Daily.PL 12.37 16.23 22.24 7.50 17.61
Std.Dev.Daily.PL.1 201.14 204.93 177.78 167.18 155.18
Ann.Sharpe 0.74 0.57 1.05 0.32 0.51
Max.Drawdown -4368.83 -6749.29 -3010.28 -4204.52 -4997.13
Profit.To.Max.Draw 2.87 1.22 5.21 0.98 1.29
Avg.WinLoss.Ratio 1.02 1.00 0.96 1.01 0.93
Med.WinLoss.Ratio 1.05 1.01 0.98 1.06 1.01
Max.Equity 13935.41 13216.89 15878.52 4375.25 9759.45
Min.Equity -281.46 0.00 0.00 -22.49 0.00
End.Equity 12558.12 8228.69 15686.23 4112.81 6421.97
EWY EWZ EZU IEF
Total.Net.Profit 13779.39 23013.79 7849.71 10099.65
Total.Days 1423.00 1499.00 1260.00 1285.00
Winning.Days 777.00 841.00 683.00 659.00
Losing.Days 646.00 658.00 577.00 626.00
Avg.Day.PL 9.68 15.35 6.23 7.86
Med.Day.PL 17.91 24.89 17.35 6.75
Largest.Winner 869.03 1099.10 664.64 1116.66
Largest.Loser -838.15 -1215.42 -995.76 -967.58
Gross.Profits 109035.17 126735.25 80243.70 99184.62
Gross.Losses -95255.78 -103721.46 -72393.99 -89084.97
Std.Dev.Daily.PL 197.08 215.29 161.49 193.96
Percent.Positive 54.60 56.10 54.21 51.28
Percent.Negative 45.40 43.90 45.79 48.72
Profit.Factor 1.14 1.22 1.11 1.11
Avg.Win.Day 140.33 150.70 117.49 150.51
Med.Win.Day 111.32 112.94 93.24 116.02
Avg.Losing.Day -147.45 -157.63 -125.47 -142.31
Med.Losing.Day -103.45 -105.36 -90.08 -108.20
Avg.Daily.PL 9.68 15.35 6.23 7.86
Med.Daily.PL 17.91 24.89 17.35 6.75
Std.Dev.Daily.PL.1 197.08 215.29 161.49 193.96
Ann.Sharpe 0.78 1.13 0.61 0.64
Max.Drawdown -4564.52 -4072.32 -5298.53 -4019.55
Profit.To.Max.Draw 3.02 5.65 1.48 2.51
Avg.WinLoss.Ratio 0.95 0.96 0.94 1.06
Med.WinLoss.Ratio 1.08 1.07 1.04 1.07
Max.Equity 13779.39 23910.96 10592.36 12909.83
Min.Equity 0.00 0.00 -165.41 -1675.30
End.Equity 13779.39 23013.79 7849.71 10099.65
IGE IYR IYZ LQD RWR
Total.Net.Profit 14095.94 12982.75 9649.19 4756.41 11097.68
Total.Days 1461.00 1314.00 1225.00 1350.00 1331.00
Winning.Days 793.00 728.00 653.00 718.00 722.00
Losing.Days 668.00 586.00 572.00 632.00 609.00
Avg.Day.PL 9.65 9.88 7.88 3.52 8.34
Med.Day.PL 21.30 16.00 9.14 9.95 13.44
Largest.Winner 663.26 578.88 516.66 591.08 614.36
Largest.Loser -819.01 -1139.51 -758.41 -491.67 -1201.72
Gross.Profits 116037.20 77715.47 60926.63 64184.63 83589.23
Gross.Losses -101941.26 -64732.72 -51277.45 -59428.22 -72491.55
Std.Dev.Daily.PL 194.37 150.80 124.66 119.90 164.61
Percent.Positive 54.28 55.40 53.31 53.19 54.24
Percent.Negative 45.72 44.60 46.69 46.81 45.76
Profit.Factor 1.14 1.20 1.19 1.08 1.15
Avg.Win.Day 146.33 106.75 93.30 89.39 115.77
Med.Win.Day 118.07 84.95 68.24 72.26 90.32
Avg.Losing.Day -152.61 -110.47 -89.65 -94.03 -119.03
Med.Losing.Day -115.51 -74.56 -64.29 -74.35 -78.63
Avg.Daily.PL 9.65 9.88 7.88 3.52 8.34
Med.Daily.PL 21.30 16.00 9.14 9.95 13.44
Std.Dev.Daily.PL.1 194.37 150.80 124.66 119.90 164.61
Ann.Sharpe 0.79 1.04 1.00 0.47 0.80
Max.Drawdown -3449.65 -4095.25 -2939.04 -3263.55 -4582.43
Profit.To.Max.Draw 4.09 3.17 3.28 1.46 2.42
Avg.WinLoss.Ratio 0.96 0.97 1.04 0.95 0.97
Med.WinLoss.Ratio 1.02 1.14 1.06 0.97 1.15
Max.Equity 14200.07 13142.58 9649.19 5704.58 12750.19
Min.Equity -88.76 -257.82 -18.03 -876.30 -336.91
End.Equity 14095.94 12982.75 9649.19 4756.41 11097.68
SHY TLT XLB XLE XLF
Total.Net.Profit 30866.81 7984.42 10276.48 15328.84 2931.55
Total.Days 1562.00 1245.00 1331.00 1456.00 1095.00
Winning.Days 874.00 644.00 731.00 798.00 570.00
Losing.Days 688.00 601.00 600.00 658.00 525.00
Avg.Day.PL 19.76 6.41 7.72 10.53 2.68
Med.Day.PL 21.92 10.54 16.37 17.80 7.67
Largest.Winner 809.44 1027.71 570.55 843.05 534.17
Largest.Loser -975.79 -728.07 -622.80 -1083.92 -930.35
Gross.Profits 113467.63 99021.87 80646.28 112733.44 54186.21
Gross.Losses -82600.83 -91037.45 -70369.80 -97404.60 -51254.66
Std.Dev.Daily.PL 170.13 202.61 148.19 196.05 130.52
Percent.Positive 55.95 51.73 54.92 54.81 52.05
Percent.Negative 44.05 48.27 45.08 45.19 47.95
Profit.Factor 1.37 1.09 1.15 1.16 1.06
Avg.Win.Day 129.83 153.76 110.32 141.27 95.06
Med.Win.Day 93.07 115.64 91.77 110.41 74.69
Avg.Losing.Day -120.06 -151.48 -117.28 -148.03 -97.63
Med.Losing.Day -92.93 -116.88 -86.95 -105.73 -68.38
Avg.Daily.PL 19.76 6.41 7.72 10.53 2.68
Med.Daily.PL 21.92 10.54 16.37 17.80 7.67
Std.Dev.Daily.PL.1 170.13 202.61 148.19 196.05 130.52
Ann.Sharpe 1.84 0.50 0.83 0.85 0.33
Max.Drawdown -3537.22 -4815.13 -3002.83 -3697.94 -3305.04
Profit.To.Max.Draw 8.73 1.66 3.42 4.15 0.89
Avg.WinLoss.Ratio 1.08 1.02 0.94 0.95 0.97
Med.WinLoss.Ratio 1.00 0.99 1.06 1.04 1.09
Max.Equity 31638.96 11680.33 10377.57 16209.04 4685.40
Min.Equity -401.25 -1228.87 -87.21 -130.15 -225.91
End.Equity 30866.81 7984.42 10276.48 15328.84 2931.55
XLI XLK XLP XLU XLV
Total.Net.Profit 11452.17 5168.06 7233.14 9654.01 1295.79
Total.Days 1323.00 1230.00 1382.00 1348.00 1179.00
Winning.Days 731.00 681.00 751.00 735.00 606.00
Losing.Days 592.00 549.00 631.00 613.00 573.00
Avg.Day.PL 8.66 4.20 5.23 7.16 1.10
Med.Day.PL 12.27 15.06 13.67 15.33 5.21
Largest.Winner 667.88 651.97 645.78 544.81 1086.79
Largest.Loser -681.83 -702.78 -743.00 -677.52 -784.28
Gross.Profits 70933.60 65526.03 68115.23 71114.61 57258.43
Gross.Losses -59481.42 -60357.97 -60882.09 -61460.60 -55962.63
Std.Dev.Daily.PL 134.55 138.48 123.71 133.61 131.08
Percent.Positive 55.25 55.37 54.34 54.53 51.40
Percent.Negative 44.75 44.63 45.66 45.47 48.60
Profit.Factor 1.19 1.09 1.12 1.16 1.02
Avg.Win.Day 97.04 96.22 90.70 96.75 94.49
Med.Win.Day 73.44 75.24 73.21 76.94 77.97
Avg.Losing.Day -100.48 -109.94 -96.49 -100.26 -97.67
Med.Losing.Day -73.30 -80.20 -73.80 -67.78 -74.02
Avg.Daily.PL 8.66 4.20 5.23 7.16 1.10
Med.Daily.PL 12.27 15.06 13.67 15.33 5.21
Std.Dev.Daily.PL.1 134.55 138.48 123.71 133.61 131.08
Ann.Sharpe 1.02 0.48 0.67 0.85 0.13
Max.Drawdown -2288.62 -3136.49 -4108.70 -3440.49 -6294.99
Profit.To.Max.Draw 5.00 1.65 1.76 2.81 0.21
Avg.WinLoss.Ratio 0.97 0.88 0.94 0.97 0.97
Med.WinLoss.Ratio 1.00 0.94 0.99 1.14 1.05
Max.Equity 11458.63 5216.66 7583.26 11588.28 4179.18
Min.Equity 0.00 -88.40 0.00 -144.19 -2115.81
End.Equity 11452.17 5168.06 7233.14 9654.01 1295.79
XLY
Total.Net.Profit 4546.69
Total.Days 1148.00
Winning.Days 603.00
Losing.Days 545.00
Avg.Day.PL 3.96
Med.Day.PL 9.85
Largest.Winner 490.31
Largest.Loser -726.59
Gross.Profits 54521.44
Gross.Losses -49974.75
Std.Dev.Daily.PL 121.37
Percent.Positive 52.53
Percent.Negative 47.47
Profit.Factor 1.09
Avg.Win.Day 90.42
Med.Win.Day 73.22
Avg.Losing.Day -91.70
Med.Losing.Day -69.21
Avg.Daily.PL 3.96
Med.Daily.PL 9.85
Std.Dev.Daily.PL.1 121.37
Ann.Sharpe 0.52
Max.Drawdown -3508.84
Profit.To.Max.Draw 1.30
Avg.WinLoss.Ratio 0.99
Med.WinLoss.Ratio 1.06
Max.Equity 4986.43
Min.Equity 0.00
End.Equity 4546.69
Compared to the previous equity curve, the drawdowns here are more pronounced. So how much do we pay for having this higher “set it and forget it” holding period?
> SharpeRatio.annualized(portfRets)
[,1]
Annualized Sharpe Ratio (Rf=0%) 1.099297
> Return.annualized(portfRets)
[,1]
Annualized Return 0.1393566
> maxDrawdown(portfRets)
[1] 0.183505
Turns out, a fair bit. The Sharpe Ratio comes down quite a bit, the returns are slightly lower, but the drawdown is much higher, crossing back under that boundary of annualized returns higher than maximum drawdown. Of course, this isn’t all attributable to stale ATR calculations, as order sizing and rebalancing won’t save a strategy from holding onto bad trades, but not rebalancing certainly does nobody any favors at the longer holding timeframes.
Here’s a picture of a single instrument, length of positions, and the indicators.
Would it have been nice to have some rebalancing for those longer timeframe trades? Yep.
Finally, is the equity curve comparison taken further, to the original 100-day period.
And the corresponding three statistics:
> SharpeRatio.annualized(portfRets)
[,1]
Annualized Sharpe Ratio (Rf=0%) 0.8681733
> Return.annualized(portfRets)
[,1]
Annualized Return 0.1366685
> maxDrawdown(portfRets)
[1] 0.2241631
Definitely not a good look. Sharpe back under 1, and drawdowns at more than 20%? What kind of returns can we get for such drawdowns? Wait until the end of the post, and I’ll show you.
The beginning of the volatility preceding the financial crisis caused some violent drawdowns (notice the actual bear market didn’t cause so much). Could some of this damage have been mitigated?
The answer? Certainly (see the monotonic rise in ATR in 2007).
So, with all of this in mind, as promised, let’s see what sort of returns we can get for the 20 day period.
What if we took our original portfolio, and simply doubled the risk allocation–in other words, leveraged the original strategy 2:1?
Here’s the one line change:
#parameters (trigger lag unchanged, defaulted at 1) delta=0 period=20 pctATR=.04 #control risk with this parameter
Well, this is what happens:
And the statistics:
> SharpeRatio.annualized(portfRets)
[,1]
Annualized Sharpe Ratio (Rf=0%) 1.465359
> Return.annualized(portfRets)
[,1]
Annualized Return 0.3088355
> maxDrawdown(portfRets)
[1] 0.2109036
About 31% annualized returns, with slightly over 20% drawdowns. Considering that the stock market has much higher drawdowns, this is a pretty good risk-return profile. If we’re willing to go above 30% drawdown, this is the resulting equity curve:
At this point, the equity curve for SPY becomes almost a flat line by comparison–not because its drawdowns are smaller (at the height of the crisis, they were over 60%), but because of proper position sizing. Here are the corresponding three statistics:
> SharpeRatio.annualized(portfRets)
[,1]
Annualized Sharpe Ratio (Rf=0%) 1.493416
> Return.annualized(portfRets)
[,1]
Annualized Return 0.4722279
> maxDrawdown(portfRets)
[1] 0.3022385
Of course, beyond this point, if one is willing to tolerate drawdowns, the annualized returns just start to get silly, but the drawdowns start to really show in 2010, when the fact that this system’s exits could still be improved, and its instrument selection (with a base correlation across all instruments of .7) starts quickly putting on the brakes on going beyond this point. For now anyway.
Thanks for reading.
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