Despite my best efforts, it’s been a month since the last post of this series. The first post replicated this simple RSI(2) strategy from the MarketSci Blog using R. The second post showed how to replicate the strategy that scales in/out of RSI(2).

This post will use the PerformanceAnalytics package to evaluate the rules that scale in/out of positions. I’ve also provided a simple function that provides some summary statistics. There is a lot of code, so I put it at the end of the post.

Table 1 contains output from my simple trade summary function (the wins and losses are in percentages, i.e. 0.69 is 69 basis points). The short side of the rule traded more often and had a lower win rate. The short side overcame its lower win rate via much higher mean and median win/loss ratios.

Table 1: RSI(2) Trade Statistics – RSI steps = 5, Size steps = 0.25

Signal	# Trades	% Win	Mean Win	Mean Loss	Median Win	Median Loss	Mean W/L	Median W/L
-1.00	133	58	0.69	-0.44	0.53	-0.25	1.55	2.12
-0.75	173	49	0.62	-0.39	0.37	-0.25	1.60	1.48
-0.50	143	54	0.43	-0.36	0.28	-0.19	1.19	1.51
-0.25	158	56	0.21	-0.19	0.14	-0.13	1.15	1.08
0.00	1262	0	NaN	NaN	NA	NA	NaN	NA
0.25	117	53	0.26	-0.31	0.18	-0.21	0.83	0.86
0.50	137	58	0.51	-0.58	0.31	-0.35	0.87	0.89
0.75	143	62	0.88	-0.89	0.50	-0.71	0.99	0.70
1.00	119	63	1.34	-1.41	0.80	-1.11	0.95	0.71

Table 2 shows the output from the PerformanceAnalytics table.Drawdowns() function. The largest percentage drawdown occurred in late 2008, but only lasted a few weeks.

The table also shows the system is prone to drawdowns that trough quickly and take months to recover from. A week of bad trades can take months to recover from.

Table 2: RSI(2) Drawdowns – RSI steps = 5, Size steps = 0.25

From	Trough	To	Depth	Length	To Trough	Recovery
2008-10-06	2008-10-10	2008-10-28	-0.157	17	5	12
2001-08-30	2001-09-21	2002-01-23	-0.091	96	12	84
2002-07-19	2002-07-23	2002-08-20	-0.088	23	3	20
2000-03-22	2000-04-14	2000-07-05	-0.076	73	18	55
2009-02-17	2009-02-23	2009-04-27	-0.070	49	5	44
2003-03-14	2003-03-21	2003-05-09	-0.055	40	6	34
2000-10-09	2000-10-12	2000-12-06	-0.052	42	4	38
2002-08-29	2002-09-24	2002-10-10	-0.051	30	18	12
2008-01-02	2008-01-22	2008-03-11	-0.045	48	14	34
2001-04-18	2001-06-18	2001-08-10	-0.045	81	43	38

Table 3 shows the output from the PerformanceAnalytics table.DownsideRisk() function. The ratio of gain/loss deviation is encouraging. I have to defer to the PerformanceAnalytics documentation and vingettes to describe the rest of the table.

Table 3: RSI(2) Downside Risk – RSI steps = 5, Size steps = 0.25

Statistic	Return
Semi Deviation	0.0050
Gain Deviation	0.0094
Loss Deviation	0.0076
Downside Deviation (MAR=10%)	0.0099
Downside Deviation (rf=0%)	0.0092
Downside Deviation (0%)	0.0092
Maximum Drawdown	-0.1572
VaR (99%)	0.0160
Beyond VaR	0.0160
Modified VaR (99%)	0.0705

The chart below shows the output from the PerformanceAnalytics charts.PerformanceSummary() function. It shows the equity curves and drawdown from peak for the long and short sides of the strategy. The middle graph shows the *daily* returns for the combined strategy.


The code below has everything that created the results above. It also contains the same results for a modified RSI(2) strategy. The modified strategy uses RSI steps of 10 and sizing steps of 0.3 (i.e. RSI<10 -> size=1, 10<20 -> size=0.7, etc.).

# Attach packages. You can install packages via:
# install.packages(c(“quantmod”,”TTR”,”PerformanceAnalytics”))
library(quantmod)
library(TTR)
library(PerformanceAnalytics)

# Pull S&P500 index data from Yahoo! Finance
getSymbols(“^GSPC”, from=”2000-01-01″)

# Calculate the RSI indicator
rsi <- RSI(Cl(GSPC), 2)

# Calculate Close-to-Close returns
ret <- ROC(Cl(GSPC))
ret[1] <- 0

# This function gives us some standard summary
# statistics for our trades.
tradeStats <- function(signals, returns) {
# Inputs:
# signals : trading signals
# returns : returns corresponding to signals

# Combine data and convert to data.frame
sysRet <- signals * returns * 100
posRet <- sysRet > 0 # Positive rule returns
negRet <- sysRet < 0 # Negative rule returns
dat <- cbind(signals,posRet*100,sysRet[posRet],sysRet[negRet],1)
dat <- as.data.frame(dat)

# Aggreate data for summary statistics
means <- aggregate(dat[,2:4], by=list(dat[,1]), mean, na.rm=TRUE)
medians <- aggregate(dat[,3:4], by=list(dat[,1]), median, na.rm=TRUE)
sums <- aggregate(dat[,5], by=list(dat[,1]), sum)

colnames(means) <- c("Signal","% Win","Mean Win","Mean Loss")
colnames(medians) <- c("Signal","Median Win","Median Loss")
colnames(sums) <- c("Signal","# Trades")

all <- merge(sums,means)
all <- merge(all,medians)

wl <- cbind( abs(all[,"Mean Win"]/all[,"Mean Loss"]),
abs(all[,”Median Win”]/all[,”Median Loss”]) )
colnames(wl) <- c("Mean W/L","Median W/L")

all <- cbind(all,wl)
return(all)
}

# This function determines position size and
# enables us to test several ideas with much
# greater speed and flexibility.
rsi2pos <- function(ind, indIncr=5, posIncr=0.25) {
# Inputs:
# ind : indicator vector
# indIncr : indicator value increments/breakpoints
# posIncr : position value increments/breakpoints

# Initialize result vector
size <- rep(0,NROW(ind))

# Long
size <- ifelse(ind < 4*indIncr, (1-posIncr*3), size)
size <- ifelse(ind < 3*indIncr, (1-posIncr*2), size)
size <- ifelse(ind < 2*indIncr, (1-posIncr*1), size)
size <- ifelse(ind < 1*indIncr, (1-posIncr*0), size)

# Short
size <- ifelse(ind > 100-4*indIncr, 3*posIncr-1, size)
size <- ifelse(ind > 100-3*indIncr, 2*posIncr-1, size)
size <- ifelse(ind > 100-2*indIncr, 1*posIncr-1, size)
size <- ifelse(ind > 100-1*indIncr, 0*posIncr-1, size)

# Today’s position (‘size’) is based on today’s
# indicator, but we need to apply today’s position
# to the Close-to-Close return at tomorrow’s close.
size <- lag(size)

# Replace missing signals with no position
# (generally just at beginning of series)
size[is.na(size)] <- 0

# Return results
return(size)
}

# Calculate signals with the ‘rsi2pos()’ function,
# using 5 as the RSI step: 5, 10, 15, 20, 80, 85, 90, 95
# and 0.25 as the size step: 0.25, 0.50, 0.75, 1.00
sig <- rsi2pos(rsi, 5, 0.25)

# Break out the long (up) and short (dn) signals
sigup <- ifelse(sig > 0, sig, 0)
sigdn <- ifelse(sig < 0, sig, 0)

# Calculate rule returns
ret_up <- ret * sigup
colnames(ret_up) <- 'Long System Return'
ret_dn <- ret * sigdn
colnames(ret_dn) <- 'Short System Return'
ret_all <- ret * sig
colnames(ret_all) <- 'Total System Return'

# Create performance graphs
png(filename=”20090606_rsi2_performance.png”, 720, 720)
charts.PerformanceSummary(cbind(ret_up,ret_dn),methods=’none’,
main=’RSI(2) Performance – RSI steps = 5, Size steps = 0.25′)
dev.off()

# Print trade statistics table
cat(‘nRSI(2) Trade Statistics – RSI steps = 5, Size steps = 0.25n’)
print(tradeStats(sig,ret))

# Print drawdown table
cat(‘nRSI(2) Drawdowns – RSI steps = 5, Size steps = 0.25n’)
print(table.Drawdowns(ret_all, top=10))

# Print downside risk table
cat(‘nRSI(2) Downside Risk – RSI steps = 5, Size steps = 0.25n’)
print(table.DownsideRisk(ret_all))

# Calculate signals with the ‘rsi2pos()’ function
# using new RSI and size step values
sig <- rsi2pos(rsi, 10, 0.3)

# Break out the long (up) and short (dn) signals
sigup <- ifelse(sig > 0, sig, 0)
sigdn <- ifelse(sig < 0, sig, 0)

# Calculate rule returns
ret_up <- ret * sigup
colnames(ret_up) <- 'Long System Return'
ret_dn <- ret * sigdn
colnames(ret_dn) <- 'Short System Return'
ret_all <- ret * sig
colnames(ret_all) <- 'Total System Return'

# Calculate performance statistics
png(filename=”20090606_rsi2_performance_updated.png”, 720, 720)
charts.PerformanceSummary(cbind(ret_up,ret_dn),methods=’none’,
main=’RSI(2) Performance – RSI steps = 10, Size steps = 0.30′)
dev.off()

# Print trade statistics table
cat(‘nRSI(2) Trade Statistics – RSI steps = 10, Size steps = 0.30n’)
print(tradeStats(sig,ret))

# Print drawdown table
cat(‘nRSI(2) Drawdowns – RSI steps = 10, Size steps = 0.30n’)
print(table.Drawdowns(ret_all, top=10))

# Print downside risk table
cat(‘nRSI(2) Downside Risk – RSI steps = 10, Size steps = 0.30n’)
print(table.DownsideRisk(ret_all))