Strategy – S&P500 Seasonal

During a previous post, S&P500 Seasonal Study + Other Commodities: https://flare9xblog.wordpress.com/2017/10/12/seasonal-study/

It was determined that the best months to be long the S&P500 was from months October through to the end of May.

As a refresher:

Rplot126
S&P500 Mean Daily Spread Per Month

We back test this theme to see how it performs over monthly bars from 1960 to present day (10.12.2017):

Rplot136

SP500seasoal.results

What we see is that we are invested 67% of the time being long from the Open bar of October and selling at the Close of May. We do beat the S&P500 and I believe this is partly due to drawing down less post 1999 bear market. Our maximum draw down is slightly less than than buy and hold at 43%.

What stands out is the average gain during this October to May holding period. We see that the average trade is 14.3%.

To see some relative benchmark, lets see what it looks like only buying May open and selling at the Close of September:

Rplot137

may to sep

> Return.cumulative(xts1, geometric = TRUE)
                        [,1]
Cumulative Return -0.1973985

We see cumulative returns for Buying May open and selling Close of September are -0.1973985. That is the growth of $1. Essentially May to September is negative to flat. The cumulative returns do not even warrant shorting May to September.

In closing we see that the majority of the S&P500 gains seem to be attributed to seasonal trends specifically buying in October and Selling in May.

Full back test R Code for the above


# S&P500 Seasonal Back Test 
# Month Bars
# Buy Open of October, Sell End of April (Based on seasonal study)
# Andrew Bannerman 10.12.2017

require(lubridate)
require(dplyr)
require(magrittr)
require(TTR)
require(zoo)
require(data.table)
require(xts)
require(PerformanceAnalytics)

# Data path
data.dir <- "C:/R Projects/Final Scripts/Seasonal Strategies/Data"
data.read.spx <- paste(data.dir,"$SPX.Monthly.csv",sep="/")

# Read data
read.spx <- read.csv(data.read.spx,header=TRUE, sep=",",skip=0,stringsAsFactors=FALSE)

# Make dataframe 
new.df <- data.frame(read.spx)

# Convert Values To Numeric 
cols <-c(3:8)
new.df[,cols] %<>% lapply(function(x) as.numeric(as.character(x)))

# Convert Date Column [1]
new.df$Date <- ymd(new.df$Date)

# Add day of month column 
# This is a helper column for creating buy/sell rules
group <- new.df %>% dplyr::mutate(month = lubridate::month(Date)) %>% group_by(month) 
new.df <- data.frame(new.df,group$month)

# Calculate Returns from open to close 
new.df$ocret <- apply(new.df[,c('Open', 'Close')], 1, function(x) { (x[2]-x[1])/x[1]} )

# Calculate Close-to-Close returns
new.df$clret <- ROC(new.df$Close, type = c("discrete"))
new.df$clret[1] <- 0

# Subset by Date
new.df <- subset(new.df, Date >= as.POSIXct("1960-01-01") )  

# Enter Long Rules 
# Buy October To End of April
x = new.df$group.month
# October to May Hold Period Rules
#new.df$enter <- ifelse(x == 1,1,0 | ifelse(x == 2,1,0 | ifelse(x == 3,1,0 | ifelse(x == 4,1,0 | ifelse(x==5,1,0 | ifelse(x == 10,1,0 | ifelse(x == 11,1,0 | ifelse(x == 12,1,0))))))))
#May to September Hold Period Rules
new.df$enter <- ifelse(x == 5,1,0 | ifelse(x == 6,1,0 | ifelse(x == 7,1,0 | ifelse(x == 8,1,0 | ifelse(x==9,1,0)))))

# Calculate equity curves
# Long
new.df <- new.df %>%
  dplyr::mutate(RunID = rleid(enter)) %>%
  group_by(RunID) %>%
  dplyr::mutate(seasonal.equity = ifelse(enter == 0, 0,
                                         ifelse(row_number() == 1, ocret, clret))) %>%
  ungroup() %>%
  select(-RunID)

# Pull select columns from data frame to make XTS whilst retaining formats 
xts1 = xts(new.df$seasonal.equity, order.by=as.POSIXct(new.df$Date, format="%Y-%m-%d")) 
xts2 = xts(new.df$clret, order.by=as.POSIXct(new.df$Date, format="%Y-%m-%d")) 
str(new.df)

# Join XTS together 
compare <- cbind(xts1,xts2)

# Use the PerformanceAnalytics package for trade statistics
colnames(compare) <- c("Seasonal","Buy And Hold")
charts.PerformanceSummary(compare,main="Long May Open To Close of September", wealth.index=TRUE, colorset=rainbow12equal)
performance.table <- rbind(table.AnnualizedReturns(compare),maxDrawdown(compare), CalmarRatio(compare),table.DownsideRisk(compare))
drawdown.table <- rbind(table.Drawdowns(compare))
#dev.off()
#logRets <- log(cumprod(1+compare))
#chart.TimeSeries(logRets, legend.loc='topleft', colorset=rainbow12equal)

print(performance.table)
print(drawdown.table)

# Find net trade result of multiple 'n' day trades
# Find start day of trade, find end day, perform (last(Close) - first(Open))/first(Open) % calculation
new.df <- new.df %>%
  dplyr::mutate(RunID = data.table::rleid(enter)) %>%
  group_by(RunID) %>%
  dplyr::mutate(perc.output = ifelse(enter == 0, 0,
                                     ifelse(row_number() == n(),
                                            (last(Close) - first(Open))/first(Open), 0))) %>%
  ungroup() %>%
  select(-RunID)

# Win / Loss % 
# All Holding Months
winning.trades <- sum(new.df$seasonal.equity > '0', na.rm=TRUE)
losing.trades <- sum(new.df$seasonal.equity < '0', na.rm=TRUE)
even.trades <- sum(new.df$seasonal.equity == '0', na.rm=TRUE)
total.days <- NROW(new.df$seasonal.equity)

# Multi Month Trades
multi.winning.trades <- sum(new.df$perc.output > '0', na.rm=TRUE)
multi.losing.trades <- sum(new.df$perc.output < '0', na.rm=TRUE)
multi.total.days <- multi.winning.trades+multi.losing.trades

# % Time Invested
time.invested <- (winning.trades + losing.trades) / total.days
winning.trades + losing.trades

# Calcualte win loss %
# All months
total <- winning.trades + losing.trades
win.percent <- winning.trades / total
loss.percent <- losing.trades / total
# Multi Month Trades
multi.total <- multi.winning.trades + multi.losing.trades
multi.win.percent <- multi.winning.trades / multi.total
multi.loss.percent <- multi.losing.trades / multi.total
# Calculate Consecutive Wins Loss 
# All Months
remove.zero <- new.df[-which(new.df$seasonal.equity == 0 ), ] # removing rows 0 values 
consec.wins <- max(rle(sign(remove.zero$seasonal.equity))[[1]][rle(sign(remove.zero$seasonal.equity))[[2]] == 1])
consec.loss <- max(rle(sign(remove.zero$seasonal.equity))[[1]][rle(sign(remove.zero$seasonal.equity))[[2]] == -1])
consec.wins

# Multi Month Trades
multi.remove.zero <- new.df[-which(new.df$perc.output == 0 ), ] # removing rows 0 values 
multi.consec.wins <- max(rle(sign(multi.remove.zero$perc.output))[[1]][rle(sign(multi.remove.zero$perc.output))[[2]] == 1])
multi.consec.loss <-max(rle(sign(multi.remove.zero$perc.output))[[1]][rle(sign(multi.remove.zero$perc.output))[[2]] == -1])

# Calculate Summary Statistics
# All Months
average.trade <- mean(new.df$seasonal.equity)
average.win <- mean(new.df$seasonal.equity[new.df$seasonal.equity >0])
average.loss <- mean(new.df$seasonal.equity[new.df$seasonal.equity <0])
median.win <- median(new.df$seasonal.equity[new.df$seasonal.equity >0])
median.loss <- median(new.df$seasonal.equity[new.df$seasonal.equity <0])
max.gain <- max(new.df$seasonal.equity)
max.loss <- min(new.df$seasonal.equity)
win.loss.ratio <- winning.trades / abs(losing.trades)
summary <- cbind(winning.trades,losing.trades,even.trades,total.days,win.percent,loss.percent,win.loss.ratio,time.invested,average.trade,average.win,average.loss,median.win,median.loss,consec.wins,consec.loss,max.gain,max.loss)
summary <- as.data.frame(summary)
colnames(summary) <- c("Winning Trades","Losing Trades","Even Trades","Total Trades","Win %","Loss %","Win Loss Ratio","Time Invested","Average Trade","Average Win","Average Loss","Median Gain","Median Loss","Consec Wins","Consec Loss","Maximum Win","Maximum Loss")
print(summary)

# Multi Month Trades
multi.average.trade <- mean(new.df$perc.output)
multi.average.win <- mean(new.df$perc.output[new.df$perc.output >0])
multi.average.loss <- mean(new.df$perc.output[new.df$perc.output <0])
multi.median.win <- median(new.df$perc.output[new.df$perc.output >0])
multi.median.loss <- median(new.df$perc.output[new.df$perc.output <0])
multi.win.loss.ratio <- multi.average.win / abs(multi.average.loss)
multi.max.gain <- max(new.df$perc.output)
multi.max.loss <- min(new.df$perc.output)
multi.summary <- cbind(multi.winning.trades,multi.losing.trades,multi.total.days,multi.win.percent,multi.loss.percent,multi.win.loss.ratio,time.invested,multi.average.trade,multi.average.win,multi.average.loss,multi.median.win,multi.median.loss,multi.consec.wins,multi.consec.loss,multi.max.gain,multi.max.loss)
multi.summary <- as.data.frame(multi.summary)
colnames(multi.summary) <- c("Winning Trades","Losing Trades","Total Trades","Win %","Loss %","Win Loss Ratio","Time Invested","Average Trade","Average Win","Average Loss","Median Gain","Median Loss","Consec Wins","Consec Loss","Maximum Win","Maximum Loss")
print(multi.summary)
print(performance.table)
print(drawdown.table)
table.Drawdowns(xts1, top=10)
Return.cumulative(xts1, geometric = TRUE)

# Write output to file
write.csv(new.df,file="C:/R Projects/SP500.Seasonal.csv")
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Simple S&P500 Linear Strategy

From our hurst exponent test during a previous post we determined that the S&P500 was a mean reverting series on an interday time frame. For this back test we have created a very simple linear model to ‘fit’ the nature of the series.

We use a rolling ‘n’ day zscore and we test using a look back of 11 days, for some reason the lookback of 11 days provided the best results. For the sake of simplicity we will test over the full sample period and we will not include any commissions or slippage.

We will use the SPY for this back test from inception to present.

Here are the parameters:
1. Rolling lookback period of z-score = 11 days
2. Entry level = < -0.2
3. Exit Time = 4 days

As you can see the parameters are kept to a minimum. The main goal here is to fit a model to the existing anomaly versus force fit a model to the data.

11.

result.

As we can see we obtain better performance than buy and hold. We have about a 21% better DD than buy and hold and a 10% annualized from 1993 to present. Notice the time invested is 48%. It means we have capital available to execute to other strategies. To offset the draw downs even further we could add another uncorrelated strategy but this as a base is not a bad attempt to capture the mean reversion nature of the S&P500 on an interday basis. Note this might not be the most stellar performance but its good example to illustrate the train of thought.

Some questions to ponder?

1. What happens if we ‘fit’ a mean reversion model to S&p500 daily data from 1929 to 1980?
2. What happens if we fit a momentum model to S&p500 daily data from 1929 to 1980?
3. What happens if we fit a momentum model for S&P500 daily data from 1993 to present?

Those questions good readers shall leave for you to answer!

The rules of this system are:
1. When zscore crosses below <-0.2 buy next days open
2. After 4 days has passed sell all, if another signal is generated while in the existing trade we will take the next signal also

Notes about the rules of the backtest:
1. We calculate S&P500 close to close returns and also open to close returns. We do this in order to set the first buying day to calculate an open to close return (At the end of a day a signal is generated, we then buy next days open, thus the returns for the first day are open to close returns, on 2 day and over the returns are close to close returns.)
2. To avoid look ahead bias, after a signal is generated, we lag +1 the time series forward a day so that we are simulating buying the NEXT days open.

All parameters can be optimized and entry and exit rules adjusted. Some ideas could be:

1. For exit, exit on specific zscore value… ie buy <-0.20 and sell when it crossed back over 0.
2. For exit, ignore repeat trades while in existing trade
3. Exit soon as the price is higher than our entry

Different rules produce slightly different results. I may go into some of these different selling rules and the code for them in future posts! For now this is a good start 🙂

# Calculate rolling z-score of SPY close price
# Sell at fixed n day hold
# 8.13.2017
# Andrew Bannerman
require(lubridate)
require(dplyr)
require(magrittr)
require(TTR)
require(zoo)
require(data.table)
require(xts)
require(PerformanceAnalytics)

# Data path
data.dir <- "D:/R Projects"
data.read.spx <- paste(data.dir,"SPY.csv",sep="/")

# Read data
read.spx <- read.csv(data.read.spx,header=TRUE, sep=",",skip=0,stringsAsFactors=FALSE)

# Make dataframe
new.df <- data.frame(read.spx)
tail(new.df)
# Convert Values To Numeric
cols <-c(3:8)
new.df[,cols] %% lapply(function(x) as.numeric(as.character(x)))

#Convert Date Column [1]
new.df$Date <- ymd(new.df$Date)

# Use TTR package to create rolling SMA n day moving average
# Create function and loop in order to repeat the desired number of SMAs for example 2:30
getSMA <- function(numdays) {
function(new.df) {
SMA(new.df[,"Close"], numdays) # Calls TTR package to create SMA
}
}
# Create a matrix to put the SMAs in
sma.matrix <- matrix(nrow=nrow(new.df), ncol=0)

# Loop for filling it
for (i in 2:60) {
sma.matrix <- cbind(sma.matrix, getSMA(i)(new.df))
}

# Rename columns
colnames(sma.matrix) <- sapply(2:60, function(n)paste("close.sma.n", n, sep=""))

# Bind to existing dataframe
new.df <- cbind(new.df, sma.matrix)

# Use TTR package to create rolling Standard Deviation
# Create function and loop in order to repeat the desired number of Stdev for example 2:30
getSD <- function(numdays) {
function(new.df) {
runSD(new.df$Close, numdays, cumulative = FALSE) # Calls TTR package to create SMA
}
}
# Create a matrix to put the SMAs in
sd.matrix <- matrix(nrow=nrow(new.df), ncol=0)

# Loop for filling it
for (i in 2:60) {
sd.matrix <- cbind(sd.matrix, getSD(i)(new.df))
}

# Rename columns
colnames(sd.matrix) <- sapply(2:60, function(n)paste("close.sd.n", n, sep=""))

# Bind to existing dataframe
new.df <- cbind(new.df, sd.matrix)

# Use base R to work out the rolling z-score (Close – roll mean) / stdev
new.df$close.zscore.n2 <- apply(new.df[,c('Close','close.sma.n2', 'close.sd.n2')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n3 <- apply(new.df[,c('Close','close.sma.n3', 'close.sd.n3')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n4 <- apply(new.df[,c('Close','close.sma.n4', 'close.sd.n4')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n5 <- apply(new.df[,c('Close','close.sma.n5', 'close.sd.n5')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n6 <- apply(new.df[,c('Close','close.sma.n6', 'close.sd.n6')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n7 <- apply(new.df[,c('Close','close.sma.n7', 'close.sd.n7')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n8 <- apply(new.df[,c('Close','close.sma.n8', 'close.sd.n8')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n9 <- apply(new.df[,c('Close','close.sma.n9', 'close.sd.n9')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n10 <- apply(new.df[,c('Close','close.sma.n10', 'close.sd.n10')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n11 <- apply(new.df[,c('Close','close.sma.n11', 'close.sd.n11')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n12 <- apply(new.df[,c('Close','close.sma.n12', 'close.sd.n12')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n13 <- apply(new.df[,c('Close','close.sma.n13', 'close.sd.n13')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n14 <- apply(new.df[,c('Close','close.sma.n14', 'close.sd.n14')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n15 <- apply(new.df[,c('Close','close.sma.n15', 'close.sd.n15')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n16 <- apply(new.df[,c('Close','close.sma.n16', 'close.sd.n16')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n17 <- apply(new.df[,c('Close','close.sma.n17', 'close.sd.n17')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n18 <- apply(new.df[,c('Close','close.sma.n18', 'close.sd.n18')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n19 <- apply(new.df[,c('Close','close.sma.n19', 'close.sd.n19')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n20 <- apply(new.df[,c('Close','close.sma.n20', 'close.sd.n20')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n21 <- apply(new.df[,c('Close','close.sma.n21', 'close.sd.n21')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n22 <- apply(new.df[,c('Close','close.sma.n22', 'close.sd.n22')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n23 <- apply(new.df[,c('Close','close.sma.n23', 'close.sd.n23')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n24 <- apply(new.df[,c('Close','close.sma.n24', 'close.sd.n24')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n25 <- apply(new.df[,c('Close','close.sma.n25', 'close.sd.n25')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n26 <- apply(new.df[,c('Close','close.sma.n26', 'close.sd.n26')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n27 <- apply(new.df[,c('Close','close.sma.n27', 'close.sd.n27')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n28 <- apply(new.df[,c('Close','close.sma.n28', 'close.sd.n28')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n29 <- apply(new.df[,c('Close','close.sma.n29', 'close.sd.n29')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n30 <- apply(new.df[,c('Close','close.sma.n30', 'close.sd.n30')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n31 <- apply(new.df[,c('Close','close.sma.n31', 'close.sd.n31')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n32 <- apply(new.df[,c('Close','close.sma.n32', 'close.sd.n32')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n33 <- apply(new.df[,c('Close','close.sma.n33', 'close.sd.n33')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n34 <- apply(new.df[,c('Close','close.sma.n34', 'close.sd.n34')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n35 <- apply(new.df[,c('Close','close.sma.n35', 'close.sd.n35')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n36 <- apply(new.df[,c('Close','close.sma.n36', 'close.sd.n36')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n37 <- apply(new.df[,c('Close','close.sma.n37', 'close.sd.n37')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n38 <- apply(new.df[,c('Close','close.sma.n38', 'close.sd.n38')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n39 <- apply(new.df[,c('Close','close.sma.n39', 'close.sd.n39')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n40 <- apply(new.df[,c('Close','close.sma.n40', 'close.sd.n40')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n41 <- apply(new.df[,c('Close','close.sma.n41', 'close.sd.n41')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n42 <- apply(new.df[,c('Close','close.sma.n42', 'close.sd.n42')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n43 <- apply(new.df[,c('Close','close.sma.n43', 'close.sd.n43')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n44 <- apply(new.df[,c('Close','close.sma.n44', 'close.sd.n44')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n45 <- apply(new.df[,c('Close','close.sma.n45', 'close.sd.n45')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n46 <- apply(new.df[,c('Close','close.sma.n46', 'close.sd.n46')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n47 <- apply(new.df[,c('Close','close.sma.n47', 'close.sd.n47')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n48 <- apply(new.df[,c('Close','close.sma.n48', 'close.sd.n48')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n49 <- apply(new.df[,c('Close','close.sma.n49', 'close.sd.n49')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n50 <- apply(new.df[,c('Close','close.sma.n50', 'close.sd.n50')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n51 <- apply(new.df[,c('Close','close.sma.n51', 'close.sd.n51')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n52 <- apply(new.df[,c('Close','close.sma.n52', 'close.sd.n52')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n53 <- apply(new.df[,c('Close','close.sma.n53', 'close.sd.n53')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n54 <- apply(new.df[,c('Close','close.sma.n54', 'close.sd.n54')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n55 <- apply(new.df[,c('Close','close.sma.n55', 'close.sd.n55')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n56 <- apply(new.df[,c('Close','close.sma.n56', 'close.sd.n56')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n57 <- apply(new.df[,c('Close','close.sma.n57', 'close.sd.n57')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n58 <- apply(new.df[,c('Close','close.sma.n58', 'close.sd.n58')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n59 <- apply(new.df[,c('Close','close.sma.n59', 'close.sd.n59')], 1, function(x) { (x[1]-x[2])/x[3] } )
new.df$close.zscore.n60 <- apply(new.df[,c('Close','close.sma.n60', 'close.sd.n60')], 1, function(x) { (x[1]-x[2])/x[3] } )

# Convert all NA to 0
new.df[is.na(new.df)] <- 0

# Calculate quartiles, where close is relation to range (Close – High) / (High – Low)
#new.df$quartile <- apply(new.df[,c('Close', 'Low', 'High')], 1, function(x) { (x[1]-x[2])/(x[3]-x[2])} )

# Calculate Returns from open to close
new.df$ocret <- apply(new.df[,c('Open', 'Close')], 1, function(x) { (x[2]-x[1])/x[1]} )

# Calculate Close-to-Close returns
new.df$clret <- ROC(new.df$Close, type = c("discrete"))
new.df$clret[1] <- 0

# Name indicators
indicator <- new.df$close.zscore.n12

# Create Long Signals
new.df$signal <- ifelse(indicator < -.2, 1, 0)

######## Fixed 'n' day hold logic ##########
# Variable for loop
indicator <- new.df$signal

# Create Vector From Signal
signal.1 <- c(indicator)

# Set variable for number of days to hold
n.day <- 4

# Loop for fixed 'n' day hold
res <- NULL
while (length(res) < length(signal.1)) {
if (signal.1[length(res)+1] == 1) {
res <- c(res, rep(1,n.day))
} else {
res <- c(res, 0)
}
}
res <- res[1:length(signal.1)]
new.df <- data.frame(new.df,response = res)

# lag signal by one forward day to signal entry next day
new.df$response %
group_by(RunID) %>%
mutate(equity.curve = ifelse(response == 0, 0,
ifelse(row_number() == 1, ocret, clret))) %>%
ungroup() %>%
select(-RunID)

# Pull select columns from data frame to make XTS whilst retaining formats
xts1 = xts(new.df$equity.curve, order.by=as.Date(new.df$Date, format=”%m/%d/%Y”))
xts2 = xts(new.df$clret, order.by=as.Date(new.df$Date, format=”%m/%d/%Y”))

# Join XTS together
compare <- cbind(xts1,xts2)

# Use the PerformanceAnalytics package for trade statistics
# install.packages("PerformanceAnalytics")
require(PerformanceAnalytics)
colnames(compare) <- c("Mean Reversion","Buy And Hold")
charts.PerformanceSummary(compare,main="Cumulative Returns", wealth.index=TRUE, colorset=rainbow12equal)
#png(filename="20090606_rsi2_performance_updated.png", 720, 720)
performance.table <- rbind(table.AnnualizedReturns(compare), maxDrawdown(compare), CalmarRatio(compare),table.DownsideRisk(compare))
drawdown.table <- rbind(table.Drawdowns(compare))
#dev.off()
logRets %
group_by(RunID) %>%
dplyr::mutate(perc.output = ifelse(response == 0, 0,
ifelse(row_number() == n(),
(last(Close) – first(Open))/first(Open), 0))) %>%
ungroup() %>%
select(-RunID)

# All NA to 0
new.df[is.na(new.df)] <- 0
# Win / Loss %
# 1 Day Hold Trades
winning.trades '0', na.rm=TRUE)
losing.trades <- sum(new.df$equity.curve < '0', na.rm=TRUE)
total.days <- NROW(new.df$equity.curve)
# Multi Day Hold Trades
multi.winning.trades '0', na.rm=TRUE)
multi.losing.trades <- sum(new.df$perc.output < '0', na.rm=TRUE)
multi.total.days <- NROW(new.df$perc.output)
multi.losing.trades
# % Time Invested (Same column for 1 day and multi hold trades)
time.invested <- (winning.trades + losing.trades) / total.days
winning.trades + losing.trades
winning.trades
losing.trades

# Calcualte win loss %
# 1 Day Hold Trades
total <- winning.trades + losing.trades
win.percent <- winning.trades / total
loss.percent <- losing.trades / total
# Multi Day Hold Trades
multi.total <- multi.winning.trades + multi.losing.trades
multi.win.percent <- multi.winning.trades / multi.total
multi.loss.percent <- multi.losing.trades / multi.total
# Calculate Consecutive Wins Loss
# 1 Day Hold Trades
remove.zero <- new.df[-which(new.df$equity.curve == 0 ), ] # removing rows 0 values
consec.wins <- max(rle(sign(remove.zero$equity.curve))[[1]][rle(sign(remove.zero$equity.curve))[[2]] == 1])
consec.loss <- max(rle(sign(remove.zero$equity.curve))[[1]][rle(sign(remove.zero$equity.curve))[[2]] == -1])

# Multi Day Hold Trades
multi.remove.zero <- new.df[-which(new.df$perc.output == 0 ), ] # removing rows 0 values
multi.consec.wins <- max(rle(sign(multi.remove.zero$perc.output))[[1]][rle(sign(multi.remove.zero$perc.output))[[2]] == 1])
multi.consec.loss <-max(rle(sign(multi.remove.zero$perc.output))[[1]][rle(sign(multi.remove.zero$perc.output))[[2]] == -1])

# Calculate Summary Statistics
# 1 Day Hold Trades OR all days if multi holding
average.trade <- mean(new.df$equity.curve)
average.win 0])
average.loss <- mean(new.df$equity.curve[new.df$equity.curve <0])
median.win 0])
median.loss <- median(new.df$equity.curve[new.df$equity.curve <0])
max.gain <- max(new.df$equity.curve)
max.loss <- min(new.df$equity.curve)
win.loss.ratio <- winning.trades / abs(losing.trades)
summary <- cbind(winning.trades,losing.trades,win.percent,loss.percent,win.loss.ratio,time.invested,average.trade,average.win,average.loss,median.win,median.loss,consec.wins,consec.loss,max.gain,max.loss)
summary <- as.data.frame(summary)
colnames(summary) <- c("Winning Trades","Losing Trades","Win %","Loss %","Win Loss Ratio","Time Invested","Average Trade","Average Win","Average Loss","Median Gain","Median Loss","Consec Wins","Consec Loss","Maximum Win","Maximum Loss")
print(summary)

# Multi Day Hold Trades
multi.average.trade <- mean(new.df$perc.output)
multi.average.win 0])
multi.average.loss <- mean(new.df$perc.output[new.df$perc.output <0])
multi.median.win 0])
multi.median.loss <- median(new.df$perc.output[new.df$perc.output <0])
multi.win.loss.ratio <- multi.average.win / abs(multi.average.loss)
multi.max.gain <- max(new.df$perc.output)
multi.max.loss <- min(new.df$perc.output)
multi.summary <- cbind(multi.winning.trades,multi.losing.trades,multi.win.percent,multi.loss.percent,multi.win.loss.ratio,time.invested,multi.average.trade,multi.average.win,multi.average.loss,multi.median.win,multi.median.loss,multi.consec.wins,multi.consec.loss,multi.max.gain,multi.max.loss)
multi.summary <- as.data.frame(multi.summary)
colnames(multi.summary) <- c("Winning Trades","Losing Trades","Win %","Loss %","Win Loss Ratio","Time Invested","Average Trade","Average Win","Average Loss","Median Gain","Median Loss","Consec Wins","Consec Loss","Maximum Win","Maximum Loss")
print(multi.summary)
print(performance.table)
print(drawdown.table)
table.Drawdowns(xts1, top=10)
charts.PerformanceSummary(compare,main="Cumulative Returns",wealth.index=TRUE,colorset=rainbow12equal)

# Write output to file
write.csv(new.df,file="D:/R Projects/spy_mean.csv")