FXEZ's Quantitative Research In R

Quoting ezcurrency

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Here is my screenshot for the same for 50:50 chance (random walk) coin flip: {image} Code: sequenceOfCoinTosses <- sample(c(-1,1), 10000, replace = TRUE, prob=c(0.5,0.5)) plot(cumsum(sequenceOfCoinTosses), type = 'l', ylab="", main="Sum of 10000 coin tosses") abline(h=0) Now change the above code to reflect probabilities of 0.52 and 0.48 we get this: {image} So if there is just a 2% edge we get a trend instead of a random walk. That is our goal. Just get a slight edge. In trading that edge is ever elusive. Systems tend to work for a while, then...

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library("ggplot2")
library("PerformanceAnalytics")
library("quantmod")
library("TTR")
lagged <- function(x, k) {
  c(rep(NA, k), x)[1 : length(x)]
}
setwd("C:/Users/Don/Documents/TRADING/FX data/1 year of data/30 min")
x <- read.csv("JPY30.csv", header=FALSE)
# if low > ema H, signal = buy
# if high < ema L, signal = sell
# otherwise signal = 0
period <- 1:50
returns <- vector()
for (i in 1:50){
x$emaH <- EMA(x[,4], period[i])
x$emaL <- EMA(x[,5], period[i])
x$emaL[is.na(x$emaL)] <- 0
x$emaH[is.na(x$emaH)] <- 0
x$signal <- 0
x$signal <- ifelse (x[,5] >= x$emaH, 1, ifelse (x[,4] <= x$emaL, -1,0))
xRet <- Delt(x[,5],k=1,type="arithmetic")
xRet[is.na(xRet)] <- 0
finalRet <- xRet * lagged(x$signal,1)
x$datetime <- paste(as.factor(x[,1]), x[,2])
tst <- data.frame(date = as.Date(x$datetime, "%Y.%m.%d %H:%M"), ret=finalRet)
tst1 <<- read.zoo(tst)
#charts.PerformanceSummary(tst1,main="X test",geometric=TRUE)
returns[i] <- Return.cumulative(tst1)
#table.Drawdowns(tst1)
}
out <- data.frame(period, returns)
write.csv(out, file="out.csv")
plot(returns, type="l")

## change for EMA of H and L
period <-47
x$emaH <- EMA(x[,4], period)
x$emaL <- EMA(x[,5], period)
x$emaL[is.na(x$emaL)] <- 0
x$emaH[is.na(x$emaH)] <- 0
x$signal<-0
x$signal <- ifelse (x[,5] >= x$emaH, 1, ifelse (x[,4] <= x$emaL, -1,0))
xRet <- Delt(x[,5],k=1,type="arithmetic")
xRet[is.na(xRet)] <- 0
finalRet <- xRet * lagged(x$signal,1)
x$datetime <- paste(as.factor(x[,1]), x[,2])
tst <- data.frame(date = as.Date(x$datetime, "%Y.%m.%d %H:%M"), ret=finalRet)
tst1 <<- read.zoo(tst)
charts.PerformanceSummary(tst1,main="X test",geometric=TRUE)
Return.cumulative(tst1)
table.Drawdowns(tst1)

Quoting PipMeUp

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This is even more important if you use neural nets. They are very good at learning by heart the dataset.

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Quoting PipMeUp

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Don't take it personally, that's not my intend but this is a terrible way of performing a optimization. Actually you optimize nothing. Essentially your code searches the EMA period that will perform best next year knowing next year.

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Quoting Dr.Phoenix

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{quote} Thoughts about a stop-loss Standart Deviation is used as a parameter for volatility description. The higher the volatility, the larger the Sigma is. So the Sigma is taken as a measure of risk, as a measure of a custom stop loss. {image}

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Quoting 9047

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{quote} Rather than focusing on automated stop generation I'm focused on identifying where the stops are. Volatility measures are a place to start with that approach. I'm back in the office tomorrow and hence back to work.... excited to get back to it! I'll spend some time on distilling something for this.

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Quoting ezcurrency

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Optimization of trading parameters and backtesting R is great because of all of the packages available for it (many trading related packages), and its vectorized so its very fast. Below is an example of a simple trading system, but the code can be easily adapted for any system. If you have any ideas to test out, post here and we can easily adapt this code to test out. ** If anyone is proficient in testing multiple timeframes in R, please post here or contact me. I have a few questions for you. ;-) This sample code to optimize an EMA length. I calculate...

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Quoting PipMeUp

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{quote} Sorry that was obvious to me. You start with some money. That's 1 time your account size. If you lose 1% of your account you lose 0.01 time your account. It remains 0.99 time your account. This loss has multiplied your account by a factor 0.99. Same thing if you win 1%, your account gets multiplied by a factor 1.01. (1-x) and (1+x) are the multiplicative factors where x is the fraction of the account you risk. They are independent of the account size. When you win then you lose your account is multiplied by (1+x)(1-x). The sequence win-win-lose-win-lose-lose...

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Quoting alphaomega

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Regarding the % risk per trade, based on my research, the optimal solution (especially for discretionary trading) is this:

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Quoting PipMeUp

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This paper may be of some interest. Note that it requires to know the expectancy of the strategy. This MM increases the size when the strategy is below its expected performance. DD are quickly recovered. But you have to be really sure of the edge because if the strategy is underperforming because the market is too far from the regime of work of the strategy you over-leverage a (temporary) loser. You need to know the expectancy in real time. Smart but quite dangerous. {image}

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bank = 1000; bank2 = bank; startbank = bank
lev = 3
trades = 3000
eq = numeric(trades); eq2 = eq
outcome = c(0.0015, -0.001)
prob = c(0.5, 0.5)
expectancy = prob[1]*outcome[1] + prob[2]*outcome[2]
wl = sample(outcome, trades, replace=T, prob = prob)
for (i in 1:trades) {
  if (bank > 0) {
    bank = bank + (bank* lev) * wl[i] # percent of equity or fixed fractional
  }
  if (bank2 > 0) {
    #bank2 = bank2 + (bank2*lev*(1+expectancy)) * wl[i]  # makes little difference
    bank2 = bank2 + (bank2*(1+lev*expectancy)^i) * wl[i] # similar to article
  }
  eq[i] = bank
  eq2[i] = bank2
}
blackplot(3,1); plot(eq, t='l', ylab="Percent of Equity (POE)", main=paste("Leverage", lev)); abline(h=0, col='red')
plot(eq2, t='l', ylab="Expectancy Sizing"); abline(h=0, col='red')
plot(eq2 - eq, t='l', ylab = "Expectancy Sizing - POE"); abline(h=0, col='red')
bank; bank2

Quoting FXEZ

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{quote} Any ideas on why this phenomenon might occur in the presence of leverage?

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# random walk simulation in one dimension
n = 100 # length of a single walk
trials = 1000 # number of walks
step = 0.001 # step size up/down
# formula to compute n root mean squared distance (rmsd) lines
dist = sqrt(1:n)*step
# create the random walks
m = matrix(0, nrow=trials, ncol = n)
for (i in 1:trials) {
  rw = sample(c(step, -step), n, replace = T)
  m[i,] = cumsum(rw)
}
# draw the (empty) chart
main = paste(trials, "random Walks with", n, "steps each")
blackplot(1,1); plot(m[1,], t='n', ylim=c(-4*sqrt(n)*step, 4*sqrt(n)*step),
 main = main, ylab = paste("Each step is", step))
# plot the walks on empty chart
for (i in 1:trials) {
  lines(m[i,], col=i)
}
# draw the rmsd deviation bands
lines(dist*1, col='white', lwd = 10)
lines(-dist*1, col='white', lwd = 10)
lines(dist*2, col='yellow', lwd = 10)
lines(-dist*2, col='yellow', lwd = 10)
# compute some stats for % outside 1*, 2* rmsd deviation band
sum(m[,n] > dist[n] | m[,n] < -dist[n]) # 248 of 1000 or 1-.248=0.752 within
sum(m[,n] > 2*dist[n] | m[,n] < -2*dist[n]) # 37 of 1000 1-0.037 = 0.963 within

Quoting FXEZ

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When I ran the following script (it changes on each iteration due to random variation) out of 1000 trials 248 or 24.8% were outside the white bands while 75.2% were inside the white band. 37 or 1-0.037 = 96.3% were inside the outer yellow bands.

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Quoting FXEZ

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If we start with expectancy measured in this way we are looking ahead or data snooping.

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Quoting FXEZ

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Any ideas on why this phenomenon might occur in the presence of leverage?

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Quoting FXEZ

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In retrospect (after you run a system test on historical data), expectancy is essentially the average profit per trade over the measured period.

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Quoting PipMeUp

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I may have found something... I generated a walk with winrate=50% and RR=1.3. The expectancy is 0.15. I used 300 samples (trades). Instead of regressing the whole equity history I cut it into 15 non-overlapping sequences of 20 trades (15x20=300). I took the average equity at each step. That's the red line. I regressed this average to get the black line. The equation of the line is y=0.1572*x-0.5063. The ground truth is y=0.15*x+0. What do you think? (Thanks to Copernicus for the boostrap idea) estimate.png;2140417 {image}

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Quoting 000

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{quote} So what are you trying to say? That's the exact definition of what a standard deviation is. The yellow line is 2 std, so by definition ~96% of the samples are inside it. {image}

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Quoting HeyYou

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{quote} you're using MA's the wrong way.. not going into details but I can tell you I tested MA's over a 20 years period and they give an edge with a variety of parameters only faster MA's give more signals, they should work on any instrument, some are more trending so you get better results.. anyway no indicators is the best but complicated to code.

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Quoting PipMeUp

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{quote} You can quite easily get rid of this bias by only using the past portion of your equity curve at each step. That's a running linear regression. Something for which the Kalman filter is exactly designed for but this can also be done with simple linear algebra => http://erikerlandson.github.io/blog/...ion-equations/ {quote}

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Quote

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I think the leverage x3 is too big for the strategy. When you go beyond the optimal size of the Kelly Criterion the expected growth falls sharply. Expectancy Sizing gets forced to overleverage. Visualy http://www.forexfactory.com/showthre...78#post7125178

Quote

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I think this is the problem. You have got one single realization. How can you estimate the edge from that?

bankPOE = 1000; bankPOEExpectancy = bankPOE; startbankPOE = bankPOE; bankPOEKelly = bankPOE
lev = 3
trades = 3000
eq = numeric(trades); eq2 = eq
outcome = c(0.0015, -0.001)
prob = c(0.5, 0.5)
#expectancy = prob[1]*outcome[1] + prob[2]*outcome[2]
expectancy = 0
Kelly = prob[1] - (1-prob[1])/(outcome[1]/abs(outcome[2]))
# alternate formula
units = outcome[1]/abs(outcome[2])
Kelly =  sum(units*prob[1] - 1*prob[2])/units; Kelly
sizePOE = numeric(trades); sizeExpectancy = numeric(trades); sizeKelly = numeric(trades)
wl = sample(outcome, trades, replace=T, prob = prob)
for (i in 1:trades) {
  if (bankPOE > 0) {
    sizePOE[i] = (bankPOE* lev)
    bankPOE = bankPOE + sizePOE[i] * wl[i] # percent of equity or fixed fractional
  }
  if (bankPOEExpectancy > 0) {
    if (i > 1) expectancy = sum(wl[1:(i-1)]) / (i-1)
    K = (Kelly*bankPOEExpectancy)/abs(outcome[2])
    sizeKelly[i] = K
    #sizeExpectancy[i] = min(bankPOEExpectancy*(1+lev*expectancy)^i, 0.5*sizeKelly[i])
    sizeExpectancy[i] = bankPOEExpectancy*(1+lev*expectancy)^i
    bankPOEExpectancy = bankPOEExpectancy + sizeExpectancy[i] * wl[i] # similar to article
  }
  eq[i] = bankPOE
  eq2[i] = bankPOEExpectancy
}
blackplot(3,1); plot(eq, t='l', ylab="Percent of Equity (POE)", main=paste("Leverage", lev)); abline(h=0, col='red')
plot(eq2, t='l', ylab="Expectancy Sizing"); abline(h=0, col='red')
plot(eq2 - eq, t='l', ylab = "Expectancy Sizing - POE"); abline(h=0, col='red')
bankPOE; bankPOEExpectancy
if (FALSE) { # plot the size comparisons separately
  plot(eq2 - eq, t='l', ylab = "Expectancy Sizing - POE"); abline(h=0, col='red')
  plot(sizeExpectancy-sizePOE, t='l'); abline(h=0, col='red')
  plot(sizeKelly/10-sizeExpectancy, t='l'); abline(h=0, col='red')
}