IM.SWING-ALO.1.0.Rmd

---
title: "Result Summary for Algorithm trading on NIFTY Options (SWING-ALO)"
output:
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keep_tex: yes
---
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# About SWING-ALO
SWING-ALO is a trading algorithm that trades based on the perdiction for NIFTY50 Index for the forthcoming day. The algorithm attempts to predict if the next business day will be an up-day or a down-day. Based on the prediction, the algorithm buys options on NIFTY50 futures. 

The investment algorithm is a combination of money management and price prediction. 

##Key Definitions

###Full Hand
The maximum quantity of NIFTY50 contracts that the client wants to trade using the algorithm.  

###Trade Size
The quantity of NIFTY50 contracts that the client actually trades using the algorithm. *Trade Size* will vary during the life of the algorithm.  

###Underlying Algorithm
The algorithm models its *Trade Size*  on the performance of an underlying algorithm that trades using *Full Hand*. The actual trades are just a mirror of trades generated by the *Full Hand* algorithm, except that the size of trades in the alogirthm is dependent on the performance of the *Full Hand* algorithm.

###HighWaterMark
The maximum profit(realized + unrealized) achieved by *Underlying Algorithm* over its life.  

###Drawdown Percent
The difference between the current profit of *Underlying Algorithm* and its *HighWaterMark*, expressed as a percentage of the notional exposure arising from a *Full Hand*.  

###Threshold Drawdown
A specifed *Drawdown Percent* below which the algorithm pauses trading.

##Money Management
1. The algorithm attempts to keep the *Trade Size* as a function of the *Drawdown Percent*. The maximum *Trade Size* will be the *Full Hand*, if *Drawdown Percent* is near zero, i.e. the underlying algorithm is near the *HighWaterMark*. As *Drawdown Percent* increases, the *Trade Size* reduces.  
2. *Trade Size* can become zero, i.e. the algorithm will pause trading, if *Drawdown Percent* rises above *Threshold Drawdown*, i.e. the *Underlying Algorithm* has incurred a drop in profit from the *HighWaterMark* greater than the *Threshold Drawdown*.  
3. The algorithm can be run with the Money Management feature or without. For SWING family of algorithm, we trade on futures with Money Management (i.e. contract sizes changes based on performance of the algorithm with *Full Hand*). Option trades are without Money Managment, and always trade with *Full Hand*


##Trading Signals
1. The algorithm predicts the direction for the next day, before the market closing. The prediction is in three categories
a. Up Day - Expect the market to make a higher high and higher low the next day.  
b. Down Day - Expect the market to make a lower high and a lower low the next day.  
2. Each trade is held till the next prediction (on the next day), or if a stop loss occurs.  
3. The strategy does not have an explict take profit signal. Profits are realized via exits generated via the predictions.  

```{r setoptions,echo=FALSE,results="hide"}
library(knitr)
opts_chunk$set(echo=FALSE,results="hide")
```
<P style="page-break-before: always">
\newpage
#Run Results [1 year committment, starting Apr 2013]
```{r maincodeline,cache=TRUE,message=FALSE}
#v1.2
#Support backtest using options
library(caret)
library(nnet)
library(doParallel)
library(RcppRoll)
library(TTR)
library(rredis)
library(log4r)
library(RTrade)
library(RQuantLib)
options(scipen=999)

args.commandline=commandArgs(trailingOnly=TRUE)
if(length(args.commandline)>0){
  args<-args.commandline
}

# args<-c("2","swing01","3")
# args[1] is a flag for model building. 0=> Build Model, 1=> Generate Signals in Production 2=> Backtest and BootStrap 4=>Save BOD Signals to Redis
# args[2] is the strategy name
# args[3] is the redisdatabase
redisConnect()
redisSelect(1)
if(length(args)>1){
  static<-redisHGetAll(toupper(args[2]))
}else{
  static<-redisHGetAll("SWINGA")
}
newargs<-unlist(strsplit(static$args,','))
if(length(args)<=1 && length(newargs>1)){
  args<-newargs
}
redisClose()


kWriteToRedis <- as.logical(static$WriteToRedis)
kGetMarketData<-as.logical(static$GetMarketData)
kDataCutOffBefore<-static$DataCutOffBefore
kBackTestStartDate<-static$BackTestStartDate
kBackTestEndDate<-static$BackTestEndDate
kFNODataFolder <- static$FNODataFolder
kNiftyDataFolder <- static$NiftyDataFolder
kTimeZone <- static$TimeZone
kIndex<-static$Index
kMLFile<-static$MLFile
kBrokerage<-as.numeric(static$SingleLegBrokerageAsPercentOfValue)/100
kPerContractBrokerage=as.numeric(static$SingleLegBrokerageAsValuePerContract)
kContractSize=as.numeric(static$ContractSize)
kMaxContracts=as.numeric(static$MaxContracts)
kHomeDirectory=static$HomeDirectory
kExchangeMargin=as.numeric(static$ExchangeMargin)
kDrawdownPercentThreshold=as.numeric(static$DrawdownPercentThreshold)
kDrawdownDaysThreshold=as.numeric(static$DrawdownDaysThreshold)
kDrawdownCost=as.numeric(static$DrawdownCost) 
kRecoveryBonus=as.numeric(static$RecoveryBonus)
kMoneyManagement=as.numeric(static$MoneyManagement)

setwd(kHomeDirectory)

today<-strftime(Sys.Date(),tz=kTimeZone,format="%Y-%m-%d")
logger <- create.logger()
logfile(logger) <- static$LogFile
level(logger) <- 'INFO'
levellog(logger,"INFO",args)
###### Load Data #############
kairos.symbol <- unlist(strsplit(kIndex, split = "_"))[1]
endtime <- format(Sys.time(), format = "%Y-%m-%d %H:%M:%S")
md <- data.frame()
if (file.exists(paste(kNiftyDataFolder,kIndex, ".Rdata", sep = ""))) {
  load(paste(kNiftyDataFolder,kIndex, ".Rdata", sep = ""))
  start <- strftime(md[nrow(md), c("date")] + 1, tz = kTimeZone, "%Y-%m-%d %H:%M:%S")
} else{
  start <- "2012-10-21 09:15:00"
}
if(kGetMarketData){
  temp <-
    kGetOHLCV(
      paste("symbol", tolower(kairos.symbol), sep = "="),
      df=md,
      start = start,
      end = endtime,
      timezone = kTimeZone,
      name = "india.nse.index.s4.daily",
      ts = c("open", "high", "low","settle", "volume"),
      aggregators = c("first", "max", "min", "last", "sum"),
      aValue = "1",
      aUnit = "days",
      splits = data.frame(
        date = as.POSIXct(character(), tz = kTimeZone),
        symbol = character(),
        oldshares = numeric(),
        newshares = numeric()
      )
    )
  if (nrow(temp) > 0) {
    temp$symbol <- kIndex
  }
  md<-temp
  save(md, file = paste(kNiftyDataFolder,kIndex, ".Rdata", sep = "")) # save new market data to disc
}
if (length(args) > 1 && args[1]==1) {
  #Backtesting with today's data from realtime sources
  newrow <- getPriceArrayFromRedis(9,"NSENIFTY_IND___","tick","close",paste(today, " 09:12:00"))
  newrow <-
    data.frame(
      "symbol" = "NSENIFTY",
      "date" = newrow$date[1],
      "open" = newrow$open[1],
      "high" = newrow$high[1],
      "low" = newrow$low[1],
      "settle" = newrow$settle[1],
      "close" = newrow$settle[1],
      "volume" = 0,
      "aopen" = newrow$open[1],
      "ahigh" = newrow$high[1],
      "alow" = newrow$low[1],
      "asettle" = newrow$settle[1],
      "aclose" = newrow$settle[1],
      "avolume" = 0,
      "splitadjust" = 1
    )
  redisString<-paste(newrow$date[1],newrow$open[1],newrow$high[1],newrow$low[1],newrow$settle[1],newrow$volume[1],sep=",")
  levellog(logger,"INFO",paste(args[2], redisString, sep = ":"))
  
  md <- rbind(md, newrow)
}

if (nrow(md) > 0) {
  #change col name of settle to close, if temp is returned with data
  md<-md[, !(names(md) %in% c("close","aclose"))]
  colnames(md) <- c( "date","open","high","low","close","volume","symbol","splitadjust",
                     "aopen","ahigh","alow","aclose","avolume")
}

md <- unique(md) # remove duplicate rows
load(kMLFile)

##### 1. Calculate Indicators ########

trend <- Trend(md$date, md$high, md$low, md$close)
md$trend <- trend$trend
sd <- roll_sd(md$close, 10) * sqrt(9 / 10)
NA9Vec <- rep(NA, 9)
sd <- c(NA9Vec, sd)
md$closezscore <- (md$close - SMA(md$close, 10)) / sd
md$highzscore <-  (md$high - SMA(md$high, 10)) / c(NA9Vec, roll_sd(md$high, 10) * sqrt(9 /10))
md$lowzscore <-  (md$low - SMA(md$low, 10)) / c(NA9Vec, roll_sd(md$low, 10) * sqrt(9 / 10))
ma <- SMA(md$close, 10)
md$mazscore <-  (ma - SMA(ma, 10)) / c(NA9Vec, roll_sd(ma, 10) * sqrt(9 / 10))
daysinupswing = BarsSince(trend$updownbar <= 0)
daysindownswing = BarsSince(trend$updownbar >= 0)
md$swing = ifelse(daysinupswing > 0, 1, 0)
md$daysinuptrend = BarsSince(trend$trend <= 0)
md$daysindowntrend = BarsSince(trend$trend >= 0)
md$daysintrend = ifelse(trend$trend == 1,md$daysinuptrend,
                        ifelse(trend$trend == -1, md$daysindowntrend, 0))
md$daysinswing = daysinupswing + daysindownswing
md$atr <- ATR(md[, c("high", "low", "close")], 10)[, 2]
md <- na.omit(md)
trainingsize = sum(md$date < "2013-01-01")
a <-(md$daysintrend - mean(md$daysintrend[md$date < "2013-01-01"])) / (3 * sd(md$daysintrend[md$date <"2013-01-01"]) * sqrt((trainingsize - 1) / trainingsize) / (2 * pi))
md$softmax_daysintrend <- 1 / (1 + exp(-a))
b <-  (md$daysinswing - mean(md$daysinswing[md$date < "2013-01-01"])) / (3 * sd(md$daysinswing[md$date <"2013-01-01"]) * sqrt((trainingsize - 1) / trainingsize) / (2 * pi))
md$softmax_daysinswing <- 1 / (1 + exp(-b))
md$dayreturn <- (log(md$close) - log(Ref(md$close, -1))) *  100

####### 2. Generate Buy/Sell Arrays ##########

md$predict.raw <- predict(fit, md, type = 'prob')
md$predict.class <- predict(fit, md)

md$buy = as.numeric(md$predict.class) == 2
md$sell = as.numeric(md$predict.class) == 1
md$short = as.numeric(md$predict.class) == 1
md$cover = as.numeric(md$predict.class) == 2
md$buy = ExRem(md$buy, md$sell)
md$sell = ExRem(md$sell, md$buy)
md$short = ExRem(md$short, md$cover)
md$cover = ExRem(md$cover, md$short)
md$buyprice <- md$close
md$sellprice <- md$close
md$shortprice <- md$close
md$coverprice <- md$close
md$inlongtrade <- Flip(md$buy, md$sell)
md$inshorttrade <- Flip(md$short, md$cover)

###### 3. Create SL/TP Array ############
md$stoploss1 <-  ifelse(md$inlongtrade == 1,md$close - md$low,
                        ifelse(md$inshorttrade == 1, md$high - md$close, 0))
md$stoploss2 <-  ifelse(md$inlongtrade == 1 | md$inshorttrade == 1,0.5 * md$atr,0)
md$stoplosslevel <- pmin(md$stoploss1, md$stoploss2)

##### 4. Generate Cash Trades #########
startindex <- which(md$date == kBackTestStartDate)
mdsubset<-md[startindex:nrow(md),]
signals <- ApplyStop(mdsubset, mdsubset$stoplosslevel)
trades <- GenerateTrades(signals)
trades$brokerage <- 2*kBrokerage
trades$netpercentprofit <-
  trades$percentprofit - trades$brokerage
equity <-
  CalculatePortfolioEquityCurve("NSENIFTY",
                                mdsubset,
                                trades,
                                rep(kMaxContracts*kContractSize, nrow(md) - startindex),
                                brokerage = kBrokerage)

##### Generate Derived Trades ########
returns <-  trades$netpercentprofit
bars <- trades$bars
amendedsize<-RTrade::calcDerivedContracts(dddays=kDrawdownDaysThreshold,ddamt=kDrawdownPercentThreshold,recoverybonus=kRecoveryBonus,ddcost=kDrawdownCost,stop=0,margin=1,charttitle="swing01",
                                          returnvector=returns,
                                          tradebarvector=bars,
                                          contractsize=kMaxContracts,
                                          derivedleg=1)
tmp<-data.frame(date=trades$entrytime,amendedsize=amendedsize)
tmp1<-merge(tmp,mdsubset,by="date",all=TRUE)
amendedsize<-na.locf(tmp1$amendedsize)
#make amendedsize of same length as nrow(mdsubset)
amendedsize<-c(rep(head(amendedsize,1),nrow(tmp1)-length(amendedsize)),amendedsize)
derivedequity <-
  CalculatePortfolioEquityCurve(kIndex, mdsubset, trades, amendedsize *
                                  kContractSize, brokerage = kBrokerage)


########### Generate Option Trades ################

signals$strike<-round((signals$buyprice+signals$shortprice) / 100) * 100
signals$currentmonthexpiry <- as.Date(sapply(signals$date, getExpiryDate), tz = kTimeZone)
nextexpiry <- as.Date(sapply(
  as.Date(signals$currentmonthexpiry + 20, tz = kTimeZone),
  getExpiryDate
), tz = kTimeZone)
signals$entrycontractexpiry <- as.Date(ifelse(
  businessDaysBetween("India",as.Date(signals$date, tz = kTimeZone),signals$currentmonthexpiry) <= 3,
  nextexpiry,signals$currentmonthexpiry),tz = kTimeZone)
optionSignals<-optionTradeSignalsLongOnly(signals,kFNODataFolder,kNiftyDataFolder)
optionTrades<-GenerateTrades(optionSignals)
optionTrades<-optionTrades[order(optionTrades$entrytime),]
for(i in 1:nrow(optionTrades)){
  if(optionTrades$exittime[i]<"2000-01-01"){
    optionTrades$exittime[i]<-strptime(NA,format="%Y-%m-%d",tz=kTimeZone)
  }
}
if(kMoneyManagement){
  amendedsizedf<-data.frame(date=mdsubset$date,close=mdsubset$close,size=amendedsize)
}else{
  amendedsize<-kMaxContracts
  amendedsizedf<-data.frame(date=mdsubset$date,close=mdsubset$close,size=amendedsize)
}
optionTrades$size<-merge(optionTrades,amendedsizedf,by.x="entrytime",by.y="date")$size*kContractSize
optionTrades$underlying<-merge(optionTrades,amendedsizedf,by.x="entrytime",by.y="date")$close

pricediff<-optionTrades$exitprice-optionTrades$entryprice
absprofit<-ifelse(grepl("BUY",optionTrades$trade),pricediff,-pricediff)
optionTrades$percentprofit<-absprofit/optionTrades$underlying
optionTrades$brokerage <-  (2*kPerContractBrokerage/kContractSize)/trades$entryprice
optionTrades$netpercentprofit <-  optionTrades$percentprofit - optionTrades$brokerage


# update option prices for trades today
# update entry prices
out <- which(as.Date(optionTrades$entrytime,tz=kTimeZone) == Sys.Date())
if(length(out)>0){
  for(o in 1:length(out)){
    index<-out[o]
    newrow <- getPriceArrayFromRedis(9,optionTrades$symbol[index],"tick","close",paste(today, " 09:12:00"))
    if(nrow(newrow)==1){
      optionTrades$entryprice[index]<-newrow$settle[1]
      optionTrades$exitprice[index]<-newrow$settle[1]
    }
  }
}



# update exit prices
out <- which(as.Date(optionTrades$exittime,tz=kTimeZone) == Sys.Date()|is.na(optionTrades$exittime))
if(length(out)>0){
  for(o in 1:length(out)){
    index<-out[o]
    newrow <- getPriceArrayFromRedis(9,optionTrades$symbol[index],"tick","close",paste(today, " 09:12:00"))
    if(nrow(newrow)==1){
      optionTrades$exitprice[index]<-newrow$settle[1]
    }
  }
}

if(length(args)>1 && args[1]==1){
  save(md,file=paste(args[2],"md.R",sep="."))
  save(optionTrades,file=paste(args[2],"optionTrades.R",sep="."))
  
}


############### METRICS ##############
if (length(args)>1 && args[1] == 2) {
  #Derived Trades
  pnl <- pnl<-data.frame(bizdays=as.Date(mdsubset$date,tz=kTimeZone),realized=0,unrealized=0,brokerage=0)
  cumpnl<-CalculateDailyPNL(optionTrades[complete.cases(optionTrades),],pnl,kFNODataFolder,kPerContractBrokerage/75,per.contract.brokerage = TRUE)
  cumpnl$daily.pnl <- (cumpnl$realized + cumpnl$unrealized-cumpnl$brokerage) - Ref(cumpnl$realized + cumpnl$unrealized-cumpnl$brokerage, -1)
  cumpnl$daily.pnl <- ifelse(is.na(cumpnl$daily.pnl), 0, cumpnl$daily.pnl)
  cumpnl$daily.return <- cumpnl$daily.pnl*100/(mdsubset$close*kContractSize*75)
  cumpnl$daily.return <- ifelse(is.na(cumpnl$daily.return), 0, cumpnl$daily.return)
  cumpnl$daily.return <- ifelse(is.infinite(cumpnl$daily.return), 0, cumpnl$daily.return)
  grosspnl<-(optionTrades$exitprice-optionTrades$entryprice)*optionTrades$size
  brokerage<- 2*optionTrades$size*kPerContractBrokerage/75
  optionTrades$grosspnl<-ifelse(grepl("BUY",optionTrades$trade),grosspnl,-grosspnl)
  optionTrades$brokerage<-brokerage
  NetProfit<-sum(optionTrades$grosspnl-optionTrades$brokerage)
  AverageMargin=sum(optionTrades$entryprice*optionTrades$size*optionTrades$bars)/sum(optionTrades$bars)
  fy.tmp <- seq( as.POSIXct('2013-04-01'), length=10, by='year')
  cumpnl$fiscalyear=(2014:2023)[ findInterval(as.POSIXct(cumpnl$bizdays,tz=kTimeZone),fy.tmp) ]
  optionTrades$fiscalyear=(2014:2023)[ findInterval(optionTrades$entrytime,fy.tmp) ]
  fiscal.pnl<-tapply(cumpnl$daily.pnl,cumpnl$fiscalyear,sum)
  fiscal.sharpe<-tapply(cumpnl$daily.return,cumpnl$fiscalyear,sharpe)
  fiscal.pnl.recon<-tapply(optionTrades$grosspnl-optionTrades$brokerage,optionTrades$fiscalyear,sum)
  fiscal.margin.num<-tapply(optionTrades$size*optionTrades$entryprice*optionTrades$bars,optionTrades$fiscalyear,sum)
  fiscal.margin.den<-tapply(optionTrades$bars,optionTrades$fiscalyear,sum)
  fiscal.margin<-fiscal.margin.num/fiscal.margin.den
  fiscal.winratio.num<-tapply((optionTrades$grosspnl-optionTrades$brokerage)>0,optionTrades$fiscalyear,sum)
  fiscal.winratio.den<-tapply(optionTrades$grosspnl,optionTrades$fiscalyear,length)
  fiscal.winratio=fiscal.winratio.num/fiscal.winratio.den  
  fiscal.underlying.max<-tapply(optionTrades$entryprice,optionTrades$fiscalyear,max)
  
  reporting<-as.data.frame(fiscal.sharpe)
  reporting=data.frame(reporting,as.data.frame(fiscal.winratio)$fiscal.winratio)
  reporting=data.frame(reporting,as.data.frame(fiscal.pnl)$fiscal.pnl)
  reporting=data.frame(reporting,as.data.frame(fiscal.margin)$fiscal.margin)
  reporting=data.frame(reporting,as.data.frame(fiscal.underlying.max)$fiscal.underlying.max*kContractSize*kMaxContracts)
  colnames(reporting)<-c("Sharpe","WinRatio","NetP&L","AverageMarginUtil","BudgetedMargin")
  reporting$Sharpe<-format(round(reporting$Sharpe,2),nsmall = 2)
  reporting$WinRatio<-format(round(reporting$WinRatio*100,2),nsmall = 2)
  reporting$`NetP&L`<-formatC(reporting$`NetP&L`,format="d", big.mark=',')
  reporting$AverageMarginUtil<- formatC(reporting$AverageMarginUtil,format="d", big.mark=',') 
  reporting$BudgetedMargin<- formatC(reporting$BudgetedMargin,format="d", big.mark=',')
}


```

The parameters for the run were set as follows:  

##Envelope Parameters  
Full Hand : `r kMaxContracts ` Contracts  
Brokerage : INR `r kPerContractBrokerage`  per contract, one-way   
Threshold Drawdown : `r kDrawdownPercentThreshold*100`%  
MoneyManagement : `r ifelse(kMoneyManagement==0,"OFF","ON")`  
BackTest Start Date : `r kBackTestStartDate`  
BackTest End Date : `r kBackTestEndDate`  


##Algorithm Performance Metrics  
The performace summary is aggregated by fiscal years - covering a 12 month period between April to March.
`r kable(reporting[c("2014","2015","2016"),],caption="Performance Metrics")`  

These metrics include brokerage costs but exclude impact of license fees to be paid for running this Algorithm. 


## Profit & Loss Graph

```{r ProfitPlot, setoptions,echo=FALSE, results="asis",fig.height=6,fig.width=10,cache=TRUE}
truncatedpnl<-cumpnl[cumpnl$bizdays<kBackTestEndDate,] 
plot(x = truncatedpnl$bizdays,
     y = (truncatedpnl$realized + truncatedpnl$unrealized - truncatedpnl$brokerage),
     type = 'l',main="Profit & Loss",xlab="Date",ylab="Profit",axes=FALSE)
axis.Date(1,truncatedpnl$bizdays,at=seq(min(truncatedpnl$bizdays), max(truncatedpnl$bizdays)+90, by="3 mon"),, format="%m-%Y")
minProfit=min(truncatedpnl$realized+truncatedpnl$unrealized-truncatedpnl$brokerage)
maxProfit=max(truncatedpnl$realized+truncatedpnl$unrealized-truncatedpnl$brokerage)
points=pretty(seq(minProfit,maxProfit,by=(maxProfit-minProfit)/5))
axis(2,at=points,labels=paste(points/1000000,"M",sep=""),las=1)

```

## BootStrap  
Bootstrapping helps us identify the variations in performance, assuming that the historical returns are a good estimate of the population. Bootstrapping over 1000 runs provides the following picture

```{r BootStrap,setoptions, message=FALSE, echo=FALSE, results="as-is",fig.height=6,fig.width=12,cache=TRUE}
library(RTrade) 
trades<-trades[complete.cases(optionTrades),]
  optionTrades<-optionTrades[complete.cases(optionTrades),] 
  #  par(mfrow = c(2, 4))
  returns <-
    trades[trades$entrytime >= "2013-04-01" & trades$entrytime <= "2016-03-31" , c("netpercentprofit")]
  derivedreturns <-
    optionTrades[optionTrades$entrytime >= "2013-04-01" & optionTrades$entrytime <= "2016-03-31" , c("netpercentprofit")]

  bars <- trades[trades$entrytime >= "2013-04-01" & trades$entrytime <= "2016-03-31", c("bars")]
  count <- length(returns)

  bootstrap.results=bootstrap(dddays=kDrawdownDaysThreshold,ddamt=kDrawdownPercentThreshold,recoverybonus=kRecoveryBonus,ddcost=kDrawdownCost,stop=0,margin=1,charttitle=args[2],
            returnvector=returns,
            derivedreturn=derivedreturns,
            tradebarvector=bars,
            samples=1000,
            samplesize=as.integer(count/3),
            contractsize=kMaxContracts,
            derivedleg=kMoneyManagement)
  
  #bootstrap estimates
  capital.at.loss=1000000
  max.exposure=capital.at.loss/bootstrap.results$ddvalue95percavg[2]
  margin.requirement = max.exposure*0.03
  return.lower.range=(as.numeric(bootstrap.results$retavg[2])-as.numeric(bootstrap.results$retsd[2]))
  return.upper.range=(as.numeric(bootstrap.results$retavg[2])+as.numeric(bootstrap.results$retsd[2]))
  pnl.lower.range=return.lower.range*capital.at.loss/ as.numeric(bootstrap.results$ddvalue95percavg[2])
  pnl.upper.range=return.upper.range*capital.at.loss/ as.numeric(bootstrap.results$ddvalue95percavg[2])
  roce.lower.range=pnl.lower.range/(capital.at.loss+margin.requirement)
  roce.upper.range=pnl.upper.range/(capital.at.loss+margin.requirement)
  
```

The first row illustrates the results over a run with *Full Hand* irrespective of any drawdown. The results are acceptable, from a return perspective. However, maximum drawdown values (chart# 4 in the first row) are high.  

This is allieviated by reducing contract size with increasing drawdown. The results from this derived algorithm are plotted in the second row. Whilst the maximum drawdown percentage reduces on implementing this money management rule, the returns are also negatively impacted. However, the returns are also postively skewed, which we believe reduces the probability of large losses.  


The bootstrap expects us to have an average of `r bootstrap.results$ddvalue95percavg*100`% maximum drawdown over a one year holding. 

Example:  
a. Trading Capital (At High Risk of Loss) : INR `r formatC(capital.at.loss,format="d",big.mark=",")`  
b. Maximum Exposure Taken by Algorithm : INR  `r formatC(max.exposure,format="d",big.mark=",")`  
c. Margin Requirement @ `r 0.03*100`% as option premium : INR  `r formatC(margin.requirement,format="d",big.mark=",")`  
d. Total Capital Needed with broker (a+c) : INR `r formatC(capital.at.loss+margin.requirement,format="d",big.mark=",")`  
e. Expected Return on Maximum Exposure at lower bound at 1 standard deviation = `r return.lower.range*100`%  
f. Expected Return on Maximum Exposure at upper bound at 1 standard deviation= `r return.upper.range*100`%  
g. Lower prediction of Absolute PNL at 1 standard deviation : INR `r formatC(pnl.lower.range,format="d",big.mark=',')`  
h. Higher prediction of Absolute PNL at 1 standard deviation : INR `r formatC(pnl.upper.range,format="d",big.mark=',')`  
i. Expected Range of annualized return on at one standard deviation = `r round(as.numeric(roce.lower.range)*100,0)`% to `r round(as.numeric(roce.upper.range)*100,0)`%  

The calculations above are illustrative based on simulation of backtested results, and provide guiding posts for allocation of funds the algorithm. By no means are any returns guaranteed. This is a strategy with a "HIGH RISK" of capital loss.  

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# Risks  

## Historical returns may not be indicator of future returns   
The reported Algorithm performance is on backtested or simulated results, unless otherwise stated. In either case, historical returns are not an indictor of the returns in future.  

## Data Quality  
The Algorithm identifies buy and sell strategies via a combination of public data and private data distributed from data providers. Any change in quality of data provided and changes in data defintions can adversely affect the performance of the Algorithm.  

## Execution  
The Algorithm performance is affected by any difference between the execution price of a contract assumed by the Algorithm, and its actual execution price in the market. The actual execution price depends on the availability of the contract for trading, liquidity of the contract and the time of execution vs the time of the trade opportunity identifed by the Algorithm. Any slippage in prices can adversely affect the performance of the Algorithm.  

## Model inadequacies  
The Algorithm is built upon a model and rules for identifying buy and sell opportunities. The model defines a relationship between some external variables, but does not cover all possible external variables. It is possible that the performance of the Algorithm will be impacted by variables outside the model. In addition, the variables used in the model might lose their efficacy over a period of time. Any such model inadequacies can adversely affect the performance of the Algorithm.  

## Regulations  
Changes to business environment and new regulations can introduce market events that are not modelled by the Algorithm. Any such development can adversely affect the performance of the Algorithm.  

## Tax Implications  
The returns illustrated by this document are before any tax payments. The returns also exclude any license fees to be paid as a result of the contract to run this Algorithm. Potential clients are urged to work with their tax consultants and review tax implications of running the Algorithm on their own funds.  

## Technology
The timely generation of buy and sell opportunities is based on the availability of technology infrastructure, including but not limited to availability of internet, market data and corporate actions. Disruption in any enabling infrastructure could delay generation of buy and sell opportunities and could adversely affect the performance of the Algorithm.