binary-Q1TD.Rmd

---
title: "<img src='www/binary-logo-resize.jpg' width='240'>"
subtitle: "[binary.com](https://github.com/englianhu/binary.com-interview-question) Interview Question I - Tick-Data-HiLo For Daily Trading <span style='color:red'>(Blooper)</span>"
author: "[®γσ, Lian Hu](https://englianhu.github.io/) <img src='www/ENG.jpg' width='24'> <img src='www/RYO.jpg' width='24'>®"
date: "`r lubridate::today('Asia/Tokyo')`"
output:
  html_document: 
    number_sections: yes
    toc: yes
    toc_depth: 4
    toc_float:
      collapsed: yes
      smooth_scroll: yes
---

```{r setup, include=FALSE}
suppressPackageStartupMessages(library('BBmisc'))
pkgs <- c('knitr', 'kableExtra', 'tint', 'devtools', 'lubridate', 'plyr', 'pryr', 'stringr', 'magrittr', 'dplyr', 'tidyr', 'tidyverse', 'tidyquant', 'turner', 'readr', 'quantmod', 'htmltools', 'highcharter', 'googleVis', 'formattable', 'ggfortify', 'DT', 'forecast', 'PerformanceAnalytics', 'broom', 'microbenchmark', 'memoise', 'doParallel', 'Boruta', 'fBasics', 'fPortfolio', 'rugarch', 'parma', 'rmgarch')

suppressAll(lib(pkgs))

## Set option to below if you want to plot an independent webpage with graph 
#'@ op <- options(gvis.plot.tag=NULL)
op <- options(gvis.plot.tag = 'chart')
options(gvis.plot.tag = 'chart', warn = -1, 'getSymbols.yahoo.warning' = FALSE)
#'@ options(rpubs.upload.method = 'internal')

rm(pkgs)
#'@ options(htmltools.dir.version = FALSE)

## filter tick data to get daily high-low price (with timeline).
source('function/filter_HL.R')
source('function/read_HL_tick_data.R')
source('function/forecastUSDJPYHL.R')
source('function/sim_predict.R')
source('function/sim_staking.R')
source('./function/plotChart2.R')#, local = TRUE)
```

# Introduction

From paper [Binary Q1](https://englianhu.github.io/2017/09/binary-forex-trading-Q1.html) or ([Alternate link](http://rpubs.com/englianhu/binary-forex-trading-Q1)) and also [Binary Q1 (Extention)](http://rpubs.com/englianhu/binary-Q1E) or ([Alternate link](http://rpubs.com/englianhu/316133)). Both papers test the accuracy of various statistical models and gain a high ROI per annum. However, as stated in the paper there has a concern which is don't know highest or lowest price came first, therefore the paper compared all possible outcomes. Finally the `Hi-Lo` and `Lo-Hi` models made highest returns. The research on this paper will be applicable to the real-life.

In order to test the timeline of daily highest and lowest price when I am writing [Real Time Trading System (Trial)](https://beta.rstudioconnect.com/content/3775/), here I created this file to read the tick-data-history to test the ROI (Return On Investment) per annum. Kindly refer to section [Reference] for further information.

# Data

## Read Data

I use more than 3 years data (from week 1 2015 until week 27 2018)^[You are feel feel to get the data via [FXCMTickData](https://github.com/fxcm/FXCMTickData)] for the question as experiment, 1st year data is burn-in data for statistical modelling and prediction purpose while following 2 years data for forecasting and staking. There have 52 trading weeks within a year.

There will be a certain spread charged by operators but the OHLC dataset does not provide the information for the course of the exchange rate. The tick-data history will be similar with rebirth model in soccer betting for normal FOREX trading market. The financial betting market similar with pre-match soccer betting.

```{r read-data1, echo=FALSE, eval=FALSE}
## ================== eval = FALSE =============================
## Do not execute...
## 
## Remove all objects include hidden objects.
#'@ rm(list = ls(all.names = TRUE))
## get currency dataset online.
yr <- c(2015, 2016, 2017, 2018)
wk <- 1:53
dr <- 'data/USDJPY/'

## https://www.epochconverter.com/years
llply(yr, function(i) {
  if(i == 2015|i == 2017) wk <- 1:53 else wk <- 1:52
  llply(wk, function(j) {
    lnk <- paste0(
      'https://tickdata.fxcorporate.com/USDJPY/', i, '/', j, '.csv.gz')
    if(!dir.exists(dr)) dir.create(dr)
    if(!file.exists(paste0(dr, 'Y', i, 'W', j, '.csv.gz'))) {
      download.file(lnk, destfile = paste0(
        dr, 'Y', i, 'W', j, '.csv.gz'))
      #cat(paste0(dr, 'Y', i, 'W', j, '.csv.gz downloaded!\n'))
    }
  })
})

## https://stackoverflow.com/questions/43642708/fread-with-gunzip-whats-the-more-memory-efficient-way/43643513
## https://stackoverflow.com/questions/37727865/how-can-i-use-fread-to-read-gz-files-in-r?noredirect=1&lq=1
#'@ data.table::fread("gunzip -c data/tickdata/Y2015W1.csv.gz")
## Due to the dataset size more than 1.5 mil rows, here I run and tidy the dataset instead of read the *.csv.gz or *.csv files.

llply(yr, function(i) {
  if(i == 2015|i == 2017) wk <- 1:53 else wk <- 1:52
  llply(wk, function(j) {
    if(file.exists(paste0(dr, 'Y', i, 'W', j, '.csv.gz')) & 
       !file.exists(paste0(dr, 'Y', i, 'W', j, '.csv'))) {
      R.utils::gunzip(paste0(dr, 'Y', i, 'W', j, '.csv.gz'), 
                      remove = FALSE)
      cat(paste0(dr, 'Y', i, 'W', j, '.csv.gz extracted!\n'))
    }
  })
})

## remove all files size less than 1MB
if(any(file.exists(paste0(dr, dir(dr, pattern = '.csv')[file.size(paste0(
  dr, dir(dr, pattern = '.csv'))) <= 1000000])))) {
  file.remove(paste0(dr, dir(dr, pattern = '.csv')[file.size(
    paste0(dr, dir(dr, pattern = '.csv'))) <= 1000000]))
  }
```

```{r read-data2, echo=FALSE, eval=FALSE}
## --------------------- Read Data -------------------------------
dr <- 'data/USDJPY/'
fls <- dir(dr, pattern = '.csv$')
#dfm <- read.csv(paste0(dr, fls), skipNul = TRUE)

# start <- seq(1, 186, 31)
# stop <- start - 1
# stop <- c(stop[-1], length(fls))
# paste0('fls = fls[', start, ':', stop, ']')

nm <- str_replace_all(fls, '.csv', '')

##
for(i in seq(length(fls))) {
  #if(!file.exists(paste0(dr, nm[i], '.rds'))) {
  assign(nm[i], read.csv(
    paste0(dr, fls[i]), skipNul = TRUE) %>% tbl_df)
  
  ## save dataset.
  eval(parse(text = paste0(
    "saveRDS(", nm[i], ", '", dr, nm[i], ".rds')")))
  eval(parse(text = paste0("rm(", nm[i], ")")))
  cat(paste0(dr, nm[i], '.rds saved!\n'))
  #}
}; rm(i, fls, nm)

## --------------------- Check Files -------------------------------
## check the number of *.rds files in directory.
drt <- dir(dr, pattern = '[^_HL].rds')

# start <- seq(1, 186, 31)
# stop <- start - 1
# stop <- c(stop[-1], length(drt))
# paste0('drt = drt[', start, ':', stop, ']')

##verify the number of files.
drt %>% str_split_fixed('Y|W|.rds', 4) %>% tbl_df %>% 
  select(V2, V3) %>% filter(V2 == 2015)

## If the downloaded files are display in Asia/Tokyo timezone, then 
##   we can change to default UTC timezone.
#'@ Y2015W2 %>% mutate(
#'@   DateTime = mdy_hms(DateTime, tz = 'Asia/Tokyo'), 
#'@   DateTime = with_tz(DateTime, 'UTC'))

## --------------------- Filter Data -------------------------------
dr <- 'data/USDJPY/'
drt <- dir(dr, pattern = '[^_HL].rds')
nm <- str_replace_all(drt, '.rds', '')
# start <- seq(1, 186, 31)
# stop <- start - 1
# stop <- c(stop[-1], length(drt))
# data.frame(drt = paste0('drt = drt[', start, ':', stop, ']'), 
#            colm = ';', 
#            nm = paste0('nm = nm[', start, ':', stop, ']'))

for(i in seq(length(drt))) {
  assign(nm[i], readRDS(paste0(dr, drt[i])))
  
  ## filter daily highest and lowest price.
  #'@ assign(paste0(nm[i], '_HL'), nm[i] %>% mutate(Date = as.Date(mdy_hms(DateTime))) %>% 
  #'@   group_by(Date) %>% 
  #'@   filter(Bid == min(Bid)|Bid == max(Bid)|Ask == min(Ask)|Ask == max(Ask)) %>% 
  #'@   filter(!duplicated(Bid)|!duplicated(Ask)))
  ## Error : assign() cannot handle nm[i] %>% mutate(...) since 'nm[i]' is class character.
  
  ## convert timezone, will take time around 20 minutes for 1 million plus rows due to not vectorised handling.
  #'@ eval(parse(text = paste0(
  #'@   nm[i], "_HL <- ", nm[i], " %>% mutate(DateTime = mdy_hms(DateTime, tz = 'UTC')) %>% rowwise() %>% do(DateTime = with_tz(.$DateTime, tzone = 'GMT')) %>% mutate(Date = as.Date(DateTime))")))
  
  ## filter daily highest and lowest price.
  eval(parse(text = paste0(
    nm[i], "_HL <- ", nm[i], " %>% mutate(DateTime = with_tz(mdy_hms(DateTime), 'GMT'), Date = as.Date(DateTime)) %>% group_by(Date) %>% filter(Bid == min(Bid)|Bid == max(Bid)|Ask == min(Ask)|Ask == max(Ask))")))
  eval(parse(text = paste0(nm[i], '_HL %<>% filter(!duplicated(Bid)|!duplicated(Ask))')))
  
  ## save dataset.
  eval(parse(text = paste0(
    "saveRDS(", nm[i], "_HL, '", dr, nm[i], "_HL.rds')")))
  eval(parse(text = paste0("rm(", nm[i], ")")))
  eval(parse(text = paste0("rm(", nm[i], "_HL)")))
  cat(paste0(dr, nm[i], '_HL.rds saved!\n'))
  }

#'@ test <- Y2018W9
#'@ test %<>% mutate(DateTime = mdy_hms(DateTime, tz = 'UTC')) %>% rowwise() %>% 
#'@   do(DateTime = with_tz(.$DateTime, tzone = 'GMT')) %>% 
#'@   mutate(Date = as.Date(DateTime))

## -----------------------------------------------------------------
## convert timezone, will take time around 20 minutes for 1 million plus rows due to not vectorised handling.
#'@ eval(parse(text = paste0(
#'@   nm[i], "_HL <- ", nm[i], " %>% mutate(DateTime = mdy_hms(DateTime, tz = 'UTC')) %>% rowwise() %>% do(DateTime = with_tz(.$DateTime, tzone = 'GMT')) %>% mutate(Date = as.Date(DateTime))")))

## check the number of *.rds files in directory.
dr <- 'data/USDJPY/'
drt <- dir(dr, pattern = '_HL.rds')

#'@ drt %>% str_split_fixed('Y|W|_HL.rds', 4) %>% tbl_df %>% 
#'@   select(V2, V3) %>% filter(V2 == 2015)

nm <- str_replace_all(drt, '.rds', '')

## filter_HL() to get daily unique high low price.
#'@ source('function/filter_HL.R')

## simulate secondary filter daily high-low price.
for(i in seq(length(drt))) {
  assign(nm[i], readRDS(paste0(dr, drt[i])))
  assign(nm[i], eval(parse(text = paste0('filter_HL(', nm[i], ')'))))
  
  ## save dataset.
  eval(parse(text = paste0(
    "saveRDS(", nm[i], ", '", dr, nm[i], ".rds')")))
  eval(parse(text = paste0("rm(", nm[i], ")")))
  cat(paste0(dr, nm[i], '.rds saved!\n'))  
  }
```

I gathered the 3 datasets from below websites: 

- **1st Dataset** - `quantmod::getSymbols(src = 'yahoo')`: which contains OHLCV data price (timezone in GMT). The place orders function required highest or lowest price come first, therefore I gathered the data via **FXCMTickData**.
- **2nd Dataset** - [FXCMTickData](https://github.com/fxcm/FXCMTickData) : which contain the timeline of highest and lowest price within a day (timezone in UTC). The daily dataset used for forecast daily price.
- **3rd Dataset** - `TFX::queryFX()`: which shows the current price. The place orders function required data history, therefore I gathered the data via **FXCMTickData**.

<span style='color:red'>There will probably occurs inconsistancy of data price among 3 datasets, however there will be cost few years time to gather all real time price via `TFX::queryFX()`. Otherwise all data gather via 1 channel (`queryFX()`) will be perfect. However, you can feel free to read futher in this paper where verified the consistancy of datasets.</span>

The will be another research project for **Real Time High Frequency Trading** where collect the real-time data and also high-frquency trading for tick-data. You are feel free to browse over [Real Time FXCM](https://github.com/scibrokes/real-time-fxcm).

Below is the dataset gather via `getSymbols(src = 'yahoo')`.

```{r data-summary1}
## read saved dataset.
mbase <- readRDS('./data/USDJPY/USDJPY.rds')
```

```{r data-summary2, echo=FALSE}
## size of dataset.
paste0('mbase : [', paste(dim(mbase), collapse = ' x '), ']')
```

```{r data-summary3, echo=FALSE, results='asis'}
summary(mbase) %>% 
  tidy %>% 
  select(-Var1) %>% 
  rename(Category = Var2) %>% 
  kable(caption = 'Table Summary') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
  scroll_box(width = '100%', height = '400px')
```

*Table 2.1.1 : 1st dataset - summary of daily price dataset.*

## Tidy Data

For 2nd dataset, here I gather the tick data via **FXCMTickData**, there are more than million rows dataset (million rows per file while there are 52 files over 52 weeks) while I tidy and filter only highest and lowest `bid/ask` price. From the table below we can know the timeline which is weather highest or lowest price came first.

```{r read-data3}
## read tick data.
HL_tick_data <- read_HL_tick_data()
dtID <- unique(HL_tick_data$Date)

## arrange the sequence of highest and lowest price.
HL_tick_data %<>% tbl_df %>% mutate(sq = rep(1:4, length(dtID)))

## Print dataset
HL_tick_data
```

*Table 2.2.1 : 2nd dataset - daily high-low price tick-data.*

For 3rd dataset, due to there is a real-time data, the **Real Time Trading System (Trial)** web application only stored the real-time `bid/ask` transaction price but not collect all tick-data in seconds. However, you are feel free to gather from [DataCollection](https://beta.rstudioconnect.com/content/3153/).

# Statistical Modelling

## Forecast Daily Hi-Lo Price

I tried to apply Lasso, Elastic Net and Ridge models to test the accuracy of prediction via [shinyApp](https://beta.rstudioconnect.com/content/2367/).

$$\begin{equation}
\sigma^2_{t} = \omega + \sum_{i=1}^{\rho}(\alpha_{i} + \gamma_{i} I_{t-i}) \varepsilon_{t-i}^{2} + \sum_{j=1}^{q}\beta_{j}\sigma^{2}_{t-j}\ \cdots\ Equation\ 3.1.1
\end{equation}$$

Here I directly apply *GJR-GARCH*^[Kindly refer to [GJR-GARCH 模型](https://vlab.stern.nyu.edu/zh/doc/3?topic=mdls) for more information] model due to I had compared few statistical models and got the best fitted model. Kindly refer to **Binary Q1** for the paper.

- Auto Arima models (Adjusted and use the optimal AR and MA parameters)
- Exponential Time Series (27 ETS models)
- Univariate Garch models (GARCH, T-GARCH, GJR-GARCH, eGARCH, etc altogather 12 models.)
- Exponential Weighted Moving Average
- <s>Monte Carlo Markov Chain</s>
- <s>Bayesian Time Series</s>
- <s>Midas</s>

![](www/ARCH-family.jpg)

*Source presentation 3.1.1 : [Univariate Garch 2012 (powerpoint)](https://github.com/englianhu/binary.com-interview-question/blob/master/reference/Univariate%20Garch%202012%20powerpoint.pdf)*

![](www/ARCH-family-formula.jpg)

Here I wrote another extention page for Q1 which is analyse the multiple currencies and also models from minutes to daily. You are feel free to browse over **Binary Q1 (Extention)**. The paper compare and get the optimal predictive model based on the various number of observations.

## GARCH Order

The `rugarch` package not only provides various GARCH models but also contains below 3 to suite our needs :

- variance.model
- mean.model
- distribution.model

Kindly refer to [rugarch包与R语言中的garch族模型](http://mob.dataguru.cn/mportal.php?mod=view&aid=794) for more information.

![](www/optimal-garchOrder-1.jpg)

*Source presentation 3.2.1 : Univariate Garch 2012 (powerpoint)*

![](www/optimal-garchOrder-2.jpg)

*Source presentation 3.2.2 : Univariate Garch 2012 (powerpoint)*

![](www/optimal-garchOrder-3.jpg)

*Source presentation 3.2.3 : Univariate Garch 2012 (powerpoint)*

Due to above presentation compares the `infocriteria` of the GARCH order, here I directly set `garchOrder(1,1)` in my model.

## ARMA Order

For ARMA order, kindly refer to **GARCH模型中的`ARMA(p,d,q)`参数最优化**^[You can read the paper by search inside section [Reference]] for more information. I used old function which is `calC()` but not `calc_fx()` in this paper.

```{r read-data4, echo=FALSE, eval=FALSE}
## get currency dataset online.
#'@ getFX('USD/JPY', from = '2014-01-01', to = '2017-01-20') #oanda only provides 180 days data. getSymbols()

## Get data.
#'@ USDJPY <- getSymbols('JPY=X', src = 'yahoo', from = '2015-01-04', 
#'@                      to = '2018-07-06', auto.assign = FALSE)
#'@ names(USDJPY) <- str_replace_all(names(USDJPY), 'JPY=X', 'USDJPY')
#'@ USDJPY %<>% na.omit
#'@ saveRDS(USDJPY, 'data/USDJPY/USDJPY.rds')

mbase <- readRDS('./data/USDJPY/USDJPY.rds')
if(!is.xts(mbase)) mbase <- xts(mbase[, -1], order.by = mbase$Date)

## dateID or timeID
timeID <- index(mbase)
timeID0 <- ymd('2016-01-04')
timeID <- timeID[timeID > dateID0] # index(mbase)[index(mbase) > ymd('2016-01-04')]

#length(timeID)
#[1] 651
#start <- seq(1, 652, 109)
#stop <- start - 1
#stop <- c(stop[-1], length(timeID))
#data.frame(timeID = paste0('timeID = timeID[', start, ':', stop, ']'))
#1   timeID = timeID[1:109] # index(mbase)[index(mbase) > ymd('2016-01-04')][1:109]
#2 timeID = timeID[110:218] # index(mbase)[index(mbase) > ymd('2016-01-04')][110:218]
#3 timeID = timeID[219:327] # index(mbase)[index(mbase) > ymd('2016-01-04')][219:327]
#4 timeID = timeID[328:436] # index(mbase)[index(mbase) > ymd('2016-01-04')][328:436]
#5 timeID = timeID[437:545] # index(mbase)[index(mbase) > ymd('2016-01-04')][437:545]
#6 timeID = timeID[546:651] # index(mbase)[index(mbase) > ymd('2016-01-04')][546:651]

## simulate financial betting.
pred.data <- sim_predict(
    mbase, #timeID = index(mbase), 
	timeID = index(mbase)[index(mbase) > ymd('2016-01-04')][546:651], 
	timeID0 = ymd('2016-01-04'), 
	.preCat = 'Op', .preCat2 = 'Hi', .preCat3 = 'Lo', .preCat4 = 'Cl', 
	.save = TRUE, currency = 'JPY=X')

#index(mbase)[index(mbase) > ymd('2016-01-04')][268:269] #error
#Latest Date (GMT): 2017-01-11 done!
#Latest Date (GMT): 2017-01-11 saved!
#
#Error in solve.default(res$hessian * n.used, A) : 
#  Lapack routine dgesv: system is exactly singular: U[1,1] = 0

#> pred.data %>% dplyr::filter(LatestDate.GMT == '2017-01-12')
## A tibble: 1 x 10
#  LatestDate.GMT Lst.Open Lst.Low Fct.High Lst.Close ForecastDate.GMT Fct.Open Lst.High  Fct.Low
#          <date>    <dbl>   <dbl>    <dbl>     <dbl>           <fctr>    <dbl>    <dbl>    <dbl>
#1     2017-01-12       NA  113.76 110.5123        NA              T+1       NA  115.219 113.6786
# ... with 1 more variables: Fct.Close <dbl>
#> pred.data %>% dplyr::filter(LatestDate.GMT == '2017-01-13')
## A tibble: 1 x 10
#  LatestDate.GMT Lst.Open Lst.Low Fct.High Lst.Close ForecastDate.GMT Fct.Open Lst.High  Fct.Low
#          <date>    <dbl>   <dbl>    <dbl>     <dbl>           <fctr>    <dbl>    <dbl>    <dbl>
#1     2017-01-13  114.696 114.284 110.5143   114.664              T+1 114.5294  115.388 114.3947
## ... with 1 more variables: Fct.Close <dbl>
#> pred.data %>% dplyr::filter(LatestDate.GMT == '2017-01-11')
## A tibble: 1 x 10
#  LatestDate.GMT Lst.Open Lst.Low Fct.High Lst.Close ForecastDate.GMT Fct.Open Lst.High  Fct.Low
#          <date>    <dbl>   <dbl>    <dbl>     <dbl>           <fctr>    #<dbl>    <dbl>    <dbl>
#1     2017-01-11  115.875 115.681 110.5116   115.872              T+1 115.7538  116.835 115.7639
## ... with 1 more variables: Fct.Close <dbl>

rm(obs.data, USDJPY)

#> pred.data %>% dplyr::filter(LatestDate.GMT == '2017-01-12')
## A tibble: 1 x 10
#  LatestDate.GMT Lst.Open Lst.High Lst.Low Lst.Close ForecastDate.GMT Fct.Open Fct.High  Fct.Low
#          <date>    <dbl>    <dbl>   <dbl>     <dbl>           <fctr>    <dbl>    <dbl>    <dbl>
#1     2017-01-12  115.055  115.219  113.76        NA              T+1 115.1867 110.5123 113.6786
## ... with 1 more variables: Fct.Close <dbl>
```

Here I read my saved dataset where forecast 1 trading day advanced for daily Hi-Lo price. Kindly refer to **Real Time Trading System (Trial)** for more information.

```{r read-data5, echo=FALSE}
pred.data <- readRDS('data/USDJPY/pred.data.rds') %>% tbl_df
pred.data %>% data.table
```

*Table 3.3.1 : Forecast high-low daily price.*

```{r tidy-data1}
pred.data %>% dplyr::filter(LatestDate.GMT == '2017-01-12') %>% 
  kable(caption = 'Data Error') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
  scroll_box(width = '100%')
```

*Table 3.3.2 : Forecast daily price missing close price.*

<s>Due to the day 2017-01-12 unable forecast the closed price.^[`armaSearch()` error on method = 'ML'], here I omit the transaction on that day.</s>

Below I combine the daily price dataset with forecast `Hi-Lo` price.

```{r tidy-data2}
## filter data.
pred.data %<>% dplyr::filter(LatestDate.GMT != '2017-01-12')

## Copied dataset.
mbase <- data.frame(Date = index(mbase), mbase) %>% tbl_df
pred.data %<>% tbl_df

## Add `Date` column as forecasted Date.
pred.data$Date <- lead(pred.data$LatestDate.GMT)
pred.data$Date[length(pred.data$Date)] <- data.table::last(pred.data$LatestDate.GMT) + days(1)

pred.data %<>% select(Date, Fct.Open, Fct.High, Fct.Low, Fct.Close) %>% data.table

## Merge dataset.
pred <- merge(tbl_df(mbase), pred.data, by = 'Date') %>% 
  tbl_df %>% select(-USDJPY.Volume, -USDJPY.Adjusted)
rm(pred.data)

## Print dataset.
pred %>% data.table
```

*Table 3.3.3 : Tidy dataset for forecast high-low daily price.*

Below I test if the dataset scrapped from `quantmod::getSymbols(src = 'yahoo')` equal to **FXCMTickData**. Unfortunately the data gathered is not tally each other.

```{r tidy-data3}
mb.dateID <- unique(mbase$Date)
td.dateID <- unique(HL_tick_data$Date)

## Check the start and end date
data.frame(MB = range(mb.dateID), 
           TD = range(td.dateID)) %>% 
  kable(caption = 'Data Range') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'), full_width = FALSE, position = 'float_left') %>%
  footnote(general = 'Date range of 1st and 2nd dataset.',
           general_title = 'Table 3.3.4 : ', footnote_as_chunk = TRUE)
```

*Table 3.3.4* shows the date range for both **MB** (mbase dataset) and **TD** (tick-data).

<span style='color:red'>Below shows all dates NOT in each dataset. Unfortunately the inconsistancy of dataset gathered from `getSymbols(src = 'yahoo')` will caused whole predictive models bias, it will affect the staking amount and evetually effect the ROI. The dataset used to working fine few years ago. There will be another research which gather only dataset from operator to solve the issue.</span>

```{r tidy-data4}
## Check if dateID not in another dataset.
mb.dateID[!mb.dateID %in% td.dateID]
td.dateID[!td.dateID %in% mb.dateID]
```

```{r plot-data1A, echo = FALSE}
## Real price.
pl.RHigh <- pred %>% 
  select(Date, USDJPY.High)
pl.RHigh <- as.xts(pl.RHigh[-1], order.by = pl.RHigh$Date)

pl.RLow <- pred %>% 
  select(Date, USDJPY.Low)
pl.RLow <- as.xts(pl.RLow[-1], order.by = pl.RLow$Date)

## Predicted price.
pl.FHigh <- pred %>% 
  select(Date, Fct.High)
pl.FHigh <- as.xts(pl.FHigh[-1], order.by = pl.FHigh$Date)

pl.FLow <- pred %>% 
  select(Date, Fct.Low)
pl.FLow <- as.xts(pl.FLow[-1], order.by = pl.FLow$Date)

## Plot graph
hc <- highchart(type = 'stock') %>% 
  hc_title(text = 'USD/JPY Currency Exchange Rate') %>% 
  hc_subtitle(text = 'Comparison of Forecast and Real Price (Highest Price)') %>% 
  hc_add_series(pl.RHigh, id = 'pl.RHigh', color = 'blue') %>% 
  hc_add_series(pl.FHigh, id = 'pl.FHigh', color = 'red')

hc
```

*Graph 3.3.1A : <span style='color:red'>Forecast daily highest price</span> vs <span style='color:blue'>real daily highest price</span>.*

```{r plot-data1B, echo = FALSE, results = 'asis'}
## Plot graph
hc <- highchart(type = 'stock') %>% 
  hc_title(text = 'USD/JPY Currency Exchange Rate') %>% 
  hc_subtitle(text = 'Comparison of Forecast and Real Price (Lowest Price)') %>% 
  hc_add_series(pl.RLow, id = 'pl.RLow', color = 'blue') %>% 
  hc_add_series(pl.FLow, id = 'pl.FLow', color = 'red')

rm(pl.RHigh, pl.RLow, pl.FHigh, pl.FLow)
hc
```

*Graph 3.3.1B : <span style='color:red'>Forecast daily lowest price</span> vs <span style='color:blue'>real daily lowest price</span>.*

*Graph 3.3.1A* and *Graph 3.3.1B* above compare the real price and forecast price. Following section will be compare the MSE (Mean Squared Error).

## Mean Squared Error

```{r mse1}
## Mean Squared Error : Comparison of accuracy.
## https://cran.r-project.org/web/packages/kableExtra/vignettes/awesome_table_in_html.html
data.frame(
  Category = c('High = ', 'Low = ', 'Close = '), 
  MSE = c(mean((pred$Fct.High - pred$USDJPY.High)^2), 
          mean((pred$Fct.Low - pred$USDJPY.Low)^2), 
          mean((pred$Fct.Close - pred$USDJPY.Close)^2))) %>% 
  kable(caption = 'Mean Squared Error') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'), full_width = FALSE, position = 'float_right') %>%
  footnote(general = 'MSE of prediction.',
           general_title = 'Table 3.4.1 : ', footnote_as_chunk = TRUE)

```

$$\begin{equation}
\frac{1}{n}\sum_{t=1}^{n}e_t^2\ \cdots\ Equation\ 3.4.1
\end{equation}$$

*Table 3.4.1* at the right-hand-side shows the accuracy of the predictive model. You can also refer to previous studies where compare the accuracy of predicted `Open`, `High`, `Low` and `Close` price. For accuracy comparison of statistical models, you might refer to **GARCH模型中的`ARMA(p,d,q)`参数最优化** or previous papers for further information.

## Univariate Preditive Error

**GARCH模型中的`ARMA(p,d,q)`参数最优化** compare the accuracy of gjrGARCH and Fi-gjrGARCH model while **Multivariate GARCH Models** states the statistical predictive error based on univariate and also use more sophistical methods for modelling. This paper I still keep using univariate gjrGARCH in mentioned paper which is not the most accurate.

```{r tidy-data5}
rx <- pred %>% 
    mutate(diff = Fct.High - Fct.Low) %>% 
    dplyr::filter(diff <= 0)

rx %>% 
  kable(caption = 'Preditive Error for Univariate gjrGARCH') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')
```

*Table 3.5.1 `r paste0('[', paste(dim(rx), collapse = ' x '), ']')` : Preditive `HiLo` Error for Univariate gjrGARCH.*

```{r tidy-data6}
rx <- pred %>% 
    mutate(Range = ifelse(Fct.Close > Fct.High | Fct.Close < Fct.Low, 0, 1)) %>% 
    dplyr::filter(Range == 0)

rx %>% 
  kable(caption = 'Preditive Error for Univariate gjrGARCH') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(width = '100%', height = '400px')
```

*Table 3.5.2 `r paste0('[', paste(dim(rx), collapse = ' x '), ']')` : Preditive `Cl` Error for Univariate gjrGARCH.*

*Table 3.5.1* states the forecast highest price lower than forecast lowest price where *Table 3.5.2* states forecast closing price not in the range of forecast highest and lowest price. [Betting Strategy] in next section will omit the error and only trade on the high winning opportunities.

# Betting Strategy

## Kelly Criterion

$$\begin{equation}
f = \frac{Edge}{Odds} = \frac{p^∗ x−(1−p^∗)}{x}
 \ \cdots Equation\ 4.1.1 
 \end{equation}$$

The section 1 inside [Application of Kelly Criterion model in Sportsbook Investment](https://github.com/scibrokes/kelly-criterion) shows the ROI for betting on sportsbook, where section 2 will be started during spared time after FOREX market.

For the betting strategy, here I need to do correction from **Binary Q1** as stated in section [Introduction]. Below I tidy the dataset to match the `bid/ask` price for close a transaction.

As we know from previous paper, the closing price will be settled price (closed transaction) if the forecast price has no occured within a day (from 12:00:01 AM until next day 12:00:00 AM, due to system calculate the price spend a minute, therefore the opening price will not in count.). There will be 2 limit orders (but and sell) placed after 12:00:00AM. Once one among the order limit stand (opened transaction), another limit order will be automatically turned to be closed transaction request. Therefore there will only transaction within a trading day unless no any order limit placed stand.

```{r data-summary4, results = 'asis'}
## Here I combine real-time dataset with the daily dataset.
pred <- merge(HL_tick_data, pred,  by = 'Date') %>% 
  tbl_df %>% 
  arrange(DateTime)

## Tidy dataset.
## bid price for sell, ask price for buy orders. bid price always lower than ask price due to banker need to earn vigorish/spread margins. We need to see bid price if we wanna sell and ask price when we wanna buy.
pred %<>% group_by(Date) %>% 
    dplyr::filter(Bid == max(Bid, na.rm = TRUE)|Ask == min(Ask, na.rm = TRUE)) %>% 
    dplyr::select(DateTime, Date, USDJPY.High, USDJPY.Low, USDJPY.Close, sq, Bid, Ask, Fct.High, Fct.Low, Fct.Close) %>% 
    rename(High = USDJPY.High, Low = USDJPY.Low, Close = USDJPY.Close) %>% tbl_df

pred %<>% mutate(
        Fct.High = round(Fct.High, 3), 
        Fct.Low = round(Fct.Low, 3), 
        Fct.Close = round(Fct.Close, 3), 
        Sell = ifelse((Fct.High <= High & 
                       Fct.High >= Low & 
                       Fct.High > Fct.Low) &        # Here I filter the 
                      (Fct.Close > Fct.High |       #  both HiLo and Cl 
                       Fct.Close < Fct.Low), 1, 0), #  predictive error.
        Buy = ifelse((Fct.Low >= Low & 
                      Fct.Low <= High & 
                      Fct.Low < Fct.High) &         # Here I filter the 
                     (Fct.Close > Fct.High |        #  both HiLo and Cl 
                      Fct.Close < Fct.Low), 1, 0))  #  predictive error.

## follow the seq to determine the buy or sell limit order stand within a day. Then the other side will be automatically switch to close transaction limit order but not placed another limit order.
pred <- ldply(split(pred, pred$Date), function(x) {
    x %<>% mutate(Trans = ifelse(!is.na(Bid), 'sell', 'buy'), 
                  Trans = ifelse(Sell == 1|Buy == 1, Trans, 0))
  
  if(x[1,]$Trans == 'sell'|x[1,]$Trans == 'buy') #if open transaction.
    x[nrow(x),]$Trans <- 'close'                 #  then close transaction.
  
  x }) %>% tbl_df

pred$.id <- NULL
pred %<>% mutate(Trans = factor(Trans))
```

Topic *2.1.4 Staking Model* in paper **Binary Q1** states that the financial market unable to know the payout rate in advanced, therefore use the forecasted pice based on statistical models. I use the amount calculated by Kelly Criterion as the stakes (possible loss or terms as stop-loss in financial market), variance of forecasted Hi/Lo and also Closed price. However it doesn't make sense in financial market.

> Hedge Fund Market Wizards has a good discussion on this in Ed Thorp's chapter.
> 
 - Kelly Criterion has highest long-term growth rate, but gives you higher drawdowns and risk of ruin.
- In gambling you know your theoretical odds, but in trading your win rate is only an estimate.
- If you estimate your win rate incorrectly, the profits you'd miss out on by underestimating are less than the losses you'd incur by being overconfident.
- If there's large uncertainty about your win rate (e.g. trend following systems) Kelly may be inappropriate.
- "Suppose you have 1MM and your max allowable drawdown is 200K - then from the Kelly perspective you don't have 1MM, you have 200K in capital."
- If you bet .5 K.C. you get .75 of the returns with .5 of the volatility - half Kelly is better psychologically.

*Source quote 4.1.1 : [Kelly Criterion in Forex primordia • Jul 22, 2017, 7:07 PM](https://amp.reddit.com/r/Forex/comments/6oxh5e/kelly_criterion_in_forex)*

> EXAMPLE
Let's look at a trading example.
> 
Say, you have a EURUSD trading strategy that wins approximately 70% of the time. The StopLoss in your strategy is 40 pips and the TakeProfit is 20 pips (spread accounted for).
> 
This means that your B and P parameters are as follows:
> 
B = 20 pips / 40 pips = 0.5
P = 70% = 0.7
Let's input these values into Kelly’s formula and see what we get:
> 
K = ( PxB – (1–P) ) / B
K = ( 0.7 x 0.5 – (1–0.7) ) / 0.5 = 0.1
> 
This means that the optimal risk for this trading strategy that will maximize your profits in the long term is 10%.
> 
If you want to be a bit more conservative, then go with the Half-Kelly of 5%.
> 
Whatever you do, don’t invest more than 10% per trade – it’s pointless.
> 
If you invest more than 20% then you will turn this great strategy into one that will ruin your account.
> 
That's how you apply the Kelly Criterion in practice.

*Source quote 4.1.2 : [ForexBoat:Kelly Criterion](https://www.forexboat.com/kelly-criterion/)^[You may feel free to read the comment onto the article [Q&A on Kelly criterion, stop-loss, take-profit and also leverage ratio](https://www.forexboat.com/kelly-criterion/#comment-2053452762) as well.]*

## Staking Model

[Chapter 20 Against the Odds: The Mathematics of Gambling](http://srdas.github.io/MLBook/Gambling.html#odds)^[Publised book [**Data Science: Theories, Models, Algorithms, and Analytics** - *Sanjiv Ranjan Das (2017-03-24)*](http://srdas.github.io/MLBook/).] elaborates the odds price, edge, Kelly Criterion staking model, portfolio, Entropy and also day trading.

$$\begin{eqnarray}
g_t(f) &=& \frac{1}{t} \ln \left( \frac{B_t}{B_0}  \right) \\
&=&  \frac{1}{t} \ln \left( \prod_{i=1}^t [1+r +f(Z_t -r)\varepsilon] \right) \\
&=&  \frac{1}{t}  \sum_{i=1}^t \ln \left( [1+r +f(Z_t -r)\varepsilon] \right)
\end{eqnarray}
 \ \cdots Equation\ 4.2.1 $$

By applying the law of central limit theorem for large data, here we get:

$$\begin{equation}
g(f) = \lim_{t \rightarrow \infty} g_t(f) = E[\ln(1+r + f (Z-r)\varepsilon)]
 \ \cdots Equation\ 4.2.2 
 \end{equation}$$

and $\varepsilon_{i}$ is a weight function where applied statistical models to forecast the price. I used some models and eventually concludes the GJR-GARCH model generated highest ROI. The weight function doesn't same with different currencies since it using substraction among 2 forecast prices but not in ratio^[The pips difference for USD/JPY different with others. Thereore there will need to compare among currencies.].

$$\begin{equation}
\varepsilon = h(x)_{1} - v
 \ \cdots Equation\ 4.2.3 
 \end{equation}$$

$v$ is a switch function to determine the settled price.

$$\begin{equation}
v
\left\{\begin{matrix}
h(x)_{2}
 & if(Lo <= h(x)_{2} <= Hi)
 & \\ Cl
 & otherwise
\end{matrix}\right.
\ \cdots Equation\ 4.2.4 
\end{equation}$$

where $Hi$, $Lo$ and $Cl$ are the daily highest, lowest and closed price.

**Binary Q1** applied a more sophisticated model as stated above to compares all possible outcomes of predicted price and ROI. Due to the financial betting only allows player place bets and awaiting for the settlement (unless placed another bet at other predicted price), there will be no any limit order and close transaction request (similar with FOREX trading market can place more than 1 limit order to lock the profit).

<span style='color:red'>The staking model in previous papers (includes **Binary Q1 (Extention)**) have only **MISTAKE** which is wrote for real FOREX trading market but not financial betting since I only think of spread betting but forgot the normal betting :</span>

- <span style='color:red'>Forecast highest price to sell and forecast lowest price to buy to maximise the profit : I wrote 2nd forecast price as settled price if it was between the daily Hi-Lo range (otherwise daily closed price will be settled price). There will be only applicable to FOREX trading market but NOT financial betting market.</span>
- <span style='color:red'>However it will be more easily since the settled price will be only daily closed price.</span>

The paper **Binary Q1** compares all outcome :

- `Hi-Cl` + `Lo-Cl` generate highest ROI in financial betting market.^[Here I will conducting another research for financial betting.]
- `Hi-Lo` or `Lo-Hi` will be best betting strategy for noarmal FOREX market.

```{r betting-strategy, echo = FALSE}
bs <- data.frame(.id = c('fundAutoArimaHICL', 'fundAutoArimaLOCL'), 
                 StartDate = ymd('2015-01-02'), 
                 LatestDate = ymd('2017-01-20'), 
                 InitFund = 1000, 
                 LatestFund = c(1401.694, 1499.818), 
                 Profit = c(401.69378, 499.81773), 
                 RR = formattable::percent(c(1.401694, 1.499818)))

sm <- data.frame(.id = 'Combine', 
                 StartDate = ymd('2015-01-02'), 
                 LatestDate = ymd('2017-01-20'), 
                 bs %>% dplyr::select(InitFund, LatestFund, Profit) %>% colSums %>% t) %>% 
    mutate(RR = formattable::percent(LatestFund/InitFund))

rbind(bs, sm) %>% 
  kable(caption = 'Return on Investment') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
  scroll_box(width = '100%')
rm(bs, sm)
```

*Table 4.2.1 : betting strategy for financial betting.*

```
No               .id  StartDate LatestDate InitFund  LatesFund    Profit        RR
07 fundAutoArimaHILO 2015-01-02 2017-01-20     1000   1637.251 637.25113 163.7251%
10 fundAutoArimaLOHI 2015-01-02 2017-01-20     1000   1716.985 716.98492 171.6985%
```
*Table 4.2.2 : betting strategy for normal FOREX market.*

Kindly refer to [2.1.5 Return of Investment in **binary Q1**](https://englianhu.github.io/2017/09/binary-forex-trading-Q1.html#return-of-investment) for full table. However, the paper does not filter the univariate preditive error.

## Optimal Edge

I don't pretend to know the optimal edge for staking. Here I need to compare above models with normal Kelly model.

<span style='color:red'>I used to use</span> <s>`Edge1 = ifelse(fB1 > 0, B1, ifelse(fS1 > 0, S1, 0))`</s> <span style='color:red'>to measure the edge for staking while it might be wrong due to I put the edge for selling as secondary edge for `Buy` as well. Here I use </span>`Edge1a = ifelse(fB1 > 0, B1, 0)`<span style='color:red'> and </span>`Edge1b = ifelse(fS1 > 0, S1, 0)`<span style='color:red'> to seperates the edge for `Buy` and `Sell`. It means that the buy action will be primary and sell action will be secondary where the edge for both `buy` and `sell` will stand. Therefore most of the observation will overcame probabilities 0.5.</span>

```{r staking1, echo = FALSE, eval = FALSE}
## =============== WRONG ==================
## http://srdas.github.io/MLBook/Gambling.html#simulation-of-the-betting-strategy
pred %>% 
    mutate(
        Fct.High = round(Fct.High, 3), 
        Fct.Low = round(Fct.Low, 3), 
        Hi = ifelse(High >= Bid, 1, 0), 
        Lo = ifelse(Low >= Ask, 1, 0)) %>% 
    tbl_df %>% 
    select(-Date) %>% 
    mutate(Buy1 = ifelse(Fct.High >= High, 1, 0), 
           Buy2 = ifelse(Fct.High >= Bid, 1, 0), 
           Buy3 = ifelse(Fct.High >= Hi, 1, 0), 
           Sell1 = ifelse(Fct.Low <= Low, 1, 0), 
           Sell2 = ifelse(Fct.Low <= Ask, 1, 0), 
           Sell3 = ifelse(Fct.Low <= Lo, 1, 0)) %>% 
    select(-High, -Low, -Close)
## A tibble: 1,244 x 14
#   DateTime               sq   Bid   Ask Fct.High Fct.Low    Hi    Lo  Buy1  Buy2  Buy3 Sell1 Sell2 Sell3
#   <dttm>              <int> <dbl> <dbl>    <dbl>   <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 2016-01-05 03:06:08     1  120.   NA      120.    119.     0    NA     1     1     1     0    NA    NA
# 2 2016-01-05 12:22:55     4   NA   119.     120.    119.    NA     1     1    NA    NA     0     0     0
# 3 2016-01-06 00:07:16     2  119.   NA      120.    119.     0    NA     1     1     1     0    NA    NA
# 4 2016-01-06 11:38:17     3   NA   118.     120.    119.    NA     1     1    NA    NA     0     0     0
# 5 2016-01-07 01:16:01     2  119.   NA      120.    119.     0    NA     1     1     1     0    NA    NA
# 6 2016-01-07 09:24:27     4   NA   117.     120.    119.    NA     1     1    NA    NA     0     0     0
# 7 2016-01-08 13:30:07     2  119.   NA      119.    119.     0    NA     1     1     1     0    NA    NA
# 8 2016-01-08 21:57:33     3   NA   117.     119.    119.    NA     1     1    NA    NA     0     0     0
# 9 2016-01-11 01:34:30     2   NA   117.     120.    119.    NA     1     1    NA    NA     0     0     0
#10 2016-01-11 13:37:52     4  118.   NA      120.    119.     0    NA     1     1     1     0    NA    NA
## ... with 1,234 more rows
```

## Application of Kelly Criterion to Normal FOREX Market

Previous paper using the forecast HiLo price and forecast closing price as settlement, the stakes will be the edge for `pnorm(Hi, mean(Lo), sd(Lo))` and vice verse. It will be $\frac{\sigma_{Hi}}{\sigma_{Lo}}$ or $\frac{\sigma_{Lo}}{\sigma_{Hi}}$ but missing the difference of pips between buy/sell price and closed price.

In this paper will count the difference of pips and also leverage ratio. The risk management on leverage will be counted into the staking model.

The papers **The Kelly Criterion and the Stock Market** and **Beat the Market - A Scientific Stock Market System** states the application of Kelly criterion onto the stock market. Kindly refer to the paper in [Reference] for further knowledge.

## Application of Kelly Criterion to Financial Betting Market

Previous paper use Kelly model to placed a certain amount and awaiting for settlement. The forecast closed price will be the settled price if it was within the range of HiLo in the day. There is not workable due to traders not allowed to placed an close transaction limit order in financial betting market.

- [Financial Spread Betting : Binary](http://www.financial-spread-betting.com/Bet-markets.html)
- [What are Binary Options or Fixed Odds Bets? Binary.com](http://winonmarkets.net/wp/2014/03/20/what-are-binary-options-or-fixed-odds-bets-binary-com/)

Due to there has no dataset for financial betting, therefore I do not have the payout rate or odds price for <s>minutely, hourly and</s> daily betting. The sample dataset and research might refer to **Application of Kelly Criterion model in Sportsbook Investment** where collected AH (Asian-Handicap) and OU (Over-Under) odds price of couple of bookmakers and placed bets^[The odds price offered by operators do not same with the probabilities of the result, similar with the exchange rate offered by different operators will be difference as well.].

I tune a bit in this paper which is set the forecast closed price cannot be settled price. There will be another research which is collect odds price from operators to test the ROI.

# Return of Investment

## Normal FOREX Market

```{r ROI-1}
sim_staking(pred) %>% 
  dplyr::select(Date, Edge1a, Edge1b, Edge2a, Edge2b, Buy, Sell, Trans, BR, Profit, Bal) %>% 
  kable(caption = 'ROI for Normal FOREX Market') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
  scroll_box(width = '100%', height = '400px')
```

*Table 5.1.1 : ROI for normal FOREX market.*

```{r plot-data2a, echo = FALSE}
fx <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'none') %>% 
  dplyr::select(Date, Bal)

names(fx)[2] <- 'None.Close'
                
plotChart2(fx, graph.title = 'Peformance of Investment Fund for FOREX Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.1.1A : ROI for normal FOREX market. (None)*

```{r plot-data2b, echo = FALSE}
fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'mixed') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'mixed') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'mixed') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'mixed') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'mixed') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'mixed') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'mixed') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'mixed') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for FOREX Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.1.1B : ROI for normal FOREX market. (Mixed Kelly model)*

```{r plot-data2c, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for FOREX Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.1.1C : ROI for normal FOREX market. (Normal Kelly model)*

```{r plot-data2d, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for FOREX Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.1.1D : ROI for normal FOREX market. (Adjusted Kelly model 1)*

```{r plot-data2e, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for FOREX Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.1.1E : ROI for normal FOREX market. (Adjusted Kelly model 2)*

```{r plot-data2f, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for FOREX Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.1.1F : ROI for normal FOREX market. (Adjusted Kelly model 3)*

```{r plot-data2g, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for FOREX Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.1.1G : ROI for normal FOREX market. (Adjusted Kelly model 4)*

```{r plot-data2h, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for FOREX Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.1.1H : ROI for normal FOREX market. (Adjusted Kelly model 5)*

```{r plot-data2i, echo = FALSE}
fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = FALSE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = FALSE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for FOREX Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.1.1G : ROI for normal FOREX market. (Adjusted Kelly model 6)*

```{r roi-ets, echo = FALSE, eval = FALSE}
## plot html table
##==================== EVAL = FALSE =====================
tagList(
  tags$div(align = "center", 
           class = "bg-info", 
           tags$h3(class = "bg-primary", "Profit and Loss of Investment (2015-Jan-02 2017-Jan-20)"), 
           tags$h5(align = "center", class = "text-muted", 
                   "Error-Trend-Seasonal or ExponenTial Smoothing Models")), 
  as.htmlwidget(ets.tbl %>% formattable(list(
    
    LatestFund = formatter('span', style = x ~ formattable::style(color = ifelse(rank(-x) <= 3, 'blue', 'grey')), x ~ paste0(round(x, 2), ' (rank: ', sprintf('%02f', rank(-x)), ')')), 
    
    Profit = formatter('span', style = x ~ formattable::style(color = ifelse(rank(-x) <= 3, 'blue', 'grey')), x ~ paste0(round(x, 2), ' (rank: ', sprintf('%02f', rank(-x)), ')')), 
    
    RR = formatter('span', style = x ~ formattable::style(color = ifelse(rank(-x) <= 3, 'blue', 'grey')), x ~ sprintf('%1.2f%% (rank: %.0f)', 100 * x, rank(-x)))))))
```

```{r plot-varAutoArima, echo = FALSE, eval = FALSE, results = 'asis'}
## Betting strategy 1 - Normal range betting
## Plot the ROI of investment fund.
plotAutoArima <- data.frame(varB1['Date'], varB1[grep('Bal', names(varB1))])
LineAutoArima <-  gvisLineChart(plotAutoArima, 'Date', names(plotAutoArima)[-1],
                        options = list(title = 'Auto Arima Models', 
                                       gvis.editor = 'Edit me!'))
plot(LineAutoArima)
```

## Financial Betting Market

```{r ROI-2}
sim_staking(pred, financial_bet = TRUE) %>% 
  #mutate(Trans = ifelse(!is.na(Bid), 'sell', 'buy')) %>% 
  dplyr::select(Date, Edge1a, Edge1b, Edge2a, Edge2b, Buy, Sell, Trans, BR, Profit, Bal) %>% 
  kable(caption = 'ROI for Financial Betting Market') %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
  scroll_box(width = '100%', height = '400px')
```

*Table 5.2.1 : ROI for financial betting market.*

```{r plot-data3a, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'normal') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1d, fx1a, fx2b, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for Financial Betting Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.2.1A : ROI for financial betting market. (Normal Kelly model)*

```{r plot-data3b, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted1') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for Financial Betting Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.2.1B : ROI for financial betting market. (Adjusted Kelly model 1)*

```{r plot-data3c, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted2') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1d, fx1a, fx2b, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for Financial Betting Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.2.1C : ROI for financial betting market. (Adjusted Kelly model 2)*

```{r plot-data3d, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted3') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for Financial Betting Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.2.1D : ROI for financial betting market. (Adjusted Kelly model 3)*

```{r plot-data3e, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted4') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for Financial Betting Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.2.1E : ROI for financial betting market. (Adjusted Kelly model 4)*

```{r plot-data3f, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted5') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for Financial Betting Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.2.1F : ROI for financial betting market. (Adjusted Kelly model 5)*

```{r plot-data3g, echo = FALSE}

fx1a <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx1b <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx1c <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx1d <- sim_staking(pred, pnorm_type = 'Bid-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx2a <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx2b <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b1-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx2c <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a1', financial_bet = TRUE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

fx2d <- sim_staking(pred, pnorm_type = 'Ask-Lo', 
                    bid_ask = 'b2-a2', financial_bet = TRUE, 
                    Kelly = 'adjusted6') %>% 
  dplyr::select(Date, Bal)

## convert to xts format.
fx1a <- xts(fx1a[-1], order.by = fx1a$Date)
fx1b <- xts(fx1b[-1], order.by = fx1b$Date)
fx1c <- xts(fx1c[-1], order.by = fx1c$Date)
fx1d <- xts(fx1d[-1], order.by = fx1d$Date)
fx2a <- xts(fx2a[-1], order.by = fx2a$Date)
fx2b <- xts(fx2b[-1], order.by = fx2b$Date)
fx2c <- xts(fx2c[-1], order.by = fx2c$Date)
fx2d <- xts(fx2d[-1], order.by = fx2d$Date)

## combine dataset.
fxm <- do.call(cbind, list(fx1a, fx1b, fx1c, fx1d, fx2a, fx2b, fx2c, fx2d))

names(fxm) <- c('BL.B1A1.Close', 'BL.B1A2.Close', 'BL.B2A1.Close', 'BL.B2A2.Close', 
                'AL.B1A1.Close', 'AL.B1A2.Close', 'AL.B2A1.Close', 'AL.B2A2.Close')

rm(fx1a, fx1b, fx1c, fx1c, fx1d, fx1a, fx2b, fx2c, fx2c, fx2d)

plotChart2(fxm, graph.title = 'Peformance of Investment Fund for Financial Betting Market', subtitle = 'Initial Fund size : ', initial = '$10,000')
```

*Graph 5.2.1G : ROI for financial betting market. (Adjusted Kelly model 6)*

# Conclusion

## Conclusion and Future Works

I can use tick-data from **FXCMTickData** for this paper while it is weekly and not up-to-date, the `getSymbols()` able to get near real-time (15 minutes late) where suite for daily trading in **Real Time Trading System (Trial)** but there are a lot of trading date is not available. 

Due to I had almost completed this paper and only noticed that I am using `calC()` but not `calc_fx()` for simulation. Therefore I wrote another paper to compare the accuacy of the arma ordered GARCH models via **GARCH模型中的`ARMA(p,d,q)`参数最优化**. There will be another paper for multivariate GARCH model upon completion of **Q1App2** web application.

Therefore High Frequency Trading in another research **Real Time FXCM** where all data price gathered from real-time will be accurate.

## Correction in Next Paper

$$\begin{equation}
\varepsilon = h(x)_{1} - h(x)_{2}
 \ \cdots Equation\ 4.2.3 
 \end{equation}$$

where $tp = abs(h(x)_{1} - h(x)_{2})$ and $tp$ is take-profit pips. As mentioned, my previous paper using `pnorm()` without weighted the most recent price, here I try to use `ppois()` to overcame the weighted data issue^[As the GARCH model has already forecast the most recent price.]. However, there has a question for stop-loss in order to make the $Equation\ 4.1.1$ stand. `B = 20 pips / 40 pips = 0.5 where 20 pips take-profit and 40 pips stop-loss` in *Source quote 4.1.2* also provides an example for mentioned equation.

Here I compare both $\sigma^2$ and VaR retrived from GARCH model to set as stop-loss pips.

```{r stop-loss1}
## Both calC() and calc_fx() added new return value.
##   paper binary-Q1-FiGJRGARCH.Rmd already completed. All 
##   dataset need to re-simulate in order to get the VaR 
##   and sigma^2 values to set as stop-loss pips. Only 
##   based on the odds price we can calculate the staking 
##   amount.

calC <- function(..){
  ...
  ...
  ...
  tmp = list(latestPrice = latestPrice, forecastPrice = res, 
             fit = fit, AIC = infocriteria(fit))
  return(tmp)
}

calc_fx <- function(..){
  ...
  ...
  ...
  tmp = list(latestPrice = latestPrice, forecastPrice = res, 
             fit = fit, AIC = infocriteria(fit))
  return(tmp)
}
```

<span style='color:red'>Here I forced to changed this paper to be blooper due to :</span>

- Existing saved simulated model files does not use most accurate Fi-gjrGARCH model.
- Existing saved simulated model files does not include VaR and $\sigma$ value in order to set as a stop-loss pips.
- When I reviewd the coding, there are statistical error occured in univariate forecasting. Although it will not affect whole staking model by filter before placed order, the multivariate models might be test the accuracy at first in order to modify the staking model.
- Existing staking model is wrong since loss bets count as 0 as shows in *Table 5.1.1* and *Table 5.2.1*, it just a small error which can be corrected but the biggest problem is that whole predictive simulation need to do gain due to lack of stop-loss pips to correct the odds price in order to make Kelly criterion model stand.
- Only know highest `bid` or lowest `ask` time in daily trading is not enough due to the stop-loss point might probably hit and close a transaction if based on the daily High-Low data.
- I want to model a dynamic fractional Kelly criterion $0.5 <= f <= 1$, and compare with `optimalf()`, normal Kelly models and also modified Kelly model^[The paper named **Modified Kelly Criteria** in [Reference]] in section 2 **Application of Kelly Criterion model in Sportsbook Investment** to test the best fit betting strategy. It will occupied a long section in [Optimal Edge] but will test it in next paper.

```{r test-HiLo}
dfm <- xts(tibble(bid = round(rnorm(100, mean = 1, sd = 0.1), 5)) %>% 
               mutate(ask = bid + 0.00003), order.by = now('Asia/Tokyo') - seconds(1:100))
```

```{r plot-HiLo}
ggplot(dfm, aes(index(dfm))) + 
    geom_line(aes(y = bid, colour = 'bid')) + 
    geom_line(aes(y = ask, colour = 'ask')) + 
    xlab('Time [Seconds]') + ylab('Currency X / Currency Y')
```

*Graph 6.2.1 : Demo real-time bid ask price moving.*

Above graph shows an example for open transaction, take-profit and stop-loss point. The Hi-Lo `bid/ask` price without whole course of price flutuation will not be able to know the exact ROI.

```{r fx-HiLo}
subset(dfm, bid == max(bid)|ask == min(ask))
```

```{r smp-HiLo}
## randomly set as example
Hi <- dfm$bid %>% as.vector %>% sort(decreasing = TRUE) %>% .[2]
Lo <- dfm$ask %>% as.vector %>% sort %>% .[2]

## forecast highest and lowest price.  
s.fct.Hi <- dfm$bid %>% as.vector %>% sort(decreasing = TRUE) %>% .[3]
s.fct.Lo <- dfm$ask %>% as.vector %>% sort %>% .[3]

##odds price for buy transaction, tk = take-profit and sl = stop-loss.
buy.tk <- s.fct.Hi - s.fct.Lo #provided the univariate Hi > Lo
buy.sl <- s.fct.Lo - 0.1 #given that 0.01 is a calculated value.

##odds price for sell transaction, tk = take-profit and sl = stop-loss.
sell.tk <- s.fct.Hi - s.fct.Lo #provided the univariate Hi > Lo 
sell.sl <- s.fct.Hi + 0.1 #given that 0.01 is a calculated value.
```

The limit order of buy on `r s.fct.Lo` or sell on `r s.fct.Hi` will open transaction, and then :

1) If first ask price hit `r s.fct.Lo`, buy order limit open transaction.

  + If bid price first hit `r buy.sl`, closed transaction and loss 0.1.
  + If bid price first hit `r s.fct.Hi`, closed transaction and gain `r buy.tk`.
  + If bid price does not appear within the day, then the closing price will be the settled price.
  
2) If first bid price hit `r s.fct.Hi`, sell order limit open transaction.

  + If ask price first hit `r sell.sl`, closed transaction and loss 0.1.
  + If ask price first hit `r s.fct.Lo`, closed transaction and gain `r buy.tk`.
  + If ask price does not appear within the day, then the closing price will be the settled price.

From the example above, The daily highest price is `r Hi` and daily lowest price is `r Lo`. The highest `bid/ask` price is not neccesary daily Hi-Lo price. We unable know if we buy first or sell first solely based on the Hi-Lo tick data and also the daily OHLCV dataset but a completed tick-data required.^[I initially think only use filted Hi-Lo tick-data to wrote this paper and also states completed tick-data will be in project **Real Time FXCM** in section [Conclusion and Future Works]. However due to noticed a lot of ommit and careless and new idea upon studied couples reference at the same time.]

Here I also publish this paper in order to let other quantitative traders or enthursiasters know the ROI of previous paper is not accurate based on mentioned equations in [Staking Model] and the table *Table 5.1.1* and *Table 5.1.1*.

```{r stopPar, echo = FALSE}
## Set options back to original options
options(op)
options(warn = 0)
#'@ stopCluster(cl)
```

# Appendix

## Documenting File Creation 

It's useful to record some information about how your file was created.

- File creation date: 2018-07-13
- File latest updated date: `r today('Asia/Tokyo')`
- `r R.version.string`
- R version (short form): `r getRversion()`
- [**rmarkdown** package](https://github.com/rstudio/rmarkdown) version: `r packageVersion('rmarkdown')`
- File version: 1.0.1
- Author Profile: [®γσ, Eng Lian Hu](https://beta.rstudioconnect.com/content/3091/ryo-eng.html)
- GitHub: [Source Code](https://github.com/englianhu/binary.com-interview-question)
- Additional session information

```{r info, echo = FALSE, warning = FALSE, results = 'asis'}
suppressMessages(require('dplyr', quietly = TRUE))
suppressMessages(require('formattable', quietly = TRUE))

lubridate::now('Asia/Tokyo')
sys1 <- devtools::session_info()$platform %>% unlist %>% data.frame(Category = names(.), session_info = .)
rownames(sys1) <- NULL
#'@ sys1 %>% formattable %>% as.htmlwidget

sys2 <- data.frame(Sys.info()) %>% mutate(Category = rownames(.)) %>% .[2:1] %>% rename(Category = Category, Sys.info =  Sys.info..)
#'@ sys2 %>% formattable %>% as.htmlwidget

sys1 %>% 
  kable %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))#, full_width = FALSE, position = 'float_left')

sys2 %>% 
  kable %>% 
  kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))#, full_width = FALSE, position = 'float_right')

rm(sys1, sys2)
```

## Reference

01. [Quant Strategies HFT](https://github.com/englianhu/Quant-Strategies-HFT)
02. [Real Time FXCM](https://github.com/scibrokes/real-time-fxcm)
03. [Real Time Trading System (Trial)](https://beta.rstudioconnect.com/content/3775/)<img src='www/hot.jpg' width='20'>
04. [The Kelly Criterion and the Stock Market](https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/reference/The%20Kelly%20Criterion%20and%20the%20Stock%20Market.pdf)
05. [Beat the Market - A Scientific Stock Market System](https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/reference/Beat%20the%20Market%20-%20A%20Scientific%20Stock%20Market%20System.pdf)
06. [GARCH模型中的`ARMA(p,d,q)`参数最优化](http://rpubs.com/englianhu/binary-Q1FiGJRGARCH)
07. [Modified Kelly Criteria](https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/reference/Modified%20Kelly%20Criteria.pdf)

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