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binary-forex-trading-Q3.Rmd
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binary-forex-trading-Q3.Rmd
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---
title: "<img src='https://raw.githubusercontent.com/englianhu/binary.com-interview-question/757b27e1e93132368b0898152078be4961b05a28/www/binary-logo-resize.jpg' width='240'>"
subtitle: "[<span style='color:blue'>binary.com</span>](https://github.com/englianhu/binary.com-interview-question) Interview Question III"
author: "[<span style='color:blue'>®γσ, Lian Hu</span>](https://englianhu.github.io/) <img src='https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/www/ENG.jpg' width='24'> <img src='https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/www/RYO.jpg?raw=true' width='24'>白戸則道®"
date: "`r Sys.Date()`"
output:
tufte::tufte_html:
toc: yes
toc_depth: 4
self_contained: no
tufte::tufte_book:
citation_package: natbib
latex_engine: xelatex
tufte::tufte_handout:
citation_package: natbib
latex_engine: xelatex
link-citations: yes
---
```{r setup, include = FALSE}
#'@ rm(list = ls(all = TRUE))
suppressPackageStartupMessages(library('BBmisc'))
pkgs <- c('knitr', 'kableExtra', 'tint', 'devtools', 'lubridate', 'data.table', 'plyr', 'stringr', 'magrittr', 'dplyr', 'tidyr', 'tidyverse', 'tidyquant', 'sparklyr', 'readr', 'quantmod', 'htmltools', 'highcharter', 'googleVis', 'formattable', 'ggfortify', 'DT', 'forecast', 'Mcomp', 'MCMCpack', 'PerformanceAnalytics', 'broom', 'microbenchmark', 'doParallel', 'engsoccerdata', 'Rmodel')
suppressAll(lib(pkgs))
#'@ install.packages(pkgs, lib = 'C:/Program Files/R/R-3.4.0/library')
## 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)
#'@ options(rpubs.upload.method = 'internal')
## R: llply fully reproducible results in parallel
## https://stackoverflow.com/questions/34946177/r-llply-fully-reproducible-results-in-parallel
cl <- makeCluster(detectCores())
registerDoParallel(cl)
## Create a cluster object to be used for rugarcgh and rmgarch models.
cluster = makePSOCKcluster(15)
## Connect to Spark.
#'@ spark_install()
#'@ sc <- spark_connect(master = 'local')
rm(pkgs)
```
# 1. Introduction
<center><iframe src="https://raw.githubusercontent.com/englianhu/binary.com-interview-question/ff20ee95aa60ef5cca3cf797066089103eb62acf/reference/quant-analyst-skills-test.pdf" width="600" height="900"></iframe></center>
For the question III, here I list down all possible scenario.
- **Observation 1 :** The bets on the first six games, if each team wins three, must land you at wining/losing zero (I call this winnings of 00). If this is not the case, then no bet^[Or in token of place bet $1] on the last game achieves ±100.
- **Observation 2 :** The bets on the first five games, if one team wins three of them, must land you at ±50 (+50 if team 1 wins three, −50 if team 2 wins three). Then (and only then) you can bet $50 on team 1 in game six and be assured of either immediately getting the proper result, or reaching a 3-3 tie at 00 winnings.
- **Observation 3 :** The bets on the first four games, if each team wins two, must land you at 00 (and you bet $50 on team 1 in the next game).
- **Observation 4 :** The bets on the first four games, if one team team wins three, must land you at ±75. Then you can bet $25 on team 1 and either terminate in the proper winnings or arrive at 3-2 at the proper amount ahead or behind.
- **Observation 5 :** The bets on the first three games, if one team wins two, must land you at some value that allows you to reach either ±75 or 00 depending on the outcome of the fourth game. That implies that the wager in that situation must be $37.5 and that the bets on the first three games, if one team wins two, must land you at ±37.5.
- **Observation 6 :** The bets on the first three games, if one team wins all three, must land you at some value that allows your next result to be ±100 or ±75 (see observation 4, which says in a 3-1 situation you need to be up or down by $75). The value that allows this is ±87.5 and the wager, of course, is $12.5.
- **Observation 7 :** The bets on the first two games, if each team wins one, must land you even, and at that point you will bet $37.5 (see observation 5).
- **Observation 8 :** The bets on the first two games, if one team wins both, must land you at some value that allows your next result to be ±87.5 or ±37.5, depending on the winner of game 3. Therefore, the bets on the first two games, if one team wins both, must land you at ±62.5 and you will bet $25.
- **Observation 9 :** The bet on the first game must land you mid-way between even and ±62.5. Than means the first bet must be $31.25.
So here is your strategy:
Bet $31.25 on team 1 in the first game. Then bet $31.25 on team 1 in the second game. At game three, if the teams are even, increase your bet for game three to $37.5. But if either team is up 2-0, decrease your bet to $25.
After three games, if one team has won all three you will be ahead or behind by $87.5 and you will bet $12.5 on the fourth game. But if either team is ahead 2-1, you will be ahead or behind by $37.5 and you will bet $37.5 on the fourth game.
After four games, if the series is not over, you will either be even and bet $50 on game five, or ahead or behind by $75, in which case you will bet on $25.
After five games either the series will be over, or you will be ahead or behind by $50, in which case you will bet $50 on game six.
And of course if the teams are tied after six games, then you are even as well, and you bet the full $100 on the final game.
Kindly refer to [Probability+Game Theory Problem [closed]](https://math.stackexchange.com/questions/1889792/probabilitygame-theory-problem?answertab=votes#tab-top) for further information.
Due to the betting strategy for question III has indenpent probability 50% without any edge, now we look at the soccer scores modelling and Kelly criterion betting strategy which is the best strategy for professional gamblers. Here I do not repeat the same model applicable to the English soccer leagues.
# 2. Data
Kindly refer to [Odds Modelling and Testing Inefficiency of Sports Bookmakers](https://github.com/scibrokes/odds-modelling-and-testing-inefficiency-of-sports-bookmakers) to know the English soccer dataset.
# 3. Statiscal Modelling
Kindly refer to [Odds Modelling and Testing Inefficiency of Sports Bookmakers](https://github.com/scibrokes/odds-modelling-and-testing-inefficiency-of-sports-bookmakers) for statistical modelling.
# 4. Betting Strategy
Kindly refer to [Application of Kelly Criterion model in Sportsbook Investment](https://github.com/scibrokes/kelly-criterion) to know the betting strategy applied to English soccer leagues over 2 years.
# 5. Return of Investment
Kindly refer to [Application of Kelly Criterion model in Sportsbook Investment](https://github.com/scibrokes/kelly-criterion) to know the return of investment applied to English soccer leagues over 2 years.
# 6. Conclusion
From the papers, we know that from my firstly betting strategy with $1 on every single match whith an edge of overcame the handicap, it might be win or loss depends the level of edge. In later paper I applied Kelly criterion method and get a confirmed ROI over 2 years.
```{r stopPar, echo = FALSE}
## Set options back to original options
options(op)
options(warn = 0)
stopCluster(cl)
```
# 7. Appendix
## 7.1 Documenting File Creation
It's useful to record some information about how your file was created.
- File creation date: 2015-10-08
- File latest updated date: `r Sys.Date()`
- `r R.version.string`
- R version (short form): `r getRversion()`
- [<span style='color:blue'>**rmarkdown** package</span>](https://github.com/rstudio/rmarkdown) version: `r packageVersion('rmarkdown')`
- [<span style='color:blue'>**tufte** package</span>](https://github.com/rstudio/tufte) version: `r packageVersion('tufte')`
- File version: 1.0.1
- Author Profile: [<span style='color:blue'>®γσ, Eng Lian Hu</span>](https://beta.rstudioconnect.com/englianhu/ryo-eng/)
- GitHub: [<span style='color:blue'>Source Code</span>](https://github.com/englianhu/binary.com-interview-question)
- Additional session information
```{r info, echo = FALSE, warning = FALSE, results = 'asis'}
suppressMessages(require('dplyr', quietly = TRUE))
suppressMessages(require('formattable', quietly = TRUE))
lubridate::now()
sys1 <- devtools::session_info()$platform %>% unlist %>% data.frame(Category = names(.), session_info = .)
rownames(sys1) <- NULL
sys1 %>% formattable %>% as.htmlwidget
data.frame(Sys.info()) %>% mutate(Category = rownames(.)) %>% .[2:1] %>% rename(Category = Category, Sys.info = Sys.info..) %>% formattable %>% as.htmlwidget
rm(sys1)
```
## 7.2 Reference
01. [<span style='color:blue'>Binary.com Interview Q1</span>](https://englianhu.github.io/2017/09/binary-forex-trading-Q1.html) (<span style='color:blue'>[Alternate link</span>](http://rpubs.com/englianhu/binary-forex-trading-Q1))
02. [<span style='color:blue'>Odds Modelling and Testing Inefficiency of Sports Bookmakers</span>](https://github.com/scibrokes/odds-modelling-and-testing-inefficiency-of-sports-bookmakers)
03. [<span style='color:blue'>Apply Kelly-Criterion on English Soccer 2011/12 to 2012/13</span>](https://github.com/scibrokes/kelly-criterion)
04. [<span style='color:blue'>Betting Strategy and Model Validation</span>](https://github.com/scibrokes/betting-strategy-and-model-validation)
05. [<span style='color:blue'>
Betting Strategy</span>](http://mathforum.org/library/drmath/view/62870.html)
06. [<span style='color:blue'>Probability+Game Theory Problem [closed]</span>](https://math.stackexchange.com/questions/1889792/probabilitygame-theory-problem)
07. [<span style='color:blue'>...</span>](...)
08. [<span style='color:blue'>...</span>](...)
09. [<span style='color:blue'>...</span>](...)
10. [<span style='color:blue'>...</span>](...)
**Powered by - Copyright® Intellectual Property Rights of <img src='https://raw.githubusercontent.com/englianhu/binary.com-interview-question/master/www/oda-army2.jpg?raw=true' width='24'> [<span style='color:blue'>Scibrokes®</span>](http://www.scibrokes.com)個人の経営企業**