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88 KiB
JavaScript
1 line
88 KiB
JavaScript
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"use strict";(self.webpackChunkspeice_io=self.webpackChunkspeice_io||[]).push([["8868"],{21450:function(s,e,a){a.r(e),a.d(e,{assets:function(){return r},contentTitle:function(){return m},default:function(){return d},frontMatter:function(){return t},metadata:function(){return n},toc:function(){return c}});var n=a(82353),l=a(85893),i=a(50065);let t={slug:"2016/02/guaranteed-money-maker",title:"Guaranteed money maker",date:new Date("2016-02-03T12:00:00.000Z"),authors:["bspeice"],tags:[]},m=void 0,r={authorsImageUrls:[void 0]},c=[{value:"Applying the Martingale Strategy",id:"applying-the-martingale-strategy",level:2},{value:"Interesting Implications",id:"interesting-implications",level:2},{value:"Running the simulation",id:"running-the-simulation",level:2},{value:"Summary",id:"summary",level:2},{value:"Side note and disclaimer",id:"side-note-and-disclaimer",level:3}];function h(s){let e={a:"a",annotation:"annotation",code:"code",em:"em",h2:"h2",h3:"h3",li:"li",math:"math",mfrac:"mfrac",mi:"mi",mn:"mn",mo:"mo",mrow:"mrow",mstyle:"mstyle",msub:"msub",msubsup:"msubsup",mtable:"mtable",mtd:"mtd",mtr:"mtr",munderover:"munderover",ol:"ol",p:"p",pre:"pre",semantics:"semantics",span:"span",strong:"strong",ul:"ul",...(0,i.a)(),...s.components};return(0,l.jsxs)(l.Fragment,{children:[(0,l.jsx)(e.p,{children:"Developing an investment strategy based on the Martingale betting strategy"}),"\n",(0,l.jsx)(e.p,{children:"If you can see into the future, that is."}),"\n",(0,l.jsxs)(e.p,{children:["My previous class in Stochastic Calculus covered a lot of interesting topics, and the important one for today is the ",(0,l.jsx)(e.a,{href:"https://en.wikipedia.org/wiki/Gambler's_ruin",children:"Gambler's Ruin"})," problem. If you're interested in some of the theory behind it, also make sure to check out ",(0,l.jsx)(e.a,{href:"https://en.wikipedia.org/wiki/Random_walk",children:"random walks"}),". The important bit is that we studied the ",(0,l.jsx)(e.a,{href:"https://en.wikipedia.org/wiki/Martingale_%28betting_system%29",children:"Martingale Betting Strategy"}),", which describes for us a ",(0,l.jsx)(e.strong,{children:"guaranteed way"})," to ",(0,l.jsx)("small",{children:"eventually"})," make money."]}),"\n",(0,l.jsx)(e.p,{children:"The strategy goes like this: You are going to toss a fair coin with a friend. If you guess heads or tails correctly, you get back double the money you bet. If you guess incorrectly, you lose money. How should you bet?"}),"\n",(0,l.jsx)(e.p,{children:"The correct answer is that you should double your bet each time you lose. Then when you finally win, you'll be guaranteed to make back everything you lost and then $1 extra! Consider the scenario:"}),"\n",(0,l.jsxs)(e.ol,{children:["\n",(0,l.jsx)(e.li,{children:"You bet $1, and guess incorrectly. You're 1 dollar in the hole."}),"\n",(0,l.jsx)(e.li,{children:"You bet $2, and guess incorrectly. You're 3 dollars in the hole now."}),"\n",(0,l.jsx)(e.li,{children:"You bet $4, and guess incorrectly. You're 7 dollars in the hole."}),"\n",(0,l.jsxs)(e.li,{children:["You bet $8, and guess correctly! You now get back those 8 dollars you bet, plus 8 extra for winning, for a ",(0,l.jsx)(e.strong,{children:"total profit of one dollar"}),"!"]}),"\n"]}),"\n",(0,l.jsx)(e.p,{children:"Mathematically, we can prove that as long as you have unlimited money to bet, you are guaranteed to make money."}),"\n",(0,l.jsx)(e.h2,{id:"applying-the-martingale-strategy",children:"Applying the Martingale Strategy"}),"\n",(0,l.jsx)(e.p,{children:"But we're all realistic people, and once you start talking about \"unlimited money\" eyebrows should be raised. Even still, this is an interesting strategy to investigate, and I want to apply it to the stock market. As long as we can guarantee there's a single day in which the stock goes up, we should be able to make money right? The question is just how much we have to invest to guarantee this."}),"\n",(0,l.jsx)(e.p,{children:"Now it's time for the math. We'll use the following definitions:"}),"\n",(0,l.jsxs)(e.ul,{children:["\n",(0,l.jsxs)(e.li,{children:[(0,l.j
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