speice.io/assets/js/818287cf.fc9a1bb7.js

"use strict";(self.webpackChunkspeice_io=self.webpackChunkspeice_io||[]).push([["5095"],{32181:function(s,e,n){n.r(e),n.d(e,{assets:function(){return c},contentTitle:function(){return r},default:function(){return d},frontMatter:function(){return l},metadata:function(){return a},toc:function(){return m}});var a=n(41915),t=n(85893),i=n(50065);let l={slug:"2015/11/welcome",title:"Welcome, and an algorithm",date:new Date("2015-11-19T12:00:00.000Z"),last_update:{date:new Date("2015-12-05T12:00:00.000Z")},authors:["bspeice"],tags:[]},r=void 0,c={authorsImageUrls:[void 0]},m=[{value:"Trading Competition Optimization",id:"trading-competition-optimization",level:2},{value:"Calculating the Return",id:"calculating-the-return",level:2},{value:"Calculating the Sharpe ratio",id:"calculating-the-sharpe-ratio",level:2},{value:"Calculating the drawdown",id:"calculating-the-drawdown",level:2}];function h(s){let e={a:"a",annotation:"annotation",code:"code",h1:"h1",h2:"h2",hr:"hr",li:"li",math:"math",mfrac:"mfrac",mi:"mi",mn:"mn",mo:"mo",mover:"mover",mrow:"mrow",mstyle:"mstyle",msub:"msub",mtable:"mtable",mtd:"mtd",mtext:"mtext",mtr:"mtr",p:"p",path:"path",pre:"pre",semantics:"semantics",span:"span",strong:"strong",svg:"svg",table:"table",tbody:"tbody",td:"td",th:"th",thead:"thead",tr:"tr",ul:"ul",...(0,i.a)(),...s.components};return(0,t.jsxs)(t.Fragment,{children:[(0,t.jsx)(e.p,{children:"Hello! Glad to meet you. I'm currently a student at Columbia University studying Financial Engineering, and want to give an overview of the projects I'm working on!"}),"\n",(0,t.jsx)(e.p,{children:"To start things off, Columbia has been hosting a trading competition that myself and another partner are competing in. I'm including a notebook of the algorithm that we're using, just to give a simple overview of a miniature algorithm."}),"\n",(0,t.jsx)(e.p,{children:"The competition is scored in 3 areas:"}),"\n",(0,t.jsxs)(e.ul,{children:["\n",(0,t.jsx)(e.li,{children:"Total return"}),"\n",(0,t.jsx)(e.li,{children:(0,t.jsx)(e.a,{href:"https://en.wikipedia.org/wiki/Sharpe_ratio",children:"Sharpe ratio"})}),"\n",(0,t.jsx)(e.li,{children:"Maximum drawdown"}),"\n"]}),"\n",(0,t.jsx)(e.p,{children:"Our algorithm uses a basic momentum strategy: in the given list of potential portfolios, pick the stocks that have been performing well in the past 30 days. Then, optimize for return subject to the drawdown being below a specific level. We didn't include the Sharpe ratio as a constraint, mostly because we were a bit late entering the competition."}),"\n",(0,t.jsx)(e.p,{children:"I'll be updating this post with the results of our algorithm as they come along!"}),"\n",(0,t.jsx)(e.hr,{}),"\n",(0,t.jsxs)(e.p,{children:[(0,t.jsx)(e.strong,{children:"UPDATE 12/5/2015"}),": Now that the competition has ended, I wanted to update how the algorithm performed. Unfortunately, it didn't do very well. I'm planning to make some tweaks over the coming weeks, and do another forward test in January."]}),"\n",(0,t.jsxs)(e.ul,{children:["\n",(0,t.jsx)(e.li,{children:"After week 1: Down .1%"}),"\n",(0,t.jsx)(e.li,{children:"After week 2: Down 1.4%"}),"\n",(0,t.jsx)(e.li,{children:"After week 3: Flat"}),"\n"]}),"\n",(0,t.jsx)(e.p,{children:"And some statistics for all teams participating in the competition:"}),"\n",(0,t.jsxs)(e.table,{children:[(0,t.jsx)(e.thead,{children:(0,t.jsxs)(e.tr,{children:[(0,t.jsx)(e.th,{children:"Statistic"}),(0,t.jsx)(e.th,{children:"Value"})]})}),(0,t.jsxs)(e.tbody,{children:[(0,t.jsxs)(e.tr,{children:[(0,t.jsx)(e.td,{children:"Max Return"}),(0,t.jsx)(e.td,{children:"74.1%"})]}),(0,t.jsxs)(e.tr,{children:[(0,t.jsx)(e.td,{children:"Min Return"}),(0,t.jsx)(e.td,{children:"-97.4%"})]}),(0,t.jsxs)(e.tr,{children:[(0,t.jsx)(e.td,{children:"Average Return"}),(0,t.jsx)(e.td,{children:"-.1%"})]}),(0,t.jsxs)(e.tr,{children:[(0,t.jsx)(e.td,{children:"Std Dev of Returns"}),(0,t.jsx)(e.td,{children:"19.6%"})]})]})]}),"\n",(0,t.jsx)(e.hr,{}),"\n",(0,t.jsx)(e.h2,{id:"trading-competition-optimization",children:"Trading Competition Optimization"}),"\n",(0,t.jsx)(e.p,{children:(0,t.jsx)(e.strong,{children:"Goal: Max return given maximum Sharpe and Drawdown"})}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-python",children:"from IPython.display import display\nimport Quandl\nfrom datetime import datetime, timedelta\n\ntickers = ['XOM', 'CVX', 'CLB', 'OXY', 'SLB']\nmarket_ticker = 'GOOG/NYSE_VOO'\nlookback = 30\nd_col = 'Close'\n\ndata = {tick: Quandl.get('YAHOO/{}'.format(tick))[-lookback:] for tick in tickers}\nmarket = Quandl.get(market_ticker)\n"})}),"\n",(0,t.jsx)(e.h2,{id:"calculating-the-return",children:"Calculating the Return"}),"\n",(0,t.jsx)(e.p,{children:"We first want to know how much each ticker returned over the prior period."}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{className:"language-python",children:"returns = {tick: data[tick][d_col].pct_change() for tick in tickers}\n\ndisplay({tick: returns[tick].mean() for tick in tickers})\n"})}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{children:"    {'CLB': -0.0016320202164526894,\n     'CVX': 0.0010319531629488911,\n     'OXY': 0.00093418904454400551,\n     'SLB': 0.00098431254720448159,\n     'XOM': 0.00044165797556096868}\n"})}),"\n",(0,t.jsx)(e.h2,{id:"calculating-the-sharpe-ratio",children:"Calculating the Sharpe ratio"}),"\n",(0,t.jsxs)(e.p,{children:["Sharpe: ",(0,t.jsxs)(e.span,{className:"katex",children:[(0,t.jsx)(e.span,{className:"katex-mathml",children:(0,t.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,t.jsxs)(e.semantics,{children:[(0,t.jsx)(e.mrow,{children:(0,t.jsxs)(e.mfrac,{children:[(0,t.jsxs)(e.mrow,{children:[(0,t.jsx)(e.mi,{children:"R"}),(0,t.jsx)(e.mo,{children:"\u2212"}),(0,t.jsxs)(e.msub,{children:[(0,t.jsx)(e.mi,{children:"R"}),(0,t.jsx)(e.mi,{children:"M"})]})]}),(0,t.jsx)(e.mi,{children:"\u03C3"})]})}),(0,t.jsx)(e.annotation,{encoding:"application/x-tex",children:"{R - 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minimizing\nreturns_a = np.array(list(map(lambda tick: returns[tick].mean(), tickers))) \n\nmeets_sharpe = lambda x: sum(abs(x) * sharpe_a) - sharpe_limit\ndef meets_dd(x):\n    portfolio = sum(abs(x))\n    if portfolio < .1:\n        # If there are no stocks in the portfolio,\n        # we can accidentally induce division by 0,\n        # or division by something small enough to cause infinity\n        return 0\n    \n    return drawdown_limit - sum(abs(x) * dd_a) / sum(abs(x))\n\nis_portfolio = lambda x: sum(x) - 1\n\ndef within_leverage(x):\n    return leverage - sum(abs(x))\n\nobjective = lambda x: sum(x * returns_a) * -1 # Because we're minimizing\nbounds = ((None, None),) * len(tickers)\nx = np.zeros(len(tickers))\n\nconstraints = [\n    {\n        'type': 'eq',\n        'fun': is_portfolio\n    }, {\n        'type': 'ineq',\n        'fun': within_leverage\n    #}, {\n    #    'type': 'ineq',\n    #    'fun': meets_sharpe\n    }, {\n        'type': 'ineq',\n        'fun': meets_dd\n    }\n]\n\noptimal = minimize(objective, x, bounds=bounds, constraints=constraints,\n                  options={'maxiter': 500})\n\n# Optimization time!\ndisplay(optimal.message)\n\ndisplay(\"Holdings: {}\".format(list(zip(tickers, optimal.x))))\n\n# multiply by -100 to scale, and compensate for minimizing\nexpected_return = optimal.fun * -100\ndisplay(\"Expected Return: {:.3f}%\".format(expected_return))\n\nexpected_drawdown = sum(abs(optimal.x) * dd_a) / sum(abs(optimal.x)) * 100\ndisplay(\"Expected Max Drawdown: {0:.2f}%\".format(expected_drawdown))\n\n# TODO: Calculate expected Sharpe\n"})}),"\n",(0,t.jsx)(e.pre,{children:(0,t.jsx)(e.code,{children:"    'Optimization terminated successfully.'\n    \"Holdings: [('XOM', 5.8337945679814904),\n                ('CVX', 42.935064321851307),\n                ('CLB', -124.5),\n                ('OXY', 36.790387773552119),\n                ('SLB', 39.940753336615096)]\"\n    'Expected Return: 32.375%'\n    'Expected Max Drawdown: 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Glad to meet you. I\'m currently a student at Columbia University studying Financial Engineering, and want to give an overview of the projects I\'m working on!","date":"2015-11-19T12:00:00.000Z","tags":[],"readingTime":4.175,"hasTruncateMarker":true,"authors":[{"name":"Bradlee Speice","socials":{"github":"https://github.com/bspeice"},"key":"bspeice","page":null}],"frontMatter":{"slug":"2015/11/welcome","title":"Welcome, and an algorithm","date":"2015-11-19T12:00:00.000Z","last_update":{"date":"2015-12-05T12:00:00.000Z"},"authors":["bspeice"],"tags":[]},"unlisted":false,"lastUpdatedAt":1449316800000,"prevItem":{"title":"Autocallable Bonds","permalink":"/2015/11/autocallable"}}')}}]);