316 lines
167 KiB
Plaintext
316 lines
167 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"printyellow (generic function with 1 method)"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"using Printf, Dates, Statistics, DelimitedFiles, StatsBase\n",
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"\n",
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"include(\"jlFiles/printmat.jl\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"using Plots\n",
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"\n",
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"gr(size=(480,320))\n",
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"default(fmt = :svg)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Load Data"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(10340, 25)"
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]
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},
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"x = readdlm(\"Data/25_Portfolios_5x5_Daily.CSV\",',',skipstart=1) #daily return data\n",
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"ym = round.(Int,x[:,1]) #yearmonthday, like 20071231\n",
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"\n",
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"dN = Date.(string.(ym),\"yyyymmdd\") #covert to Julia date, eg. 2001-12-31\n",
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"\n",
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"\n",
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"vv = Date(1980,1,1) .<= dN .<= Date(2020,12,31) #pick out the correct sample\n",
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"ym = ym[vv]\n",
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"R = x[vv,2:end] #returns\n",
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"\n",
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"(T,n) = size(R) #number of data points, number of assets"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Task 1: Two Simple Strategies\n",
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"\n",
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"`R_1`: go long each of asset 1-24 (each with the weight 1/24) and short asset 25\n",
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"\n",
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"`R_2`: go long asset 1 and short asset 25\n",
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"\n",
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"The returns of these portfolios are easy to calculate without having to explicitly construct the portfolio weights, but it still a good preparation for later to do the explicit calculations as follows:\n",
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"\n",
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"1. Construct the vector of portfolio weights `w`\n",
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"2. The portfolio return in `t` is `w'*R[t,:]`.\n",
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"\n",
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"Also, do not be afraid of loops: they are quick.\n",
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"\n",
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"Show means and standard deviations of the two strategies. Annualize the mean by `*252` and the standard deviation by `*sqrt(252)`.\n",
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"\n",
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"Plot histograms with bins that are 0.25 wide. (Don't annualize anything in the histograms.)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [],
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"source": [
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"w1 = [ones(24)/24;-1] #static\n",
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"w2 = [1;zeros(23);-1]\n",
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"\n",
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"(R_1,R_2) = (fill(NaN,T),fill(NaN,T))\n",
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"for t = 1:T \n",
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" R_1[t] = w1'*R[t,:]\n",
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" R_2[t] = w2'*R[t,:]\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" R_1 R_2\n",
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"mean -0.348 -8.665\n",
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"std 13.860 18.996\n",
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"SR -0.025 -0.456\n",
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"\n"
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]
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}
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],
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"source": [
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"R_all = [R_1 R_2]\n",
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"\n",
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"μ = mean(R_all,dims=1)*252\n",
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"σ = std(R_all,dims=1)*sqrt(252)\n",
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"SR = μ./σ\n",
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"\n",
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"printmat([μ;σ;SR],colNames=[\"R_1\",\"R_2\"],rowNames=[\"mean\",\"std\",\"SR\"])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
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"data": {
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"plt = histogram( R_1,bins = -12:0.25:12,normalize=true,legend=false,title=\"strategy 1\" )\n",
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"display(plt)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\"?>\n<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"480\" height=\"320\" viewBox=\"0 0 1920 1280\">\n<defs>\n <clipPath id=\"clip240\">\n <rect x=\"0\" y=\"0\" width=\"1920\" height=\"1280\"/>\n </clipPath>\n</defs>\n<path clip-path=\"url(#clip240)\" d=\"\nM0 1280 L1920 1280 L1920 0 L0 0 Z\n \" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n<defs>\n <clipPath id=\"clip241\">\n <rect x=\"384\" y=\"0\" width=\"1345\" height=\"1280\"/>\n </clipPath>\n</defs>\n<path clip-path=\"url(#clip240)\" d=\"\nM151.798 1169.65 L1872.76 1169.65 L1872.76 123.472 L151.798 123.472 Z\n \" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n<defs>\n <clipPath id=\"clip242\">\n <rect x=\"151\" y=\"123\" width=\"1722\" height=\"1047\"/>\n </clipPath>\n</defs>\n<polyline clip-path=\"url(#clip242)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"\n 374.091,1169.65 374.091,123.472 \n \"/>\n<polyline clip-path=\"url(#clip242)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"\n 693.184,1169.65 693.184,123.472 \n \"/>\n<polyline clip-path=\"url(#clip242)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"\n 1012.28,1169.65 1012.28,123.472 \n \"/>\n<polyline clip-path=\"url(#clip242)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"\n 1331.37,1169.65 1331.37,123.472 \n \"/>\n<polyline clip-path=\"url(#clip242)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:2; stroke-opacity:0.1; fill:none\" points=\"\n 1650.46,1169.65 1650.46,123.472 \n \"/>\n<polyline clip-path=\"url(#clip240)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n 151.798,1169.65 1872.76,1169.65 \n \"/>\n<polyline clip-path=\"url(#clip240)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n 374.091,1169.65 374.091,1150.75 \n \"/>\n<polyline clip-path=\"url(#clip240)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n 693.184,1169.65 693.184,1150.75 \n \"/>\n<polyline clip-path=\"url(#clip240)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n 1012.28,1169.65 1012.28,1150.75 \n \"/>\n<polyline clip-path=\"url(#clip240)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n 1331.37,1169.65 1331.37,1150.75 \n \"/>\n<polyline clip-path=\"url(#clip240)\" style=\"stroke:#000000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n 1650.46,1169.65 1650.46,1150.75 \n \"/>\n<path clip-path=\"url(#clip240)\" d=\"M328.154 1209.65 L357.83 1209.65 L357.83 1213.59 L328.154 1213.59 L328.154 1209.65 Z\" fill=\"#000000\" fill-rule=\"evenodd\" fill-opacity=\"1\" /><path clip-path=\"url(#clip240)\" d=\"M368.732 1222.54 L376.371 1222.54 L376.371 1196.18 L368.061 1197.85 L368.061 1193.59 L376.325 1191.92 L381.001 1191.92 L381.001 1222.54 L388.64 1222.54 L388.64 1226.48 L368.732 1226.48 L368.732 1222.54 Z\" fill=\"#000000\" fill-rule=\"evenodd\" fill-opacity=\"1\" /><path clip-path=\"url(#clip240)\" d=\"M408.084 1195 Q404.473 1195 402.644 1198.56 Q400.839 1202.11 400.839 1209.23 Q400.839 1216.34 402.644 1219.91 Q404.473 1223.45 408.084 1223.45 Q411.718 1223.45 413.524 1219.91 Q415.353 1216.34 415.353 1209.23 Q415.353 1202.11 413.524 1198.56 Q411.718 1195 408.084 1195 M408.084 1191.29 Q413.894 1191.29 416.95 1195.9 Q420.028 1200.48 420.028 1209.23 Q420.028 1217.96 416.95 1222.5
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"plt = histogram( R_2,bins = -12:0.25:12,normalize=true,legend=false,title=\"strategy 2\" )\n",
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"display(plt)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Task 2: Another Trading Strategy\n",
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"\n",
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"We now do simple volatility based trading strategy.\n",
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"\n",
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"1. Find the 3 least volatile assets over `t-22:t-1` and give each a portfolio weight `w[t,i]=1/3`. \n",
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"\n",
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"2. Find the 3 most volatile assets over `t-22:t-1` and give each a portfolio weight `w[t,i]=-1/3`. \n",
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"\n",
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"3. The portfolio return in `t` is `w[t,:]'*R[t,:]`.\n",
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"\n",
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"4. Compare the average and std (annualized) with the previous portfolios, over periods `23:T`\n",
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"\n",
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"Hint: `v = sortperm(x)` gives indices such that `v[1:2]` are the indices of the lowest 2 elements in x. Try `sortperm([12,11,13])` to see."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" 2 \n",
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" 1 \n",
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" 3 \n",
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"\n",
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" 2 \n",
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" 1 \n",
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"\n"
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]
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}
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],
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"source": [
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"v = sortperm([12,11,13])\n",
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"printmat(v)\n",
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"printmat(v[1:2])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"σ_moving = fill(NaN,T,n)\n",
|
|||
|
|
"for t = 22:T\n",
|
|||
|
|
" σ_moving[t,:] = std(R[t-21:t,:],dims=1)\n",
|
|||
|
|
"end "
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 20,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
"-0.36666666666666664"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"m = 3 #number of long/short positions \n",
|
|||
|
|
"\n",
|
|||
|
|
"R_3 = fill(NaN,T)\n",
|
|||
|
|
"for t = 23:T #loop over periods, save portfolio returns\n",
|
|||
|
|
" #local s,w #local/global is needed in script\n",
|
|||
|
|
" s = sortperm(σ_moving[t-1,:])\n",
|
|||
|
|
" w = zeros(n)\n",
|
|||
|
|
" w[s[1:m]] .= 1/m\n",
|
|||
|
|
" w[s[end-m+1:end]] .= -1/m\n",
|
|||
|
|
" R_3[t] = w'R[t,:]\n",
|
|||
|
|
"end\n",
|
|||
|
|
"\n",
|
|||
|
|
"print(R_3[23])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 19,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"name": "stdout",
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"text": [
|
|||
|
|
" R_1 R_2 Vol sort\n",
|
|||
|
|
"avg return -0.281 -8.739 3.628\n",
|
|||
|
|
"std 13.867 19.002 14.867\n",
|
|||
|
|
"SR -0.020 -0.460 0.244\n",
|
|||
|
|
"\n"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"R_all = [R_1[23:end] R_2[23:end] R_3[23:end]]\n",
|
|||
|
|
"\n",
|
|||
|
|
"μ = mean(R_all,dims=1)*252\n",
|
|||
|
|
"σ = std(R_all,dims=1)*sqrt(252)\n",
|
|||
|
|
"SR = μ./σ\n",
|
|||
|
|
"\n",
|
|||
|
|
"printmat([μ;σ;SR],colNames=[\"R_1\",\"R_2\",\"Vol sort\"],rowNames=[\"avg return\",\"std\",\"SR\"])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": null,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": []
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"metadata": {
|
|||
|
|
"@webio": {
|
|||
|
|
"lastCommId": null,
|
|||
|
|
"lastKernelId": null
|
|||
|
|
},
|
|||
|
|
"anaconda-cloud": {},
|
|||
|
|
"kernelspec": {
|
|||
|
|
"display_name": "Julia 1.7.0-rc1",
|
|||
|
|
"language": "julia",
|
|||
|
|
"name": "julia-1.7"
|
|||
|
|
},
|
|||
|
|
"language_info": {
|
|||
|
|
"file_extension": ".jl",
|
|||
|
|
"mimetype": "application/julia",
|
|||
|
|
"name": "julia",
|
|||
|
|
"version": "1.7.0"
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
"nbformat": 4,
|
|||
|
|
"nbformat_minor": 4
|
|||
|
|
}
|