1743 lines
397 KiB
Plaintext
1743 lines
397 KiB
Plaintext
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{
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"cells": [
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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 Packages and Extra Functions"
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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": 1,
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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": 1,
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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 Statistics, Printf, Dates, DelimitedFiles, Distributions, LinearAlgebra\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": 2,
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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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"#pyplot(size=(600,400))\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 from a csv File"
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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": 3,
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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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"\n",
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"first four lines of x:\n",
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"1970-01-01 -5.480 -4.875 -8.100\n",
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"1970-02-01 1.465 7.546 5.130\n",
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"1970-03-01 -7.232 1.061 -1.060\n",
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"1970-04-01 -24.488 -8.481 -11.000\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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"x = readdlm(\"Data/Portfolios_SGLV.csv\",',',skipstart=1) #reading the csv file\n",
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" #skip 1st line\n",
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"println(\"\\nfirst four lines of x:\")\n",
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"printmat(x[1:4,:])\n",
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"\n",
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"dN = Date.(x[:,1]) #creating variables\n",
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"Re = convert.(Float64,x[:,2:3]) #small growth (SG), large value (LV)\n",
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"Rme = convert.(Float64,x[:,end]); #market"
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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: Means and Standard Deviations\n",
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"\n",
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"Estimate and print the means and standard deviations of the three series (in `Re` and `Rme`)."
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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": 4,
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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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" SG LV Market\n",
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"mean 0.218 0.677 0.593\n",
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"std 8.079 5.772 4.595\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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"μ = mean([Re Rme],dims=1) \n",
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"σ = std([Re Rme],dims=1) \n",
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"\n",
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"printmat([μ;σ],colNames=[\"SG\",\"LV\",\"Market\"],rowNames=[\"mean\",\"std\"])"
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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: Correlations\n",
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"\n",
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"Estimate and print the correlation matrix."
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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": 5,
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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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" 1.000 0.563 0.804\n",
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" 0.563 1.000 0.774\n",
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" 0.804 0.774 1.000\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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"printmat(cor([Re Rme]))"
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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 3: OLS\n",
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"\n",
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"Code up a function to do OLS. It should take `y` and `x` as inputs and return the slope coefficients, the standard errors and R2 as output. Notice that you can calculate the standard erors as follows\n",
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"1. `cov_b = inv(x'x)*var(u)` where `u` are the residuals\n",
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"2. `std_b = sqrt.(diag(cov_b))`\n",
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"\n",
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"Hint: cell 3 (or so) in [OLS notebook on Paul Söderlind's Github](https://github.com/PaulSoderlind/FinancialEconometrics/blob/master/Ch02_OLS1.ipynb)\n",
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"\n",
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"Then, regress each of return `Re[:,1]` and `Re[:,2]` on the market `Rme` and a constant. Report the coefficients and standard errors."
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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": 6,
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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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"OLS (generic function with 1 method)"
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]
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},
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"execution_count": 6,
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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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"function OLS(y,x) \n",
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" b = x\\y\n",
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" u = y - x*b\n",
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" R2 = 1 - var(u)/var(y)\n",
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" cov_b = inv(x'x)*var(u)\n",
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" std_b = sqrt.(diag(cov_b))\n",
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" return b, std_b, R2\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": 7,
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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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"Small growth\n",
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" coef StdErr\n",
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"c -0.620 0.196\n",
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"Rme 1.414 0.042\n",
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"\n",
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"Large value\n",
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" coef StdErr\n",
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"c 0.100 0.149\n",
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"Rme 0.972 0.032\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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"T = size(Re,1) #number of time periods\n",
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"\n",
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"c = ones(T) #a vector with ones\n",
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"x = [c Rme] #x is a Tx2 matrix\n",
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"b1 = x\\Re[:,1] \n",
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"b2 = x\\Re[:,2] \n",
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"(b1,std_b1,) = OLS(Re[:,1],x)\n",
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"(b2,std_b2,) = OLS(Re[:,2],x)\n",
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"\n",
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"println(\"Small growth\")\n",
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"printmat([b1 std_b1],colNames=[\"coef\",\"StdErr\"],rowNames=[\"c\",\"Rme\"])\n",
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"println(\"Large value\")\n",
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"printmat([b2 std_b2],colNames=[\"coef\",\"StdErr\"],rowNames=[\"c\",\"Rme\"])"
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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 4: Scatter Plot\n",
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"\n",
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"Make a scatter plot of `Rme` (on the horizontal axis) and `SG`. Do the same for `Rme` and `LV`. Add a 45 degree line and also the regression line from OLS."
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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": 8,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"<defs>\n",
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" \"/>\n",
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"</svg>\n"
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]
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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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|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"xGrid = range(-40,40,length=5)\n",
|
|||
|
|
"yLine = b1[1] .+ b1[2]*xGrid\n",
|
|||
|
|
"\n",
|
|||
|
|
"p1 = scatter( Rme,Re[:,1],\n",
|
|||
|
|
" fillcolor = :blue,\n",
|
|||
|
|
" legend = false,\n",
|
|||
|
|
" xlim = (-40,40),\n",
|
|||
|
|
" ylim = (-40,40),\n",
|
|||
|
|
" title = \"Scatter plot: two monthly return series\",\n",
|
|||
|
|
" titlefont = font(10),\n",
|
|||
|
|
" xlabel = \"Market excess return, %\",\n",
|
|||
|
|
" ylabel = \"Excess returns on small growth stocks, %\",\n",
|
|||
|
|
" guidefont = font(8) )\n",
|
|||
|
|
"plot!([-40;40],[-40;40],color=:black,linewidth=0.5) \n",
|
|||
|
|
"plot!(xGrid,yLine,color=:red,linestyle=:dash)\n",
|
|||
|
|
"display(p1)"
|
|||
|
|
]
|
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|
|
},
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|
|
{
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|
|
"cell_type": "code",
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"execution_count": 9,
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|
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"metadata": {},
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|
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"outputs": [
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|
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{
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"data": {
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" 224.375,1119.34 1872.76,106.192 \n",
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" \"/>\n",
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"<polyline clip-path=\"url(#clip802)\" style=\"stroke:#ff0000; stroke-linecap:butt; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" stroke-dasharray=\"16, 10\" points=\"\n",
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|
" 224.375,1104.05 636.47,857.773 1048.57,611.496 1460.66,365.219 1872.76,118.942 \n",
|
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|
|
" \"/>\n",
|
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|
|
"</svg>\n"
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|
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]
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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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|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"xGrid = range(-40,40,length=5)\n",
|
|||
|
|
"yLine = b2[1] .+ b2[2]*xGrid\n",
|
|||
|
|
"\n",
|
|||
|
|
"p1 = scatter( Rme,Re[:,2],\n",
|
|||
|
|
" fillcolor = :blue,\n",
|
|||
|
|
" legend = false,\n",
|
|||
|
|
" xlim = (-40,40),\n",
|
|||
|
|
" ylim = (-40,40),\n",
|
|||
|
|
" title = \"Scatter plot: two monthly return series\",\n",
|
|||
|
|
" titlefont = font(10),\n",
|
|||
|
|
" xlabel = \"Market excess return, %\",\n",
|
|||
|
|
" ylabel = \"Excess returns on large value stocks, %\",\n",
|
|||
|
|
" guidefont = font(8) )\n",
|
|||
|
|
"plot!([-40;40],[-40;40],color=:black,linewidth=0.5)\n",
|
|||
|
|
"plot!(xGrid,yLine,color=:red,linestyle=:dash)\n",
|
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|
|
"display(p1)"
|
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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": null,
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|
"metadata": {},
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|
|
"outputs": [],
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|
|
"source": []
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|
|
}
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|
],
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|
|
"metadata": {
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"@webio": {
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"lastCommId": null,
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"lastKernelId": null
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},
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"anaconda-cloud": {},
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"kernelspec": {
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|
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"display_name": "Julia 1.6.3",
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|
|
"language": "julia",
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|
|
"name": "julia-1.6"
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|
|
},
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|
|
"language_info": {
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|
|
"file_extension": ".jl",
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|
|
"mimetype": "application/julia",
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|
|
"name": "julia",
|
|||
|
|
"version": "1.6.3"
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
"nbformat": 4,
|
|||
|
|
"nbformat_minor": 4
|
|||
|
|
}
|