341 lines
389 KiB
Plaintext
341 lines
389 KiB
Plaintext
{
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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": 2,
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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": 2,
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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": 3,
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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": 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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"\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": 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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"Mean:\n",
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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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"println(\"Mean:\")\n",
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"a = mean([Re Rme], dims=1)\n",
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"b = std([Re Rme], dims=1)\n",
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"\n",
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"printmat([a;b],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": 6,
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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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"c = cor([Re Rme])\n",
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"\n",
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"printmat(c)"
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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": 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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"\n",
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" coef stdErr\n",
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"c -0.620 0.196\n",
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"Rme (slope) 1.414 0.042\n",
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"\n",
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"Large value:\n",
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"\n",
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" coef stdErr\n",
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"c 0.100 0.149\n",
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"Rme (slope) 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)\n",
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"\n",
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"c = ones(T)\n",
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"X = [c Rme]\n",
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"# b1 = X\\Re[:,1]\n",
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"# b2 = X\\Re[:,2]\n",
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"\n",
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"function OlsGMFn(Y,X)\n",
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"\n",
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" T = size(Y,1)\n",
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"\n",
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" b = X\\Y\n",
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" Yhat = X*b\n",
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" u = Y - Yhat\n",
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"\n",
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" σ2 = var(u)\n",
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" cov_b = inv(X'X)*σ2\n",
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" std_b = sqrt.(diag(cov_b))\n",
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" R2 = 1 - σ2/var(Y)\n",
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"\n",
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" return b, std_b, R2\n",
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"\n",
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"end\n",
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"\n",
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"(b1, std_b1) = OlsGMFn(Re[:,1],X)\n",
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"(b2, std_b2) = OlsGMFn(Re[:,2],X)\n",
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"\n",
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"println(\"Small growth:\\n\")\n",
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"printmat([b1 std_b1],colNames=[\"coef\",\"stdErr\"],rowNames=[\"c\", \"Rme (slope)\"])\n",
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"println(\"Large value:\\n\")\n",
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"printmat([b2 std_b2],colNames=[\"coef\",\"stdErr\"],rowNames=[\"c\", \"Rme (slope)\"])"
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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": 15,
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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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{
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"name": "stdout",
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"text": [
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" -0.620 1.414\n",
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"\n",
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" -28.895\n",
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"\n",
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" -40.000\n",
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" -20.000\n",
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" 0.000\n",
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" 20.000\n",
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" 40.000\n",
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"\n",
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" -57.169\n",
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" -28.895\n",
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" -0.620\n",
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" 27.655\n",
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" 55.930\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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"xGrid = range(-40,40, length=5)\n",
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||
"yLine = b1[1] .+ b1[2]*xGrid\n",
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||
"\n",
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"printmat(b1[1], b1[2])\n",
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"printmat(b1[1] + b1[2]*xGrid[2])\n",
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"printmat(xGrid)\n",
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"printmat(yLine)\n",
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||
"\n",
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||
"p1 = scatter( Rme, Re[:,1],\n",
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" fillcolor = :blue,\n",
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" legend = false,\n",
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" xlim = (-60,40),\n",
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" ylim = (-60,40),\n",
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" title = \"Scatter plot: two monthly return series\",\n",
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" titlefont = font(10),\n",
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||
" xlabel = \"Market excess return, %\",\n",
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||
" ylabel = \"Excess returns on small growth stocks, %\",\n",
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" guidefont = font(8))\n",
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"plot!([-40;40],[-40;40],color=:black,linewidth=0.5) #easier to keep this outside plot()\n",
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"plot!(xGrid, yLine ,color=:red,linestyle=:dash) #easier to keep this outside plot()\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": 9,
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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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"yLine = b2[1] .+ b2[2]*xGrid\n",
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"\n",
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"p1 = scatter( Rme,Re[:,2],\n",
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" fillcolor = :blue,\n",
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" legend = false,\n",
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" xlim = (-40,40),\n",
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" ylim = (-40,60),\n",
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" title = \"Scatter plot: two monthly return series\",\n",
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" titlefont = font(10),\n",
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" xlabel = \"Market excess return, %\",\n",
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" ylabel = \"Excess returns on large value stocks, %\",\n",
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" guidefont = font(8) )\n",
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"plot!([-40;60],[-40;60],color=:black,linewidth=0.5) #easier to keep this outside plot()\n",
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"plot!(xGrid, yLine ,color=:red,linestyle=:dash) #easier to keep this outside plot()\n",
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"display(p1)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.7.0-rc1",
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"language": "julia",
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"name": "julia-1.7"
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},
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"language_info": {
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"name": "julia",
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"version": "1.7.0"
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