diff --git a/.gitignore b/.gitignore
index 2170e45..aba41e0 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1,3 @@
/.DS_Store
-/.ipynb_checkpoints
\ No newline at end of file
+/.ipynb_checkpoints
+.DS_Store
\ No newline at end of file
diff --git a/Exam1/Exam1_Solution.ipynb b/Exam1/Exam1_Solution.ipynb
new file mode 100644
index 0000000..5452850
--- /dev/null
+++ b/Exam1/Exam1_Solution.ipynb
@@ -0,0 +1,2405 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "printyellow (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using Printf, Dates, Statistics, DelimitedFiles, StatsBase\n",
+ "\n",
+ "include(\"jlFiles/printmat.jl\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using Plots\n",
+ "\n",
+ "gr(size=(480,320))\n",
+ "default(fmt = :svg)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Load Data \n",
+ "\n",
+ "Returns from FX investments (for a US investor) in percent are in `Data_Returns.csv` (extract the returns into a matrix `R`) and log forward premia in percent are in `Data_Forwardpremia.csv` (extract the forward premia into a matrix `fp`). Convert the first columns to Julia dates.\n",
+ "\n",
+ "Test if the dates in the two files are the same.\n",
+ "\n",
+ "The currency names/abbreviations are\n",
+ "`[\"AUD\",\"CAD\",\"EUR\",\"JPY\",\"NZD\",\"NOK\",\"SEK\",\"CHF\",\"GBP\"]` "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(300, 9)"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "CurrNames = [\"AUD\",\"CAD\",\"EUR\",\"JPY\",\"NZD\",\"NOK\",\"SEK\",\"CHF\",\"GBP\"]\n",
+ "\n",
+ "x = readdlm(\"Data_Returns.csv\",',',skipstart=1) #return data\n",
+ "dN = Date.(x[:,1]) #covert to Julia date, eg. 2001-12-31\n",
+ "R = Float64.(x[:,2:end])\n",
+ "\n",
+ "x = readdlm(\"Data_Forwardpremia.csv\",',',skipstart=2) #forward premia, skip 2 rows\n",
+ "dN2 = Date.(x[:,1]) \n",
+ "fp = Float64.(x[:,2:end])\n",
+ "\n",
+ "(T,n) = size(R) #number of data points, number of currencies"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Same dates? true\n"
+ ]
+ }
+ ],
+ "source": [
+ "println(\"Same dates? \",dN == dN2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Plot the forward premia\n",
+ "\n",
+ "against time. Create a figure with 3x3 subplots. In the plot show the forward premia multiplied by 12 so they can be interpreted as the (annualised) interest rate differential (foreign minus US). \n",
+ "\n",
+ "Make sure to \n",
+ "1. have tick marks on the x-axis at `[Date(2000),Date(2010),Date(2020)]`\n",
+ "\n",
+ "2. limit the y-axis to `(-6,6)`\n",
+ "\n",
+ "3. Put the currency name/abbreviation in the title of each subfigure."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "xTicksLoc = [Date(2000),Date(2010),Date(2020)]\n",
+ "xTicksLab = Dates.format.(xTicksLoc,\"Y\")\n",
+ "\n",
+ "p1 = plot( dN,fp*12,\n",
+ " layout = (3,3),\n",
+ " legend = false,\n",
+ " size = (800,600),\n",
+ " linecolor = :blue,\n",
+ " xticks = (xTicksLoc,xTicksLab),\n",
+ " ylims = (-6,6),\n",
+ " title = reshape(CurrNames,1,:),\n",
+ " titlefont = font(10) )\n",
+ "display(p1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Plot cumulated log returns\n",
+ "\n",
+ "in a 3x3 figure (similar to before). The cumulated log returns for a given currency are $r_1,r_1+r_2,r_1+r_2+r_3,...$ etc where $r_t$ is the log return in period $t$.\n",
+ "\n",
+ "Make sure to\n",
+ "1. use the same tick marks on the x-axis as before\n",
+ "2. limit the y-axis to (-1,1)\n",
+ "\n",
+ "Hints:\n",
+ "1. log returns are $r= \\ln(1+R/100)$ since the returns in `R` are in percent. In Julia, use `log()` for the natural logarithm.\n",
+ "2. cumulate using `cumsum()` or by a loop so you get a $T \\times 9$ matrix."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "r = log.(1.0.+R/100)\n",
+ "P = cumsum(r,dims=1)\n",
+ "\n",
+ "p1 = plot( dN,P,\n",
+ " layout = (3,3),\n",
+ " legend = false,\n",
+ " size = (800,600),\n",
+ " linecolor = :blue,\n",
+ " xticks = (xTicksLoc,xTicksLab),\n",
+ " ylims = (-1,1),\n",
+ " title = reshape(CurrNames,1,:),\n",
+ " titlefont = font(10) )\n",
+ "display(p1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Implement a carry trade strategy\n",
+ "\n",
+ "\n",
+ "1. Find the 4 currencies with the highest forward premia (interest rate differential) in $t-1$ and give each a portfolio weight `w[t,i]=1/4`. These are the investment currencies.\n",
+ "\n",
+ "2. Find the 4 currencies with the lowest forward premia in $t-1$ and give each a portfolio weight `w[t,i]=-1/4`. These are the funding currencies.\n",
+ "\n",
+ "3. The portfolio return in t is `w[t,:]'*R[t,:]`. For all periods that lacks data, set the portfolio return to 0.\n",
+ "\n",
+ "4. Create log returns, cumulate and plot (as above).\n",
+ "\n",
+ "5. In the plot, add a comparison with an equally weighted portfolio (1/9 in each currency). "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "m = 4 #number of long/short positions \n",
+ "\n",
+ "(R_CT,w_CT) = (zeros(T),zeros(T,n))\n",
+ "for t = 2:T #loop over periods, save portfolio returns\n",
+ " #local v,wt #local/global is needed in script\n",
+ " v = sortperm(fp[t-1,:])\n",
+ " w = zeros(n)\n",
+ " w[v[1:m]] .= -1/m #low interest rate currencies\n",
+ " w[v[end-m+1:end]] .= 1/m #high interest rate currencies \n",
+ " R_CT[t] = w'R[t,:]\n",
+ " w_CT[t,:] = w \n",
+ "end\n",
+ "\n",
+ "R_EW = vec(mean(R,dims=2)); #equally weighted portfolio"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "P_CT = cumsum(log.(1.0.+R_CT/100))\n",
+ "P_EW = cumsum(log.(1.0.+R_EW/100));\n",
+ "\n",
+ "p1 = plot( dN,[P_CT P_EW],\n",
+ " label = [\"CT\" \"EW\"],\n",
+ " size = (800,600),\n",
+ " linecolor = [:red :blue],\n",
+ " xticks = (xTicksLoc,xTicksLab),\n",
+ " ylims = (-1,1),\n",
+ " title = \"Comparison of performance\")\n",
+ "display(p1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Report some return statistics\n",
+ "\n",
+ "1. For each of the two portfolio returns, report the average returns, standard deviation and their ratio (the \"Sharpe ratio\").\n",
+ "\n",
+ "2. For each currency, report the frequency of periods that the currency is in the \"high\" carry trade portfolio."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " CT EW\n",
+ "mean 0.283 0.018\n",
+ "std 2.038 2.255\n",
+ "SR 0.139 0.008\n",
+ "\n",
+ "and in case you want annualised numbers...\n",
+ " CT EW\n",
+ "mean 3.401 0.221\n",
+ "std 7.061 7.813\n",
+ "SR 0.482 0.028\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "μ = mean([R_CT R_EW],dims=1)\n",
+ "σ = std([R_CT R_EW],dims=1)\n",
+ "SR = μ./σ\n",
+ "\n",
+ "printmat([μ;σ;SR],colNames=[\"CT\",\"EW\"],rowNames=[\"mean\",\"std\",\"SR\"])\n",
+ "\n",
+ "println(\"and in case you want annualised numbers...\")\n",
+ "(μ_a,σ_a,SR_a) = (μ*12,σ*sqrt(12),SR*sqrt(12))\n",
+ "printmat([μ_a;σ_a;SR_a],colNames=[\"CT\",\"EW\"],rowNames=[\"mean\",\"std\",\"SR\"])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "...and for log returns, in %\n",
+ " CT EW\n",
+ "mean 0.262 -0.007\n",
+ "std 2.046 2.256\n",
+ "SR 0.128 -0.003\n",
+ "\n",
+ "and in case you want annualised numbers...\n",
+ " CT EW\n",
+ "mean 3.147 -0.083\n",
+ "std 7.089 7.816\n",
+ "SR 0.444 -0.011\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "println(\"...and for log returns, in %\")\n",
+ "\n",
+ "μ = mean(log.(1.0.+[R_CT R_EW]/100),dims=1)*100\n",
+ "σ = std(log.(1.0.+[R_CT R_EW]/100),dims=1)*100\n",
+ "SR = μ./σ\n",
+ "\n",
+ "printmat([μ;σ;SR],colNames=[\"CT\",\"EW\"],rowNames=[\"mean\",\"std\",\"SR\"])\n",
+ "\n",
+ "println(\"and in case you want annualised numbers...\")\n",
+ "(μ_a,σ_a,SR_a) = (μ*12,σ*sqrt(12),SR*sqrt(12))\n",
+ "printmat([μ_a;σ_a;SR_a],colNames=[\"CT\",\"EW\"],rowNames=[\"mean\",\"std\",\"SR\"])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "AUD 0.983\n",
+ "CAD 0.467\n",
+ "EUR 0.023\n",
+ "JPY 0.000\n",
+ "NZD 0.957\n",
+ "NOK 0.710\n",
+ "SEK 0.317\n",
+ "CHF 0.000\n",
+ "GBP 0.530\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "FreqInHi = mean(0 .< w_CT,dims=1) #frequence of times the weight is positive\n",
+ "\n",
+ "printmat(vec(FreqInHi),rowNames=CurrNames)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "@webio": {
+ "lastCommId": null,
+ "lastKernelId": null
+ },
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Julia 1.6.3",
+ "language": "julia",
+ "name": "julia-1.6"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.6.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Exam1/Exam2021_1_Feedback.jl b/Exam1/Exam2021_1_Feedback.jl
new file mode 100644
index 0000000..dc318e8
--- /dev/null
+++ b/Exam1/Exam2021_1_Feedback.jl
@@ -0,0 +1,22 @@
+
+using Printf
+include("jlFiles/printmat.jl")
+
+println("Three ways of doing the same thing")
+
+fp = [1 2;
+ 1.1 2.1]
+
+x1 = fp*10 #easiest and fastest
+printmat(x1)
+
+x2 = map(i->fp[:,i]*10,1:2) #cumbersome
+x2 = hcat(x2...)
+printmat(x2)
+
+x3 = zeros(size(fp)) #even more cumbersome
+for i=1:size(fp,1),j=1:size(fp,2)
+ x3[i,j] = fp[i,j]*10
+end
+printmat(x3)
+
diff --git a/Exam2.zip b/Exam2.zip
new file mode 100644
index 0000000..f5a44fc
Binary files /dev/null and b/Exam2.zip differ
diff --git a/Exam2/Exam2.ipynb b/Exam2/Exam2.ipynb
new file mode 100644
index 0000000..3af9ea8
--- /dev/null
+++ b/Exam2/Exam2.ipynb
@@ -0,0 +1,1147 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Load Packages"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 90,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "TaskLocalRNG()"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "using Printf, Statistics, StatsBase, Random, Distributions\n",
+ "include(\"jlFiles/printmat.jl\")\n",
+ "Random.seed!(678) #set the random number generator to this starting point"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 91,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using Plots\n",
+ "\n",
+ "gr(size=(480,320))\n",
+ "default(fmt = :svg)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Introduction\n",
+ "\n",
+ "This exam explores how autocorrelation ought to change how we test statistical hypotheses."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 1\n",
+ "\n",
+ "Code a function for simulating $T$ observations from an AR(1) series\n",
+ "\n",
+ "$\n",
+ "y_t = (1-\\rho)\\mu + \\rho y_{t-1} + \\varepsilon_t \\sigma\n",
+ "$\n",
+ "where $\\varepsilon_t$ is N(0,1).\n",
+ "\n",
+ "That is, generate $y_1,y_2,...,y_T$ from this formula.\n",
+ "\n",
+ "To make also the starting value ($y_0$) random, simulate $T+100$ data points, but then discard the first 100 values of $y_t$.\n",
+ "\n",
+ "Generate a single \"sample\" using `(T,ρ,σ,μ) = (500,0,3,2)`. Calculate and report the average (mean) and the first 5 autocorrelations (hint: `autocor()`) of this sample. Redo a 2nd time, but with `ρ=0.75`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 92,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "SimAR1 (generic function with 1 method)"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "function SimAR1(T,ρ,σ,μ)\n",
+ " y = fill(NaN, T + 100)\n",
+ " e = rand(Normal(0, 1), T + 100)\n",
+ " y[1] = 1\n",
+ " for i = 2:T + 100\n",
+ " y[i] = (1-ρ)μ + ρ*y[i-1] + e[i]*σ\n",
+ " end\n",
+ " return y[101:end]\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 93,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average from one sample with ρ=0 1.986\n",
+ "\n",
+ "autocorrelations with ρ=0\n",
+ "\n",
+ " 1 -0.016\n",
+ " 2 0.027\n",
+ " 3 0.004\n",
+ " 4 0.004\n",
+ " 5 0.008\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "y1 = SimAR1(500,0,3,2)\n",
+ "\n",
+ "printmat(\"average from one sample with ρ=0\", mean(y1))\n",
+ "\n",
+ "printmat(\"autocorrelations with ρ=0\")\n",
+ "printmat(1:5, autocor(y1)[2:6])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 94,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average from one sample with ρ=0.75 3.187\n",
+ "\n",
+ "autocorrelations with ρ=0.75\n",
+ "\n",
+ " 1 0.766\n",
+ " 2 0.580\n",
+ " 3 0.495\n",
+ " 4 0.441\n",
+ " 5 0.372\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "y2 = SimAR1(500,0.75,3,2)\n",
+ "\n",
+ "printmat(\"average from one sample with ρ=0.75\", mean(y2))\n",
+ "\n",
+ "printmat(\"autocorrelations with ρ=0.75\")\n",
+ "printmat(1:5, autocor(y2)[2:6])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 2\n",
+ "\n",
+ "Do a Monte Carlo simulation. Use the parameters `(T,ρ,σ,μ) = (500,0,3,2)`.\n",
+ "\n",
+ "1. Generate a sample with $T$ observations and calculate the average. Repeat $M=10,000$ times and store the estimated averages in a vector of length $M$. (The rest of the question uses the symbol $\\mu_i$ to denote the average from sample $i$.)\n",
+ "\n",
+ "2. What is average $\\mu_i$ across the $M$ estimates? (That is, what is $\\frac{1}{M}\\sum\\nolimits_{i=1}^{M}\\mu_i$?) _Report_ the result.\n",
+ "\n",
+ "3. What is the standard deviation of $\\mu_i$ across the $M$ estimates? Compare with the theoretical standard deviation (see below). _Report_ the result.\n",
+ "\n",
+ "4. Does the distribution of $\\mu_i$ look normal? _Plot_ a histogram and compare with the theoretical pdf (see below).\n",
+ "\n",
+ "\n",
+ "## ...basic stats (the theoretical results)\n",
+ "\n",
+ "says that the sample average of an iid (\"independently and identically distributed\") data series is normally distributed with a mean equal to the true (population) mean $\\mu$ and a standard deviation equal to $s=\\sigma_y/\\sqrt{T}$ where $\\sigma_y$ is the standard deviation of $y$.\n",
+ "\n",
+ "To compare with our simulation results, you could estimate $\\sigma_y$ from a single simulation with very many observations (say 10'000)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 95,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Average across the simulations: 2.001\n",
+ "\n",
+ "Std across the samples (with ρ=0) and in theory:\n",
+ "simulations theory\n",
+ " 0.134 0.133\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "M = 10_000\n",
+ "\n",
+ "(T,ρ1,σ,μ) = (500,0,3,2)\n",
+ "\n",
+ "μi1 = fill(NaN, M)\n",
+ "σi1 = fill(NaN, M)\n",
+ "\n",
+ "# Monte Carlo simulation\n",
+ "for i = 1:M\n",
+ " y = SimAR1(T, ρ1, σ, μ)\n",
+ " μi1[i] = mean(y)\n",
+ " σi1[i] = std(y)\n",
+ "end\n",
+ "\n",
+ "# Theoretical results\n",
+ "y1 = SimAR1(10_000,ρ1,σ,μ)\n",
+ "σy1 = std(y1)\n",
+ "s1 = σy1/sqrt(T)\n",
+ "\n",
+ "printmat(\"Average across the simulations:\", mean(μi1))\n",
+ "println(\"Std across the samples (with ρ=0) and in theory:\")\n",
+ "printmat([\"simulations\", std(μi1)], [\"theory\", s1])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 96,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": "\n\n",
+ "text/html": [
+ "\n",
+ "\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "histogram(μi1,bins=0:0.1:4,normalize=true,legend=false,title=\"Histogram of 10000 averages with ρ=0\")\n",
+ "plot!(μi1->pdf(Normal(μ, s1), μi1))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 3\n",
+ "\n",
+ "Redo task 2, but now use `ρ=0.75` (the other parameters are unchanged)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 97,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Average across the simulations: 1.989\n",
+ "\n",
+ "Std across the samples (with ρ=0.75) and in theory:\n",
+ "simulations theory\n",
+ " 0.534 0.206\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "M = 10_000\n",
+ "\n",
+ "(T,ρ2,σ,μ) = (500,0.75,3,2)\n",
+ "\n",
+ "μi2 = fill(NaN, M)\n",
+ "σi2 = fill(NaN, M)\n",
+ "\n",
+ "# Monte Carlo simulation\n",
+ "for i = 1:M\n",
+ " y = SimAR1(T, ρ2, σ, μ)\n",
+ " μi2[i] = mean(y)\n",
+ " σi2[i] = std(y)\n",
+ "end\n",
+ "\n",
+ "# Theoretical results\n",
+ "y2 = SimAR1(10_000,ρ2,σ,μ)\n",
+ "σy2 = std(y2)\n",
+ "s2 = σy2/sqrt(T)\n",
+ "\n",
+ "printmat(\"Average across the simulations:\", mean(μi2))\n",
+ "println(\"Std across the samples (with ρ=0.75) and in theory:\")\n",
+ "printmat([\"simulations\", std(μi2)], [\"theory\", s2])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 98,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": "\n\n",
+ "text/html": [
+ "\n",
+ "\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "histogram(μi2,bins=0:0.1:4,normalize=true,legend=false,title=\"Histogram of 10000 averages with ρ=0.75\")\n",
+ "plot!(μi2->pdf(Normal(μ, s2), μi2))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 4\n",
+ "\n",
+ "You decide to test the hypothesis that $\\mu=2$. Your decision rule is \n",
+ "\n",
+ "- reject the hypothesis if $|(\\mu_i-2)/s|>1.645$ with $s=\\sigma_y/\\sqrt{T}$\n",
+ "\n",
+ "With this decision rule, you are clearly assuming that the theoretical result (definition of $s$) is correct.\n",
+ "\n",
+ "Estimate both $\\mu_i$ and $\\sigma_y$ from each sample.\n",
+ "\n",
+ "In what fraction of the $M$ simulation do you reject your hypothesis when $\\rho=0$ and when $\\rho=0.75$? For the other parameters, use `(T,σ,μ) = (500,3,2)` (same as before)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 99,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Frequency of rejections:\n",
+ " with ρ=0 with ρ=0.75 \n",
+ " 0.098 0.536\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "(T,σ,μ) = (500,3,2)\n",
+ "\n",
+ "rejection1 = 0\n",
+ "rejection2 = 0\n",
+ "\n",
+ "# Count how many times we reject the hypothesis\n",
+ "for i = 1:M\n",
+ " # rejections for ρ = 0\n",
+ " s1 = σi1[i]/sqrt(T)\n",
+ " if abs((μi1[i] - 2)/s1) > 1.645\n",
+ " rejection1 += 1\n",
+ " end\n",
+ "\n",
+ " # rejections for ρ = 0.75\n",
+ " s2 = σi2[i]/sqrt(T)\n",
+ " if abs((μi2[i] - 2)/s2) > 1.645\n",
+ " rejection2 += 1\n",
+ " end\n",
+ "end\n",
+ "\n",
+ "println(\"Frequency of rejections:\")\n",
+ "printmat([\"with ρ=0 \", rejection1 / (M)], [\"with ρ=0.75 \", rejection2 / (M)])"
+ ]
+ }
+ ],
+ "metadata": {
+ "@webio": {
+ "lastCommId": null,
+ "lastKernelId": null
+ },
+ "kernelspec": {
+ "display_name": "Julia 1.7.1",
+ "language": "julia",
+ "name": "julia-1.7"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Exam2/Exam2_FakeResults.pdf b/Exam2/Exam2_FakeResults.pdf
new file mode 100644
index 0000000..96e0e2d
Binary files /dev/null and b/Exam2/Exam2_FakeResults.pdf differ
diff --git a/Exam2/jlFiles/printmat.jl b/Exam2/jlFiles/printmat.jl
new file mode 100644
index 0000000..18df2ba
--- /dev/null
+++ b/Exam2/jlFiles/printmat.jl
@@ -0,0 +1,246 @@
+#------------------------------------------------------------------------------
+"""
+ printmat([fh::IO],x...;colNames=[],rowNames=[],
+ width=10,prec=3,NoPrinting=false,StringFmt="",cell00="")
+
+Print all elements of a matrix (or several) with predefined formatting. It can also handle
+OffsetArrays. StringFmt = "csv" prints using a csv format.
+
+# Input
+- `fh::IO`: (optional) file handle. If not supplied, prints to screen
+- `x::Array(s)`: (of numbers, dates, strings, ...) to print
+- `colNames::Array`: of strings with column headers
+- `rowNames::Array`: of strings with row labels
+- `width::Int`: (keyword) scalar, minimum width of printed cells
+- `prec::Int`: (keyword) scalar, precision of printed cells
+- `NoPrinting::Bool`: (keyword) bool, true: no printing, just return formatted string [false]
+- `StringFmt::String`: (keyword) string, "", "csv"
+- `cell00::String`: (keyword) string, for row 0, column 0
+
+# Output
+- str (if NoPrinting) string, (otherwise nothing)
+
+# Examples
+```
+x = [11 12;21 22]
+printmat(x)
+```
+```
+x = [1 "ab"; Date(2018,10,7) 3.14]
+printmat(x,width=20,colNames=["col 1","col 2"])
+```
+```
+printmat([11,12],[21,22])
+```
+Can also call as
+```
+opt = Dict(:rowNames=>["1";"4"],:width=>10,:prec=>3,:NoPrinting=>false,:StringFmt=>"")
+printmat(x;colNames=["a","b"],opt...) #notice ; and ...
+```
+(not all keywords are needed)
+
+# Requires
+- fmtNumPs
+
+# Notice
+- The prefixN and suffixN could potentially be made function inputs. This would allow
+a fairly flexible way to format tables.
+
+
+Paul.Soderlind@unisg.ch
+
+"""
+function printmat(fh::IO,x...;colNames=[],rowNames=[],
+ width=10,prec=3,NoPrinting=false,StringFmt="",cell00="")
+
+ isempty(x) && return nothing #do nothing is isempty(x)
+
+ typeTestQ = any(!=(eltype(x[1])),[eltype(z) for z in x]) #test if eltype(x[i]) differs
+ if typeTestQ #create matrix from tuple created by x...
+ x = hcat(Matrix{Any}(hcat(x[1])),x[2:end]...) #preserving types of x[i]
+ else
+ x = hcat(x...)
+ end
+
+ (m,n) = (size(x,1),size(x,2))
+
+ (length(rowNames) == 1 < m) && (rowNames = [string(rowNames[1],i) for i = 1:m]) #"ri"
+ (length(colNames) == 1 < n) && (colNames = [string(colNames[1],i) for i = 1:n]) #"ci"
+
+ if StringFmt == "csv"
+ (prefixN,suffixN) = (fill("",n),vcat(fill(",",n-1),"")) #prefix and suffix for column 1:n
+ (prefixC0,suffixC0) = ("",",") #prefix and suffix for column 0
+ else
+ (prefixN,suffixN) = (fill("",n),fill("",n))
+ (prefixC0,suffixC0) = ("","")
+ end
+
+ if length(rowNames) == 0 #width of column 0 (cell00 and rowNames)
+ col0Width = 0
+ else
+ col0Width = maximum(length,vcat(cell00,rowNames)) + length(prefixC0) + length(suffixC0)
+ end
+
+ colWidth = [width + length(prefixN[j]) + length(suffixN[j]) for j=1:n] #widths of column 1:n
+
+ iob = IOBuffer()
+
+ if !isempty(colNames) #print (cell00,colNames), if any
+ !isempty(cell00) ? txt0 = string(prefixC0,cell00,suffixC0) : txt0 = ""
+ print(iob,rpad(txt0,col0Width))
+ for j = 1:n #loop over columns
+ print(iob,lpad(string(prefixN[j],colNames[j],suffixN[j]),colWidth[j]))
+ end
+ print(iob,"\n")
+ end
+ #print rowNames and x
+ (i0,j0) = (1 - first(axes(x,1)),1 - first(axes(x,2))) #i+i0,j+j0 give traditional indices
+ for i in axes(x,1) #loop over rows
+ !isempty(rowNames) && print(iob,rpad(string(prefixC0,rowNames[i+i0],suffixC0),col0Width))
+ for j in axes(x,2) #loop over columns
+ print(iob,fmtNumPs(x[i,j],width,prec,"right",prefix=prefixN[j+j0],suffix=suffixN[j+j0]))
+ end
+ print(iob,"\n")
+ end
+ str = String(take!(iob))
+
+ if NoPrinting #no printing, just return str
+ return str
+ else #print, return nothing
+ print(fh,str,"\n")
+ return nothing
+ end
+
+end
+ #when fh is not supplied: printing to screen
+printmat(x...;colNames=[],rowNames=[],width=10,prec=3,NoPrinting=false,StringFmt="",cell00="") =
+ printmat(stdout::IO,x...;colNames,rowNames,width,prec,NoPrinting,StringFmt,cell00)
+#------------------------------------------------------------------------------
+
+
+#------------------------------------------------------------------------------
+"""
+ printlnPs([fh::IO],z...;width=10,prec=3)
+
+Subsitute for println, with predefined formatting.
+
+
+# Input
+- `fh::IO`: (optional) file handle. If not supplied, prints to screen
+- `z::String`: string, numbers and arrays to print
+
+Paul.Soderlind@unisg.ch
+
+"""
+function printlnPs(fh::IO,z...;width=10,prec=3)
+
+ for x in z #loop over inputs in z...
+ if isa(x,AbstractArray)
+ iob = IOBuffer()
+ for i = 1:length(x)
+ print(iob,fmtNumPs(x[i],width,prec,"right"))
+ end
+ print(fh,String(take!(iob)))
+ else
+ print(fh,fmtNumPs(x,width,prec,"right"))
+ end
+ end
+
+ print(fh,"\n")
+
+end
+ #when fh is not supplied: printing to screen
+printlnPs(z...;width=10,prec=3) = printlnPs(stdout::IO,z...;width,prec)
+#------------------------------------------------------------------------------
+
+
+#------------------------------------------------------------------------------
+"""
+ fmtNumPs(z,width=10,prec=2,justify="right";prefix="",suffix="")
+
+Create a formatted string of a float (eg, "%10.4f"), nothing (""),
+while other values are passed through. Strings are right (or left) justified
+and can optionally be given prefix and suffix (eg, ",")
+
+# Notice
+- With prec > 0 and isa(z,Integer), then the string is padded with 1+prec spaces
+to align with the printing of floats with the same prec.
+
+# Requires
+- Printf (for 1.6-), fmtNumPsC (for < 1.6)
+
+"""
+function fmtNumPs(z,width=10,prec=2,justify="right";prefix="",suffix="")
+
+ isa(z,Bool) && (z = convert(Int,z)) #Bool -> Int
+
+ if isa(z,AbstractFloat) #example: 101.0234, prec=3
+ if VERSION < v"1.6-"
+ fmt = "%$(width).$(prec)f"
+ zRound = round(z,digits=prec)
+ strLR = fmtNumPsC(fmt,zRound) #C fallback solution
+ else
+ fmt = Printf.Format("%$(width).$(prec)f")
+ strLR = Printf.format(fmt,z)
+ end
+ elseif isa(z,Nothing)
+ strLR = ""
+ elseif isa(z,Integer) && prec > 0 #integer followed by (1+prec spaces)
+ strLR = string(z," "^(1+prec))
+ else #Int, String, Date, Missing, etc
+ strLR = string(z)
+ end
+
+ strLR = string(prefix,strLR,suffix)
+
+ if justify == "left" #justification
+ strLR = rpad(strLR,width+length(prefix)+length(suffix))
+ else
+ strLR = lpad(strLR,width+length(prefix)+length(suffix))
+ end
+
+ return strLR
+
+end
+#------------------------------------------------------------------------------
+
+
+#------------------------------------------------------------------------------
+"""
+ fmtNumPsC(fmt,z)
+
+c fallback solution for formatting of floating point number. Used if VERSION < v"1.6-"
+"""
+function fmtNumPsC(fmt,z) #c fallback solution
+ if ismissing(z) || isnan(z) || isinf(z) #asprintf does not work for these cases
+ str = string(z)
+ else
+ strp = Ref{Ptr{Cchar}}(0)
+ len = ccall(:asprintf,Cint,(Ptr{Ptr{Cchar}},Cstring,Cdouble...),strp,fmt,z)
+ str = unsafe_string(strp[],len)
+ Libc.free(strp[])
+ end
+ return str
+end
+#------------------------------------------------------------------------------
+
+
+#------------------------------------------------------------------------------
+function printblue(x...)
+ foreach(z->printstyled(z,color=:blue,bold=true),x)
+ print("\n")
+end
+function printred(x...)
+ foreach(z->printstyled(z,color=:red,bold=true),x)
+ print("\n")
+end
+function printmagenta(x...)
+ foreach(z->printstyled(z,color=:magenta,bold=true),x)
+ print("\n")
+end
+function printyellow(x...)
+ foreach(z->printstyled(z,color=:yellow,bold=true),x)
+ print("\n")
+end
+#------------------------------------------------------------------------------
+
diff --git a/Problemsets/.DS_Store b/Problemsets/.DS_Store
index 5008ddf..ab50143 100644
Binary files a/Problemsets/.DS_Store and b/Problemsets/.DS_Store differ
diff --git a/Problemsets/Data/FFmFactorsPs.csv b/Problemsets/Data/FFmFactorsPs.csv
new file mode 100644
index 0000000..3a663da
--- /dev/null
+++ b/Problemsets/Data/FFmFactorsPs.csv
@@ -0,0 +1,389 @@
+date,Mkt-RF,SMB,HML,RF,Mom,ST_Rev,LT_Rev
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diff --git a/Problemsets/Data/Options_prices_US_Canada.csv b/Problemsets/Data/Options_prices_US_Canada.csv
new file mode 100644
index 0000000..ac4ff9a
--- /dev/null
+++ b/Problemsets/Data/Options_prices_US_Canada.csv
@@ -0,0 +1,13953 @@
+symbol,exchange,date,adjusted close,option symbol,expiration,strike,call/put,style,ask,bid,volume,open interest,unadjusted
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+XEG,TSX,03/30/17,12.69,XEG 170407P00011500,04/07/17,11.5,P,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407C00012000,04/07/17,12,C,A,0.73,0.67,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407P00012000,04/07/17,12,P,A,0.05,0,0,32,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407C00012500,04/07/17,12.5,C,A,0.28,0.25,0,32,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407P00012500,04/07/17,12.5,P,A,0.09,0.05,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407C00013000,04/07/17,13,C,A,0.07,0.01,0,10,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407P00013000,04/07/17,13,P,A,0.38,0.32,0,30,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407C00013500,04/07/17,13.5,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407P00013500,04/07/17,13.5,P,A,0.84,0.79,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407C00014000,04/07/17,14,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407P00014000,04/07/17,14,P,A,1.34,1.28,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407C00014500,04/07/17,14.5,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407P00014500,04/07/17,14.5,P,A,1.84,1.78,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407C00015000,04/07/17,15,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170407P00015000,04/07/17,15,P,A,2.34,2.28,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413C00010500,04/13/17,10.5,C,A,2.22,2.17,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413P00010500,04/13/17,10.5,P,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413C00011000,04/13/17,11,C,A,1.72,1.67,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413P00011000,04/13/17,11,P,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413C00011500,04/13/17,11.5,C,A,1.22,1.17,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413P00011500,04/13/17,11.5,P,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413C00012000,04/13/17,12,C,A,0.74,0.69,0,10,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413P00012000,04/13/17,12,P,A,0.07,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413C00012500,04/13/17,12.5,C,A,0.32,0.27,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413P00012500,04/13/17,12.5,P,A,0.13,0.09,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413C00013000,04/13/17,13,C,A,0.08,0.04,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413P00013000,04/13/17,13,P,A,0.4,0.36,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413C00013500,04/13/17,13.5,C,A,0.06,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413P00013500,04/13/17,13.5,P,A,0.85,0.79,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413C00014000,04/13/17,14,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413P00014000,04/13/17,14,P,A,1.34,1.29,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413C00014500,04/13/17,14.5,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413P00014500,04/13/17,14.5,P,A,1.84,1.78,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413C00015000,04/13/17,15,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170413P00015000,04/13/17,15,P,A,2.34,2.28,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00010000,04/21/17,10,C,A,2.72,2.67,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00010000,04/21/17,10,P,A,0.03,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00011000,04/21/17,11,C,A,1.72,1.67,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00011000,04/21/17,11,P,A,0.04,0,0,77,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00011250,04/21/17,11.25,C,A,1.47,1.42,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00011250,04/21/17,11.25,P,A,0.04,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00011500,04/21/17,11.5,C,A,1.23,1.17,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00011500,04/21/17,11.5,P,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00011750,04/21/17,11.75,C,A,0.99,0.94,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00011750,04/21/17,11.75,P,A,0.06,0.01,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00012000,04/21/17,12,C,A,0.76,0.72,0,20,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00012000,04/21/17,12,P,A,0.07,0.03,0,100369,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00012250,04/21/17,12.25,C,A,0.55,0.5,0,30,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00012250,04/21/17,12.25,P,A,0.11,0.07,0,201,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00012500,04/21/17,12.5,C,A,0.36,0.32,120,156,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00012500,04/21/17,12.5,P,A,0.17,0.14,0,144,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00012750,04/21/17,12.75,C,A,0.21,0.18,0,84,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00012750,04/21/17,12.75,P,A,0.28,0.24,0,10,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00013000,04/21/17,13,C,A,0.12,0.08,0,756,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00013000,04/21/17,13,P,A,0.43,0.39,0,57,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00013250,04/21/17,13.25,C,A,0.07,0.03,0,324,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00013250,04/21/17,13.25,P,A,0.64,0.59,0,20,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00013500,04/21/17,13.5,C,A,0.06,0.01,0,11000,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00013500,04/21/17,13.5,P,A,0.85,0.8,0,10,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00013750,04/21/17,13.75,C,A,0.04,0,0,20,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00013750,04/21/17,13.75,P,A,1.09,1.05,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00014000,04/21/17,14,C,A,0.04,0,0,152,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00014000,04/21/17,14,P,A,1.35,1.29,0,242,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00014250,04/21/17,14.25,C,A,0.03,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00014250,04/21/17,14.25,P,A,1.6,1.54,0,100,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00014500,04/21/17,14.5,C,A,0.03,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00014500,04/21/17,14.5,P,A,1.84,1.79,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00014750,04/21/17,14.75,C,A,0.03,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00014750,04/21/17,14.75,P,A,2.09,2.04,0,50,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00015000,04/21/17,15,C,A,0.03,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00015000,04/21/17,15,P,A,2.34,2.29,0,50,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00015250,04/21/17,15.25,C,A,0.03,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00015250,04/21/17,15.25,P,A,2.59,2.54,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00015500,04/21/17,15.5,C,A,0.03,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00015500,04/21/17,15.5,P,A,2.84,2.79,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00015750,04/21/17,15.75,C,A,0.03,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00015750,04/21/17,15.75,P,A,3.09,3.04,0,50,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421C00016000,04/21/17,16,C,A,0.03,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170421P00016000,04/21/17,16,P,A,3.34,3.29,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428C00011000,04/28/17,11,C,A,1.73,1.68,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428P00011000,04/28/17,11,P,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428C00011500,04/28/17,11.5,C,A,1.24,1.19,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428P00011500,04/28/17,11.5,P,A,0.06,0.01,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428C00012000,04/28/17,12,C,A,0.78,0.74,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428P00012000,04/28/17,12,P,A,0.1,0.05,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428C00012500,04/28/17,12.5,C,A,0.4,0.36,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428P00012500,04/28/17,12.5,P,A,0.21,0.17,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428C00013000,04/28/17,13,C,A,0.15,0.11,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428P00013000,04/28/17,13,P,A,0.48,0.42,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428C00013500,04/28/17,13.5,C,A,0.07,0.02,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428P00013500,04/28/17,13.5,P,A,0.87,0.83,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428C00014000,04/28/17,14,C,A,0.06,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428P00014000,04/28/17,14,P,A,1.35,1.3,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428C00014500,04/28/17,14.5,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428P00014500,04/28/17,14.5,P,A,1.86,1.79,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428C00015000,04/28/17,15,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170428P00015000,04/28/17,15,P,A,2.35,2.29,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00010000,05/19/17,10,C,A,2.73,2.67,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00010000,05/19/17,10,P,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00011000,05/19/17,11,C,A,1.74,1.68,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00011000,05/19/17,11,P,A,0.07,0.02,0,29,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00011250,05/19/17,11.25,C,A,1.5,1.46,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00011250,05/19/17,11.25,P,A,0.08,0.03,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00011500,05/19/17,11.5,C,A,1.27,1.22,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00011500,05/19/17,11.5,P,A,0.1,0.05,0,20,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00011750,05/19/17,11.75,C,A,1.05,1.01,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00011750,05/19/17,11.75,P,A,0.12,0.08,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00012000,05/19/17,12,C,A,0.85,0.8,0,53,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00012000,05/19/17,12,P,A,0.16,0.12,0,535,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00012250,05/19/17,12.25,C,A,0.66,0.61,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00012250,05/19/17,12.25,P,A,0.22,0.19,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00012500,05/19/17,12.5,C,A,0.49,0.45,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00012500,05/19/17,12.5,P,A,0.3,0.27,0,31,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00012750,05/19/17,12.75,C,A,0.34,0.3,51,51,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00012750,05/19/17,12.75,P,A,0.41,0.37,0,31,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00013000,05/19/17,13,C,A,0.22,0.18,10,481,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00013000,05/19/17,13,P,A,0.54,0.51,20,81,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00013250,05/19/17,13.25,C,A,0.15,0.11,0,31,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00013250,05/19/17,13.25,P,A,0.72,0.68,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00013500,05/19/17,13.5,C,A,0.1,0.07,0,81,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00013500,05/19/17,13.5,P,A,0.92,0.87,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00013750,05/19/17,13.75,C,A,0.07,0.04,0,31,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00013750,05/19/17,13.75,P,A,1.14,1.09,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00014000,05/19/17,14,C,A,0.07,0.01,0,28,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00014000,05/19/17,14,P,A,1.37,1.32,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00014250,05/19/17,14.25,C,A,0.06,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00014250,05/19/17,14.25,P,A,1.61,1.56,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00014500,05/19/17,14.5,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00014500,05/19/17,14.5,P,A,1.85,1.8,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00014750,05/19/17,14.75,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00014750,05/19/17,14.75,P,A,2.1,2.04,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00015000,05/19/17,15,C,A,0.04,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00015000,05/19/17,15,P,A,2.35,2.3,0,3,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00015250,05/19/17,15.25,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00015250,05/19/17,15.25,P,A,2.6,2.55,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00015500,05/19/17,15.5,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00015500,05/19/17,15.5,P,A,2.85,2.79,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519C00015750,05/19/17,15.75,C,A,0.05,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170519P00015750,05/19/17,15.75,P,A,3.1,3.05,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616C00010000,06/17/17,10,C,A,2.74,2.68,0,49,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616P00010000,06/17/17,10,P,A,0.06,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616C00011000,06/17/17,11,C,A,1.79,1.72,0,7,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616P00011000,06/17/17,11,P,A,0.1,0.05,0,30,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616C00012000,06/17/17,12,C,A,0.93,0.87,10,193,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616P00012000,06/17/17,12,P,A,0.24,0.19,0,3102,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616C00013000,06/17/17,13,C,A,0.33,0.29,0,394,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616P00013000,06/17/17,13,P,A,0.66,0.6,135,1682,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616C00014000,06/17/17,14,C,A,0.1,0.05,0,81,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616P00014000,06/17/17,14,P,A,1.43,1.36,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616C00015000,06/17/17,15,C,A,0.04,0,0,5,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616P00015000,06/17/17,15,P,A,2.38,2.3,0,20,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616C00016000,06/17/17,16,C,A,0.04,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616P00016000,06/17/17,16,P,A,3.35,3.29,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616C00017000,06/17/17,17,C,A,0.04,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170616P00017000,06/17/17,17,P,A,4.36,4.29,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915C00010000,09/16/17,10,C,A,2.79,2.7,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915P00010000,09/16/17,10,P,A,0.13,0.06,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915C00011000,09/16/17,11,C,A,1.91,1.8,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915P00011000,09/16/17,11,P,A,0.25,0.16,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915C00012000,09/16/17,12,C,A,1.16,1.06,0,50,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915P00012000,09/16/17,12,P,A,0.5,0.43,0,230,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915C00013000,09/16/17,13,C,A,0.62,0.52,0,281,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915P00013000,09/16/17,13,P,A,0.97,0.89,0,364,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915C00014000,09/16/17,14,C,A,0.3,0.21,0,194,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915P00014000,09/16/17,14,P,A,1.69,1.56,0,320,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915C00015000,09/16/17,15,C,A,0.16,0.07,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915P00015000,09/16/17,15,P,A,2.53,2.4,0,50,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915C00016000,09/16/17,16,C,A,0.09,0.02,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915P00016000,09/16/17,16,P,A,3.45,3.35,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915C00017000,09/16/17,17,C,A,0.07,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 170915P00017000,09/16/17,17,P,A,4.42,4.33,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215C00010000,12/16/17,10,C,A,2.86,2.74,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215P00010000,12/16/17,10,P,A,0.2,0.1,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215C00011000,12/16/17,11,C,A,2.04,1.9,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215P00011000,12/16/17,11,P,A,0.38,0.26,0,40,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215C00012000,12/16/17,12,C,A,1.34,1.21,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215P00012000,12/16/17,12,P,A,0.69,0.57,0,90,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215C00013000,12/16/17,13,C,A,0.81,0.69,20,8,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215P00013000,12/16/17,13,P,A,1.17,1.05,90,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215C00014000,12/16/17,14,C,A,0.48,0.35,0,5,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215P00014000,12/16/17,14,P,A,1.86,1.68,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215C00015000,12/16/17,15,C,A,0.26,0.17,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 171215P00015000,12/16/17,15,P,A,2.65,2.49,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316C00005000,03/16/18,5,C,A,7.74,7.65,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316P00005000,03/16/18,5,P,A,0.09,0,0,25,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316C00006000,03/16/18,6,C,A,6.74,6.64,0,1,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316P00006000,03/16/18,6,P,A,0.09,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316C00007000,03/16/18,7,C,A,5.74,5.64,0,40,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316P00007000,03/16/18,7,P,A,0.09,0,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316C00008000,03/16/18,8,C,A,4.74,4.66,0,48,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316P00008000,03/16/18,8,P,A,0.12,0.03,0,66,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316C00009000,03/16/18,9,C,A,3.81,3.68,0,221,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316P00009000,03/16/18,9,P,A,0.17,0.07,0,65,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316C00010000,03/16/18,10,C,A,2.92,2.77,0,162,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316P00010000,03/16/18,10,P,A,0.28,0.18,0,4,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316C00011000,03/16/18,11,C,A,2.15,2,0,196,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316P00011000,03/16/18,11,P,A,0.49,0.39,0,1205,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316C00012000,03/16/18,12,C,A,1.44,1.33,0,12704,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316P00012000,03/16/18,12,P,A,0.84,0.75,25,627,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316C00013000,03/16/18,13,C,A,0.94,0.82,0,1095,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316P00013000,03/16/18,13,P,A,1.34,1.24,0,225,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316C00014000,03/16/18,14,C,A,0.59,0.48,0,251,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316P00014000,03/16/18,14,P,A,2,1.88,0,320,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316C00015000,03/16/18,15,C,A,0.34,0.26,0,526,12.69
+XEG,TSX,03/30/17,12.69,XEG 180316P00015000,03/16/18,15,P,A,2.78,2.62,0,240,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315C00009000,03/15/19,9,C,A,4.05,3.78,0,35,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315P00009000,03/15/19,9,P,A,0.4,0.26,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315C00010000,03/15/19,10,C,A,3.27,3.02,0,0,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315P00010000,03/15/19,10,P,A,0.64,0.43,0,30,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315C00011000,03/15/19,11,C,A,2.61,2.4,0,7,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315P00011000,03/15/19,11,P,A,0.92,0.74,0,3274,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315C00012000,03/15/19,12,C,A,1.88,1.79,0,3068,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315P00012000,03/15/19,12,P,A,1.29,1.07,0,139,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315C00013000,03/15/19,13,C,A,1.37,1.22,0,99,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315P00013000,03/15/19,13,P,A,1.84,1.61,20,20,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315C00014000,03/15/19,14,C,A,1.1,0.89,0,24,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315P00014000,03/15/19,14,P,A,2.46,2.19,0,2,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315C00015000,03/15/19,15,C,A,0.81,0.57,0,55,12.69
+XEG,TSX,03/30/17,12.69,XEG 190315P00015000,03/15/19,15,P,A,3.18,2.9,0,14,12.69
+XIU,TSX,03/30/17,23.06,XIU 170331C00020500,03/31/17,20.5,C,A,2.58,2.54,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331P00020500,03/31/17,20.5,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331C00021000,03/31/17,21,C,A,2.08,2.04,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331P00021000,03/31/17,21,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331C00021500,03/31/17,21.5,C,A,1.58,1.54,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331P00021500,03/31/17,21.5,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331C00022000,03/31/17,22,C,A,1.08,1.04,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331P00022000,03/31/17,22,P,A,0.05,0,0,50,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331C00022500,03/31/17,22.5,C,A,0.59,0.55,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331P00022500,03/31/17,22.5,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331C00023000,03/31/17,23,C,A,0.11,0.06,6,122,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331P00023000,03/31/17,23,P,A,0.06,0.01,0,99,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331C00023500,03/31/17,23.5,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331P00023500,03/31/17,23.5,P,A,0.46,0.43,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331C00024000,03/31/17,24,C,A,0.09,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331P00024000,03/31/17,24,P,A,0.96,0.93,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331C00024500,03/31/17,24.5,C,A,0.09,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331P00024500,03/31/17,24.5,P,A,1.46,1.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331C00025000,03/31/17,25,C,A,0.09,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170331P00025000,03/31/17,25,P,A,1.96,1.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407C00020500,04/07/17,20.5,C,A,2.59,2.56,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407P00020500,04/07/17,20.5,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407C00021000,04/07/17,21,C,A,2.09,2.06,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407P00021000,04/07/17,21,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407C00021500,04/07/17,21.5,C,A,1.59,1.56,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407P00021500,04/07/17,21.5,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407C00022000,04/07/17,22,C,A,1.09,1.06,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407P00022000,04/07/17,22,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407C00022500,04/07/17,22.5,C,A,0.6,0.57,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407P00022500,04/07/17,22.5,P,A,0.05,0,0,200,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407C00023000,04/07/17,23,C,A,0.17,0.15,0,56,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407P00023000,04/07/17,23,P,A,0.11,0.08,0,199,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407C00023500,04/07/17,23.5,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407P00023500,04/07/17,23.5,P,A,0.46,0.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407C00024000,04/07/17,24,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407P00024000,04/07/17,24,P,A,0.96,0.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407C00024500,04/07/17,24.5,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407P00024500,04/07/17,24.5,P,A,1.46,1.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407C00025000,04/07/17,25,C,A,0.09,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170407P00025000,04/07/17,25,P,A,1.96,1.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413C00020500,04/13/17,20.5,C,A,2.59,2.56,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413P00020500,04/13/17,20.5,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413C00021000,04/13/17,21,C,A,2.09,2.06,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413P00021000,04/13/17,21,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413C00021500,04/13/17,21.5,C,A,1.6,1.56,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413P00021500,04/13/17,21.5,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413C00022000,04/13/17,22,C,A,1.11,1.06,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413P00022000,04/13/17,22,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413C00022500,04/13/17,22.5,C,A,0.62,0.59,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413P00022500,04/13/17,22.5,P,A,0.06,0.02,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413C00023000,04/13/17,23,C,A,0.22,0.19,54,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413P00023000,04/13/17,23,P,A,0.15,0.12,0,64,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413C00023500,04/13/17,23.5,C,A,0.05,0.01,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413P00023500,04/13/17,23.5,P,A,0.46,0.44,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413C00024000,04/13/17,24,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413P00024000,04/13/17,24,P,A,0.96,0.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413C00024500,04/13/17,24.5,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413P00024500,04/13/17,24.5,P,A,1.46,1.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413C00025000,04/13/17,25,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170413P00025000,04/13/17,25,P,A,1.96,1.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00017000,04/21/17,17,C,A,6.09,6.06,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00017000,04/21/17,17,P,A,0.03,0,0,8264,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00018000,04/21/17,18,C,A,5.09,5.06,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00018000,04/21/17,18,P,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00018500,04/21/17,18.5,C,A,4.59,4.56,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00018500,04/21/17,18.5,P,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00019000,04/21/17,19,C,A,4.09,4.06,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00019000,04/21/17,19,P,A,0.03,0,0,5509,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00019500,04/21/17,19.5,C,A,3.59,3.56,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00019500,04/21/17,19.5,P,A,0.04,0,0,20,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00020000,04/21/17,20,C,A,3.1,3.06,0,35,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00020000,04/21/17,20,P,A,0.04,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00020500,04/21/17,20.5,C,A,2.6,2.57,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00020500,04/21/17,20.5,P,A,0.04,0,0,24,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00021000,04/21/17,21,C,A,2.1,2.07,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00021000,04/21/17,21,P,A,0.04,0,0,141,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00021250,04/21/17,21.25,C,A,1.85,1.82,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00021250,04/21/17,21.25,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00021500,04/21/17,21.5,C,A,1.6,1.57,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00021500,04/21/17,21.5,P,A,0.05,0.01,0,670,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00021750,04/21/17,21.75,C,A,1.36,1.33,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00021750,04/21/17,21.75,P,A,0.06,0.01,0,745,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00022000,04/21/17,22,C,A,1.12,1.09,10,70,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00022000,04/21/17,22,P,A,0.05,0.02,5000,9634,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00022250,04/21/17,22.25,C,A,0.88,0.85,0,634,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00022250,04/21/17,22.25,P,A,0.06,0.03,0,160205,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00022500,04/21/17,22.5,C,A,0.65,0.62,0,327,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00022500,04/21/17,22.5,P,A,0.08,0.05,50,4912,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00022750,04/21/17,22.75,C,A,0.44,0.4,0,981,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00022750,04/21/17,22.75,P,A,0.12,0.09,4000,50938,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00023000,04/21/17,23,C,A,0.26,0.23,0,1981,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00023000,04/21/17,23,P,A,0.19,0.16,430,217027,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00023250,04/21/17,23.25,C,A,0.13,0.1,430,5422,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00023250,04/21/17,23.25,P,A,0.3,0.28,140,663,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00023500,04/21/17,23.5,C,A,0.06,0.03,0,22940,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00023500,04/21/17,23.5,P,A,0.48,0.45,25,3097,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00023750,04/21/17,23.75,C,A,0.04,0,0,1397,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00023750,04/21/17,23.75,P,A,0.71,0.68,0,45,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00024000,04/21/17,24,C,A,0.03,0,0,3850,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00024000,04/21/17,24,P,A,0.96,0.93,0,1571,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00024250,04/21/17,24.25,C,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00024250,04/21/17,24.25,P,A,1.21,1.18,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00024500,04/21/17,24.5,C,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00024500,04/21/17,24.5,P,A,1.46,1.43,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00024750,04/21/17,24.75,C,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00024750,04/21/17,24.75,P,A,1.71,1.68,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00025000,04/21/17,25,C,A,0.03,0,0,50,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00025000,04/21/17,25,P,A,1.96,1.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00025250,04/21/17,25.25,C,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00025250,04/21/17,25.25,P,A,2.21,2.18,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00025500,04/21/17,25.5,C,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00025500,04/21/17,25.5,P,A,2.46,2.43,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00025750,04/21/17,25.75,C,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00025750,04/21/17,25.75,P,A,2.71,2.68,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00026000,04/21/17,26,C,A,0.04,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00026000,04/21/17,26,P,A,2.96,2.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00026500,04/21/17,26.5,C,A,0.04,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00026500,04/21/17,26.5,P,A,3.46,3.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00027000,04/21/17,27,C,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00027000,04/21/17,27,P,A,3.96,3.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00027500,04/21/17,27.5,C,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00027500,04/21/17,27.5,P,A,4.46,4.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00028000,04/21/17,28,C,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00028000,04/21/17,28,P,A,4.96,4.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421C00029000,04/21/17,29,C,A,0.03,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170421P00029000,04/21/17,29,P,A,5.96,5.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428C00021000,04/28/17,21,C,A,2.11,2.08,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428P00021000,04/28/17,21,P,A,0.05,0.01,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428C00021500,04/28/17,21.5,C,A,1.62,1.59,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428P00021500,04/28/17,21.5,P,A,0.06,0.02,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428C00022000,04/28/17,22,C,A,1.14,1.11,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428P00022000,04/28/17,22,P,A,0.06,0.03,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428C00022500,04/28/17,22.5,C,A,0.68,0.65,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428P00022500,04/28/17,22.5,P,A,0.11,0.08,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428C00023000,04/28/17,23,C,A,0.3,0.27,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428P00023000,04/28/17,23,P,A,0.23,0.2,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428C00023500,04/28/17,23.5,C,A,0.08,0.05,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428P00023500,04/28/17,23.5,P,A,0.51,0.47,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428C00024000,04/28/17,24,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428P00024000,04/28/17,24,P,A,0.96,0.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428C00024500,04/28/17,24.5,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428P00024500,04/28/17,24.5,P,A,1.46,1.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428C00025000,04/28/17,25,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170428P00025000,04/28/17,25,P,A,1.96,1.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00017000,05/19/17,17,C,A,6.1,6.05,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00017000,05/19/17,17,P,A,0.05,0,0,8194,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00018000,05/19/17,18,C,A,5.11,5.06,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00018000,05/19/17,18,P,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00018500,05/19/17,18.5,C,A,4.61,4.56,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00018500,05/19/17,18.5,P,A,0.05,0.01,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00019000,05/19/17,19,C,A,4.12,4.07,0,41,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00019000,05/19/17,19,P,A,0.04,0.01,0,4327,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00019500,05/19/17,19.5,C,A,3.62,3.58,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00019500,05/19/17,19.5,P,A,0.06,0.01,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00020000,05/19/17,20,C,A,3.12,3.07,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00020000,05/19/17,20,P,A,0.06,0.01,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00020500,05/19/17,20.5,C,A,2.63,2.58,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00020500,05/19/17,20.5,P,A,0.06,0.02,0,1600,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00021000,05/19/17,21,C,A,2.15,2.1,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00021000,05/19/17,21,P,A,0.07,0.04,0,30,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00021250,05/19/17,21.25,C,A,1.9,1.86,20,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00021250,05/19/17,21.25,P,A,0.08,0.04,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00021500,05/19/17,21.5,C,A,1.67,1.63,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00021500,05/19/17,21.5,P,A,0.08,0.05,100,170466,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00021750,05/19/17,21.75,C,A,1.43,1.39,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00021750,05/19/17,21.75,P,A,0.1,0.07,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00022000,05/19/17,22,C,A,1.19,1.16,0,970,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00022000,05/19/17,22,P,A,0.11,0.09,0,1716,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00022250,05/19/17,22.25,C,A,0.97,0.94,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00022250,05/19/17,22.25,P,A,0.15,0.11,0,500,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00022500,05/19/17,22.5,C,A,0.75,0.72,0,845,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00022500,05/19/17,22.5,P,A,0.18,0.15,0,103161,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00022750,05/19/17,22.75,C,A,0.56,0.53,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00022750,05/19/17,22.75,P,A,0.23,0.2,0,1371,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00023000,05/19/17,23,C,A,0.38,0.36,200,18606,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00023000,05/19/17,23,P,A,0.3,0.28,242,7115,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00023250,05/19/17,23.25,C,A,0.26,0.22,100,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00023250,05/19/17,23.25,P,A,0.41,0.38,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00023500,05/19/17,23.5,C,A,0.14,0.11,0,1003,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00023500,05/19/17,23.5,P,A,0.57,0.53,0,2318,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00023750,05/19/17,23.75,C,A,0.07,0.04,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00023750,05/19/17,23.75,P,A,0.75,0.71,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00024000,05/19/17,24,C,A,0.06,0.01,0,83,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00024000,05/19/17,24,P,A,0.96,0.93,13,180,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00024250,05/19/17,24.25,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00024250,05/19/17,24.25,P,A,1.21,1.18,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00024500,05/19/17,24.5,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00024500,05/19/17,24.5,P,A,1.46,1.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00024750,05/19/17,24.75,C,A,0.04,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00024750,05/19/17,24.75,P,A,1.71,1.68,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00025000,05/19/17,25,C,A,0.04,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00025000,05/19/17,25,P,A,1.96,1.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00025250,05/19/17,25.25,C,A,0.04,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00025250,05/19/17,25.25,P,A,2.21,2.18,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00025500,05/19/17,25.5,C,A,0.04,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00025500,05/19/17,25.5,P,A,2.46,2.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00025750,05/19/17,25.75,C,A,0.04,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00025750,05/19/17,25.75,P,A,2.71,2.68,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00026000,05/19/17,26,C,A,0.04,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00026000,05/19/17,26,P,A,2.96,2.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00026500,05/19/17,26.5,C,A,0.04,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00026500,05/19/17,26.5,P,A,3.46,3.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00027000,05/19/17,27,C,A,0.04,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00027000,05/19/17,27,P,A,3.96,3.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00027500,05/19/17,27.5,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00027500,05/19/17,27.5,P,A,4.46,4.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00028000,05/19/17,28,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00028000,05/19/17,28,P,A,4.96,4.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00028500,05/19/17,28.5,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00028500,05/19/17,28.5,P,A,5.46,5.43,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519C00029000,05/19/17,29,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170519P00029000,05/19/17,29,P,A,5.96,5.93,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00017000,06/17/17,17,C,A,6.12,6.05,0,5,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00017000,06/17/17,17,P,A,0.08,0.01,0,9882,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00017500,06/17/17,17.5,C,A,5.62,5.55,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00017500,06/17/17,17.5,P,A,0.08,0.01,0,1120,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00018000,06/17/17,18,C,A,5.13,5.05,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00018000,06/17/17,18,P,A,0.08,0.02,0,180,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00018500,06/17/17,18.5,C,A,4.63,4.55,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00018500,06/17/17,18.5,P,A,0.07,0.02,0,290,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00019000,06/17/17,19,C,A,4.14,4.05,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00019000,06/17/17,19,P,A,0.1,0.02,0,4444,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00019500,06/17/17,19.5,C,A,3.64,3.57,0,150,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00019500,06/17/17,19.5,P,A,0.1,0.01,0,50,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00020000,06/17/17,20,C,A,3.15,3.06,0,100,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00020000,06/17/17,20,P,A,0.11,0.02,0,4472,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00020500,06/17/17,20.5,C,A,2.66,2.58,0,23,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00020500,06/17/17,20.5,P,A,0.11,0.05,0,1597,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00021000,06/17/17,21,C,A,2.18,2.1,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00021000,06/17/17,21,P,A,0.17,0.09,0,411,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00021500,06/17/17,21.5,C,A,1.73,1.64,0,132,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00021500,06/17/17,21.5,P,A,0.18,0.15,0,180,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00022000,06/17/17,22,C,A,1.29,1.19,0,75,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00022000,06/17/17,22,P,A,0.31,0.21,0,1926,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00022500,06/17/17,22.5,C,A,0.87,0.79,0,1349,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00022500,06/17/17,22.5,P,A,0.42,0.33,0,2509,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00023000,06/17/17,23,C,A,0.54,0.42,54,274,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00023000,06/17/17,23,P,A,0.57,0.48,40,651,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00023500,06/17/17,23.5,C,A,0.27,0.18,40,38379,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00023500,06/17/17,23.5,P,A,0.85,0.74,0,985,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00024000,06/17/17,24,C,A,0.12,0.04,0,6526,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00024000,06/17/17,24,P,A,1.19,1.14,0,194,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00024500,06/17/17,24.5,C,A,0.07,0,0,30120,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00024500,06/17/17,24.5,P,A,1.63,1.57,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00025000,06/17/17,25,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00025000,06/17/17,25,P,A,2.11,2.06,0,145,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00025500,06/17/17,25.5,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00025500,06/17/17,25.5,P,A,2.61,2.54,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00026000,06/17/17,26,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00026000,06/17/17,26,P,A,3.11,3.04,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00027000,06/17/17,27,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00027000,06/17/17,27,P,A,4.11,4.04,0,40,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00028000,06/17/17,28,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00028000,06/17/17,28,P,A,5.09,5.03,0,50,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616C00029000,06/17/17,29,C,A,0.05,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170616P00029000,06/17/17,29,P,A,6.11,6.03,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00018000,09/16/17,18,C,A,5.14,5.03,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00018000,09/16/17,18,P,A,0.14,0.04,0,14685,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00018500,09/16/17,18.5,C,A,4.66,4.54,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00018500,09/16/17,18.5,P,A,0.15,0.05,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00019000,09/16/17,19,C,A,4.15,4.06,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00019000,09/16/17,19,P,A,0.18,0.06,0,30,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00019500,09/16/17,19.5,C,A,3.69,3.57,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00019500,09/16/17,19.5,P,A,0.2,0.09,0,20,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00020000,09/16/17,20,C,A,3.23,3.09,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00020000,09/16/17,20,P,A,0.24,0.12,0,7574,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00020500,09/16/17,20.5,C,A,2.75,2.63,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00020500,09/16/17,20.5,P,A,0.3,0.18,0,83,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00021000,09/16/17,21,C,A,2.27,2.17,0,175,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00021000,09/16/17,21,P,A,0.36,0.23,0,8622,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00021500,09/16/17,21.5,C,A,1.87,1.74,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00021500,09/16/17,21.5,P,A,0.47,0.33,0,1095,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00022000,09/16/17,22,C,A,1.44,1.33,5,1,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00022000,09/16/17,22,P,A,0.53,0.45,0,1695,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00022500,09/16/17,22.5,C,A,1.06,0.91,0,1,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00022500,09/16/17,22.5,P,A,0.74,0.6,0,4579,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00023000,09/16/17,23,C,A,0.75,0.61,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00023000,09/16/17,23,P,A,0.91,0.8,0,23,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00023500,09/16/17,23.5,C,A,0.49,0.36,0,136,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00023500,09/16/17,23.5,P,A,1.23,1.06,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00024000,09/16/17,24,C,A,0.28,0.18,0,24,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00024000,09/16/17,24,P,A,1.56,1.38,0,20,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00024500,09/16/17,24.5,C,A,0.2,0.07,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00024500,09/16/17,24.5,P,A,1.95,1.74,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00025000,09/16/17,25,C,A,0.12,0.02,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00025000,09/16/17,25,P,A,2.32,2.18,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00025500,09/16/17,25.5,C,A,0.08,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00025500,09/16/17,25.5,P,A,2.78,2.65,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00026000,09/16/17,26,C,A,0.07,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00026000,09/16/17,26,P,A,3.29,3.14,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00026500,09/16/17,26.5,C,A,0.06,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00026500,09/16/17,26.5,P,A,3.75,3.64,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00027000,09/16/17,27,C,A,0.06,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00027000,09/16/17,27,P,A,4.25,4.14,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00027500,09/16/17,27.5,C,A,0.06,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00027500,09/16/17,27.5,P,A,4.74,4.64,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00028000,09/16/17,28,C,A,0.06,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00028000,09/16/17,28,P,A,5.24,5.15,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915C00029000,09/16/17,29,C,A,0.06,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 170915P00029000,09/16/17,29,P,A,6.25,6.14,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00018000,12/16/17,18,C,A,5.14,5.04,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00018000,12/16/17,18,P,A,0.26,0.11,0,14696,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00018500,12/16/17,18.5,C,A,4.65,4.54,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00018500,12/16/17,18.5,P,A,0.28,0.14,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00019000,12/16/17,19,C,A,4.17,4.05,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00019000,12/16/17,19,P,A,0.33,0.18,0,100,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00019500,12/16/17,19.5,C,A,3.71,3.6,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00019500,12/16/17,19.5,P,A,0.36,0.22,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00020000,12/16/17,20,C,A,3.3,3.14,0,10,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00020000,12/16/17,20,P,A,0.4,0.28,1,7846,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00020500,12/16/17,20.5,C,A,2.87,2.69,40,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00020500,12/16/17,20.5,P,A,0.51,0.36,0,120,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00021000,12/16/17,21,C,A,2.39,2.2,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00021000,12/16/17,21,P,A,0.59,0.45,0,50,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00021500,12/16/17,21.5,C,A,1.99,1.8,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00021500,12/16/17,21.5,P,A,0.72,0.57,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00022000,12/16/17,22,C,A,1.62,1.43,0,70,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00022000,12/16/17,22,P,A,0.88,0.7,0,361,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00022500,12/16/17,22.5,C,A,1.28,1.1,0,150,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00022500,12/16/17,22.5,P,A,1.08,0.89,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00023000,12/16/17,23,C,A,0.97,0.81,0,170,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00023000,12/16/17,23,P,A,1.3,1.09,0,220,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00023500,12/16/17,23.5,C,A,0.74,0.55,0,40,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00023500,12/16/17,23.5,P,A,1.56,1.34,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00024000,12/16/17,24,C,A,0.52,0.34,0,387,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00024000,12/16/17,24,P,A,1.87,1.65,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00024500,12/16/17,24.5,C,A,0.38,0.2,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00024500,12/16/17,24.5,P,A,2.22,2.01,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00025000,12/16/17,25,C,A,0.25,0.1,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00025000,12/16/17,25,P,A,2.62,2.38,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00025500,12/16/17,25.5,C,A,0.18,0.03,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00025500,12/16/17,25.5,P,A,3.05,2.8,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00026000,12/16/17,26,C,A,0.13,0.02,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00026000,12/16/17,26,P,A,3.51,3.26,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00026500,12/16/17,26.5,C,A,0.09,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00026500,12/16/17,26.5,P,A,3.98,3.79,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00027000,12/16/17,27,C,A,0.08,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00027000,12/16/17,27,P,A,4.47,4.2,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00027500,12/16/17,27.5,C,A,0.07,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00027500,12/16/17,27.5,P,A,4.88,4.7,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215C00028000,12/16/17,28,C,A,0.08,0,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 171215P00028000,12/16/17,28,P,A,5.37,5.2,0,0,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316C00014000,03/16/18,14,C,A,9.15,9.03,0,3,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316P00014000,03/16/18,14,P,A,0.24,0.03,0,61,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316C00015000,03/16/18,15,C,A,8.16,8.01,0,11,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316P00015000,03/16/18,15,P,A,0.27,0.05,0,7,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316C00016000,03/16/18,16,C,A,7.12,7.02,0,5,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316P00016000,03/16/18,16,P,A,0.3,0.08,0,23,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316C00017000,03/16/18,17,C,A,6.15,6.03,0,64,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316P00017000,03/16/18,17,P,A,0.34,0.07,0,171,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316C00018000,03/16/18,18,C,A,5.21,5.05,0,85,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316P00018000,03/16/18,18,P,A,0.27,0.16,0,26337,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316C00019000,03/16/18,19,C,A,4.31,4.08,0,161,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316P00019000,03/16/18,19,P,A,0.36,0.24,0,1346,23.06
+XIU,TSX,03/30/17,23.06,XIU 180316C00020000,03/16/18,20,C,A,3.42,3.15,0,218,23.06
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+XIU,TSX,03/30/17,23.06,XIU 180316C00021000,03/16/18,21,C,A,2.44,2.33,0,437,23.06
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diff --git a/Problemsets/Data/PS08_Data.xlsx b/Problemsets/Data/PS08_Data.xlsx
new file mode 100644
index 0000000..8212ff2
Binary files /dev/null and b/Problemsets/Data/PS08_Data.xlsx differ
diff --git a/Problemsets/PS07_Optimisation.ipynb b/Problemsets/PS07_Optimisation.ipynb
new file mode 100644
index 0000000..5fceee6
--- /dev/null
+++ b/Problemsets/PS07_Optimisation.ipynb
@@ -0,0 +1,420 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Mean Variance Frontier with Short Sales Constraints"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Load Packages and Utility Functions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "printyellow (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using Printf, LinearAlgebra, Optim\n",
+ "\n",
+ "include(\"jlFiles/printmat.jl\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using Plots\n",
+ "\n",
+ "#pyplot(size=(600,400)) #use pyplot or gr\n",
+ "gr(size=(480,320))\n",
+ "default(fmt = :svg)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Traditional MV Calculations \n",
+ "\n",
+ "(no constraints)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "3"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "μ = [11.5, 9.5, 6]/100 #expected returns\n",
+ "Σ = [166 34 58; #covariance matrix\n",
+ " 34 64 4;\n",
+ " 58 4 100]/100^2\n",
+ "\n",
+ "assetNames = [\"A\",\"B\",\"C\"];\n",
+ "n = length(μ)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## A Function for Calculating the (traditional) Mean-Variance Frontier\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "MVCalc"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "\"\"\"\n",
+ " MVCalc(μstar,μ,Σ)\n",
+ "\n",
+ "Calculate the std and weights of a portfolio (with mean return μstar) on MVF of risky assets.\n",
+ "\n",
+ "# Remark\n",
+ "- Only (λ,δ) and thus (w,stdRp) depend on μstar. We could therefore speed up the computations a bit\n",
+ "by doing the loop over different μstar values inside the function (and thus not recalculate Σ_1,a,b,c).\n",
+ "\"\"\"\n",
+ "function MVCalc(μstar,μ,Σ)\n",
+ " n = length(μ)\n",
+ " Σ_1 = inv(Σ)\n",
+ " a = μ'Σ_1*μ\n",
+ " b = μ'Σ_1*ones(n)\n",
+ " c = ones(n)'Σ_1*ones(n)\n",
+ " λ = (c*μstar - b)/(a*c-b^2)\n",
+ " δ = (a-b*μstar)/(a*c-b^2)\n",
+ " w = Σ_1 *(μ*λ.+δ)\n",
+ " StdRp = sqrt(w'Σ*w)\n",
+ " return StdRp,w\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "μstar_range = range(0.04,0.15,length=201)\n",
+ "L = length(μstar_range)\n",
+ "\n",
+ "StdRp = fill(NaN,L)\n",
+ "for i = 1:L\n",
+ " StdRp[i] = MVCalc(μstar_range[i],μ,Σ)[1]\n",
+ "end\n",
+ "\n",
+ "p1 = plot( StdRp*100,μstar_range*100,\n",
+ " linecolor = :red,\n",
+ " linewidth = 2,\n",
+ " label = \"MVF\",\n",
+ " legend = :topleft,\n",
+ " xlim = (0,15),\n",
+ " ylim = (0,15),\n",
+ " title = \"MVF (no portfolio constraints)\",\n",
+ " xlabel = \"Std(Rp), %\",\n",
+ " ylabel = \"ERp, %\" )\n",
+ "scatter!(sqrt.(diag(Σ))*100,μ*100,color=:red,label=\"assets\")\n",
+ "display(p1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# The Maximization Problem\n",
+ "\n",
+ "The investor maximizes:\n",
+ "\n",
+ "$\\text{E}R_{p}-\\frac{k}{2} \\text{Var}(R_{p})$,\n",
+ "\n",
+ "where $\\text{E}R_{p}= w'\\mu$ and $\\text{Var}(R_{p}=w'\\Sigma w$\n",
+ "\n",
+ "subject to $\\Sigma_{i=1}^n w_{i} = 1$.\n",
+ "\n",
+ "We can trace out the mean-variance frontier by solving this problem for different values of $k$.\n",
+ "\n",
+ "To impose the restriction, optimise over `v` and let `w=[v;1-sum(v)]`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "objfun1 (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "function objfun1(v,k,μ,Σ)\n",
+ " w = [v;1-sum(v)]\n",
+ " ERp = w'μ\n",
+ " VarRp = w'Σ*w\n",
+ " StdRp = sqrt(VarRp)\n",
+ " U = ERp - k/2*VarRp\n",
+ " loss = -U #minimise this\n",
+ " return loss, w, ERp, StdRp\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "A 0.313\n",
+ "B 0.695\n",
+ "C -0.008\n",
+ "\n",
+ "σₚ 0.079\n",
+ "μₚ 0.102\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "k = 10\n",
+ "Sol = optimize(v -> objfun1(v,k,μ,Σ)[1],zeros(n-1))\n",
+ "\n",
+ "v = Optim.minimizer(Sol)\n",
+ "(_,w,ERp,StdRp) = objfun1(v,k,μ,Σ)\n",
+ "\n",
+ "printmat(w,rowNames=assetNames)\n",
+ "printmat([StdRp,ERp],rowNames=[\"σₚ\",\"μₚ\"])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 1\n",
+ "\n",
+ "Redo the optimisation for the following range of $k$ values:\n",
+ "`k = [range(0.1,1.9,length=30);range(1,30,length=25)]`\n",
+ "\n",
+ "Then plot the resulting \"efficient frontier\" (similar to the MV plot above). Is is the same as the plot above?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 2\n",
+ "\n",
+ "Change the optimisation problem to `U = ERp + cost - k/2*VarRp` where `cost` is (sum of the *negative* portfolio weights)*0.05. This is a (crude/dramatic) attaempt to illustrate the impact of costs of short selling ($w_i<0$) assets. Plot the new \"effecient frontier\" together with the old one."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 3\n",
+ "\n",
+ "Compare the portfolio weights (with/without the extra `cost`)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "@webio": {
+ "lastCommId": null,
+ "lastKernelId": null
+ },
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Julia 1.6.3",
+ "language": "julia",
+ "name": "julia-1.6"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.6.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Problemsets/PS08_Volatility.ipynb b/Problemsets/PS08_Volatility.ipynb
new file mode 100644
index 0000000..25c98b9
--- /dev/null
+++ b/Problemsets/PS08_Volatility.ipynb
@@ -0,0 +1,579 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Load Packages and Extra Functions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "printyellow (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using Printf, Dates, Statistics, Distributions, XLSX\n",
+ "\n",
+ "include(\"jlFiles/printmat.jl\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using Plots\n",
+ "\n",
+ "gr(size=(480,320))\n",
+ "default(fmt = :svg)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Loading Daily S&P 500 Data\n",
+ "\n",
+ "The data file contains some missing values indicated by the value -999.99. Do not use those observations when the S&P level is missing. \n",
+ "\n",
+ "1. Calculate daily returns (treat missing days as if they do not exist).\n",
+ "\n",
+ "2. Create a vector of dates (from the first column in the data set)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Number of days in the sample: 17864\n"
+ ]
+ }
+ ],
+ "source": [
+ "xx = XLSX.readxlsx(\"Data/PS08_Data.xlsx\") #reads a sheet from the xlsx file\n",
+ "x = xx[\"SP500RfPs!A2:B17870\"] #pick out some cells\n",
+ "\n",
+ "...do the rest"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 1\n",
+ "\n",
+ "1. Show a normalised histogram of the returns. Use the bins `-5:0.25:5`\n",
+ "2. Add a curve for the density of the best fitting $N(\\mu,\\sigma)$ distribution."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "(μ,σ) = (mean(R),std(R))\n",
+ "\n",
+ "xGrid = -5:0.25:5\n",
+ "pdfX = pdf.(Normal(μ,σ),xGrid) #\"Distributions\" wants σ, not σ^2\n",
+ "\n",
+ "do the rest..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 2\n",
+ "\n",
+ "1. Calculate the quantile 0.01 in the data and according to the fitted normal distribution. Change the sign and call it \"99% Value at Risk\". Hint: `quantile(R,0.01)`and `quantile(Normal(μ,σ),0.01)`\n",
+ "\n",
+ "2. Calculate the expected return conditional on the return being less than the 5th quantile, both in data and according to the normal distribution. Change sign and call it \"expected shortfall\". Hint: `mean(TruncatedNormal(μ,σ,-Inf,quantile001))`\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 3\n",
+ "\n",
+ "Construct an simple estimate of $\\sigma_t^2$ as a backward looking exponential moving average\n",
+ "\n",
+ "$\\sigma_t^2 = \\lambda \\sigma_{t-1}^2 + (1-\\lambda) (R_{t-1} -\\mu_{t-1})^2$,\n",
+ "where $\\mu_{t}=\\lambda \\mu_{t-1} + (1-\\lambda) R_{t-1}$ \n",
+ "\n",
+ "Use $\\lambda=0.94$\n",
+ "\n",
+ "Plot the standard deviation in a time series plot."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 4\n",
+ "\n",
+ "Calculate 99% VaR and ES according to time-varying normal distributions `Normal(μ[t],sqrt(σ²[t]))` and plot the results (as time series plots)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "@webio": {
+ "lastCommId": null,
+ "lastKernelId": null
+ },
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Julia 1.6.3",
+ "language": "julia",
+ "name": "julia-1.6"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.6.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Problemsets/PS09a_PyCall.ipynb b/Problemsets/PS09a_PyCall.ipynb
new file mode 100644
index 0000000..945fc52
--- /dev/null
+++ b/Problemsets/PS09a_PyCall.ipynb
@@ -0,0 +1,271 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Python\n",
+ "\n",
+ "using the [PyCall.jl](https://github.com/JuliaPy/PyCall.jl) package."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "CovNWFn"
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using Printf, DelimitedFiles, LinearAlgebra, Statistics\n",
+ "\n",
+ "include(\"jlFiles/printmat.jl\")\n",
+ "include(\"jlFiles/OlsNW.jl\") #functions for OLS"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Sample size: (388,)\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = readdlm(\"Data/FFmFactorsPs.csv\",',',skipstart=1)\n",
+ "\n",
+ " #yearmonth, market, small minus big, high minus low\n",
+ "(ym,Rme,RSMB,RHML) = (x[:,1],x[:,2]/100,x[:,3]/100,x[:,4]/100) \n",
+ "x = nothing\n",
+ "\n",
+ "printlnPs(\"Sample size:\",size(Rme))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Do OLS (in Julia)\n",
+ "\n",
+ "use the function sin the file OlsNW.jl to do OLS. Report point estimates and standard errors."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\u001b[34m\u001b[1mOLS Results (assuming iid residuals):\u001b[22m\u001b[39m\n",
+ "\n",
+ " b std_iid\n",
+ "c 0.007 0.002\n",
+ "SMB 0.217 0.073\n",
+ "HML -0.429 0.074\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "Y = Rme\n",
+ "T = size(Y,1)\n",
+ "X = [ones(T) RSMB RHML]\n",
+ "\n",
+ "(b,u,Yhat,V,R2) = OlsGMFn(Y,X)\n",
+ "std_iid = sqrt.(diag(V))\n",
+ "\n",
+ "printblue(\"OLS Results (assuming iid residuals):\\n\")\n",
+ "xNames = [\"c\",\"SMB\",\"HML\"]\n",
+ "printmat([b std_iid],colNames=[\"b\",\"std_iid\"],rowNames=xNames)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Getting Started with PyCall"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using PyCall\n",
+ "sm = pyimport(\"statsmodels.api\"); #activate this package"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "PyObject \n",
+ "\"\"\"\n",
+ " OLS Regression Results \n",
+ "==============================================================================\n",
+ "Dep. Variable: y R-squared: 0.134\n",
+ "Model: OLS Adj. R-squared: 0.130\n",
+ "Method: Least Squares F-statistic: 29.85\n",
+ "Date: Mon, 08 Nov 2021 Prob (F-statistic): 8.88e-13\n",
+ "Time: 16:17:13 Log-Likelihood: 672.28\n",
+ "No. Observations: 388 AIC: -1339.\n",
+ "Df Residuals: 385 BIC: -1327.\n",
+ "Df Model: 2 \n",
+ "Covariance Type: nonrobust \n",
+ "==============================================================================\n",
+ " coef std err t P>|t| [0.025 0.975]\n",
+ "------------------------------------------------------------------------------\n",
+ "const 0.0070 0.002 3.167 0.002 0.003 0.011\n",
+ "x1 0.2170 0.074 2.949 0.003 0.072 0.362\n",
+ "x2 -0.4291 0.074 -5.821 0.000 -0.574 -0.284\n",
+ "==============================================================================\n",
+ "Omnibus: 58.863 Durbin-Watson: 1.849\n",
+ "Prob(Omnibus): 0.000 Jarque-Bera (JB): 146.539\n",
+ "Skew: -0.749 Prob(JB): 1.51e-32\n",
+ "Kurtosis: 5.612 Cond. No. 38.8\n",
+ "==============================================================================\n",
+ "\n",
+ "Notes:\n",
+ "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
+ "\"\"\"\n"
+ ]
+ }
+ ],
+ "source": [
+ "resultsP = sm.OLS(Y, X).fit() #can use Python functions directly\n",
+ "\n",
+ "println(resultsP.summary())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[:HC0_se, :HC1_se, :HC2_se, :HC3_se, :_HCCM, :__class__, :__delattr__, :__dict__, :__dir__, :__doc__, :__eq__, :__format__, :__ge__, :__getattribute__, :__gt__, :__hash__, :__init__, :__init_subclass__, :__le__, :__lt__, :__module__, :__ne__, :__new__, :__reduce__, :__reduce_ex__, :__repr__, :__setattr__, :__sizeof__, :__str__, :__subclasshook__, :__weakref__, :_abat_diagonal, :_cache, :_data_attr, :_data_in_cache, :_get_robustcov_results, :_is_nested, :_use_t, :_wexog_singular_values, :aic, :bic, :bse, :centered_tss, :compare_f_test, :compare_lm_test, :compare_lr_test, :condition_number, :conf_int, :conf_int_el, :cov_HC0, :cov_HC1, :cov_HC2, :cov_HC3, :cov_kwds, :cov_params, :cov_type, :df_model, :df_resid, :diagn, :eigenvals, :el_test, :ess, :f_pvalue, :f_test, :fittedvalues, :fvalue, :get_influence, :get_prediction, :get_robustcov_results, :info_criteria, :initialize, :k_constant, :llf, :load, :model, :mse_model, :mse_resid, :mse_total, :nobs, :normalized_cov_params, :outlier_test, :params, :predict, :pvalues, :remove_data, :resid, :resid_pearson, :rsquared, :rsquared_adj, :save, :scale, :ssr, :summary, :summary2, :t_test, :t_test_pairwise, :tvalues, :uncentered_tss, :use_t, :wald_test, :wald_test_terms, :wresid]\n"
+ ]
+ }
+ ],
+ "source": [
+ "println(keys(resultsP)) #print all keys (field names)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 1\n",
+ "\n",
+ "Print the Julia and Python estimates (of the coefficients) in a table so we can compare directly."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 2\n",
+ "\n",
+ "Print the smallest and largest values of the difference between the residuals according to Julia and those according to Python."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# OLS (in Julia) with Robust Standard Errors\n",
+ "\n",
+ "Use standard errors that are robust to heteroskedastcity and autocorrelation (2 lags)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\u001b[34m\u001b[1mOLS Results (robust std):\u001b[22m\u001b[39m\n",
+ "\n",
+ " b std_nw\n",
+ "c 0.007 0.002\n",
+ "SMB 0.217 0.129\n",
+ "HML -0.429 0.118\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "(b,u,Yhat,V,R2) = OlsNWFn(Y,X,2)\n",
+ "std_nw = sqrt.(diag(V))\n",
+ "\n",
+ "printblue(\"OLS Results (robust std):\\n\")\n",
+ "xNames = [\"c\",\"SMB\",\"HML\"]\n",
+ "printmat([b std_nw],colNames=[\"b\",\"std_nw\"],rowNames=xNames)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 3 \n",
+ "\n",
+ "Now redo the Python estimation with the same sort of robust standard errors. Hint: `resultsP.get_robustcov_results()`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "@webio": {
+ "lastCommId": null,
+ "lastKernelId": null
+ },
+ "kernelspec": {
+ "display_name": "Julia 1.6.3",
+ "language": "julia",
+ "name": "julia-1.6"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.6.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Problemsets/PS09b_RCall.ipynb b/Problemsets/PS09b_RCall.ipynb
new file mode 100644
index 0000000..ef5536b
--- /dev/null
+++ b/Problemsets/PS09b_RCall.ipynb
@@ -0,0 +1,284 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# R\n",
+ "\n",
+ "using the [RCall.jl](https://juliainterop.github.io/RCall.jl/stable/) package."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "CovNWFn"
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using Printf, DelimitedFiles, LinearAlgebra, Statistics\n",
+ "\n",
+ "include(\"jlFiles/printmat.jl\")\n",
+ "include(\"jlFiles/OlsNW.jl\") #functions for OLS"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Sample size: (388,)\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = readdlm(\"Data/FFmFactorsPs.csv\",',',skipstart=1)\n",
+ "\n",
+ " #yearmonth, market, small minus big, high minus low\n",
+ "(ym,Rme,RSMB,RHML) = (x[:,1],x[:,2]/100,x[:,3]/100,x[:,4]/100) \n",
+ "x = nothing\n",
+ "\n",
+ "printlnPs(\"Sample size:\",size(Rme))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Do OLS (in Julia)\n",
+ "\n",
+ "use the function sin the file OlsNW.jl to do OLS. Report point estimates and standard errors."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\u001b[34m\u001b[1mOLS Results (assuming iid residuals):\u001b[22m\u001b[39m\n",
+ "\n",
+ " b std_iid\n",
+ "c 0.007 0.002\n",
+ "SMB 0.217 0.073\n",
+ "HML -0.429 0.074\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "Y = Rme\n",
+ "T = size(Y,1)\n",
+ "X = [ones(T) RSMB RHML]\n",
+ "\n",
+ "(b,u,Yhat,V,R2) = OlsGMFn(Y,X)\n",
+ "std_iid = sqrt.(diag(V))\n",
+ "\n",
+ "printblue(\"OLS Results (assuming iid residuals):\\n\")\n",
+ "xNames = [\"c\",\"SMB\",\"HML\"]\n",
+ "printmat([b std_iid],colNames=[\"b\",\"std_iid\"],rowNames=xNames)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Getting Started with RCall"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using RCall"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "RObject{VecSxp}\n",
+ "\n",
+ "Call:\n",
+ "lm(formula = Y ~ X + 0)\n",
+ "\n",
+ "Residuals:\n",
+ " Min 1Q Median 3Q Max \n",
+ "-0.20224 -0.02477 0.00335 0.02663 0.11840 \n",
+ "\n",
+ "Coefficients:\n",
+ " Estimate Std. Error t value Pr(>|t|) \n",
+ "X1 0.006983 0.002205 3.167 0.00166 ** \n",
+ "X2 0.216968 0.073565 2.949 0.00338 ** \n",
+ "X3 -0.429088 0.073710 -5.821 1.23e-08 ***\n",
+ "---\n",
+ "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
+ "\n",
+ "Residual standard error: 0.04295 on 385 degrees of freedom\n",
+ "Multiple R-squared: 0.1488,\tAdjusted R-squared: 0.1422 \n",
+ "F-statistic: 22.44 on 3 and 385 DF, p-value: 2.07e-13\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "RObject{VecSxp}\n",
+ "\n",
+ "Call:\n",
+ "lm(formula = Y ~ X + 0)\n",
+ "\n",
+ "Coefficients:\n",
+ " X1 X2 X3 \n",
+ " 0.006983 0.216968 -0.429088 \n",
+ "\n"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "@rput X Y\n",
+ "\n",
+ "ResultsR = reval(\"summary(mod <- lm(Y ~ X+0))\") #print summary of regression\n",
+ "println(ResultsR)\n",
+ "\n",
+ "resultsR = reval(\"mod <- lm(Y ~ X+0)\") #get all output"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[:coefficients, :residuals, :effects, :rank, Symbol(\"fitted.values\"), :assign, :qr, Symbol(\"df.residual\"), :xlevels, :call, :terms, :model]\n"
+ ]
+ }
+ ],
+ "source": [
+ "println(names(resultsR)) #print all keys (field names)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 1\n",
+ "\n",
+ "Print the Julia and Python estimates (of the coefficients) in a table so we can compare directly."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 2\n",
+ "\n",
+ "Print the smallest and largest values of the difference between the residuals according to Julia and those according to Python."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# OLS (in Julia) with Robust Standard Errors\n",
+ "\n",
+ "Use standard errors that are robust to heteroskedastcity and autocorrelation (2 lags)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\u001b[34m\u001b[1mOLS Results (robust std):\u001b[22m\u001b[39m\n",
+ "\n",
+ " b std_nw\n",
+ "c 0.007 0.002\n",
+ "SMB 0.217 0.129\n",
+ "HML -0.429 0.118\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "(b,u,Yhat,V,R2) = OlsNWFn(Y,X,2)\n",
+ "std_nw = sqrt.(diag(V))\n",
+ "\n",
+ "printblue(\"OLS Results (robust std):\\n\")\n",
+ "xNames = [\"c\",\"SMB\",\"HML\"]\n",
+ "printmat([b std_nw],colNames=[\"b\",\"std_nw\"],rowNames=xNames)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 3 \n",
+ "\n",
+ "Now redo the R estimation with the same sort of robust standard errors. Hint: the `NeweyWest` in the `sandwich`package."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "@webio": {
+ "lastCommId": null,
+ "lastKernelId": null
+ },
+ "kernelspec": {
+ "display_name": "Julia 1.6.3",
+ "language": "julia",
+ "name": "julia-1.6"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.6.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Problemsets/PS09c_WarAndPeace.ipynb b/Problemsets/PS09c_WarAndPeace.ipynb
new file mode 100644
index 0000000..f9cfec7
--- /dev/null
+++ b/Problemsets/PS09c_WarAndPeace.ipynb
@@ -0,0 +1,132 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using Downloads"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Download a Book from Internet\n",
+ "\n",
+ "and read it into a string in Julia. Then report the number of letters etc (see below)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "File to download: http://www.gutenberg.org/files/2600/2600-0.txt\n",
+ "\n",
+ "check the subfolder Results\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "if !isdir(\"Results\")\n",
+ " error(\"create the subfolder Results before running this program\")\n",
+ "end\n",
+ "\n",
+ "http = \"http://www.gutenberg.org/files/2600/2600-0.txt\"\n",
+ "\n",
+ "println(\"File to download: \",http)\n",
+ "Downloads.download(http,\"Results/WarAndPeace.txt\")\n",
+ "\n",
+ "println(\"\\ncheck the subfolder Results\\n\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [],
+ "source": [
+ "fh = open(\"Results/WarAndPeace.txt\")\n",
+ "str = read(fh,String) \n",
+ "close(fh)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 1\n",
+ "\n",
+ "1. Count the number of letters and the unique letters in `str`. Hint: `length() and `unique()`\n",
+ "\n",
+ "2. Count the number of word and lines. Hint: `split(str)` and `split(str,\"\\n\")`\n",
+ "\n",
+ "3. Count the number of unique words."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 2\n",
+ "\n",
+ "1. How often is Borodinó mentioned. Hint: `occursin.(,words)`\n",
+ "\n",
+ "2. Print all lines that contain the word Borodinó. Hint: `occursin(,line)`"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 3\n",
+ "\n",
+ "1. Change Borodinó everywhere to Berëzina and then count the occurances"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "@webio": {
+ "lastCommId": null,
+ "lastKernelId": null
+ },
+ "anaconda-cloud": {},
+ "kernel_info": {
+ "name": "julia-1.2"
+ },
+ "kernelspec": {
+ "display_name": "Julia 1.6.3",
+ "language": "julia",
+ "name": "julia-1.6"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.6.3"
+ },
+ "nteract": {
+ "version": "0.24.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Problemsets/PS10_DataFrames.ipynb b/Problemsets/PS10_DataFrames.ipynb
new file mode 100644
index 0000000..3f85bc5
--- /dev/null
+++ b/Problemsets/PS10_DataFrames.ipynb
@@ -0,0 +1,210 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Load Packages"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "printyellow (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using Printf, Dates, Statistics, CSV, DataFrames\n",
+ "include(\"jlFiles/printmat.jl\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Loading Some Data with CSV.jl"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The first 4 lines of Data/Options_prices_US_Canada.csv:\n",
+ "\n",
+ "symbol,exchange,date,adjusted close,option symbol,expiration,strike,call/put,style,ask,bid,volume,open interest,unadjusted\n",
+ "SPX,CBOE,03/30/17,2368.06,SPXW 170331C00300000,03/31/17,300,C,E,2073.9,2062.9,0,0,2368.927\n",
+ "SPX,CBOE,03/30/17,2368.06,SPXW 170331P00300000,03/31/17,300,P,E,0.1,0,0,0,2368.927\n",
+ "SPX,CBOE,03/30/17,2368.06,SPXW 170331C00400000,03/31/17,400,C,E,1974.1,1962.7,0,0,2368.927\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "DataFile = \"Data/Options_prices_US_Canada.csv\"\n",
+ "\n",
+ "println(\"The first 4 lines of $(DataFile):\\n\")\n",
+ "txt = readlines(DataFile)\n",
+ "printmat(txt[1:4])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Use `normalizenames` to get names that can be used in Julia as variables names and specify the `dateformat` used in the csv file (to convert to proper Julia dates). The dates in the file are given as `03/30/17` which CSV/DataFrames interpret as 30 March year 17 (AD). We add `Dates.Year(2000)` to get year 2017."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\u001b[1m13952×10 DataFrame\u001b[0m\n",
+ "\u001b[1m Row \u001b[0m│\u001b[1m symbol \u001b[0m\u001b[1m date \u001b[0m\u001b[1m close \u001b[0m\u001b[1m expiration \u001b[0m\u001b[1m strike \u001b[0m\u001b[1m call_put \u001b[0m\u001b[1m ask \u001b[0m\u001b[1m\u001b[0m ⋯\n",
+ "\u001b[1m \u001b[0m│\u001b[90m String3 \u001b[0m\u001b[90m Date \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Date \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m String1 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m\u001b[0m ⋯\n",
+ "───────┼────────────────────────────────────────────────────────────────────────\n",
+ " 1 │ SPX 2017-03-30 2368.06 2017-03-31 300.0 C 2073.9 ⋯\n",
+ " 2 │ SPX 2017-03-30 2368.06 2017-03-31 300.0 P 0.1\n",
+ " 3 │ SPX 2017-03-30 2368.06 2017-03-31 400.0 C 1974.1\n",
+ " 4 │ SPX 2017-03-30 2368.06 2017-03-31 400.0 P 0.05\n",
+ " 5 │ SPX 2017-03-30 2368.06 2017-03-31 500.0 C 1874.1 ⋯\n",
+ " 6 │ SPX 2017-03-30 2368.06 2017-03-31 500.0 P 0.05\n",
+ " 7 │ SPX 2017-03-30 2368.06 2017-03-31 600.0 C 1774.1\n",
+ " 8 │ SPX 2017-03-30 2368.06 2017-03-31 600.0 P 0.05\n",
+ " 9 │ SPX 2017-03-30 2368.06 2017-03-31 700.0 C 1673.9 ⋯\n",
+ " 10 │ SPX 2017-03-30 2368.06 2017-03-31 700.0 P 0.05\n",
+ " 11 │ SPX 2017-03-30 2368.06 2017-03-31 750.0 C 1624.1\n",
+ " ⋮ │ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱\n",
+ " 13943 │ XIU 2017-03-30 23.06 2019-03-15 21.0 C 3.21\n",
+ " 13944 │ XIU 2017-03-30 23.06 2019-03-15 21.0 P 1.71 ⋯\n",
+ " 13945 │ XIU 2017-03-30 23.06 2019-03-15 22.0 C 2.53\n",
+ " 13946 │ XIU 2017-03-30 23.06 2019-03-15 22.0 P 2.03\n",
+ " 13947 │ XIU 2017-03-30 23.06 2019-03-15 23.0 C 1.97\n",
+ " 13948 │ XIU 2017-03-30 23.06 2019-03-15 23.0 P 2.51 ⋯\n",
+ " 13949 │ XIU 2017-03-30 23.06 2019-03-15 24.0 C 1.5\n",
+ " 13950 │ XIU 2017-03-30 23.06 2019-03-15 24.0 P 3.12\n",
+ " 13951 │ XIU 2017-03-30 23.06 2019-03-15 25.0 C 1.13\n",
+ " 13952 │ XIU 2017-03-30 23.06 2019-03-15 25.0 P 3.64 ⋯\n",
+ "\u001b[36m 3 columns and 13931 rows omitted\u001b[0m"
+ ]
+ }
+ ],
+ "source": [
+ "df1 = CSV.read(DataFile,DataFrame,normalizenames=true,dateformat=\"mm/dd/yy\")\n",
+ "\n",
+ "df1.date .+= Dates.Year(2000) #03/30/17 to 03/30/2017\n",
+ "df1.expiration .+= Dates.Year(2000)\n",
+ "\n",
+ "select!(df1,Not([:exchange,:option_symbol,:style,:unadjusted])) #deleting some columns\n",
+ "rename!(df1,:adjusted_close => :close) #renaming a column\n",
+ "\n",
+ "show(df1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 1\n",
+ "\n",
+ "Create a new DataFrame that contains only the data for SPX and those option contracts that were traded (volume > 0). Hint: `df1[vv, :]` picks out the rows of the data frame for which `vv` is `true`. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 2\n",
+ "\n",
+ "Create a *group* for each expiration date. These groups can be referred to as `dataG2[key]`.\n",
+ "\n",
+ "Hints: `groupby()`"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 3\n",
+ "\n",
+ "Print the number of contracts (`nrow`) and the sum of the open interest `:open_interest=>sum` for each of the expiration dates.\n",
+ "\n",
+ "Hint: `combine()`"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 4 \n",
+ "Creating two new DataFrames: for expiration date 2017-04-21 and another for 2017-06-16.\n",
+ "\n",
+ "Hint: `dataG2[(expiration = Date(\"2017-04-21\"),)]`"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 5\n",
+ "\n",
+ "For the expiration date 2017-04-21, calculate the mid price as the average of the `.ask` and `.bid`. \n",
+ "\n",
+ "Plot the mid price as a function of the strike price `.strike` for put options. Add a curve another curve for the call options."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "@webio": {
+ "lastCommId": null,
+ "lastKernelId": null
+ },
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Julia 1.7.0",
+ "language": "julia",
+ "name": "julia-1.7"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.7.0"
+ },
+ "nteract": {
+ "version": "0.23.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Problemsets/PS10b_OptionDeltas.ipynb b/Problemsets/PS10b_OptionDeltas.ipynb
new file mode 100644
index 0000000..36de03f
--- /dev/null
+++ b/Problemsets/PS10b_OptionDeltas.ipynb
@@ -0,0 +1,229 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Load Packages and Extra Functions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "printyellow (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using Printf, Distributions, OffsetArrays, FiniteDiff\n",
+ "\n",
+ "include(\"jlFiles/OptionsCalculations.jl\")\n",
+ "include(\"jlFiles/printmat.jl\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using Plots\n",
+ "#pyplot(size=(600,400))\n",
+ "gr(size=(480,320))\n",
+ "default(fmt = :svg)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# The Black-Scholes Model\n",
+ "\n",
+ "The next cell calculates call `C` and put prices `P` from the Black-Scholes formula.\n",
+ "\n",
+ "The key parameters are:\n",
+ "`(S,K,m,y,σ) = (current undelying price, strike price,time to expiration,interest rate, volatility)`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "call price at K=42: 2.893 \n",
+ "\n",
+ "put price at K=42: 1.856 \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "(S,K,m,y,σ) = (42,42,0.5,0.05,0.2)\n",
+ "\n",
+ "C = OptionBlackSPs(S,K,m,y,σ)\n",
+ "printlnPs(\"call price at K=$K: \",C,\"\\n\")\n",
+ "\n",
+ "P = OptionBlackSPs(S,K,m,y,σ,0,true)\n",
+ "printlnPs(\"put price at K=$K: \",P,\"\\n\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 1\n",
+ "\n",
+ "For a range of different prices of the underlying asset `S=30.0:60.0`, calculat the call and put prices and plot them (with `S` on the hoizontal axis)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# The Binomial Option Pricing Model\n",
+ "\n",
+ "The next cell contains functions to implement a binomial option pricing model for European style (exercise at expiration only) and American style (exercise any day) options. We use the CRR (Cox-Ross-Rubinstein) parameterisation.\n",
+ "\n",
+ "The key parameters are the same as before, but also `n` which is the number of time steps used in the calculations (which defaults to 250)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "BOPM_American (generic function with 3 methods)"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "\"\"\"\n",
+ "CRRparams(σ,m,n,y)\n",
+ "\n",
+ " BOPM parameters according to CRR\n",
+ "\"\"\"\n",
+ "function CRRparams(σ,m,y,n)\n",
+ " h = m/n #time step size (in years)\n",
+ " u = exp(σ*sqrt(h)) #up move\n",
+ " d = exp(-σ*sqrt(h)) #down move\n",
+ " p = (exp(y*h) - d)/(u-d) #rn prob of up move\n",
+ " return h,u,d,p\n",
+ "end \n",
+ "\n",
+ "function BOPM_European(S,K,m,y,σ,isPut=false,n=250)\n",
+ " (h,u,d,p) = CRRparams(σ,m,y,n)\n",
+ " STree = BuildSTree(S,n,u,d)\n",
+ " price = EuOptionPrice(STree,K,y,h,p,isPut)[0][]\n",
+ " return price\n",
+ "end\n",
+ "\n",
+ "function BOPM_American(S,K,m,y,σ,isPut=false,n=250)\n",
+ " (h,u,d,p) = CRRparams(σ,m,y,n)\n",
+ " STree = BuildSTree(S,n,u,d)\n",
+ " price = AmOptionPrice(STree,K,y,h,p,isPut)[1][0][1]\n",
+ " return price\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "call (Eu) 2.891\n",
+ "put (Eu) 1.854\n",
+ "call (Am) 2.891\n",
+ "put (Am) 1.954\n",
+ "\n",
+ "\u001b[31m\u001b[1mNotice that c_e=c_a but that p_a>=p_e\u001b[22m\u001b[39m\n"
+ ]
+ }
+ ],
+ "source": [
+ "c_e = BOPM_European(S,K,m,y,σ,false) #call price, European style\n",
+ "p_e = BOPM_European(S,K,m,y,σ,true) #put price, European\n",
+ "\n",
+ "c_a = BOPM_American(S,K,m,y,σ,false) #call, American\n",
+ "p_a = BOPM_American(S,K,m,y,σ,true) #put, American\n",
+ "\n",
+ "printmat([c_e,p_e,c_a,p_a],rowNames=[\"call (Eu)\",\"put (Eu)\",\"call (Am)\",\"put (Am)\"])\n",
+ "\n",
+ "printred(\"Notice that c_e=c_a but that p_a>=p_e\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Task 2\n",
+ "\n",
+ "Redo the calculation of p_e and p_a for `S=30:60` and plot the prices."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Delta\n",
+ "\n",
+ "To hedge an option contract (eg. if we are short one option contract), we buy $\\Delta$ units of the underlying asset, where $\\Delta$ is the partial derivative of the option price with respect to the price of the underlying asset.\n",
+ "\n",
+ "Calculate $\\Delta$ for both the European and American puts, using the BOPM function. Do the calculation for each value in `S_range` and plot the results.\n",
+ "\n",
+ "To calculate the derivatives we could use, for instance, \n",
+ "`FiniteDiff.finite_difference_derivative(the function,an S value)`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "@webio": {
+ "lastCommId": null,
+ "lastKernelId": null
+ },
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Julia 1.6.3",
+ "language": "julia",
+ "name": "julia-1.6"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.6.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Problemsets/Solutions/PS01_Basics_Solution.ipynb b/Problemsets/Solutions/PS01_Basics_Solution.ipynb
new file mode 100644
index 0000000..31199ec
--- /dev/null
+++ b/Problemsets/Solutions/PS01_Basics_Solution.ipynb
@@ -0,0 +1,1688 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Basic Julia Tutorial"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Running/Installing Julia\n",
+ "\n",
+ "This is a notebook. To run in you need Julia and jupyter or nteract (see below).\n",
+ "\n",
+ "1. To run Julia without a local installation, use (for instance) [CoCalc](https://cocalc.com).\n",
+ "\n",
+ "2. To install Julia on your machine, [download and install it](https://julialang.org/downloads/). \n",
+ "\n",
+ "3. You may also want to use [VS Code with the Julia extension](https://github.com/julia-vscode/julia-vscode) IDE. See also the [julia-vscode.org](https://www.julia-vscode.org/) for more information.\n",
+ "\n",
+ "4. To run notebooks with either jupyter or nteract from your local installation, see [IJulia](https://github.com/JuliaLang/IJulia.jl) for instructions. See also below for some hints.\n",
+ "\n",
+ "5. As an alternative to jupyter/nteract you can also run notebooks in VS Code (see above).\n",
+ "\n",
+ "\n",
+ "\n",
+ "## More Details on Installing jupyter and nteract\n",
+ "\n",
+ "1. If you want to use nteract do as follows: install IJulia, but do *not* call on `notebook()` to avoid the automatic Python installation. Then install nteract.\n",
+ "\n",
+ "2. After installing IJulia and issuing the command `notebook()` a new local Python installation will be made - unless IJulia finds an existing installation.\n",
+ "\n",
+ "3. If you already have a Python installation, run `ENV[\"JUPYTER\"] = \"C:\\\\Miniconda3\\\\Scripts\\\\jupyter.exe\"` (change the path as needed) before you install IJulia. The best is perhaps to add this to your startup.jl file (~/.julia/config/startup.jl, for instance, C:\\Users\\yourusername\\.julia\\config\\startup.jl if you are on Windows). You can test whether it works by running ```run(`$(ENV[\"JUPYTER\"]) --version`)``` from the Julia REPL.\n",
+ "\n",
+ "4. On Windows, it helps to allow the Python installer to add python to the system path."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Documentation and Help\n",
+ "\n",
+ "1. Cheat sheet at [QuantEcon](https://cheatsheets.quantecon.org/julia-cheatsheet.html)\n",
+ "2. [Wiki book](https://en.wikibooks.org/wiki/Introducing_Julia)\n",
+ "3. [Short tutorials](https://techytok.com/from-zero-to-julia/) \n",
+ "4. [ThinkJulia](https://benlauwens.github.io/ThinkJulia.jl/latest/book.html) is a free on-line book\n",
+ "5. The [official Julia on-line manual](https://docs.julialang.org)\n",
+ "6. Discussion lists are found at\n",
+ " * https://discourse.julialang.org/\n",
+ " * https://stackoverflow.com/questions/tagged/julia-lang\n",
+ " * https://www.reddit.com/r/Julia/\n",
+ " * https://gitter.im/JuliaLang/julia\n",
+ "7. In Julia, do ```? cos``` to get help with the cos function "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# About Notebooks\n",
+ "\n",
+ "This cell is a \"Markdown\" cell. This is meant for comments and documentation, not computations.\n",
+ "\n",
+ "You can change a cell to \"Code\" or \"Markdown\" in the menu.\n",
+ "\n",
+ "Markdown cells can handle LaTeX. An example: $\\alpha = \\beta/2$. A Markdown cell can also contain some *formatting*, like lists of this kind\n",
+ "\n",
+ "1. To insert a new cell, use the menu. \n",
+ "\n",
+ "2. The next cell is \"Code\". You can run it. Text after a # sign is treated as a comment.\n",
+ "\n",
+ "3. The subsequent cell shows how to get help on a command."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "2"
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "a = 2 #this is a comment\n",
+ " #run this cell by using the menu, or by Shift+Enter"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "search: \u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ms\u001b[22m \u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ms\u001b[22mh \u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ms\u001b[22md \u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ms\u001b[22mc \u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ms\u001b[22mpi a\u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ms\u001b[22m a\u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ms\u001b[22mh a\u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ms\u001b[22md sin\u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ms\u001b[22m sin\u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ms\u001b[22md sin\u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22m\u001b[0m\u001b[1ms\u001b[22mpi \u001b[0m\u001b[1mc\u001b[22m\u001b[0m\u001b[1mo\u001b[22mn\u001b[0m\u001b[1ms\u001b[22mt\n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "text/latex": [
+ "\\begin{verbatim}\n",
+ "cos(x)\n",
+ "\\end{verbatim}\n",
+ "Compute cosine of \\texttt{x}, where \\texttt{x} is in radians.\n",
+ "\n",
+ "\\rule{\\textwidth}{1pt}\n",
+ "\\begin{verbatim}\n",
+ "cos(A::AbstractMatrix)\n",
+ "\\end{verbatim}\n",
+ "Compute the matrix cosine of a square matrix \\texttt{A}.\n",
+ "\n",
+ "If \\texttt{A} is symmetric or Hermitian, its eigendecomposition (\\href{@ref}{\\texttt{eigen}}) is used to compute the cosine. Otherwise, the cosine is determined by calling \\href{@ref}{\\texttt{exp}}.\n",
+ "\n",
+ "\\section{Examples}\n",
+ "\\begin{verbatim}\n",
+ "julia> cos(fill(1.0, (2,2)))\n",
+ "2×2 Matrix{Float64}:\n",
+ " 0.291927 -0.708073\n",
+ " -0.708073 0.291927\n",
+ "\\end{verbatim}\n"
+ ],
+ "text/markdown": [
+ "```\n",
+ "cos(x)\n",
+ "```\n",
+ "\n",
+ "Compute cosine of `x`, where `x` is in radians.\n",
+ "\n",
+ "---\n",
+ "\n",
+ "```\n",
+ "cos(A::AbstractMatrix)\n",
+ "```\n",
+ "\n",
+ "Compute the matrix cosine of a square matrix `A`.\n",
+ "\n",
+ "If `A` is symmetric or Hermitian, its eigendecomposition ([`eigen`](@ref)) is used to compute the cosine. Otherwise, the cosine is determined by calling [`exp`](@ref).\n",
+ "\n",
+ "# Examples\n",
+ "\n",
+ "```jldoctest\n",
+ "julia> cos(fill(1.0, (2,2)))\n",
+ "2×2 Matrix{Float64}:\n",
+ " 0.291927 -0.708073\n",
+ " -0.708073 0.291927\n",
+ "```\n"
+ ],
+ "text/plain": [
+ "\u001b[36m cos(x)\u001b[39m\n",
+ "\n",
+ " Compute cosine of \u001b[36mx\u001b[39m, where \u001b[36mx\u001b[39m is in radians.\n",
+ "\n",
+ " ────────────────────────────────────────────────────────────────────────────\n",
+ "\n",
+ "\u001b[36m cos(A::AbstractMatrix)\u001b[39m\n",
+ "\n",
+ " Compute the matrix cosine of a square matrix \u001b[36mA\u001b[39m.\n",
+ "\n",
+ " If \u001b[36mA\u001b[39m is symmetric or Hermitian, its eigendecomposition (\u001b[36meigen\u001b[39m) is used to\n",
+ " compute the cosine. Otherwise, the cosine is determined by calling \u001b[36mexp\u001b[39m.\n",
+ "\n",
+ "\u001b[1m Examples\u001b[22m\n",
+ "\u001b[1m ≡≡≡≡≡≡≡≡≡≡\u001b[22m\n",
+ "\n",
+ "\u001b[36m julia> cos(fill(1.0, (2,2)))\u001b[39m\n",
+ "\u001b[36m 2×2 Matrix{Float64}:\u001b[39m\n",
+ "\u001b[36m 0.291927 -0.708073\u001b[39m\n",
+ "\u001b[36m -0.708073 0.291927\u001b[39m"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "? cos #to get help on the cos() function"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Load Packages and Extra Functions\n",
+ "\n",
+ "There are many packages for Julia, for instance, for plotting or statistical methods (see [JuliaHub](https://juliahub.com/) for a list). To install a package, you do either \n",
+ "\n",
+ "1. (works everywhere) run `import Pkg` and then `Pkg.add(\"Packagename\")`\n",
+ "\n",
+ "2. (works in the Julia console, REPL) enter the \"package manager mode\" by typing `]`, then run `add PackageName`. You leave the package manager mode by ctrl-c or backspace.\n",
+ "\n",
+ "Once a package is installed, you can use it by running\n",
+ "\n",
+ "```\n",
+ "using PackageName\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "printyellow (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using Printf\n",
+ "\n",
+ "include(\"jlFiles/printmat.jl\") #just a function for prettier matrix printing"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using Plots #this loads the Plots package\n",
+ "\n",
+ "#pyplot(size=(600,400)) #choice of plotting backend\n",
+ "gr(size=(480,320))\n",
+ "default(fmt = :svg) #try :png or :svg"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Scalars and Matrices\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Create a Scalar and a Matrix"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "q is a scalar. To print, use println() or printlnPs()\n",
+ "1\n",
+ "\n",
+ "Q is a matrix. To print, use display() or printmat()\n",
+ " 1 2 3 \n",
+ " 4 5 6 \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "q = 1 #create a scalar\n",
+ "Q = [ 1 2 3; #create 2x3 matrix\n",
+ " 4 5 6 ] \n",
+ "println(\"q is a scalar. To print, use println() or printlnPs()\")\n",
+ "println(q)\n",
+ "\n",
+ "println(\"\\nQ is a matrix. To print, use display() or printmat()\")\n",
+ "printmat(Q) #case sensitive (q and Q are different)\n",
+ " #the \\n adds a line break"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Picking Out Parts of a Matrix"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "element [1,2] of Q: 2\n",
+ "\n",
+ "columns 2 and 3 of Q: \n",
+ " 2 3 \n",
+ " 5 6 \n",
+ "\n",
+ "\n",
+ "line 1 of Q (as a vector): \n",
+ " 1 \n",
+ " 2 \n",
+ " 3 \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "println(\"\\n\",\"element [1,2] of Q: \", #commands continue on\n",
+ " Q[1,2]) #the next line (until finished)\n",
+ "\n",
+ "println(\"\\ncolumns 2 and 3 of Q: \")\n",
+ "printmat(Q[:,2:3])\n",
+ "\n",
+ "println(\"\\nline 1 of Q (as a vector): \")\n",
+ "printmat(Q[1,:])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task\n",
+ "Create a 2x2 matrix A\n",
+ "\n",
+ "```\n",
+ "10 10\n",
+ "21 22\n",
+ "```\n",
+ "\n",
+ "Print it\n",
+ "\n",
+ "Change the second row to `[1 2]`. Print again."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " 10 10 \n",
+ " 21 22 \n",
+ "\n",
+ " 10 10 \n",
+ " 1 2 \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "A = [10 10;\n",
+ " 21 22]\n",
+ "printmat(A)\n",
+ "A[2,:] = [1 2]\n",
+ "printmat(A)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Basic Linear Algebra\n",
+ "\n",
+ "The syntax for linear algebra is similar to the standard text book approach. For instance, \n",
+ "* `Q'Q` (or `Q'*Q`) multiplies the transpose ($Q'$) with the matrix ($Q$)\n",
+ "* `A*B` does matrix multiplication\n",
+ "* `100*Q` multiplies each element of the matrix ($Q$) by 100. (You can also do `100Q`.)\n",
+ "\n",
+ "However, to add a scalar to each element of a matrix, use `100 .+ Q`. Notice the dot."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "transpose of Q:\n",
+ " 1 4 \n",
+ " 2 5 \n",
+ " 3 6 \n",
+ "\n",
+ "Q'Q:\n",
+ " 17 22 27 \n",
+ " 22 29 36 \n",
+ " 27 36 45 \n",
+ "\n",
+ "scalar * matrix:\n",
+ " 100 200 300 \n",
+ " 400 500 600 \n",
+ "\n",
+ "scalar .+ matrix:\n",
+ " 101 102 103 \n",
+ " 104 105 106 \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "println(\"transpose of Q:\")\n",
+ "printmat(Q')\n",
+ "\n",
+ "println(\"Q'Q:\")\n",
+ "printmat(Q'Q)\n",
+ "\n",
+ "println(\"scalar * matrix:\")\n",
+ "printmat(100*Q)\n",
+ "\n",
+ "println(\"scalar .+ matrix:\") #notice the dot\n",
+ "printmat(100 .+ Q)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task\n",
+ "\n",
+ "Consider the system of linear equations\n",
+ "\n",
+ "$\n",
+ "Ax = q\n",
+ "$, \n",
+ "\n",
+ "where \n",
+ "$ \n",
+ "q = \\begin{bmatrix} 1 \\\\2 \\end{bmatrix}\n",
+ "$\n",
+ "\n",
+ "You could solve it as\n",
+ "$\n",
+ "x = A^{-1}q\n",
+ "$\n",
+ "\n",
+ "\n",
+ "Solve (numrically) for the vector $x$. Hint: `inv()` Then check that $Ax$ indeed equals $q$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " x\n",
+ " -1.800\n",
+ " 1.900\n",
+ "\n",
+ " A*x q\n",
+ " 1.000 1.000\n",
+ " 2.000 2.000\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ "\n",
+ "q = [1,2]\n",
+ "x = inv(A)*q\n",
+ "printmat(x,colNames=[\"x\"])\n",
+ "\n",
+ "printmat([A*x q],colNames=[\"A*x\",\"q\"])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Creating a Sequence and a Vector"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "θ is a sequence: 1:10:21\n",
+ "\n",
+ "ρ is a vector: \n",
+ " 1 \n",
+ " 11 \n",
+ " 21 \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "θ = 1:10:21 #a range, type \\theta[TAB] to get this symbol\n",
+ "println(\"\\n\",\"θ is a sequence: \",θ)\n",
+ "\n",
+ "ρ = collect(θ) #make the sequence into a vector, \\rho[TAB]\n",
+ "println(\"\\n\",\"ρ is a vector: \")\n",
+ "printmat(ρ)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task\n",
+ "\n",
+ "Create a sequence $\\alpha$ which starts at 0 and ends at 1, taking 11 steps. (Hint: you can also use `range()`)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " 0.000\n",
+ " 0.100\n",
+ " 0.200\n",
+ " 0.300\n",
+ " 0.400\n",
+ " 0.500\n",
+ " 0.600\n",
+ " 0.700\n",
+ " 0.800\n",
+ " 0.900\n",
+ " 1.000\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "α = 0:0.1:1\n",
+ "#α = range(0,1,length=11)\n",
+ "printmat(α)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Comparing Things\n",
+ "\n",
+ "To see if the scalar z <= 0, do \n",
+ "```\n",
+ "vv = z <= 0\n",
+ "```\n",
+ "to get a single output (true or false).\n",
+ "\n",
+ "Instead, if x is an array, do \n",
+ "```\n",
+ "vv = x .<= 0 #notice the dot.\n",
+ "```\n",
+ "to get an array of outputs (same dimension as x)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "x values: \n",
+ " -1.500\n",
+ " -1.000\n",
+ " -0.500\n",
+ " 0.000\n",
+ " 0.500\n",
+ "\n",
+ "true if x is in (-1,0]: \n",
+ " 0 \n",
+ " 0 \n",
+ " 1 \n",
+ " 1 \n",
+ " 0 \n",
+ "\n",
+ "x values that are in (-1,0]: \n",
+ " -0.500\n",
+ " 0.000\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = [-1.5,-1.0,-0.5,0,0.5] #this is a vector\n",
+ "\n",
+ "println(\"x values: \")\n",
+ "printmat(x)\n",
+ "\n",
+ "vv = -1 .< x .<= 0 #true for x values (-1,0], vv is a vector\n",
+ "println(\"true if x is in (-1,0]: \")\n",
+ "printmat(vv)\n",
+ "\n",
+ "x2 = x[vv] #x values for which vv==true\n",
+ "println(\"x values that are in (-1,0]: \")\n",
+ "printmat(x2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task\n",
+ "\n",
+ "Which elements of $\\alpha$ are (weakly) between 0.6 and 0.99?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " vv[-1.5, -1.0, -0.5, 0.0, 0.5]\n",
+ " 0 0.000\n",
+ " 0 0.100\n",
+ " 0 0.200\n",
+ " 0 0.300\n",
+ " 0 0.400\n",
+ " 0 0.500\n",
+ " 1 0.600\n",
+ " 1 0.700\n",
+ " 1 0.800\n",
+ " 1 0.900\n",
+ " 0 1.000\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "vv = 0.6 .<= α .<= 0.99\n",
+ "printmat(vv,α,colNames=[\"vv\",x])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Finding Things\n",
+ "\n",
+ "can be done by, for instance, `findfirst()`, `findall()` and `indexin()`. \n",
+ "\n",
+ "Instead, if you just need to check if the number `z` is in an array (or any collection) `x`, then use `in(z,x)`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "x values: \n",
+ " -1.500\n",
+ " -1.000\n",
+ " -0.500\n",
+ " 0.000\n",
+ " 0.500\n",
+ "\n",
+ "(first) index v in x such x[v]==0: 4\n",
+ "\n",
+ "all indices v in x such x[v]>=0: \n",
+ " 4 \n",
+ " 5 \n",
+ "\n",
+ "\n",
+ "indices in x so that x[v] equals the vector y=[-1.0, 0.0]: \n",
+ " 2 \n",
+ " 4 \n",
+ "\n",
+ "\n",
+ "testing if 0 is in x: true\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = [-1.5,-1.0,-0.5,0,0.5] #this is a vector\n",
+ "\n",
+ "println(\"x values: \")\n",
+ "printmat(x)\n",
+ "\n",
+ "v1 = findfirst(x.==0)\n",
+ "println(\"(first) index v in x such x[v]==0: \",v1)\n",
+ "\n",
+ "v2 = findall(x.>=0)\n",
+ "println(\"\\nall indices v in x such x[v]>=0: \")\n",
+ "printmat(v2)\n",
+ "\n",
+ "y = [-1.0,0]\n",
+ "v3 = indexin(y,x)\n",
+ "println(\"\\nindices in x so that x[v] equals the vector y=$y: \")\n",
+ "printmat(v3)\n",
+ "\n",
+ "v4 = in(0,x)\n",
+ "println(\"\\ntesting if 0 is in x: \",v4)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# if-else\n",
+ "\n",
+ "allows you to run different comman ddepending on a condition which you specify.\n",
+ "\n",
+ "(extra) There are also other (more compact) possibilities for `if-else` case\n",
+ "\n",
+ "1. `y = ifelse(z <= 2,z,2)` or \n",
+ "2. `z <= 2 ? y = z : y = 2`\n",
+ "(In this partcular case, `y=minimum(z,2)` also works.)\n",
+ "\n",
+ "You can also insert an `ifelse` command."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1.05\n"
+ ]
+ }
+ ],
+ "source": [
+ "z = 1.05\n",
+ "\n",
+ "if z <= 2 #(a) if true, run the next command (y=z) and then jump to end\n",
+ " y = z\n",
+ "else #(b) if (a) is false, do this instead\n",
+ " y = 2\n",
+ "end\n",
+ "\n",
+ "#y = ifelse(z <= 2,z,2) #these two versions also work\n",
+ "#z <= 2 ? y = z : y = 2\n",
+ "\n",
+ "println(y)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1.05\n"
+ ]
+ }
+ ],
+ "source": [
+ "if z < 1 #(a) if true, run the next command (y=1) and then jump to end\n",
+ " y = 1\n",
+ "elseif 1 <= z <= 2 #(b) if (a) is false, try this instead \n",
+ " y = z\n",
+ "else #(c) if also (b) is false, do this\n",
+ " y = 2\n",
+ "end\n",
+ "\n",
+ "println(y)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task\n",
+ "\n",
+ "\n",
+ "Use `if-else` to calculate the tax paid by someone with an income of $X$. The tax schedule is progressive so the first 100 of the income pays 40% tax, while income above 100 has a marginal tax rate of 0.6 (that is, $X-100$ pays 60% if $X>100)$. What is the total tax paid and the average tax rate.\n",
+ "Report the results for an income of 150."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " 70.000 0.467\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "X = 150\n",
+ "\n",
+ "if X <= 100\n",
+ " tax = 0.4*X\n",
+ "else\n",
+ " tax = 0.4*100 + 0.6*(X-100)\n",
+ "end\n",
+ "\n",
+ "avgtax = tax/X\n",
+ "printmat(tax,avgtax)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Loops\n",
+ "\n",
+ "The are two types of loops: \"for loops\" and \"while loops\". \n",
+ "\n",
+ "The *for loop* is best when you know how many times you want to loop (for instance, over all $m$ rows in a matrix). \n",
+ "\n",
+ "The *while loop* is best when you want to keep looping until something happens, for instance, that $x_0$ and $x_1$ get really close.\n",
+ "\n",
+ "The default behaviour in *IJulia*, *inside functions* and at the *REPL* promt is that assignments of `x` inside the loop overwrites `x` defined before the loop. To get the same behavior in scripts, you need to add `global x` somewhere inside the loop.\n",
+ "\n",
+ "To make sure that the `y` calculated inside the loop does not affect `y` outside the loop, add `local y`.\n",
+ "\n",
+ "A variable (here `z2`) that does not exist before the loop is local to the loop."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### A Simple \"for loop\"\n",
+ "\n",
+ "The \"for loop\" in the next cell makes 3 iterations and changes a global $x$ variable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "i=3, x=3 and z2=-998\n",
+ "i=6, x=9 and z2=-998\n",
+ "i=9, x=18 and z2=-998\n",
+ "\n",
+ "After loop: x=18 and y=-999\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = 0\n",
+ "y = -999\n",
+ "for i = 3:3:9 #or `i in 3:3:9`, or `v=[3,6,9]; i in v`\n",
+ " #global x #only needed in script\n",
+ " local y #don't overwrite y outside loop\n",
+ " x = x + i #adding i to the \"old\" x\n",
+ " y = i\n",
+ " z2 = -998 #notice: z2 has not been used before \n",
+ " println(\"i=$i, x=$x and z2=$z2\") #$x prints the value of x\n",
+ "end\n",
+ "\n",
+ "println(\"\\nAfter loop: x=$x and y=$y\")\n",
+ "#println(z2) #does not work: z2 is local to the loop"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task\n",
+ "\n",
+ "You have the following financial data\n",
+ "\n",
+ "```\n",
+ "P = [100;108;109] #price series, after dividends\n",
+ "D = [0;2;0] #dividends\n",
+ "```\n",
+ "\n",
+ "For each $t$, calculate the returns\n",
+ "\n",
+ "$\n",
+ "R_t = (P_t+D_t)/P_{t-1} - 1\n",
+ "$,\n",
+ "\n",
+ "by using a loop."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Return\n",
+ "period 2 0.100\n",
+ "period 3 0.009\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "P = [100;108;109] #price series, after dividends\n",
+ "D = [0;2;0] #dividends\n",
+ "\n",
+ "R = zeros(length(P)) #where to store the results\n",
+ "for t = 2:length(P) #P[2] is the 2nd element of P \n",
+ " R[t] = (P[t] + D[t])/P[t-1] - 1\n",
+ "end\n",
+ "R = R[2:end]\n",
+ "\n",
+ "printmat(R,colNames=[\"Return\"],rowNames=string.(\"period \",2:3))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### A Double \"for loop\"\n",
+ "\n",
+ "An example of a nested for for loop\n",
+ "\n",
+ "```\n",
+ "for j = 1:n, i = 1:m\n",
+ " #do something\n",
+ "end\n",
+ "```\n",
+ "\n",
+ "If you prefer, could also write a longer version to do the same thing\n",
+ "```\n",
+ "for j = 1:n \n",
+ " for i = 1:m\n",
+ " #do something\n",
+ " end \n",
+ "end\n",
+ "```\n",
+ "\n",
+ "The next cell uses a double loop to fill a matrix. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "new x matrix: \n",
+ "\n",
+ " 11 12 13 \n",
+ " 21 22 23 \n",
+ " 31 32 33 \n",
+ " 41 42 43 \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "(m,n) = (4,3) #same as m=4;n=3\n",
+ "x = fill(-999,(m,n)) #to put results in, initialized as -999\n",
+ "for i = 1:m, j = 1:n\n",
+ " x[i,j] = 10*i + j\n",
+ "end\n",
+ "\n",
+ "println(\"new x matrix: \\n\")\n",
+ "printmat(x)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## A Simple \"while loop\"\n",
+ "\n",
+ "The \"while loop\" in the next cell iterates until two variables ($x_0$ and $x_1$) get close.\n",
+ "\n",
+ "The background to the example is that we want to solve a function $f(x)=x^2$ for the $x$ value that makes $f(x)=2$. The Newton-Raphson algorithm starts with a value $x_0$ and updates it to\n",
+ "$\n",
+ "x_1 = x_0 + (2-f(x_0))/f'(x_0)\n",
+ "$\n",
+ "where $f'(x_0)$ is the derivative of $f()$ evaluated at $x_0$. The algorithm iterates until $x_0$ and $x_1$ are close. Clearly, we are trying to find the square root of 2."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Solving x^2 = 2 with Newton-Raphson:\n",
+ "\n",
+ " 10 is changed to 5.100\n",
+ " 5.100 is changed to 2.746\n",
+ " 2.746 is changed to 1.737\n",
+ " 1.737 is changed to 1.444\n",
+ " 1.444 is changed to 1.415\n",
+ " 1.415 is changed to 1.414\n",
+ "\n",
+ "The result should be close to 1.414\n"
+ ]
+ }
+ ],
+ "source": [
+ "println(\"Solving x^2 = 2 with Newton-Raphson:\\n\")\n",
+ "\n",
+ "x₀ = Inf #x\\_0[TAB]\n",
+ "x₁ = 10\n",
+ "\n",
+ "while abs(x₁-x₀) > 0.001 #keep going until they get similar\n",
+ " #global x₀, x₁ #only needed in script\n",
+ " local y, dy #don't overwrite any y,dy outside loop\n",
+ " x₀ = x₁ #initial guess is taken from old guess\n",
+ " y = x₀^2 #value of function\n",
+ " dy = 2*x₀ #derivative of function\n",
+ " x₁ = x₀ + (2 - y)/dy #updating the guess, Newton-Raphson\n",
+ " printlnPs(x₀,\" is changed to \",x₁)\n",
+ "end\n",
+ "\n",
+ "printlnPs(\"\\nThe result should be close to \",sqrt(2))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task\n",
+ "\n",
+ "Start at `x=1` and create a while loop that multiplies the previous $x$ by 1.1.(That is, you earn a 10% return each year.) Continue while `x<2`. Print the iterations (iteration number, `x`). So, how many years did it take to double the investment?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " 1 1.100\n",
+ " 2 1.210\n",
+ " 3 1.331\n",
+ " 4 1.464\n",
+ " 5 1.611\n",
+ " 6 1.772\n",
+ " 7 1.949\n",
+ " 8 2.144\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = 1\n",
+ "iter = 0\n",
+ "while x < 2\n",
+ " x = x*1.1\n",
+ " iter = iter + 1 \n",
+ " printlnPs(iter,x)\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# A Simple Function\n",
+ "\n",
+ "The next cell defines a new function, `fn1()`. It takes a scalar input (`x`) and returns a scalar output (`y`).\n",
+ "\n",
+ "If you instead use a vector as the input, then the computation fails. (The reason is that you cannot do x^2 on a vector. You could on a square matrix, though.)\n",
+ "\n",
+ "However, using the \"dot\" syntax\n",
+ "```\n",
+ "y = fn1.(x)\n",
+ "```\n",
+ "gives an array as output where element `y[i,j] = fn1(x[i,j])`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "fn1 (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 23,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "function fn1(x) #define a new function \n",
+ " y = (x-1.1)^2 - 0.5\n",
+ " return y\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "result from fn1(1.5): -0.340\n",
+ "\n",
+ "result from fn1.(x): \n",
+ " -0.490\n",
+ " -0.340\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "y = fn1(1.5)\n",
+ "printlnPs(\"result from fn1(1.5): \",y)\n",
+ "\n",
+ "x = [1;1.5]\n",
+ "#y = fn1(x) #would give an error \n",
+ "y = fn1.(x) #calling on the function, dot. to do for each element in x\n",
+ "printlnPs(\"\\nresult from fn1.(x): \")\n",
+ "printmat(y)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task\n",
+ "\n",
+ "Write a function to calculate \n",
+ "$B =\\exp{(-my)}$, \n",
+ "where $B$ is the price of a bond and $m$ is the time to maturity (measured in years) and $y$ is the (continously compounded) interest rate.\n",
+ "\n",
+ "If $y=0.103$ and $m=0.5$, what is $B$?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " 0.950\n"
+ ]
+ }
+ ],
+ "source": [
+ "BondPrice(y,m) = exp(-m*y) #B as fn of y\n",
+ "\n",
+ "printlnPs(BondPrice(0.103,0.5))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# A First Plot\n",
+ "\n",
+ "With the Plots package you create a a simple plot like this:\n",
+ "\n",
+ "1. Plot two curve by using the `plot([x1 x2],[y1 y2])` command\n",
+ "2. Configure curves by `linecolor =`, `linestyle =` etc\n",
+ "2. Add titles and labels by `title = `, `xlabel = `, etc\n",
+ "\n",
+ "Notice: the *first plot is slow*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x = -3:6/99:6 \n",
+ "\n",
+ "p1 = plot( [x x],[fn1.(x) cos.(x)],\n",
+ " linecolor = [:red :blue],\n",
+ " linestyle = [:solid :dash],\n",
+ " linewidth = [2 1],\n",
+ " label = [\"fn1()\" \"cos\"],\n",
+ " title = \"My Results\",\n",
+ " xlabel = \"x\",\n",
+ " ylabel = \"my output value\" )\n",
+ "display(p1) #not needed in notebook, but useful in script"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task\n",
+ "\n",
+ "Consider different interest rates in the interval (-0.05,0.1). Plot the prices of 3-month and 10-year bonds as functions of the interest rate."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ]
+ },
+ "execution_count": 27,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "y = -0.05:0.001:0.10\n",
+ "\n",
+ "B3m = BondPrice.(y,3/12)\n",
+ "B10y = BondPrice.(y,10)\n",
+ "\n",
+ "plot([y y],[B3m B10y],label = [\"3m\" \"10y\"],xlabel=\"interest rate\",ylabel=\"Bond price\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Types: Integers, Floats, Bools and Others\n",
+ "\n",
+ "Julia has many different types of variables: signed integers (like 2 or -5), floating point numbers (2.0 and -5.1), bools (false/true), bitarrays (similar to bools, but with more efficient use of memory), strings (\"hello\"), Dates (2017-04-23) and many more types."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Integers and Floats"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Finding the type of a, b, A and B:\n",
+ "Int64 Float64 Vector{Int64} Vector{Float64}\n"
+ ]
+ }
+ ],
+ "source": [
+ "a = 2 #integer, Int (Int64 on most machines)\n",
+ "b = 2.0 #floating point, (Float64 on most machines)\n",
+ "A = [1,2]\n",
+ "B = [1.0,2.0]\n",
+ "\n",
+ "println(\"Finding the type of a, b, A and B:\")\n",
+ "println(typeof(a),\" \",typeof(b),\" \",typeof(A),\" \",typeof(B))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bools and BitArrays\n",
+ "\n",
+ "Bools are \"true\" or \"false\". BitArrays are (more memory efficient) versions of this."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Finding the type of c and C:\n",
+ "Bool BitVector\n"
+ ]
+ }
+ ],
+ "source": [
+ "c = 2 > 1.1\n",
+ "C = A .> 1.5 #A is an array, so C is too\n",
+ "\n",
+ "println(\"Finding the type of c and C:\")\n",
+ "println(typeof(c),\" \",typeof(C))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Calculations with Mixed Types\n",
+ "\n",
+ "A calculation like \"integer\" + \"float\" works and the type of the result will be a float (the more flexible type). Similarly, \"bool\" + \"integer\" will give an integer. These promotion rules make it easy to have mixed types in calculations, and also provide a simple way of converting a variable from one type to another. (There are also an explicit convert() function that might be quicker.)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "3.0\n",
+ "3\n"
+ ]
+ }
+ ],
+ "source": [
+ "println(1+2.0) #integer + Float\n",
+ "println((1>0) + 2) #bool + integer"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "@webio": {
+ "lastCommId": null,
+ "lastKernelId": null
+ },
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Julia 1.6.3",
+ "language": "julia",
+ "name": "julia-1.6"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.6.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Problemsets/Solutions/PS02_Stats_Solution.ipynb b/Problemsets/Solutions/PS02_Stats_Solution.ipynb
new file mode 100644
index 0000000..4752b12
--- /dev/null
+++ b/Problemsets/Solutions/PS02_Stats_Solution.ipynb
@@ -0,0 +1,1742 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Load Packages and Extra Functions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "printyellow (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using Statistics, Printf, Dates, DelimitedFiles, Distributions, LinearAlgebra\n",
+ "\n",
+ "include(\"jlFiles/printmat.jl\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using Plots\n",
+ "\n",
+ "#pyplot(size=(600,400))\n",
+ "gr(size=(480,320))\n",
+ "default(fmt = :svg)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Load Data from a csv File"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "first four lines of x:\n",
+ "1970-01-01 -5.480 -4.875 -8.100\n",
+ "1970-02-01 1.465 7.546 5.130\n",
+ "1970-03-01 -7.232 1.061 -1.060\n",
+ "1970-04-01 -24.488 -8.481 -11.000\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = readdlm(\"Data/Portfolios_SGLV.csv\",',',skipstart=1) #reading the csv file\n",
+ " #skip 1st line\n",
+ "println(\"\\nfirst four lines of x:\")\n",
+ "printmat(x[1:4,:])\n",
+ "\n",
+ "dN = Date.(x[:,1]) #creating variables\n",
+ "Re = convert.(Float64,x[:,2:3]) #small growth (SG), large value (LV)\n",
+ "Rme = convert.(Float64,x[:,end]); #market"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task 1: Means and Standard Deviations\n",
+ "\n",
+ "Estimate and print the means and standard deviations of the three series (in `Re` and `Rme`)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " SG LV Market\n",
+ "mean 0.218 0.677 0.593\n",
+ "std 8.079 5.772 4.595\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "μ = mean([Re Rme],dims=1) \n",
+ "σ = std([Re Rme],dims=1) \n",
+ "\n",
+ "printmat([μ;σ],colNames=[\"SG\",\"LV\",\"Market\"],rowNames=[\"mean\",\"std\"])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task 2: Correlations\n",
+ "\n",
+ "Estimate and print the correlation matrix."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " 1.000 0.563 0.804\n",
+ " 0.563 1.000 0.774\n",
+ " 0.804 0.774 1.000\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "printmat(cor([Re Rme]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task 3: OLS\n",
+ "\n",
+ "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",
+ "1. `cov_b = inv(x'x)*var(u)` where `u` are the residuals\n",
+ "2. `std_b = sqrt.(diag(cov_b))`\n",
+ "\n",
+ "Hint: cell 3 (or so) in [OLS notebook on Paul Söderlind's Github](https://github.com/PaulSoderlind/FinancialEconometrics/blob/master/Ch02_OLS1.ipynb)\n",
+ "\n",
+ "Then, regress each of return `Re[:,1]` and `Re[:,2]` on the market `Rme` and a constant. Report the coefficients and standard errors."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "OLS (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "function OLS(y,x) \n",
+ " b = x\\y\n",
+ " u = y - x*b\n",
+ " R2 = 1 - var(u)/var(y)\n",
+ " cov_b = inv(x'x)*var(u)\n",
+ " std_b = sqrt.(diag(cov_b))\n",
+ " return b, std_b, R2\n",
+ "end "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Small growth\n",
+ " coef StdErr\n",
+ "c -0.620 0.196\n",
+ "Rme 1.414 0.042\n",
+ "\n",
+ "Large value\n",
+ " coef StdErr\n",
+ "c 0.100 0.149\n",
+ "Rme 0.972 0.032\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "T = size(Re,1) #number of time periods\n",
+ "\n",
+ "c = ones(T) #a vector with ones\n",
+ "x = [c Rme] #x is a Tx2 matrix\n",
+ "b1 = x\\Re[:,1] \n",
+ "b2 = x\\Re[:,2] \n",
+ "(b1,std_b1,) = OLS(Re[:,1],x)\n",
+ "(b2,std_b2,) = OLS(Re[:,2],x)\n",
+ "\n",
+ "println(\"Small growth\")\n",
+ "printmat([b1 std_b1],colNames=[\"coef\",\"StdErr\"],rowNames=[\"c\",\"Rme\"])\n",
+ "println(\"Large value\")\n",
+ "printmat([b2 std_b2],colNames=[\"coef\",\"StdErr\"],rowNames=[\"c\",\"Rme\"])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Task 4: Scatter Plot\n",
+ "\n",
+ "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."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "