317 lines
495 KiB
Plaintext
317 lines
495 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Load Data \n",
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"\n",
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"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",
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"\n",
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"Test if the dates in the two files are the same.\n",
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"\n",
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"The currency names/abbreviations are\n",
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"`[\"AUD\",\"CAD\",\"EUR\",\"JPY\",\"NZD\",\"NOK\",\"SEK\",\"CHF\",\"GBP\"]` "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [],
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"source": [
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"using DelimitedFiles, Printf, Dates, Plots, Statistics\n",
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"\n",
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"include(\"jlFiles/printmat.jl\")\n",
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"gr(size=(480,320))\n",
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"default(fmt = :svg)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"All dates are the same"
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]
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}
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],
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"source": [
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"# Load data\n",
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"R = readdlm(\"Data/Data_Returns.csv\",',',skipstart=1) \n",
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"fp = readdlm(\"Data/Data_Forwardpremia.csv\",',',skipstart=2) \n",
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"\n",
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"# Convert to julia dates\n",
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"R[:,1] .= Date.(R[:,1])\n",
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"fp[:,1] .= Date.(fp[:,1])\n",
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"\n",
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"# Check if all dates are the same\n",
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"if all(fp[:,1] .== R[:,1])\n",
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" print(\"All dates are the same\")\n",
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"else \n",
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" print(\"Some dates are different\")\n",
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"end\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Plot the forward premia\n",
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"\n",
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"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",
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"\n",
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"Make sure to \n",
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"1. have tick marks on the x-axis at `[Date(2000),Date(2010),Date(2020)]`\n",
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"\n",
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"2. limit the y-axis to `(-6,6)`\n",
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"\n",
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"3. Put the currency name/abbreviation in the title of each subfigure."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {},
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"outputs": [
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{
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"data": {
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||
},
|
||
"execution_count": 16,
|
||
"metadata": {},
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||
"output_type": "execute_result"
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||
}
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||
],
|
||
"source": [
|
||
"# Dates\n",
|
||
"dates = fp[:,1]\n",
|
||
"\n",
|
||
"# Function to create the Plots\n",
|
||
"function getForwardPremiaPlot(y, title)\n",
|
||
" return plot(dates, y .* 12, \n",
|
||
" size = (1280, 720),\n",
|
||
" ylim = (-6, 6),\n",
|
||
" xticks = ([Date(2000),Date(2010),Date(2020)], [\"2000\",\"2010\",\"2020\"]),\n",
|
||
" legend = false,\n",
|
||
" title = title,\n",
|
||
" color = \"blue\",\n",
|
||
" )\n",
|
||
"end\n",
|
||
"\n",
|
||
"# Create plot with 3x3 subplots \n",
|
||
"plot(getForwardPremiaPlot(fp[:,2], \"AUD\"), getForwardPremiaPlot(fp[:,3], \"CAD\"), getForwardPremiaPlot(fp[:,4], \"EUR\"),\n",
|
||
"getForwardPremiaPlot(fp[:,5], \"JPY\"),getForwardPremiaPlot(fp[:,6], \"NZD\"),getForwardPremiaPlot(fp[:,7], \"NOK\"),\n",
|
||
"getForwardPremiaPlot(fp[:,8], \"SEK\"),getForwardPremiaPlot(fp[:,9], \"CHF\"),getForwardPremiaPlot(fp[:,10], \"GBP\"))"
|
||
]
|
||
},
|
||
{
|
||
"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": 17,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
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"data": {
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},
|
||
"execution_count": 17,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
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||
}
|
||
],
|
||
"source": [
|
||
"# Function to create the Plots\n",
|
||
"function getCumulatedLogReturnsPlot(y, title)\n",
|
||
" return plot(dates, cumsum(log.(1 .+ y./100)), \n",
|
||
" size = (1280, 720),\n",
|
||
" ylim = (-1, 1),\n",
|
||
" xticks = ([Date(2000),Date(2010),Date(2020)], [\"2000\",\"2010\",\"2020\"]),\n",
|
||
" legend = false,\n",
|
||
" title = title,\n",
|
||
" color = \"blue\"\n",
|
||
" )\n",
|
||
"end\n",
|
||
"\n",
|
||
"# Create plot with 3x3 subplots \n",
|
||
"plot(getCumulatedLogReturnsPlot(R[:,2], \"AUD\"), getCumulatedLogReturnsPlot(R[:,3], \"CAD\"), getCumulatedLogReturnsPlot(R[:,4], \"EUR\"),\n",
|
||
"getCumulatedLogReturnsPlot(R[:,5], \"JPY\"),getCumulatedLogReturnsPlot(R[:,6], \"NZD\"),getCumulatedLogReturnsPlot(R[:,7], \"NOK\"),\n",
|
||
"getCumulatedLogReturnsPlot(R[:,8], \"SEK\"),getCumulatedLogReturnsPlot(R[:,9], \"CHF\"),getCumulatedLogReturnsPlot(R[:,10], \"GBP\"))\n"
|
||
]
|
||
},
|
||
{
|
||
"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": 18,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
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|
||
},
|
||
"execution_count": 18,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Remove date from matrix\n",
|
||
"fpNoDates = fp[:,2:10]\n",
|
||
"RNoDates = R[:,2:10]\n",
|
||
"\n",
|
||
"(T, n) = size(fpNoDates)\n",
|
||
"\n",
|
||
"#number of high/low positions \n",
|
||
"m = 4 \n",
|
||
"\n",
|
||
"# Create empty array\n",
|
||
"R_1 = fill(NaN,T)\n",
|
||
"EW = fill(NaN,T)\n",
|
||
"Frequency = fill(0, (1, n))\n",
|
||
"\n",
|
||
"#loop over periods\n",
|
||
"for t = 2:T \n",
|
||
" s = sortperm(fpNoDates[t-1,:])\n",
|
||
" w = zeros(n)\n",
|
||
" # Set portfolio weight to -1/4 for the lowest 4 forward premia\n",
|
||
" w[s[1:m]] .= -1/m\n",
|
||
" # Set portfolio weight to 1/4 for the highest 4 forward premia\n",
|
||
" w[s[end-m+1:end]] .= 1/m\n",
|
||
" # Calculate weighted portfolio returns\n",
|
||
" R_1[t] = w'RNoDates[t,:]\n",
|
||
" # Calculate EW portfolio returns\n",
|
||
" EW[t] = fill(1/n, n)'RNoDates[t,:]\n",
|
||
" # Calculate frequency of currencies for the highest 4 forward premia\n",
|
||
" Frequency[s[end-m+1:end]] .+= 1\n",
|
||
"end\n",
|
||
"\n",
|
||
"# Replace NaN with 0\n",
|
||
"R_1[isnan.(R_1)] .= 0\n",
|
||
"EW[isnan.(EW)] .= 0\n",
|
||
"\n",
|
||
"plot(dates, [cumsum(log.(1 .+ R_1./100)) cumsum(log.(1 .+ EW./100))], \n",
|
||
" size = (1280, 720),\n",
|
||
" ylim = (-1, 1),\n",
|
||
" xticks = ([Date(2000),Date(2010),Date(2020)], [\"2000\",\"2010\",\"2020\"]),\n",
|
||
" label = [\"CT\" \"EW\"],\n",
|
||
" title = \"Comparison of performance\",\n",
|
||
" color = [\"red\" \"blue\"]\n",
|
||
" )\n"
|
||
]
|
||
},
|
||
{
|
||
"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": 19,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"1.\n",
|
||
" CT EW\n",
|
||
"avg return 0.284 0.018\n",
|
||
"std 2.042 2.259\n",
|
||
"SR 0.139 0.008\n",
|
||
"\n",
|
||
"2. frequency of periods in high carry trade portfolio\n",
|
||
" amount\n",
|
||
"AUD 295 \n",
|
||
"CAD 140 \n",
|
||
"EUR 7 \n",
|
||
"JPY 0 \n",
|
||
"NZD 287 \n",
|
||
"NOK 213 \n",
|
||
"SEK 95 \n",
|
||
"CHF 0 \n",
|
||
"GBP 159 \n",
|
||
"\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Calculate avg, std, sr\n",
|
||
"R_all = [R_1[2:end] EW[2:end]]\n",
|
||
"\n",
|
||
"μ = mean(R_all,dims=1)\n",
|
||
"σ = std(R_all,dims=1)\n",
|
||
"SR = μ./σ\n",
|
||
"\n",
|
||
"println(\"1.\")\n",
|
||
"printmat([μ;σ;SR],colNames=[\"CT\",\"EW\"],rowNames=[\"avg return\",\"std\",\"SR\"])\n",
|
||
"\n",
|
||
"println(\"2. frequency of periods in high carry trade portfolio\")\n",
|
||
"printmat(Frequency[:] ,colNames=[\"amount\"],rowNames=[\"AUD\",\"CAD\",\"EUR\",\"JPY\",\"NZD\",\"NOK\",\"SEK\",\"CHF\",\"GBP\"])"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"@webio": {
|
||
"lastCommId": null,
|
||
"lastKernelId": null
|
||
},
|
||
"anaconda-cloud": {},
|
||
"kernelspec": {
|
||
"display_name": "Julia 1.7.0-rc1",
|
||
"language": "julia",
|
||
"name": "julia-1.7"
|
||
},
|
||
"language_info": {
|
||
"file_extension": ".jl",
|
||
"mimetype": "application/julia",
|
||
"name": "julia",
|
||
"version": "1.7.0"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 4
|
||
}
|