{ "cells": [ { "cell_type": "markdown", "id": "0af08339-9e59-4ccc-8066-4761e7a714d8", "metadata": {}, "source": [ "# Sample R notebook - Example Financial Analysis\n", "\n", "In this notebook, we illustrate the use of R with several code examples showing how to gather and use financial data, as well as fit financial models, eventually with deep learning.\n", "\n", "The code below is R code. Please make sure to execute this only after you've installed the R kernel as in the previous notebook titled `1._InstallR.ipynb`\n", "\n", "This notebook uses the R kernel. You will find this in the launcher. " ] }, { "cell_type": "markdown", "id": "d7d2383e-cf10-4559-a111-3dac38f6e32e", "metadata": {}, "source": [ "## Check that plotting works\n", "\n", "It's good to start by checking that plots work in the notebook so that we know the graphical support in R is working. Here we generate 1 million standard normal random variates and plot the histogram, which shows that it is normally distributed. We also overlay a grid on the plot. " ] }, { "cell_type": "code", "execution_count": 24, "id": "a7a80d0d-3f8a-40d4-b5ef-cfc33aee286f", "metadata": {}, "outputs": [ { "data": { "image/png": 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Ih1k2VFiOQPiKQFnkVa3qXb0/YzhPoZ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\nPkskq29hD76NHlexPiaS1ffjEaxr1eM1rI+JFN9dM+JZ1ld2LBs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"text/plain": [ "Plot with title “Histogram of x”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = rnorm(1000000) # normal random numbers\n", "hist(x,100) # histogram with 100 bins\n", "grid(lwd=2) # a grid with adjusted line width" ] }, { "cell_type": "markdown", "id": "2e808a80-cdd9-4f3e-96a0-9ec359d0b00a", "metadata": {}, "source": [ "## Installing R packages\n", "\n", "You can install multiple R packages in this notebook as follows. The `install.packages` function in R can take a list of packages, concatenated together using the `c()` function. We install below two packages: (i) `quantmod` (https://www.quantmod.com/) a financial data package, and `magrittr` (https://cran.r-project.org/web/packages/magrittr/vignettes/magrittr.html) used for piping. \n", "\n", "You can install these once and not every time you use this notebook. The first time you use `install.packages` you will also be required to choose a [CRAN](https://cran.r-project.org/) mirror for the download. " ] }, { "cell_type": "code", "execution_count": 46, "id": "d59163df-4408-4859-9d40-13675eb1e671", "metadata": {}, "outputs": [], "source": [ "install.packages(c(\"quantmod\", \"magrittr\"))" ] }, { "cell_type": "markdown", "id": "d9fe7164-a6f9-40bf-a4bf-a91df92e02c2", "metadata": {}, "source": [ "We now use the quantmod package to download stock prices as a basic example. \n", "\n", "We use the S&P 500 index here. " ] }, { "cell_type": "code", "execution_count": 26, "id": "fe878940-31b0-42a6-9bc8-d362b1d2fde4", "metadata": {}, "outputs": [], "source": [ "ticker = '^GSPC'" ] }, { "cell_type": "markdown", "id": "a0e29f21-3cac-43e5-8edd-6b17dcf8a31b", "metadata": {}, "source": [ "Next, we will invoke the quantmod package. Then we use the `getSymbols` function to get the chosen ticker (or tickers in a concatenated list), we then convert the table into a dataframe. \n", "\n", "We can examine the dataframe and also plot the adjusted prices of the ticker. " ] }, { "cell_type": "code", "execution_count": 27, "id": "75288599-d59c-4159-9b02-5135ff945881", "metadata": {}, "outputs": [ { "data": { "text/html": [ "'^GSPC'" ], "text/latex": [ "'\\textasciicircum{}GSPC'" ], "text/markdown": [ "'^GSPC'" ], "text/plain": [ "[1] \"^GSPC\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "library(quantmod)\n", "getSymbols(ticker)\n", "GSPC = as.data.frame(GSPC)" ] }, { "cell_type": "code", "execution_count": 5, "id": "cc078550-6f78-459a-a2e9-68d4fda48b54", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
GSPC.OpenGSPC.HighGSPC.LowGSPC.CloseGSPC.VolumeGSPC.Adjusted
2007-01-031418.03 1429.42 1407.86 1416.60 34291600001416.60
2007-01-041416.60 1421.84 1408.43 1418.34 30044600001418.34
2007-01-051418.34 1418.34 1405.75 1409.71 29194000001409.71
2007-01-081409.26 1414.98 1403.97 1412.84 27633400001412.84
2007-01-091412.84 1415.61 1405.42 1412.11 30383800001412.11
2007-01-101408.70 1415.99 1405.32 1414.85 27646600001414.85
\n" ], "text/latex": [ "\\begin{tabular}{r|llllll}\n", " & GSPC.Open & GSPC.High & GSPC.Low & GSPC.Close & GSPC.Volume & GSPC.Adjusted\\\\\n", "\\hline\n", "\t2007-01-03 & 1418.03 & 1429.42 & 1407.86 & 1416.60 & 3429160000 & 1416.60 \\\\\n", "\t2007-01-04 & 1416.60 & 1421.84 & 1408.43 & 1418.34 & 3004460000 & 1418.34 \\\\\n", "\t2007-01-05 & 1418.34 & 1418.34 & 1405.75 & 1409.71 & 2919400000 & 1409.71 \\\\\n", "\t2007-01-08 & 1409.26 & 1414.98 & 1403.97 & 1412.84 & 2763340000 & 1412.84 \\\\\n", "\t2007-01-09 & 1412.84 & 1415.61 & 1405.42 & 1412.11 & 3038380000 & 1412.11 \\\\\n", "\t2007-01-10 & 1408.70 & 1415.99 & 1405.32 & 1414.85 & 2764660000 & 1414.85 \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "| | GSPC.Open | GSPC.High | GSPC.Low | GSPC.Close | GSPC.Volume | GSPC.Adjusted |\n", "|---|---|---|---|---|---|---|\n", "| 2007-01-03 | 1418.03 | 1429.42 | 1407.86 | 1416.60 | 3429160000 | 1416.60 |\n", "| 2007-01-04 | 1416.60 | 1421.84 | 1408.43 | 1418.34 | 3004460000 | 1418.34 |\n", "| 2007-01-05 | 1418.34 | 1418.34 | 1405.75 | 1409.71 | 2919400000 | 1409.71 |\n", "| 2007-01-08 | 1409.26 | 1414.98 | 1403.97 | 1412.84 | 2763340000 | 1412.84 |\n", "| 2007-01-09 | 1412.84 | 1415.61 | 1405.42 | 1412.11 | 3038380000 | 1412.11 |\n", "| 2007-01-10 | 1408.70 | 1415.99 | 1405.32 | 1414.85 | 2764660000 | 1414.85 |\n", "\n" ], "text/plain": [ " GSPC.Open GSPC.High GSPC.Low GSPC.Close GSPC.Volume GSPC.Adjusted\n", "2007-01-03 1418.03 1429.42 1407.86 1416.60 3429160000 1416.60 \n", "2007-01-04 1416.60 1421.84 1408.43 1418.34 3004460000 1418.34 \n", "2007-01-05 1418.34 1418.34 1405.75 1409.71 2919400000 1409.71 \n", "2007-01-08 1409.26 1414.98 1403.97 1412.84 2763340000 1412.84 \n", "2007-01-09 1412.84 1415.61 1405.42 1412.11 3038380000 1412.11 \n", "2007-01-10 1408.70 1415.99 1405.32 1414.85 2764660000 1414.85 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "head(GSPC)" ] }, { "cell_type": "code", "execution_count": 28, "id": "77f7571a-faa7-4443-8844-5b5e34533170", "metadata": {}, "outputs": [ { "data": { "image/png": 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0yelYzFE8KxeEI49v/evDtCZYkTJbzjcifniYEdkdY4FyMWbz2Rm/fgdUwMcC6k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\nICAgNTW1e/fuNpvNYrGUlZUdO3bs4MGDc+bM2bZtW05OTphXHkeL62C1XhH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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(GSPC$GSPC.Adjusted, type='l', col='blue', lwd=1.5)\n", "grid()" ] }, { "cell_type": "markdown", "id": "94023ebe-5e64-4662-9722-514d00183a45", "metadata": {}, "source": [ "We can invoke the same functionality in R using pipes with the `magrittr` package. Can you see why the package is so named? " ] }, { "cell_type": "code", "execution_count": 29, "id": "bcb52893-4069-4ad3-a166-a097b1569553", "metadata": {}, "outputs": [ { "data": { "image/png": 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VprTHanVuUTFphkk1ZlGiOR2cCfgO1fG/GxNzGWXO8ejJhS5liGa+3cr4xlbLkQ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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "library(magrittr)\n", "GSPC$GSPC.Adjusted %>% plot(type='l'); grid()" ] }, { "cell_type": "markdown", "id": "e1c50667-7dc1-4541-93f5-0a6e7a912e7a", "metadata": {}, "source": [ "## Regression Analysis \n", "\n", "We can examine a simple regression of a chosen stock's return on the market index returns so that we can see how it is related to moves in the broad stock market. We choose Tesla here. \n", "\n", "Let's collect the two time series first for both the index and the stock. Note that we already downloaded the S&P 500 index data above. Below, we add a column of dates to that dataframe. We also download Tesla stock prices and add a date column as well. " ] }, { "cell_type": "code", "execution_count": 30, "id": "154018ac-136e-4a0e-9852-cbbeac0e8149", "metadata": {}, "outputs": [ { "data": { "text/html": [ "'TSLA'" ], "text/latex": [ "'TSLA'" ], "text/markdown": [ "'TSLA'" ], "text/plain": [ "[1] \"TSLA\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "GSPC$dt = rownames(GSPC)\n", "\n", "getSymbols('TSLA')\n", "TSLA = as.data.frame(TSLA)\n", "TSLA$dt = rownames(TSLA)" ] }, { "cell_type": "code", "execution_count": 31, "id": "f43fe5b1-4cf3-40f8-bab0-0e52b640d0fa", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
TSLA.OpenTSLA.HighTSLA.LowTSLA.CloseTSLA.VolumeTSLA.Adjusteddt
2010-06-293.800 5.000 3.508 4.778 93831500 4.778 2010-06-29
2010-06-305.158 6.084 4.660 4.766 85935500 4.766 2010-06-30
2010-07-015.000 5.184 4.054 4.392 41094000 4.392 2010-07-01
2010-07-024.600 4.620 3.742 3.840 25699000 3.840 2010-07-02
2010-07-064.000 4.000 3.166 3.222 34334500 3.222 2010-07-06
2010-07-073.280 3.326 2.996 3.160 34608500 3.160 2010-07-07
\n" ], "text/latex": [ "\\begin{tabular}{r|lllllll}\n", " & TSLA.Open & TSLA.High & TSLA.Low & TSLA.Close & TSLA.Volume & TSLA.Adjusted & dt\\\\\n", "\\hline\n", "\t2010-06-29 & 3.800 & 5.000 & 3.508 & 4.778 & 93831500 & 4.778 & 2010-06-29\\\\\n", "\t2010-06-30 & 5.158 & 6.084 & 4.660 & 4.766 & 85935500 & 4.766 & 2010-06-30\\\\\n", "\t2010-07-01 & 5.000 & 5.184 & 4.054 & 4.392 & 41094000 & 4.392 & 2010-07-01\\\\\n", "\t2010-07-02 & 4.600 & 4.620 & 3.742 & 3.840 & 25699000 & 3.840 & 2010-07-02\\\\\n", "\t2010-07-06 & 4.000 & 4.000 & 3.166 & 3.222 & 34334500 & 3.222 & 2010-07-06\\\\\n", "\t2010-07-07 & 3.280 & 3.326 & 2.996 & 3.160 & 34608500 & 3.160 & 2010-07-07\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "| | TSLA.Open | TSLA.High | TSLA.Low | TSLA.Close | TSLA.Volume | TSLA.Adjusted | dt |\n", "|---|---|---|---|---|---|---|---|\n", "| 2010-06-29 | 3.800 | 5.000 | 3.508 | 4.778 | 93831500 | 4.778 | 2010-06-29 |\n", "| 2010-06-30 | 5.158 | 6.084 | 4.660 | 4.766 | 85935500 | 4.766 | 2010-06-30 |\n", "| 2010-07-01 | 5.000 | 5.184 | 4.054 | 4.392 | 41094000 | 4.392 | 2010-07-01 |\n", "| 2010-07-02 | 4.600 | 4.620 | 3.742 | 3.840 | 25699000 | 3.840 | 2010-07-02 |\n", "| 2010-07-06 | 4.000 | 4.000 | 3.166 | 3.222 | 34334500 | 3.222 | 2010-07-06 |\n", "| 2010-07-07 | 3.280 | 3.326 | 2.996 | 3.160 | 34608500 | 3.160 | 2010-07-07 |\n", "\n" ], "text/plain": [ " TSLA.Open TSLA.High TSLA.Low TSLA.Close TSLA.Volume TSLA.Adjusted\n", "2010-06-29 3.800 5.000 3.508 4.778 93831500 4.778 \n", "2010-06-30 5.158 6.084 4.660 4.766 85935500 4.766 \n", "2010-07-01 5.000 5.184 4.054 4.392 41094000 4.392 \n", "2010-07-02 4.600 4.620 3.742 3.840 25699000 3.840 \n", "2010-07-06 4.000 4.000 3.166 3.222 34334500 3.222 \n", "2010-07-07 3.280 3.326 2.996 3.160 34608500 3.160 \n", " dt \n", "2010-06-29 2010-06-29\n", "2010-06-30 2010-06-30\n", "2010-07-01 2010-07-01\n", "2010-07-02 2010-07-02\n", "2010-07-06 2010-07-06\n", "2010-07-07 2010-07-07" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "head(TSLA)" ] }, { "cell_type": "markdown", "id": "6caf88f6-b39e-4bd4-bc39-15d4b08936dd", "metadata": {}, "source": [ "## Merging two dataframes\n", "\n", "We have two separate dataframes, one for GSPC and the other for TSLA. They cover different date ranges, and we wish to line up the data for the two tickers. One way to do this is to join the two dataframes on date using an intersection (inner) join, so that the rows that are retained are the ones for which the two tickers have common dates. It is really easy to do so in R using the `merge` function. The key for the join is the date column. " ] }, { "cell_type": "code", "execution_count": 32, "id": "e4cde865-2a00-4852-a6aa-8dbefcbd3c8b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
dtGSPC.OpenGSPC.HighGSPC.LowGSPC.CloseGSPC.VolumeGSPC.AdjustedTSLA.OpenTSLA.HighTSLA.LowTSLA.CloseTSLA.VolumeTSLA.Adjusted
2010-06-291071.10 1071.10 1035.18 1041.24 61367000001041.24 3.800 5.000 3.508 4.778 93831500 4.778
2010-06-301040.56 1048.08 1028.33 1030.71 50670800001030.71 5.158 6.084 4.660 4.766 85935500 4.766
2010-07-011031.10 1033.58 1010.91 1027.37 64357700001027.37 5.000 5.184 4.054 4.392 41094000 4.392
2010-07-021027.65 1032.95 1015.93 1022.58 39685000001022.58 4.600 4.620 3.742 3.840 25699000 3.840
2010-07-061028.09 1042.50 1018.35 1028.06 46912400001028.06 4.000 4.000 3.166 3.222 34334500 3.222
2010-07-071028.54 1060.89 1028.54 1060.27 49312200001060.27 3.280 3.326 2.996 3.160 34608500 3.160
\n" ], "text/latex": [ "\\begin{tabular}{r|lllllllllllll}\n", " dt & GSPC.Open & GSPC.High & GSPC.Low & GSPC.Close & GSPC.Volume & GSPC.Adjusted & TSLA.Open & TSLA.High & TSLA.Low & TSLA.Close & TSLA.Volume & TSLA.Adjusted\\\\\n", "\\hline\n", "\t 2010-06-29 & 1071.10 & 1071.10 & 1035.18 & 1041.24 & 6136700000 & 1041.24 & 3.800 & 5.000 & 3.508 & 4.778 & 93831500 & 4.778 \\\\\n", "\t 2010-06-30 & 1040.56 & 1048.08 & 1028.33 & 1030.71 & 5067080000 & 1030.71 & 5.158 & 6.084 & 4.660 & 4.766 & 85935500 & 4.766 \\\\\n", "\t 2010-07-01 & 1031.10 & 1033.58 & 1010.91 & 1027.37 & 6435770000 & 1027.37 & 5.000 & 5.184 & 4.054 & 4.392 & 41094000 & 4.392 \\\\\n", "\t 2010-07-02 & 1027.65 & 1032.95 & 1015.93 & 1022.58 & 3968500000 & 1022.58 & 4.600 & 4.620 & 3.742 & 3.840 & 25699000 & 3.840 \\\\\n", "\t 2010-07-06 & 1028.09 & 1042.50 & 1018.35 & 1028.06 & 4691240000 & 1028.06 & 4.000 & 4.000 & 3.166 & 3.222 & 34334500 & 3.222 \\\\\n", "\t 2010-07-07 & 1028.54 & 1060.89 & 1028.54 & 1060.27 & 4931220000 & 1060.27 & 3.280 & 3.326 & 2.996 & 3.160 & 34608500 & 3.160 \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "| dt | GSPC.Open | GSPC.High | GSPC.Low | GSPC.Close | GSPC.Volume | GSPC.Adjusted | TSLA.Open | TSLA.High | TSLA.Low | TSLA.Close | TSLA.Volume | TSLA.Adjusted |\n", "|---|---|---|---|---|---|---|---|---|---|---|---|---|\n", "| 2010-06-29 | 1071.10 | 1071.10 | 1035.18 | 1041.24 | 6136700000 | 1041.24 | 3.800 | 5.000 | 3.508 | 4.778 | 93831500 | 4.778 |\n", "| 2010-06-30 | 1040.56 | 1048.08 | 1028.33 | 1030.71 | 5067080000 | 1030.71 | 5.158 | 6.084 | 4.660 | 4.766 | 85935500 | 4.766 |\n", "| 2010-07-01 | 1031.10 | 1033.58 | 1010.91 | 1027.37 | 6435770000 | 1027.37 | 5.000 | 5.184 | 4.054 | 4.392 | 41094000 | 4.392 |\n", "| 2010-07-02 | 1027.65 | 1032.95 | 1015.93 | 1022.58 | 3968500000 | 1022.58 | 4.600 | 4.620 | 3.742 | 3.840 | 25699000 | 3.840 |\n", "| 2010-07-06 | 1028.09 | 1042.50 | 1018.35 | 1028.06 | 4691240000 | 1028.06 | 4.000 | 4.000 | 3.166 | 3.222 | 34334500 | 3.222 |\n", "| 2010-07-07 | 1028.54 | 1060.89 | 1028.54 | 1060.27 | 4931220000 | 1060.27 | 3.280 | 3.326 | 2.996 | 3.160 | 34608500 | 3.160 |\n", "\n" ], "text/plain": [ " dt GSPC.Open GSPC.High GSPC.Low GSPC.Close GSPC.Volume GSPC.Adjusted\n", "1 2010-06-29 1071.10 1071.10 1035.18 1041.24 6136700000 1041.24 \n", "2 2010-06-30 1040.56 1048.08 1028.33 1030.71 5067080000 1030.71 \n", "3 2010-07-01 1031.10 1033.58 1010.91 1027.37 6435770000 1027.37 \n", "4 2010-07-02 1027.65 1032.95 1015.93 1022.58 3968500000 1022.58 \n", "5 2010-07-06 1028.09 1042.50 1018.35 1028.06 4691240000 1028.06 \n", "6 2010-07-07 1028.54 1060.89 1028.54 1060.27 4931220000 1060.27 \n", " TSLA.Open TSLA.High TSLA.Low TSLA.Close TSLA.Volume TSLA.Adjusted\n", "1 3.800 5.000 3.508 4.778 93831500 4.778 \n", "2 5.158 6.084 4.660 4.766 85935500 4.766 \n", "3 5.000 5.184 4.054 4.392 41094000 4.392 \n", "4 4.600 4.620 3.742 3.840 25699000 3.840 \n", "5 4.000 4.000 3.166 3.222 34334500 3.222 \n", "6 3.280 3.326 2.996 3.160 34608500 3.160 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df = merge(GSPC,TSLA,by=\"dt\")\n", "head(df)" ] }, { "cell_type": "markdown", "id": "b3211ffe-7e73-48ff-86ce-a90357cc4225", "metadata": {}, "source": [ "## Preparing the dataframe needed for regression analysis\n", "\n", "We only need the adjusted closing prices for each ticker, and the dates, so we take a subset of the merged dataframe. This is shown next. " ] }, { "cell_type": "code", "execution_count": 33, "id": "40970c23-53b7-45e5-a4cc-7e28076598d0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
DATEGSPCTSLA
2010-06-291041.24 4.778
2010-06-301030.71 4.766
2010-07-011027.37 4.392
2010-07-021022.58 3.840
2010-07-061028.06 3.222
2010-07-071060.27 3.160
\n" ], "text/latex": [ "\\begin{tabular}{r|lll}\n", " DATE & GSPC & TSLA\\\\\n", "\\hline\n", "\t 2010-06-29 & 1041.24 & 4.778 \\\\\n", "\t 2010-06-30 & 1030.71 & 4.766 \\\\\n", "\t 2010-07-01 & 1027.37 & 4.392 \\\\\n", "\t 2010-07-02 & 1022.58 & 3.840 \\\\\n", "\t 2010-07-06 & 1028.06 & 3.222 \\\\\n", "\t 2010-07-07 & 1060.27 & 3.160 \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "| DATE | GSPC | TSLA |\n", "|---|---|---|\n", "| 2010-06-29 | 1041.24 | 4.778 |\n", "| 2010-06-30 | 1030.71 | 4.766 |\n", "| 2010-07-01 | 1027.37 | 4.392 |\n", "| 2010-07-02 | 1022.58 | 3.840 |\n", "| 2010-07-06 | 1028.06 | 3.222 |\n", "| 2010-07-07 | 1060.27 | 3.160 |\n", "\n" ], "text/plain": [ " DATE GSPC TSLA \n", "1 2010-06-29 1041.24 4.778\n", "2 2010-06-30 1030.71 4.766\n", "3 2010-07-01 1027.37 4.392\n", "4 2010-07-02 1022.58 3.840\n", "5 2010-07-06 1028.06 3.222\n", "6 2010-07-07 1060.27 3.160" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df = df[c(\"dt\",\"GSPC.Adjusted\",\"TSLA.Adjusted\")]\n", "names(df) = c(\"DATE\",\"GSPC\",\"TSLA\")\n", "head(df)" ] }, { "cell_type": "code", "execution_count": 34, "id": "151d9548-ad92-4a2e-abb4-ff73dabbb867", "metadata": {}, "outputs": [ { "data": { "text/plain": [ " DATE GSPC TSLA \n", " Length:2873 Min. :1023 Min. : 3.16 \n", " Class :character 1st Qu.:1598 1st Qu.: 11.16 \n", " Mode :character Median :2099 Median : 46.01 \n", " Mean :2287 Mean : 115.12 \n", " 3rd Qu.:2804 3rd Qu.: 66.18 \n", " Max. :4705 Max. :1229.91 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# DESCRIPTIVE STATISTICS\n", "summary(df)" ] }, { "cell_type": "markdown", "id": "f28f6706-e6e9-4b1f-82be-afa9f988676e", "metadata": {}, "source": [ "## Convert prices to returns\n", "\n", "We want to use regression analysis to examine the relationship of returns on the two tickers. So we convert the prices into percentage returns from one date to the next. This is easy to using the twp columns of ticker prices. Note that we create two vectors of returns. " ] }, { "cell_type": "code", "execution_count": 35, "id": "a3dde1b5-68e9-4d5d-b178-ed5453ebb2b6", "metadata": {}, "outputs": [], "source": [ "n = dim(df)[1]\n", "gspc_ret = (df$GSPC[2:n] - df$GSPC[1:(n-1)])/df$GSPC[1:(n-1)]\n", "tsla_ret = (df$TSLA[2:n] - df$TSLA[1:(n-1)])/df$TSLA[1:(n-1)]" ] }, { "cell_type": "markdown", "id": "b1c52ae2-254f-44d8-92c9-f84131aa7434", "metadata": { "tags": [] }, "source": [ "## Fitting the regression\n", "\n", "In R, ordinary least squares (OLS) regression is fitted using the function `lm` (for linear model). We want to fit the model by regressing Tesla's return on the return of the S&P 500 index. The single line of code below runs the model and the `summary` function prints out all the details of the regression. " ] }, { "cell_type": "code", "execution_count": 36, "id": "c91e38ba-c581-4ca1-a457-304556d4d535", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "lm(formula = tsla_ret ~ gspc_ret)\n", "\n", "Residuals:\n", " Min 1Q Median 3Q Max \n", "-0.188661 -0.016457 -0.001094 0.014901 0.246938 \n", "\n", "Coefficients:\n", " Estimate Std. Error t value Pr(>|t|) \n", "(Intercept) 0.0017693 0.0006088 2.906 0.00369 ** \n", "gspc_ret 1.2900404 0.0567632 22.727 < 2e-16 ***\n", "---\n", "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n", "\n", "Residual standard error: 0.03258 on 2870 degrees of freedom\n", "Multiple R-squared: 0.1525,\tAdjusted R-squared: 0.1522 \n", "F-statistic: 516.5 on 1 and 2870 DF, p-value: < 2.2e-16\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "res = lm(tsla_ret ~ gspc_ret)\n", "summary(res)" ] }, { "cell_type": "markdown", "id": "3f240ded-fc81-46d3-a64a-d5f0f5ee1db6", "metadata": {}, "source": [ "Notice that the intercept is very small (0.0017) and the coefficient on the GSPC return is 1.29, which approximates what is known as the \"beta\" of the stock. What this means is that when the market moves by 1%, Tesla stock changes by 1.29% (up or down). So TSLA is relatively more risky than GSPC. \n", "\n", "Note that the t-statistics show that GSPC is statistically significant in being able to explain the return of TSLA. \n", "\n", "Also, see that the F-statistic has a p-value = 0, which means that the regression model provides a good fit to the data. We see that the R-square is 15%. \n", "\n", "It is useful to plot one series against the other to see this relationship and also plot the regression line using the output of the regression model. This is done next. " ] }, { "cell_type": "code", "execution_count": 37, "id": "38177c08-df3c-4d93-8fe7-145082a6bf04", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correlation of stock and market return:[1] 0.3905358\n" ] }, { "data": { "image/png": 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jyJiIhITk4uLS0lhMjIyOjr69vb21tY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\nQBIEOwAAAEkQ7AAAACTxH+CxCIuCr9MCAAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(gspc_ret, tsla_ret)\n", "cat(\"Correlation of stock and market return:\"); print(cor(gspc_ret, tsla_ret))\n", "abline(res, col=\"red\")" ] }, { "cell_type": "markdown", "id": "255b1888-3c72-4157-ad29-0e08d9d1641a", "metadata": {}, "source": [ "Next, let's explore a different topic to see how functions are written in R, and to implement some deep learning as well. " ] }, { "cell_type": "markdown", "id": "866d4527-7666-4a66-a2ba-b3b8d8bffce1", "metadata": {}, "source": [ "## Pricing Equity Options \n", "\n", "[Options](https://www.investopedia.com/terms/o/option.asp) are traded in large numbers. The basic model for pricing options is the famous Black-Scholes equation. The price of a call option in this model is given by the following formula (see: https://www.investopedia.com/terms/b/blackscholes.asp)\n", "\n", "$$\n", "C=Se^{-qT} N(d_1) - Ke^{-rT}⋅N(d_2)\n", "$$\n", "\n", "where\n", "\n", "$$\n", "d_1=\\frac{\\ln(S/K)+(r-q+v^2/2)T]}{v\\sqrt{T}}\n", "$$\n", "\n", "and $d_2=d_1-v\\sqrt{T}$. \n", "\n", "Here $S$ is the stock price, $K$ is the strike price, $T$ is option maturity in years, $v$ is the annualized volatility of the stock, and $r$ is the continuous risk free rate of interest for maturity $T$. Finally, $q$\n", "is the annual dividend rate, assuming it is paid continuously.\n", "\n", "Likewise, the formula for a put option is\n", "\n", "$$\n", "P=Ke^{-rT}N(-d_2) - Se^{-qT}N(-d_1)\n", "$$\n", "\n", "and $d_1$ and $d_2$ are the same as for the call option.\n", "\n", "We build a simple R function to price options. It returns both the price of a call and a put option for the input parameters. " ] }, { "cell_type": "code", "execution_count": 38, "id": "9e5b0efc-6a25-465f-a8ad-2e870504cce1", "metadata": {}, "outputs": [], "source": [ "#Generate Black-Scholes values\n", "BS = function(S,K,T,v,rf,dv) {\n", " d1 = (log(S/K) + (rf-dv+0.5*v^2)*T)/(v*sqrt(T))\n", " d2 = d1 - v*sqrt(T)\n", " bscall = S*exp(-dv*T)*pnorm(d1) - K*exp(-rf*T)*pnorm(d2)\n", " bsput = -S*exp(-dv*T)*pnorm(-d1) + K*exp(-rf*T)*pnorm(-d2)\n", " res = c(bscall,bsput)\n", "}" ] }, { "cell_type": "markdown", "id": "ead6227d-b629-4335-9433-574904d61417", "metadata": {}, "source": [ "We install `ggplot` which is a popular package in R. See: https://ggplot2.tidyverse.org/\n", "\n", "This will be used to plot the option prices generated from this function. " ] }, { "cell_type": "code", "execution_count": 47, "id": "42c367e3-a2c3-413a-b9d8-2228ebce46de", "metadata": {}, "outputs": [], "source": [ "install.packages(\"ggplot2\")\n", "library(ggplot2)" ] }, { "cell_type": "code", "execution_count": 40, "id": "a4814e57-db48-48dc-9c16-8fee22a61f6b", "metadata": {}, "outputs": [ { "data": { "image/png": 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a98/PHHH3zwwbrF+6P+/v5yudyAD+rp6Vm/fn0DPmgBCsOwt7e3VCoNDAzEnSWZ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\n4447dnR0TH7PZz/72e2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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Add in the parameter values for pricing options\n", "S = 100\n", "K = 100\n", "T = 1\n", "v = 0.20\n", "rf = 0.05\n", "dv = 0.01\n", "\n", "# Create null vectors to hold the option prices\n", "vcall = NULL; vput = NULL\n", "strikes = seq(K-30,K+30)\n", "\n", "# Loop to compute all option prices\n", "for (k in strikes) {\n", " vcall = c(vcall,BS(S,k,T,v,rf,dv)[1])\n", " vput = c(vput,BS(S,k,T,v,rf,dv)[2])\n", "}\n", "\n", "# Construct a dataframe with the option values\n", "df = data.frame(strikes,vcall,vput)\n", "ggplot(df,aes(x=strikes,y=vput)) + geom_point(color=strikes)" ] }, { "cell_type": "markdown", "id": "f2a88173-393c-4bd2-9d91-99799c8921f8", "metadata": {}, "source": [ "This shows the expected relationship of put prices to the strike price of the option, i.e., as the strike is increase, ceteris paribus, the price of puts increases. " ] }, { "cell_type": "markdown", "id": "1af89664-303a-45b2-942a-60be6f6a08c4", "metadata": {}, "source": [ "## Create a synthetic dataset of option prices for a deep learning example\n", "\n", "We now create a synthetic dataset of option prices and inputs to fit a deep learning model to \"learn\" the Black-Scholes option pricing model from synthetically generated data. We generate 100,000 option prices. The six input parameters are chosen randomly and then the call prices are generated from the random input parameters. " ] }, { "cell_type": "code", "execution_count": 41, "id": "6ebfbec9-ab82-47d4-946c-26a1d4ad401b", "metadata": {}, "outputs": [], "source": [ "n = 100000\n", "S = runif(n, 80, 120) # Uniform random numbers between 80\n", "K = runif(n, 80, 120) \n", "T = runif(n, 0.25, 2)\n", "v = runif(n, 0.05, 0.25)\n", "rf = runif(n, 0.01, 0.05)\n", "dv = runif(n, 0.005, 0.02)" ] }, { "cell_type": "code", "execution_count": 42, "id": "8bff20bc-c657-45ed-9390-fc2bb5d5720a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
SKTvrfdvcallPrices
92.45267 86.48318 0.8339456 0.06401861 0.01174064 0.017899846 5.830030
109.37121 84.52778 0.8588396 0.24332395 0.04839114 0.01583179827.833251
103.00767 92.33301 1.8619172 0.20795091 0.03477433 0.01632140018.519266
85.46472 99.33980 1.3971280 0.24506076 0.01582442 0.013232990 5.090455
82.75917 85.48530 1.6095747 0.16418166 0.01132484 0.014381646 5.406382
85.97294 87.77193 1.2422152 0.09356906 0.04713541 0.005021026 4.986066
\n" ], "text/latex": [ "\\begin{tabular}{r|lllllll}\n", " S & K & T & v & rf & dv & callPrices\\\\\n", "\\hline\n", "\t 92.45267 & 86.48318 & 0.8339456 & 0.06401861 & 0.01174064 & 0.017899846 & 5.830030 \\\\\n", "\t 109.37121 & 84.52778 & 0.8588396 & 0.24332395 & 0.04839114 & 0.015831798 & 27.833251 \\\\\n", "\t 103.00767 & 92.33301 & 1.8619172 & 0.20795091 & 0.03477433 & 0.016321400 & 18.519266 \\\\\n", "\t 85.46472 & 99.33980 & 1.3971280 & 0.24506076 & 0.01582442 & 0.013232990 & 5.090455 \\\\\n", "\t 82.75917 & 85.48530 & 1.6095747 & 0.16418166 & 0.01132484 & 0.014381646 & 5.406382 \\\\\n", "\t 85.97294 & 87.77193 & 1.2422152 & 0.09356906 & 0.04713541 & 0.005021026 & 4.986066 \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "| S | K | T | v | rf | dv | callPrices |\n", "|---|---|---|---|---|---|---|\n", "| 92.45267 | 86.48318 | 0.8339456 | 0.06401861 | 0.01174064 | 0.017899846 | 5.830030 |\n", "| 109.37121 | 84.52778 | 0.8588396 | 0.24332395 | 0.04839114 | 0.015831798 | 27.833251 |\n", "| 103.00767 | 92.33301 | 1.8619172 | 0.20795091 | 0.03477433 | 0.016321400 | 18.519266 |\n", "| 85.46472 | 99.33980 | 1.3971280 | 0.24506076 | 0.01582442 | 0.013232990 | 5.090455 |\n", "| 82.75917 | 85.48530 | 1.6095747 | 0.16418166 | 0.01132484 | 0.014381646 | 5.406382 |\n", "| 85.97294 | 87.77193 | 1.2422152 | 0.09356906 | 0.04713541 | 0.005021026 | 4.986066 |\n", "\n" ], "text/plain": [ " S K T v rf dv callPrices\n", "1 92.45267 86.48318 0.8339456 0.06401861 0.01174064 0.017899846 5.830030 \n", "2 109.37121 84.52778 0.8588396 0.24332395 0.04839114 0.015831798 27.833251 \n", "3 103.00767 92.33301 1.8619172 0.20795091 0.03477433 0.016321400 18.519266 \n", "4 85.46472 99.33980 1.3971280 0.24506076 0.01582442 0.013232990 5.090455 \n", "5 82.75917 85.48530 1.6095747 0.16418166 0.01132484 0.014381646 5.406382 \n", "6 85.97294 87.77193 1.2422152 0.09356906 0.04713541 0.005021026 4.986066 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "callPrices = NULL\n", "for (i in 1:n) {\n", " callPrices = c(callPrices,BS(S[i],K[i],T[i],v[i],rf[i],dv[i])[1])\n", "}\n", "df = data.frame(S, K, T, v, rf, dv, callPrices)\n", "head(df)" ] }, { "cell_type": "markdown", "id": "a42e9e41-b708-44be-90b3-7d63979c841d", "metadata": {}, "source": [ "Above, we see the dataframe of input values and in the last column, the option price generated by the Black-Scholes model. " ] } ], "metadata": { "kernelspec": { "display_name": "default:R", "language": "R", "name": "conda-env-default-r" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 5 }