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Code Issues Releases Wiki Activity

Work on converting old blog posts

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Bradlee Speice 2024-10-14 00:48:31 +00:00
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293
blog/2015-11-14-welcome/2015-11-14-welcome.ipynb Normal file
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Trading Competition Optimization\n",
"\n",
"### Goal: Max return given maximum Sharpe and Drawdown"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from IPython.display import display\n",
"import Quandl\n",
"from datetime import datetime, timedelta\n",
"\n",
"tickers = ['XOM', 'CVX', 'CLB', 'OXY', 'SLB']\n",
"market_ticker = 'GOOG/NYSE_VOO'\n",
"lookback = 30\n",
"d_col = 'Close'\n",
"\n",
"data = {tick: Quandl.get('YAHOO/{}'.format(tick))[-lookback:] for tick in tickers}\n",
"market = Quandl.get(market_ticker)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Calculating the Return\n",
"We first want to know how much each ticker returned over the prior period."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"{'CLB': -0.0016320202164526894,\n",
" 'CVX': 0.0010319531629488911,\n",
" 'OXY': 0.00093418904454400551,\n",
" 'SLB': 0.00098431254720448159,\n",
" 'XOM': 0.00044165797556096868}"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"returns = {tick: data[tick][d_col].pct_change() for tick in tickers}\n",
"\n",
"display({tick: returns[tick].mean() for tick in tickers})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Calculating the Sharpe ratio\n",
"Sharpe: ${R - R_M \\over \\sigma}$\n",
"\n",
"We use the average return over the lookback period, minus the market average return, over the ticker standard deviation to calculate the Sharpe. Shorting a stock turns a negative Sharpe positive."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"{'CLB': -0.10578734457846127,\n",
" 'CVX': 0.027303529817677398,\n",
" 'OXY': 0.022622210057414487,\n",
" 'SLB': 0.026950946344858676,\n",
" 'XOM': -0.0053519259698605499}"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"market_returns = market.pct_change()\n",
"\n",
"sharpe = lambda ret: (ret.mean() - market_returns[d_col].mean()) / ret.std()\n",
"sharpes = {tick: sharpe(returns[tick]) for tick in tickers}\n",
"\n",
"display(sharpes)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Calculating the drawdown\n",
"This one is easy - what is the maximum daily change over the lookback period? That is, because we will allow short positions, we are not concerned strictly with maximum downturn, but in general, what is the largest 1-day change?"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"{'CLB': 0.043551495607375035,\n",
" 'CVX': 0.044894389686214398,\n",
" 'OXY': 0.051424517867144637,\n",
" 'SLB': 0.034774627850375328,\n",
" 'XOM': 0.035851524605672758}"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"drawdown = lambda ret: ret.abs().max()\n",
"drawdowns = {tick: drawdown(returns[tick]) for tick in tickers}\n",
"\n",
"display(drawdowns)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Performing the optimization\n",
"\n",
"$\\begin{align}\n",
"max\\ \\ & \\mu \\cdot \\omega\\\\\n",
"s.t.\\ \\ & \\vec{1} \\omega = 1\\\\\n",
"& \\vec{S} \\omega \\ge s\\\\\n",
"& \\vec{D} \\cdot | \\omega | \\le d\\\\\n",
"& \\left|\\omega\\right| \\le l\\\\\n",
"\\end{align}$\n",
"\n",
"We want to maximize average return subject to having a full portfolio, Sharpe above a specific level, drawdown below a level, and leverage not too high - that is, don't have huge long/short positions."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"'Optimization terminated successfully.'"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"\"Holdings: [('XOM', 5.8337945679814904), ('CVX', 42.935064321851307), ('CLB', -124.5), ('OXY', 36.790387773552119), ('SLB', 39.940753336615096)]\""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"'Expected Return: 32.375%'"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"'Expected Max Drawdown: 4.34%'"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.optimize import minimize\n",
"\n",
"#sharpe_limit = .1\n",
"drawdown_limit = .05\n",
"leverage = 250\n",
"\n",
"# Use the map so we can guarantee we maintain the correct order\n",
"# sharpe_a = np.array(list(map(lambda tick: sharpes[tick], tickers))) * -1 # So we can write as upper-bound\n",
"dd_a = np.array(list(map(lambda tick: drawdowns[tick], tickers)))\n",
"returns_a = np.array(list(map(lambda tick: returns[tick].mean(), tickers))) # Because minimizing\n",
"\n",
"meets_sharpe = lambda x: sum(abs(x) * sharpe_a) - sharpe_limit\n",
"def meets_dd(x):\n",
" portfolio = sum(abs(x))\n",
" if portfolio < .1:\n",
" # If there are no stocks in the portfolio,\n",
" # we can accidentally induce division by 0,\n",
" # or division by something small enough to cause infinity\n",
" return 0\n",
" \n",
" return drawdown_limit - sum(abs(x) * dd_a) / sum(abs(x))\n",
"\n",
"is_portfolio = lambda x: sum(x) - 1\n",
"\n",
"def within_leverage(x):\n",
" return leverage - sum(abs(x))\n",
"\n",
"objective = lambda x: sum(x * returns_a) * -1 # Because we're minimizing\n",
"bounds = ((None, None),) * len(tickers)\n",
"x = np.zeros(len(tickers))\n",
"\n",
"constraints = [\n",
" {\n",
" 'type': 'eq',\n",
" 'fun': is_portfolio\n",
" }, {\n",
" 'type': 'ineq',\n",
" 'fun': within_leverage\n",
" #}, {\n",
" # 'type': 'ineq',\n",
" # 'fun': meets_sharpe\n",
" }, {\n",
" 'type': 'ineq',\n",
" 'fun': meets_dd\n",
" }\n",
"]\n",
"\n",
"optimal = minimize(objective, x, bounds=bounds, constraints=constraints,\n",
" options={'maxiter': 500})\n",
"\n",
"# Optimization time!\n",
"display(optimal.message)\n",
"\n",
"display(\"Holdings: {}\".format(list(zip(tickers, optimal.x))))\n",
"\n",
"expected_return = optimal.fun * -100 # multiply by -100 to scale, and compensate for minimizing\n",
"display(\"Expected Return: {:.3f}%\".format(expected_return))\n",
"\n",
"expected_drawdown = sum(abs(optimal.x) * dd_a) / sum(abs(optimal.x)) * 100\n",
"display(\"Expected Max Drawdown: {0:.2f}%\".format(expected_drawdown))\n",
"\n",
"# TODO: Calculate expected Sharpe"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.0"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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**Goal: Max return given maximum Sharpe and Drawdown**
```python
from IPython.display import display
import Quandl
from datetime import datetime, timedelta
tickers = ['XOM', 'CVX', 'CLB', 'OXY', 'SLB']
market_ticker = 'GOOG/NYSE_VOO'
lookback = 30
d_col = 'Close'
data = {tick: Quandl.get('YAHOO/{}'.format(tick))[-lookback:] for tick in tickers}
market = Quandl.get(market_ticker)
```
## Calculating the Return
We first want to know how much each ticker returned over the prior period.
```python
returns = {tick: data[tick][d_col].pct_change() for tick in tickers}
display({tick: returns[tick].mean() for tick in tickers})
```
```
{'CLB': -0.0016320202164526894,
'CVX': 0.0010319531629488911,
'OXY': 0.00093418904454400551,
'SLB': 0.00098431254720448159,
'XOM': 0.00044165797556096868}
```
## Calculating the Sharpe ratio
Sharpe: $R - R_M \over \sigma$
We use the average return over the lookback period, minus the market average return, over the ticker standard deviation to calculate the Sharpe. Shorting a stock turns a negative Sharpe positive.
```python
market_returns = market.pct_change()
sharpe = lambda ret: (ret.mean() - market_returns[d_col].mean()) / ret.std()
sharpes = {tick: sharpe(returns[tick]) for tick in tickers}
display(sharpes)
```
```
{'CLB': -0.10578734457846127,
'CVX': 0.027303529817677398,
'OXY': 0.022622210057414487,
'SLB': 0.026950946344858676,
'XOM': -0.0053519259698605499}
```
## Calculating the drawdown
This one is easy - what is the maximum daily change over the lookback period? That is, because we will allow short positions, we are not concerned strictly with maximum downturn, but in general, what is the largest 1-day change?
```python
drawdown = lambda ret: ret.abs().max()
drawdowns = {tick: drawdown(returns[tick]) for tick in tickers}
display(drawdowns)
```
```
{'CLB': 0.043551495607375035,
'CVX': 0.044894389686214398,
'OXY': 0.051424517867144637,
'SLB': 0.034774627850375328,
'XOM': 0.035851524605672758}
```
## Performing the optimization
$$
\begin{align*}
max\ \ & \mu \cdot \omega \\
s.t.\ \ & \vec{1} \omega = 1\\
& \vec{S} \omega \ge s\\
& \vec{D} \cdot | \omega | \le d\\
& \left|\omega\right| \le l\\
\end{align*}
$$
We want to maximize average return subject to having a full portfolio, Sharpe above a specific level, drawdown below a level, and leverage not too high - that is, don't have huge long/short positions.
```python
import numpy as np
from scipy.optimize import minimize
#sharpe_limit = .1
drawdown_limit = .05
leverage = 250
# Use the map so we can guarantee we maintain the correct order
# sharpe_a = np.array(list(map(lambda tick: sharpes[tick], tickers))) * -1 # So we can write as upper-bound
dd_a = np.array(list(map(lambda tick: drawdowns[tick], tickers)))
returns_a = np.array(list(map(lambda tick: returns[tick].mean(), tickers))) # Because minimizing
meets_sharpe = lambda x: sum(abs(x) * sharpe_a) - sharpe_limit
def meets_dd(x):
portfolio = sum(abs(x))
if portfolio < .1:
# If there are no stocks in the portfolio,
# we can accidentally induce division by 0,
# or division by something small enough to cause infinity
return 0
return drawdown_limit - sum(abs(x) * dd_a) / sum(abs(x))
is_portfolio = lambda x: sum(x) - 1
def within_leverage(x):
return leverage - sum(abs(x))
objective = lambda x: sum(x * returns_a) * -1 # Because we're minimizing
bounds = ((None, None),) * len(tickers)
x = np.zeros(len(tickers))
constraints = [
{
'type': 'eq',
'fun': is_portfolio
}, {
'type': 'ineq',
'fun': within_leverage
#}, {
# 'type': 'ineq',
# 'fun': meets_sharpe
}, {
'type': 'ineq',
'fun': meets_dd
}
]
optimal = minimize(objective, x, bounds=bounds, constraints=constraints,
options={'maxiter': 500})
# Optimization time!
display(optimal.message)
display("Holdings: {}".format(list(zip(tickers, optimal.x))))
expected_return = optimal.fun * -100 # multiply by -100 to scale, and compensate for minimizing
display("Expected Return: {:.3f}%".format(expected_return))
expected_drawdown = sum(abs(optimal.x) * dd_a) / sum(abs(optimal.x)) * 100
display("Expected Max Drawdown: {0:.2f}%".format(expected_drawdown))
# TODO: Calculate expected Sharpe
```
```
'Optimization terminated successfully.'
"Holdings: [('XOM', 5.8337945679814904), ('CVX', 42.935064321851307), ('CLB', -124.5), ('OXY', 36.790387773552119), ('SLB', 39.940753336615096)]"
'Expected Return: 32.375%'
'Expected Max Drawdown: 4.34%'
```

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---
title: Welcome, and an algorithm
date: 2015-11-19
last_update:
date: 2015-12-05
slug: 2015/11/welcome
authors: [bspeice]
tags: [trading]
---
import Notebook from './_notebook.md'
Hello! Glad to meet you. I'm currently a student at Columbia University
studying Financial Engineering, and want to give an overview of the projects
I'm working on!
<!-- truncate -->
To start things off, Columbia has been hosting a trading competition that
myself and another partner are competing in. I'm including a notebook of the
algorithm that we're using, just to give a simple overview of a miniature
algorithm.
The competition is scored in 3 areas:
- Total return
- [Sharpe ratio](https://en.wikipedia.org/wiki/Sharpe_ratio)
- Maximum drawdown
Our algorithm uses a basic momentum strategy: in the given list of potential
portfolios, pick the stocks that have been performing well in the past 30
days. Then, optimize for return subject to the drawdown being below a specific
level. We didn't include the Sharpe ratio as a constraint, mostly because
we were a bit late entering the competition.
I'll be updating this post with the results of our algorithm as they come along!
---
**UPDATE 12/5/2015**: Now that the competition has ended, I wanted to update
how the algorithm performed. Unfortunately, it didn't do very well. I'm planning
to make some tweaks over the coming weeks, and do another forward test in January.
- After week 1: Down .1%
- After week 2: Down 1.4%
- After week 3: Flat
And some statistics for all teams participating in the competition:
<table>
<tr>
<td>Max Return</td>
<td>74.1%</td>
</tr>
<tr>
<td>Min Return</td>
<td>-97.4%</td>
</tr>
<tr>
<td>Average Return</td>
<td>-.1%</td>
</tr>
<tr>
<td>Std Dev of Returns</td>
<td>19.6%</td>
</tr>
</table>
---
<Notebook/>

6
blog/2021-08-01-mdx-blog-post.mdx
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@ -12,6 +12,12 @@ Hello?
Blog posts support [Docusaurus Markdown features](https://docusaurus.io/docs/markdown-features), such as [MDX](https://mdxjs.com/).
<details>
<summary>Hello</summary>
Testing - {1 + 2}
</details>
:::tip

3
blog/2021-08-01-second.mdx
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@ -1,3 +0,0 @@
---
title: Another title
---

18
docusaurus.config.ts
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@ -1,6 +1,8 @@
import {themes as prismThemes} from 'prism-react-renderer';
import type {Config} from '@docusaurus/types';
import type * as Preset from '@docusaurus/preset-classic';
import remarkMath from 'remark-math';
import rehypeKatex from 'rehype-katex';
const config: Config = {
title: 'The Old Speice Guy',
@ -34,6 +36,7 @@ const config: Config = {
blog: {
routeBasePath: "/",
showReadingTime: true,
showLastUpdateTime: true,
feedOptions: {
type: ['rss', 'atom'],
xslt: true,
@ -42,10 +45,12 @@ const config: Config = {
onInlineTags: 'warn',
onInlineAuthors: 'warn',
onUntruncatedBlogPosts: 'warn',
remarkPlugins: [remarkMath],
rehypePlugins: [rehypeKatex]
},
theme: {
customCss: ['./src/css/custom.css']
}
},
} satisfies Preset.Options,
],
],
@ -75,7 +80,16 @@ const config: Config = {
darkTheme: prismThemes.oneDark,
},
} satisfies Preset.ThemeConfig,
plugins: [require.resolve('docusaurus-lunr-search')]
plugins: [require.resolve('docusaurus-lunr-search')],
stylesheets: [
{
href: 'https://cdn.jsdelivr.net/npm/katex@0.13.24/dist/katex.min.css',
type: 'text/css',
integrity:
'sha384-odtC+0UGzzFL/6PNoE8rX/SPcQDXBJ+uRepguP4QkPCm2LBxH3FA3y+fKSiJ+AmM',
crossorigin: 'anonymous',
},
]
};
export default config;

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package-lock.json generated
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@ -15,7 +15,9 @@
"docusaurus-lunr-search": "^3.5.0",
"prism-react-renderer": "^2.3.0",
"react": "^18.0.0",
"react-dom": "^18.0.0"
"react-dom": "^18.0.0",
"rehype-katex": "^7.0.1",
"remark-math": "^6.0.0"
},
"devDependencies": {
"@docusaurus/module-type-aliases": "3.5.2",
@ -3762,6 +3764,12 @@
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"license": "MIT"
},
"node_modules/@types/mdast": {
"version": "4.0.4",
"resolved": "https://registry.npmjs.org/@types/mdast/-/mdast-4.0.4.tgz",
@ -7837,6 +7845,55 @@
"node": ">= 0.4"
}
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"license": "ISC",
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"@types/hast": "^3.0.0",
"hastscript": "^8.0.0",
"web-namespaces": "^2.0.0"
},
"funding": {
"type": "opencollective",
"url": "https://opencollective.com/unified"
}
},
"node_modules/hast-util-from-html": {
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"devlop": "^1.1.0",
"hast-util-from-parse5": "^8.0.0",
"parse5": "^7.0.0",
"vfile": "^6.0.0",
"vfile-message": "^4.0.0"
},
"funding": {
"type": "opencollective",
"url": "https://opencollective.com/unified"
}
},
"node_modules/hast-util-from-html-isomorphic": {
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"license": "MIT",
"dependencies": {
"@types/hast": "^3.0.0",
"hast-util-from-dom": "^5.0.0",
"hast-util-from-html": "^2.0.0",
"unist-util-remove-position": "^5.0.0"
},
"funding": {
"type": "opencollective",
"url": "https://opencollective.com/unified"
}
},
"node_modules/hast-util-from-parse5": {
"version": "8.0.1",
"resolved": "https://registry.npmjs.org/hast-util-from-parse5/-/hast-util-from-parse5-8.0.1.tgz",
@ -9190,6 +9247,31 @@
"graceful-fs": "^4.1.6"
}
},
"node_modules/katex": {
"version": "0.16.11",
"resolved": "https://registry.npmjs.org/katex/-/katex-0.16.11.tgz",
"integrity": "sha512-RQrI8rlHY92OLf3rho/Ts8i/XvjgguEjOkO1BEXcU3N8BqPpSzBNwV/G0Ukr+P/l3ivvJUE/Fa/CwbS6HesGNQ==",
"funding": [
"https://opencollective.com/katex",
"https://github.com/sponsors/katex"
],
"license": "MIT",
"dependencies": {
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},
"bin": {
"katex": "cli.js"
}
},
"node_modules/katex/node_modules/commander": {
"version": "8.3.0",
"resolved": "https://registry.npmjs.org/commander/-/commander-8.3.0.tgz",
"integrity": "sha512-OkTL9umf+He2DZkUq8f8J9of7yL6RJKI24dVITBmNfZBmri9zYZQrKkuXiKhyfPSu8tUhnVBB1iKXevvnlR4Ww==",
"license": "MIT",
"engines": {
"node": ">= 12"
}
},
"node_modules/keyv": {
"version": "4.5.4",
"resolved": "https://registry.npmjs.org/keyv/-/keyv-4.5.4.tgz",
@ -9678,6 +9760,25 @@
"url": "https://opencollective.com/unified"
}
},
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@ -13773,6 +13949,68 @@
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4
package.json
View File

@ -22,7 +22,9 @@
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8
src/css/custom.css
View File

@ -1,12 +1,6 @@
.container {
margin: 0 1rem;
}
.footer__col {
margin-bottom: calc(var(--ifm-spacing-vertical))
}
:root {
--ifm-container-width: 1280px;
--ifm-footer-padding-vertical: 1rem;
--ifm-footer-padding-vertical: .5rem;
}
.header-github-link:hover {