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"source": [
"### Python Implementation of Modern Portfolio Theory\n",
"\n",
"This code relates to my article on Medium.\n",
"\n",
"For any questions, please leave a comment on the article or here on Github."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"\n",
"from tqdm import tqdm\n",
"\n",
"import plotly\n",
"import plotly.graph_objects as go\n",
"from plotly.subplots import make_subplots\n",
"import plotly.express as px\n",
"import plotly.figure_factory as ff"
]
},
{
"cell_type": "code",
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"source": [
"#-- Plot the risk vs. return of randomly generated portfolios\n",
"#-- Convert the list from before into an array for easy plotting\n",
"mean_variance_pairs = np.array(mean_variance_pairs)\n",
"\n",
"risk_free_rate=0 #-- Include risk free rate here\n",
"\n",
"fig = go.Figure()\n",
"fig.add_trace(go.Scatter(x=mean_variance_pairs[:,1]**0.5, y=mean_variance_pairs[:,0], \n",
" marker=dict(color=(mean_variance_pairs[:,0]-risk_free_rate)/(mean_variance_pairs[:,1]**0.5), \n",
" showscale=True, \n",
" size=7,\n",
" line=dict(width=1),\n",
" colorscale=\"RdBu\",\n",
" colorbar=dict(title=\"Sharpe
Ratio\")\n",
" ), \n",
" mode='markers'))\n",
"fig.update_layout(template='plotly_white',\n",
" xaxis=dict(title='Annualised Risk (Volatility)'),\n",
" yaxis=dict(title='Annualised Return'),\n",
" title='Sample of Random Portfolios',\n",
" width=850,\n",
" height=500)\n",
"fig.update_xaxes(range=[0.18, 0.32])\n",
"fig.update_yaxes(range=[0.02,0.27])\n",
"fig.update_layout(coloraxis_colorbar=dict(title=\"Sharpe Ratio\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sample only from efficient frontier"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 10000/10000 [00:02<00:00, 4743.72it/s]\n"
]
}
],
"source": [
"#-- Create random portfolio weights and indexes\n",
"#- How many assests in the portfolio\n",
"n_assets = 5\n",
"\n",
"mean_variance_pairs = []\n",
"weights_list=[]\n",
"tickers_list=[]\n",
"\n",
"for i in tqdm(range(10000)):\n",
" next_i = False\n",
" while True:\n",
" #- Choose assets randomly without replacement\n",
" assets = np.random.choice(list(daily_returns.columns), n_assets, replace=False)\n",
" #- Choose weights randomly ensuring they sum to one\n",
" weights = np.random.rand(n_assets)\n",
" weights = weights/sum(weights)\n",
"\n",
" #-- Loop over asset pairs and compute portfolio return and variance\n",
" portfolio_E_Variance = 0\n",
" portfolio_E_Return = 0\n",
" for i in range(len(assets)):\n",
" portfolio_E_Return += weights[i] * mus.loc[assets[i]]\n",
" for j in range(len(assets)):\n",
" portfolio_E_Variance += weights[i] * weights[j] * cov.loc[assets[i], assets[j]]\n",
"\n",
" #-- Skip over dominated portfolios\n",
" for R,V in mean_variance_pairs:\n",
" if (R > portfolio_E_Return) & (V < portfolio_E_Variance):\n",
" next_i = True\n",
" break\n",
" if next_i:\n",
" break\n",
"\n",
" #-- Add the mean/variance pairs to a list for plotting\n",
" mean_variance_pairs.append([portfolio_E_Return, portfolio_E_Variance])\n",
" weights_list.append(weights)\n",
" tickers_list.append(assets)\n",
" break"
]
},
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"source": [
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"source": [
"#-- Plot the risk vs. return of randomly generated portfolios\n",
"#-- Convert the list from before into an array for easy plotting\n",
"mean_variance_pairs = np.array(mean_variance_pairs)\n",
"\n",
"risk_free_rate=0 #-- Include risk free rate here\n",
"\n",
"fig = go.Figure()\n",
"fig.add_trace(go.Scatter(x=mean_variance_pairs[:,1]**0.5, y=mean_variance_pairs[:,0], \n",
" marker=dict(color=(mean_variance_pairs[:,0]-risk_free_rate)/(mean_variance_pairs[:,1]**0.5), \n",
" showscale=True, \n",
" size=7,\n",
" line=dict(width=1),\n",
" colorscale=\"RdBu\",\n",
" colorbar=dict(title=\"Sharpe
Ratio\")\n",
" ), \n",
" mode='markers',\n",
" text=[str(np.array(tickers_list[i])) + \"
\" + str(np.array(weights_list[i]).round(2)) for i in range(len(tickers_list))]))\n",
"fig.update_layout(template='plotly_white',\n",
" xaxis=dict(title='Annualised Risk (Volatility)'),\n",
" yaxis=dict(title='Annualised Return'),\n",
" title='Sample of Random Portfolios',\n",
" width=850,\n",
" height=500)\n",
"fig.update_xaxes(range=[0.18, 0.35])\n",
"fig.update_yaxes(range=[0.05,0.29])\n",
"fig.update_layout(coloraxis_colorbar=dict(title=\"Sharpe Ratio\"))"
]
}
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