from io import BytesIO
import numpy as np
import pandas as pd
import holoviews as hv
import panel as pn
from scipy.optimize import minimize
pn.extension('tabulator', design='material', template='material', loading_indicator=True)
import hvplot.pandas
@pn.cache
def get_stocks(data):
if data is None:
stock_file = 'https://datasets.holoviz.org/stocks/v1/stocks.csv'
else:
stock_file = BytesIO(data)
return pd.read_csv(stock_file, index_col='Date', parse_dates=True)
file_input = pn.widgets.FileInput(sizing_mode='stretch_width')
stocks = hvplot.bind(get_stocks, file_input).interactive()
selector = pn.widgets.MultiSelect(
name='Select stocks', sizing_mode='stretch_width',
options=stocks.columns.to_list()
)
selected_stocks = stocks.pipe(
lambda df, cols: df[cols] if cols else df, selector
)
def compute_random_allocations(log_return, num_ports=15000):
_, ncols = log_return.shape
# Compute log and mean return
mean_return = np.nanmean(log_return, axis=0)
# Allocate normalized weights
weights = np.random.random((num_ports, ncols))
normed_weights = (weights.T / np.sum(weights, axis=1)).T
data = dict(zip(log_return.columns, normed_weights.T))
# Compute expected return and volatility of random portfolios
data['Return'] = expected_return = np.sum((mean_return * normed_weights) * 252, axis=1)
return_covariance = np.cov(log_return[1:], rowvar=False) * 252
if not return_covariance.shape:
return_covariance = np.array([[252.]])
data['Volatility'] = volatility = np.sqrt((normed_weights * np.tensordot(return_covariance, normed_weights.T, axes=1).T).sum(axis=1))
data['Sharpe'] = sharpe_ratio = expected_return/volatility
df = pd.DataFrame(data)
df.attrs['mean_return'] = mean_return
df.attrs['log_return'] = log_return
return df
def check_sum(weights):
return np.sum(weights) - 1
def get_return(mean_ret, weights):
return np.sum(mean_ret * weights) * 252
def get_volatility(log_ret, weights):
return np.sqrt(np.dot(weights.T, np.dot(np.cov(log_ret[1:], rowvar=False) * 252, weights)))
def compute_frontier(df, n=30):
frontier_ret = np.linspace(df.Return.min(), df.Return.max(), n)
frontier_volatility = []
cols = len(df.columns) - 3
bounds = tuple((0, 1) for i in range(cols))
init_guess = [1./cols for i in range(cols)]
for possible_return in frontier_ret:
cons = (
{'type':'eq', 'fun': check_sum},
{'type':'eq', 'fun': lambda w: get_return(df.attrs['mean_return'], w) - possible_return}
)
result = minimize(lambda w: get_volatility(df.attrs['log_return'], w), init_guess, bounds=bounds, constraints=cons)
frontier_volatility.append(result['fun'])
return pd.DataFrame({'Volatility': frontier_volatility, 'Return': frontier_ret})
def minimize_difference(weights, des_vol, des_ret, log_ret, mean_ret):
ret = get_return(mean_ret, weights)
vol = get_volatility(log_ret, weights)
return abs(des_ret-ret) + abs(des_vol-vol)
@pn.cache
def find_best_allocation(log_return, vol, ret):
cols = log_return.shape[1]
vol = vol or 0
ret = ret or 0
mean_return = np.nanmean(log_return, axis=0)
bounds = tuple((0, 1) for i in range(cols))
init_guess = [1./cols for i in range(cols)]
cons = (
{'type':'eq','fun': check_sum},
{'type':'eq','fun': lambda w: get_return(mean_return, w) - ret},
{'type':'eq','fun': lambda w: get_volatility(log_return, w) - vol}
)
opt = minimize(
minimize_difference, init_guess, args=(vol, ret, log_return, mean_return),
bounds=bounds, constraints=cons
)
ret = get_return(mean_return, opt.x)
vol = get_volatility(log_return, opt.x)
return pd.Series(list(opt.x)+[ret, vol], index=list(log_return.columns)+['Return', 'Volatility'], name='Weight')
n_samples = pn.widgets.IntSlider(
name='Random samples', value=10_000, start=1000, end=20_000, step=1000, sizing_mode='stretch_width'
)
button = pn.widgets.Button(name='Run Analysis', sizing_mode='stretch_width')
posxy = hv.streams.Tap(x=None, y=None)
text = """
# Portfolio optimization
This application performs portfolio optimization given a set of stock time series.
To optimize your portfolio:
1. Upload a CSV of the daily stock time series for the stocks you are considering
2. Select the stocks to be included.
3. Run the Analysis
4. Click on the Return/Volatility plot to select the desired risk/reward profile
Upload a CSV containing stock data:
"""
explanation = """
The code for this app was taken from [this excellent introduction to Python for Finance](https://github.com/PrateekKumarSingh/Python/tree/master/Python%20for%20Finance/Python-for-Finance-Repo-master).
To learn some of the background and theory about portfolio optimization see [this notebook](https://github.com/PrateekKumarSingh/Python/blob/master/Python%20for%20Finance/Python-for-Finance-Repo-master/09-Python-Finance-Fundamentals/02-Portfolio-Optimization.ipynb).
"""
sidebar = pn.layout.WidgetBox(
pn.pane.Markdown(text, margin=(0, 10)),
file_input,
selector,
n_samples,
explanation,
max_width=350,
sizing_mode='stretch_width'
).servable(area='sidebar')
sidebar
# Set up data pipelines
log_return = np.log(selected_stocks/selected_stocks.shift(1))
random_allocations = log_return.pipe(compute_random_allocations, n_samples)
closest_allocation = log_return.pipe(find_best_allocation, posxy.param.x, posxy.param.y)
efficient_frontier = random_allocations.pipe(compute_frontier)
max_sharpe = random_allocations.pipe(lambda df: df[df.Sharpe==df.Sharpe.max()])
# Generate plots
opts = {'x': 'Volatility', 'y': 'Return', 'responsive': True}
allocations_scatter = random_allocations.hvplot.scatter(
alpha=0.1, color='Sharpe', cmap='plasma', **opts
).dmap().opts(tools=[])
frontier_curve = efficient_frontier.hvplot(
line_dash='dashed', color='green', **opts
).dmap()
max_sharpe_point = max_sharpe.hvplot.scatter(
line_color='black', size=50, **opts
).dmap()
closest_point = closest_allocation.to_frame().T.hvplot.scatter(color='green', line_color='black', size=50, **opts).dmap()
posxy.source = allocations_scatter
summary = pn.pane.Markdown(
pn.bind(lambda p: f"""
The selected portfolio has a volatility of {p.Volatility:.2f}, a return of {p.Return:.2f}
and Sharpe ratio of {p.Return/p.Volatility:.2f}.""", closest_allocation), width=250
)
table = pn.widgets.Tabulator(closest_allocation.to_frame().iloc[:-2])
plot = (allocations_scatter * frontier_curve * max_sharpe_point * closest_point).opts(min_height=400, show_grid=True)
pn.Row(plot, pn.Column(summary, table), sizing_mode='stretch_both')
investment = pn.widgets.Spinner(name='Investment Value in $', value=5000, step=1000, start=1000, end=100000)
year = pn.widgets.DateRangeSlider(name='Year', value=(stocks.index.min().eval(), stocks.index.max().eval()), start=stocks.index.min(), end=stocks.index.max())
stocks_between_dates = selected_stocks[year.param.value_start:year.param.value_end]
price_on_start_date = selected_stocks[year.param.value_start:].iloc[0]
allocation = (closest_allocation.iloc[:-2] * investment)
performance_plot = (stocks_between_dates * allocation / price_on_start_date).sum(axis=1).rename().hvplot.line(
ylabel='Total Value ($)', title='Portfolio performance', responsive=True, min_height=400
).dmap()
performance = pn.Column(
pn.Row(year, investment),
performance_plot,
sizing_mode='stretch_both'
)
performance
timeseries = selected_stocks.hvplot.line(
'Date', group_label='Stock', value_label='Stock Price ($)', title='Daily Stock Price',
min_height=300, responsive=True, grid=True, legend='top_left'
).dmap()
timeseries
log_ret_hists = log_return.hvplot.hist(min_height=300, min_width=400, responsive=True, bins=100, subplots=True, group_label='Stock').cols(2).opts(sizing_mode='stretch_both').panel()
log_ret_hists
main = pn.Tabs(
('Analysis', pn.Column(
pn.Row(
plot, pn.Column(summary, table),
sizing_mode='stretch_both'
),
performance,
sizing_mode='stretch_both'
)
),
('Timeseries', timeseries),
('Log Return', pn.Column(
'## Daily normalized log returns',
'Width of distribution indicates volatility and center of distribution the mean daily return.',
log_ret_hists,
sizing_mode='stretch_both'
)),
sizing_mode='stretch_both', min_height=1000
).servable(title='Portfolio Optimizer')
pn.Row(sidebar, main)