Integrating a histogram in a bootstrap simulation graph

Question

I have a dataframe with 1000 simulations of a portfolio's returns. I am able to graph the simulations and do the respective histogram separately, but I have absolutely no idea how to merge them in order to resemble the following image:

please take this example of data in order to facilitate answers:

import numpy as np
import pandas as pd

def simulate_panel(T, N):

    """" This function simulates return paths"""

    dates = pd.date_range("20210218", periods=T, freq='D')
    columns = []

    for i in range(N):
        columns.append(str(i+1))

    return pd.DataFrame(np.random.normal(0, 0.01, size=(T, N)), index=dates, 
    columns=columns)

df=(1+simulate_panel(1000,1000)).cumprod()

df.plot(figsize=(8,6),title=('Bootstrap'), legend=False)

Thank you very much in advance.

user_12046409 · Answer

To color the curves via their last value, they can be drawn one-by-one. With a colormap and a norm, the value can be converted to the appropriate color. Using some transparency (alpha), the most visited positions will be colored stronger.

In a second subplot, a vertical histogram can be drawn, with the bars colored similarly.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

def simulate_panel(T, N):
    """" This function simulates return paths"""
    dates = pd.date_range("20210218", periods=T, freq='D')
    columns = [(str(i + 1)) for i in range(N)]
    return pd.DataFrame(np.random.normal(0, 0.01, size=(T, N)), index=dates, columns=columns)

df = (1 + simulate_panel(1000, 1000)).cumprod()

fig, (ax1, ax2) = plt.subplots(ncols=2, sharey=True, figsize=(12, 4),
                               gridspec_kw={'width_ratios': [5, 1], 'wspace': 0})
data = df.to_numpy().T
cmap = plt.cm.get_cmap('turbo')
norm = plt.Normalize(min(data[:, -1]), max(data[:, -1]))

for row in data:
    ax1.plot(df.index, row, c=cmap(norm(row[-1])), alpha=0.1)
ax1.margins(x=0)
_, bin_edges, bars = ax2.hist(data[:, -1], bins=20, orientation='horizontal')
for x0, x1, bar in zip(bin_edges[:-1], bin_edges[1:], bars):
    bar.set_color(cmap(norm((x0 + x1) / 2)))
ax2.tick_params(left=False)
plt.tight_layout()
plt.show()

user_6792743 · Answer

You can use GridSpec to set up axes for line chart and the histogram next to each other:

import matplotlib.pyplot as plt
import matplotlib.cm as cm

# layout
fig = plt.figure()
gs = fig.add_gridspec(1, 2, wspace=0, width_ratios=[9, 1])
ax = gs.subplots(sharey=True)

# line chart
z = df.iloc[-1]
df.plot(figsize=(8,6), title=('Bootstrap'), legend=False, ax=ax[0],
        color=cm.RdYlBu_r((z - z.min()) / (z.max() - z.min())))

# histogram
n_bins = 20
cnt, bins, patches = ax[1].hist(
    z, np.linspace(z.min(), z.max(), n_bins),
    ec='k', orientation='horizontal')

colors = cm.RdYlBu_r((bins - z.min()) / (z.max() - z.min()))
for i, p in enumerate(patches):
    p.set_color(colors[i])

Integrating a histogram in a bootstrap simulation graph

2 Answers