The Python Quants

Importance of Large Returns¶

Dr. Yves J. Hilpisch | The Python Quants GmbH | http://tpq.io

Imports & Data¶

In [1]:
import numpy as np
import pandas as pd
from pylab import plt, mpl
plt.style.use('seaborn')
mpl.rcParams['figure.dpi'] = 300
%config InlineBackend.figure_format = 'jpg'
In [2]:
# data from Refinitiv Workspace/Eikon data API
url = 'https://certificate.tpq.io/mlfin.csv'
In [3]:
raw = pd.read_csv(url, index_col=0, parse_dates=True)
In [4]:
raw.columns
Out[4]:
Index(['AAPL.O', 'MSFT.O', 'INTC.O', 'AMZN.O', 'GS.N', '.SPX', '.VIX', 'SPY',
       'EUR=', 'XAU=', 'GDX', 'GLD', 'BTC='],
      dtype='object')
In [5]:
del raw['BTC=']
In [6]:
raw.dropna(inplace=True)

Log Returns¶

In [7]:
sym = '.SPX'
# sym = 'AAPL.O'
In [8]:
rets = np.log(raw / raw.shift(1)).dropna()
In [9]:
mean = rets[sym].mean()
mean
Out[9]:
0.0003947829170345228
In [10]:
std = rets[sym].std()
std
Out[10]:
0.011018002078001089
In [11]:
tail_right = mean + 2 * std
tail_right
Out[11]:
0.022430787073036702
In [12]:
tail_left = mean - 2 * std
tail_left
Out[12]:
-0.021641221238967653
In [13]:
nor = len(rets[sym][rets[sym].sort_values() > tail_right].values)
nor  # number of large positive returns
Out[13]:
45
In [14]:
nol = len(rets[sym][rets[sym].sort_values() < tail_left].values)
nol  # number of large negative returns
Out[14]:
72
In [15]:
rets[sym].cumsum().apply(np.exp).plot();
In [16]:
np.exp(rets.sort_values(sym)[sym].values.cumsum())
Out[16]:
array([0.8801595 , 0.79644517, 0.73593948, ..., 2.25957578, 2.46942528,
       2.70112567])
In [17]:
plt.bar(np.arange(len(rets)),
        np.exp(rets.sort_values(sym)[sym].values.cumsum()));
plt.axvline(len(rets) - nor, c='r', lw=1)
plt.axvline(nol, c='r', lw=1);

Missing Large Positive Movements¶

... as a long investor.

In [18]:
x_ = range(0, 51, 5)
In [19]:
# gross performance when missing the x largest positive returns
r_ = list()
for x in x_:
    r = np.exp(rets.sort_values(sym)[sym].values.cumsum())[-1-x]
    r_.append(r)
    print(f'{x:3d} | {r:.3f}')

  0 | 2.701
  5 | 1.875
 10 | 1.503
 15 | 1.279
 20 | 1.108
 25 | 0.972
 30 | 0.857
 35 | 0.758
 40 | 0.673
 45 | 0.600
 50 | 0.538
In [20]:
plt.bar(x_, r_)
for label, value in zip(x_, r_):
    plt.text(label - 1, value + 0.025, str(round(value, 1)));

Avoiding Large Negative Movements¶

... as a long investor.

In [21]:
# gross performance when avoiding the x largest negative returns
r_ = list()
for x in x_:
    r = np.exp(rets.sort_values(sym)[sym].values[x:].sum())
    r_.append(r)
    print(f'{x:3d} | {r:.3f}')

  0 | 2.701
  5 | 4.113
 10 | 5.172
 15 | 6.324
 20 | 7.582
 25 | 8.992
 30 | 10.576
 35 | 12.314
 40 | 14.250
 45 | 16.402
 50 | 18.679
In [22]:
plt.bar(x_, r_)
for label, value in zip(x_, r_):
    plt.text(label - 1, value + 0.2, str(round(value, 1)));

The Python Quants