devanshdalal/portfolio-optimization-pypfopt

Portfolio Optimization

Disclaimer: Past does not always repeat itself, we can just learn the wisom from it.

This is a small experiment done with the help of very nice library pyportfolioopt where we are trying to find a portfolio distribution with maximum sharpe ratio (return/risk) from past nifty index data(MPT). And also explore the efficient frontier and where nifty index lie(blue triangle in graph) in terms of risk and reurns.

import pandas as pd
from pypfopt import EfficientFrontier
from pypfopt import risk_models
from pypfopt import expected_returns
from pypfopt import plotting
import os
import numpy as np
from datetime import datetime
import matplotlib.pyplot as plt
import time
from ipynb.fs.full.prepare import index_df, topk
plt.rcParams['figure.dpi'] = 200

split RELIANCE 1645.4 2.0112455690013444 818.1
split RELIANCE 2194.7 8.345758072013917 528.9011030752401
split HDFCBANK 2187.75 1.9869669860587622 1101.05
split HDFCBANK 2519.7 19.661766684358625 254.6343263627014
split INFY 1434.25 1.9456691311130707 737.15
split INFY 1975.05 7.548897276749774 509.05366393585496
split INFY 4349.85 116.56160069377809 281.71001962761125
split INFY 3385.65 27348.90761583446 14.429709183719028
split HDFC 3008.95 4.84377012234385 621.2
split ICICIBANK 1794.1 4.953340695748206 362.2
split TCS 3514.1 2.018379713391344 1741.05
split TCS 778.0 8.144572754105939 192.80316652912552
split TCS 1899.7 135.72602072222847 113.99615769064606
split KOTAKBANK 1425.6 2.016122189223589 707.1
split KOTAKBANK 864.6 7.729011898731478 225.53196548821552
split KOTAKBANK 464.75 136.93248427402247 26.232331203070895
split AXISBANK 1985.75 5.022764638927533 395.35

print('Start')

Start

index_df

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	RELIANCE	HDFCBANK	INFY	HDFC	ICICIBANK	TCS	KOTAKBANK	HINDUNILVR	AXISBANK
Date
2005-01-07	64.973127	24.934178	0.074987	149.955506	72.415774	9.872462	2.074745	141.05	37.847682
2005-01-10	64.002574	24.908748	0.072943	150.801954	70.437311	9.780365	2.084969	142.75	38.245869
2005-01-11	62.996075	24.585787	0.072092	148.954220	70.810796	9.679426	1.990762	141.15	37.419631
2005-01-12	62.091424	24.461179	0.069701	149.078090	69.670152	9.563752	1.921385	139.40	36.105614
2005-01-13	62.319084	25.374119	0.071972	148.582609	71.477014	9.525808	1.989302	140.05	34.970781
...	...	...	...	...	...	...	...	...	...
2021-04-26	1937.850000	1404.800000	1343.550000	2509.800000	591.100000	3100.800000	1759.650000	2360.65	700.450000
2021-04-27	1988.650000	1438.700000	1348.500000	2518.400000	598.750000	3132.000000	1750.300000	2379.85	699.550000
2021-04-28	1997.300000	1476.800000	1356.000000	2577.000000	621.350000	3124.100000	1811.450000	2406.55	708.150000
2021-04-29	2024.050000	1472.500000	1356.350000	2538.850000	621.450000	3115.250000	1805.000000	2407.60	719.400000
2021-04-30	1994.500000	1412.300000	1354.350000	2420.100000	600.500000	3035.650000	1748.800000	2353.75	714.900000

4045 rows × 9 columns

topk.plot(y='WEIGHTAGE(%)', x='SYMBOL',  kind='bar', rot=60)

<AxesSubplot:xlabel='SYMBOL'>

index_df.plot(y='HDFCBANK', kind='line', rot=60)

<AxesSubplot:xlabel='Date'>

# index_df.plot(kind='line',y='LT',color='red')

# Calculate expected returns and sample covariance
mu = expected_returns.mean_historical_return(index_df, compounding=True)

mu

RELIANCE      0.237850
HDFCBANK      0.286014
INFY          0.841863
HDFC          0.189236
ICICIBANK     0.140899
TCS           0.428985
KOTAKBANK     0.521663
HINDUNILVR    0.191715
AXISBANK      0.200953
dtype: float64

expected_returns.mean_historical_return(index_df, compounding=False)

RELIANCE      0.290637
HDFCBANK      0.315050
INFY          7.862403
HDFC          0.236050
ICICIBANK     0.216091
TCS           0.739331
KOTAKBANK     0.811720
HINDUNILVR    0.214057
AXISBANK      0.272611
dtype: float64

S = risk_models.exp_cov(index_df)

# Optimize for maximal Sharpe ratio
ef = EfficientFrontier(mu, S)
ef

<pypfopt.efficient_frontier.efficient_frontier.EfficientFrontier at 0x132e8deb0>

# raw_weights = ef.max_sharpe()

# w = ef.nonconvex_objective(objective_functions.sharpe_ratio, objective_args=(ef.expected_returns, ef.cov_matrix), weights_sum_to_one=True)

# raw_weights

# cleaned_weights = ef.clean_weights()
# ef.save_weights_to_file("weights.csv")  # saves to file
# print(cleaned_weights)
# ef.portfolio_performance(verbose=True)

fig, ax = plt.subplots()
plotting.plot_efficient_frontier(ef, ax=ax, show_assets=False)

# Find the tangency portfolio
raw_weights = ef.max_sharpe()
ret_tangent, std_tangent, _ = ef.portfolio_performance()
ax.scatter(std_tangent, ret_tangent, marker="*", s=100, c="g", label="Max Sharpe")

# Generate random portfolios
n_samples = 10000
w = np.random.dirichlet(np.ones(len(mu)), n_samples)
rets = w.dot(mu)
stds = np.sqrt(np.diag(w @ S @ w.T))
sharpes = rets / stds
ax.scatter(stds, rets, marker=".", c=sharpes, cmap="viridis_r")

# Nifty Top
nifty = np.array([(topk["WEIGHTAGE(%)"]/sum(topk["WEIGHTAGE(%)"])).values])
rets1 = nifty.dot(mu)
stds1 = np.sqrt(np.diag(nifty @ S @ nifty.T))
ax.scatter(stds1, rets1, marker="^", c='b', s=200)

# # Output
# ax.set_title("Efficient Frontier with random portfolios")
# ax.legend()
# plt.tight_layout()
# plt.savefig("ef_scatter.png", dpi=200)
# plt.show()

<matplotlib.collections.PathCollection at 0x134fae190>

# nifty.dot(mu)
# w.dot(mu).shape
# np.sqrt(np.diag(w @ S @ w.T)).shape
rets1
# stds1

array([0.3494463])

np.sqrt(np.diag(nifty @ S @ nifty.T)).shape

(1,)

nifty * S

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	RELIANCE	HDFCBANK	INFY	HDFC	ICICIBANK	TCS	KOTAKBANK	HINDUNILVR	AXISBANK
RELIANCE	0.019174	0.007469	0.004650	0.004972	0.006003	0.002778	0.002661	0.001389	0.002650
HDFCBANK	0.008237	0.018093	0.004144	0.010680	0.011066	0.001919	0.004818	0.001004	0.003656
INFY	0.005952	0.004811	0.043097	0.003603	0.002809	0.005419	0.002829	0.001493	0.001204
HDFC	0.007882	0.015351	0.004462	0.016174	0.012722	0.002347	0.005200	0.001343	0.004499
ICICIBANK	0.009905	0.016556	0.003621	0.013241	0.019703	0.001898	0.005595	0.001104	0.006705
TCS	0.005863	0.003673	0.008933	0.003125	0.002428	0.006553	0.001204	0.001461	0.000956
KOTAKBANK	0.007459	0.012243	0.006193	0.009194	0.009503	0.001599	0.007797	0.001326	0.003459
HINDUNILVR	0.004477	0.002934	0.003761	0.002731	0.002157	0.002233	0.001525	0.003544	0.000744
AXISBANK	0.010276	0.012855	0.003647	0.011006	0.015760	0.001757	0.004787	0.000895	0.009024

topk["WEIGHTAGE(%)"]/sum(topk["WEIGHTAGE(%)"])

0    0.187846
1    0.170331
2    0.146738
3    0.118499
4    0.113852
5    0.089008
6    0.067024
7    0.058266
8    0.048436
Name: WEIGHTAGE(%), dtype: float64

raw_weights

OrderedDict([('RELIANCE', 0.0),
             ('HDFCBANK', 0.0),
             ('INFY', 0.1974132196509596),
             ('HDFC', 0.0),
             ('ICICIBANK', 0.0),
             ('TCS', 0.4157200297654416),
             ('KOTAKBANK', 0.3868667505835988),
             ('HINDUNILVR', 0.0),
             ('AXISBANK', 0.0)])

plt.bar(list(raw_weights.keys()), raw_weights.values(), color='g')
plt.xticks(rotation=60)

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Leanings

I always used to feel that index is safest and the most efficient bet(max sharpe ratio), because markets fill up all inefficiencies and are always self correcting, but this might not be always true.
Index top 10 have still very good risk to reward ratio, hence a good investment choice among all passively managed vehicles.
"Compounding is the eight wonder": Einstein

devanshdalal / portfolio-optimization-pypfopt

Portfolio Optimization

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