Riskfolio-Lib Tutorial:¶

__[Financionerioncios](https://financioneroncios.wordpress.com)__
__[Orenji](https://www.linkedin.com/company/orenj-i)__
__[Riskfolio-Lib](https://riskfolio-lib.readthedocs.io/en/latest/)__
__[Dany Cajas](https://www.linkedin.com/in/dany-cajas/)__

Tutorial 10: Risk Parity Portfolio Optimization¶

1. Downloading the data:¶

In [2]:

import numpy as np
import pandas as pd
import yfinance as yf
import warnings

warnings.filterwarnings("ignore")
pd.options.display.float_format = '{:.4%}'.format

# Date range
start = '2016-01-01'
end = '2019-12-30'

# Tickers of assets
assets = ['JCI', 'TGT', 'CMCSA', 'CPB', 'MO', 'APA', 'MMC', 'JPM',
          'ZION', 'PSA', 'BAX', 'BMY', 'LUV', 'PCAR', 'TXT', 'TMO',
          'DE', 'MSFT', 'HPQ', 'SEE', 'VZ', 'CNP', 'NI', 'T', 'BA']
assets.sort()

# Downloading data
data = yf.download(assets, start = start, end = end)
data = data.loc[:,('Adj Close', slice(None))]
data.columns = assets

[*********************100%%**********************]  25 of 25 completed

In [3]:

# Calculating returns

Y = data[assets].pct_change().dropna()

display(Y.head())

	APA	BA	BAX	BMY	CMCSA	CNP	CPB	DE	HPQ	JCI	...	NI	PCAR	PSA	SEE	T	TGT	TMO	TXT	VZ	ZION
Date
2016-01-05	-2.0257%	0.4057%	0.4036%	1.9693%	0.0180%	0.9305%	0.3678%	0.5783%	0.9483%	-1.1954%	...	1.5881%	0.0212%	2.8236%	0.9758%	0.6987%	1.7539%	-0.1730%	0.2410%	1.3734%	-1.0858%
2016-01-06	-11.4863%	-1.5879%	0.2411%	-1.7557%	-0.7727%	-1.2473%	-0.1736%	-1.1239%	-3.5867%	-0.9551%	...	0.5547%	0.0212%	0.1592%	-1.5646%	0.3108%	-1.0155%	-0.7653%	-3.0048%	-0.9034%	-2.9145%
2016-01-07	-5.1389%	-4.1922%	-1.6573%	-2.7699%	-1.1047%	-1.9770%	-1.2206%	-0.8855%	-4.6058%	-2.5394%	...	-2.2066%	-3.0310%	-1.0410%	-3.1557%	-1.6148%	-0.2700%	-2.2844%	-2.0570%	-0.5492%	-3.0019%
2016-01-08	0.2736%	-2.2705%	-1.6037%	-2.5425%	0.1098%	-0.2240%	0.5707%	-1.6402%	-1.7642%	-0.1649%	...	-0.1538%	-1.1366%	-0.7308%	-0.1448%	0.0895%	-3.3839%	-0.1117%	-1.1387%	-0.9719%	-1.1254%
2016-01-11	-4.3383%	0.1692%	-1.6851%	-1.0215%	0.0915%	-1.1792%	0.5674%	0.5287%	0.6616%	0.0330%	...	1.6436%	0.0000%	0.9869%	-0.1450%	1.2224%	1.4569%	0.5367%	-0.4607%	0.5800%	-1.9919%

5 rows × 25 columns

2. Estimating Mean Variance Portfolios¶

2.1 Calculating the portfolio that maximizes Sharpe ratio.¶

In [5]:

import riskfolio as rp

# Building the portfolio object
port = rp.Portfolio(returns=Y)

# Calculating optimal portfolio

# Select method and estimate input parameters:

method_mu='hist' # Method to estimate expected returns based on historical data.
method_cov='hist' # Method to estimate covariance matrix based on historical data.

port.assets_stats(method_mu=method_mu, method_cov=method_cov)

# Estimate optimal portfolio:

model='Classic' # Could be Classic (historical), BL (Black Litterman) or FM (Factor Model)
rm = 'MV' # Risk measure used, this time will be variance
obj = 'Sharpe' # Objective function, could be MinRisk, MaxRet, Utility or Sharpe
hist = True # Use historical scenarios for risk measures that depend on scenarios
rf = 0 # Risk free rate
l = 0 # Risk aversion factor, only useful when obj is 'Utility'

w = port.optimization(model=model, rm=rm, obj=obj, rf=rf, l=l, hist=hist)

display(w.T)

	APA	BA	BAX	BMY	CMCSA	CNP	CPB	DE	HPQ	JCI	...	NI	PCAR	PSA	SEE	T	TGT	TMO	TXT	VZ	ZION
weights	0.0000%	6.1590%	11.5019%	0.0000%	0.0000%	8.4806%	0.0000%	3.8193%	0.0000%	0.0000%	...	10.8264%	0.0000%	0.0000%	0.0000%	0.0000%	7.1804%	0.0000%	0.0000%	4.2740%	0.0000%

1 rows × 25 columns

2.2 Plotting portfolio composition¶

In [7]:

# Plotting the composition of the portfolio

ax = rp.plot_pie(w=w, title='Sharpe Mean Variance', others=0.05, nrow=25, cmap = "tab20",
                 height=6, width=10, ax=None)

2.3 Plotting Risk Composition¶

In [9]:

# Plotting the risk composition of the portfolio

ax = rp.plot_risk_con(w, cov=port.cov, returns=port.returns, rm=rm, rf=0, alpha=0.01,
                      color="tab:blue", height=6, width=10, ax=None)

3. Estimating Risk Parity Portfolios for Other Risk Measures¶

In this part I will calculate risk parity portfolios. First I'm going to calculate risk parity portfolio when we use variance as risk measure, then I'm going to calculate the risk parity portfolios for all available risk measures.

3.1 Calculating the risk parity portfolio for variance.¶

In [11]:

b = None # Risk contribution constraints vector

w_rp = port.rp_optimization(model=model, rm=rm, rf=rf, b=b, hist=hist)

display(w.T)

	APA	BA	BAX	BMY	CMCSA	CNP	CPB	DE	HPQ	JCI	...	NI	PCAR	PSA	SEE	T	TGT	TMO	TXT	VZ	ZION
weights	0.0000%	6.1590%	11.5019%	0.0000%	0.0000%	8.4806%	0.0000%	3.8193%	0.0000%	0.0000%	...	10.8264%	0.0000%	0.0000%	0.0000%	0.0000%	7.1804%	0.0000%	0.0000%	4.2740%	0.0000%

1 rows × 25 columns

3.2 Plotting portfolio composition¶

In [13]:

ax = rp.plot_pie(w=w_rp, title='Risk Parity Variance', others=0.05, nrow=25, cmap = "tab20",
                 height=6, width=10, ax=None)

3.3 Plotting Risk Composition¶

In [15]:

ax = rp.plot_risk_con(w_rp, cov=port.cov, returns=port.returns, rm=rm, rf=0, alpha=0.01,
                      color="tab:blue", height=6, width=10, ax=None)

3.4 Calculate Optimal Portfolios for Several Risk Measures¶

In [17]:

# Risk Measures available:
#
# 'MV': Standard Deviation.
# 'MAD': Mean Absolute Deviation.
# 'MSV': Semi Standard Deviation.
# 'FLPM': First Lower Partial Moment (Omega Ratio).
# 'SLPM': Second Lower Partial Moment (Sortino Ratio).
# 'CVaR': Conditional Value at Risk.
# 'EVaR': Entropic Value at Risk.
# 'CDaR': Conditional Drawdown at Risk of uncompounded cumulative returns.
# 'EDaR': Entropic Drawdown at Risk of uncompounded cumulative returns.
# 'UCI': Ulcer Index of uncompounded cumulative returns.

rms = ['MV', 'MAD', 'MSV', 'FLPM', 'SLPM', 'CVaR',
       'EVaR', 'CDaR', 'UCI', 'EDaR']

w_s = pd.DataFrame([])
port.solvers = ['MOSEK']

for i in rms:
    w = port.rp_optimization(model=model, rm=i, rf=rf, b=b, hist=hist)
    w_s = pd.concat([w_s, w], axis=1)
    
w_s.columns = rms

In [18]:

w_s.style.format("{:.2%}").background_gradient(cmap='YlGn')

Out[18]:

	MV	MAD	MSV	FLPM	SLPM	CVaR	EVaR	CDaR	UCI	EDaR
APA	2.40%	2.20%	2.51%	2.03%	2.40%	2.45%	2.80%	1.16%	1.16%	1.05%
BA	3.08%	3.22%	2.99%	3.30%	3.04%	2.87%	2.76%	6.48%	6.10%	4.23%
BAX	4.03%	4.40%	3.93%	4.64%	4.02%	3.77%	3.49%	2.67%	3.41%	2.69%
BMY	4.12%	4.24%	4.19%	4.07%	4.07%	3.83%	4.67%	2.01%	1.59%	2.24%
CMCSA	3.89%	4.01%	3.89%	3.86%	3.90%	3.72%	3.52%	2.66%	2.52%	3.59%
CNP	5.20%	5.06%	5.22%	5.11%	5.34%	5.63%	5.50%	7.25%	5.67%	9.14%
CPB	5.10%	4.54%	5.69%	4.48%	5.66%	6.94%	7.73%	2.83%	2.51%	2.64%
DE	3.04%	3.02%	2.91%	3.08%	2.94%	2.79%	2.95%	5.21%	5.33%	7.12%
HPQ	2.83%	2.95%	2.64%	2.91%	2.62%	2.36%	2.69%	2.57%	2.57%	2.43%
JCI	3.61%	3.51%	3.60%	3.50%	3.58%	3.37%	3.27%	1.90%	2.03%	1.97%
JPM	3.35%	3.67%	3.35%	3.89%	3.40%	2.99%	3.08%	3.70%	3.75%	3.17%
LUV	3.42%	3.37%	3.33%	3.13%	3.28%	2.92%	3.80%	1.98%	1.82%	1.76%
MMC	4.41%	4.69%	4.33%	5.03%	4.44%	4.09%	4.36%	5.64%	6.52%	5.05%
MO	5.18%	5.02%	4.98%	4.82%	4.83%	5.01%	4.04%	2.27%	2.01%	2.14%
MSFT	3.26%	3.88%	3.25%	4.27%	3.34%	2.94%	3.15%	6.07%	9.19%	4.42%
NI	6.54%	6.54%	6.63%	6.95%	6.77%	6.70%	6.40%	5.80%	6.74%	5.50%
PCAR	2.99%	2.81%	3.04%	2.81%	3.06%	3.25%	3.23%	1.89%	1.92%	2.25%
PSA	6.87%	6.29%	7.30%	5.79%	7.14%	7.98%	6.09%	13.37%	10.92%	12.54%
SEE	3.54%	3.45%	3.38%	3.14%	3.25%	3.32%	3.58%	1.96%	1.83%	2.36%
T	4.59%	4.56%	4.41%	4.50%	4.39%	4.31%	4.04%	3.43%	3.55%	3.05%
TGT	3.97%	3.66%	4.19%	3.88%	4.34%	4.80%	5.59%	2.00%	2.22%	1.74%
TMO	3.43%	3.60%	3.36%	3.72%	3.41%	3.08%	3.25%	4.57%	4.70%	4.00%
TXT	2.95%	2.93%	2.86%	2.68%	2.75%	2.66%	3.12%	1.58%	1.58%	1.37%
VZ	5.19%	5.19%	5.15%	5.19%	5.19%	5.69%	4.10%	7.75%	6.36%	11.08%
ZION	3.00%	3.19%	2.86%	3.21%	2.85%	2.54%	2.79%	3.25%	4.02%	2.47%

In [19]:

import matplotlib.pyplot as plt

# Plotting a comparison of assets weights for each portfolio

fig = plt.gcf()
fig.set_figwidth(16)
fig.set_figheight(6)
ax = fig.subplots(nrows=1, ncols=1)

w_s.plot.bar(ax=ax)

Out[19]:

<Axes: >