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 8: Short and Leveraged Portfolios¶

1. Downloading the data:¶

In [1]:

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 [2]:

# Calculating returns

Y = data.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%	-1.0857%
2016-01-06	-11.4863%	-1.5879%	0.2411%	-1.7557%	-0.7727%	-1.2473%	-0.1735%	-1.1239%	-3.5867%	-0.9551%	...	0.5547%	0.0212%	0.1592%	-1.5647%	0.3108%	-1.0155%	-0.7653%	-3.0048%	-0.9034%	-2.9145%
2016-01-07	-5.1388%	-4.1922%	-1.6573%	-2.7699%	-1.1047%	-1.9769%	-1.2207%	-0.8856%	-4.6059%	-2.5394%	...	-2.2066%	-3.0309%	-1.0411%	-3.1556%	-1.6148%	-0.2700%	-2.2845%	-2.0570%	-0.5492%	-3.0019%
2016-01-08	0.2736%	-2.2705%	-1.6037%	-2.5425%	0.1099%	-0.2241%	0.5706%	-1.6402%	-1.7642%	-0.1649%	...	-0.1539%	-1.1366%	-0.7308%	-0.1448%	0.0895%	-3.3839%	-0.1117%	-1.1387%	-0.9720%	-1.1254%
2016-01-11	-4.3383%	0.1693%	-1.6851%	-1.0215%	0.0914%	-1.1791%	0.5674%	0.5287%	0.6616%	0.0331%	...	1.6436%	0.0000%	0.9869%	-0.1451%	1.2224%	1.4570%	0.5367%	-0.4607%	0.5800%	-1.9919%

5 rows × 25 columns

2. Estimating Mean Variance Portfolios with Short Weights¶

2.1 Calculating the portfolio that maximizes Sharpe ratio.¶

In [3]:

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)

# Configuring short weights options

port.sht = True # Allows to use Short Weights

port.uppersht = 0.3 # Maximum absolute value of individual negative weights
port.upperlng = 1.3 # Maximum value of individual positive weights
port.budget = 1.0 # Sum of all weights
port.budgetsht = 0.3 # Maximum absolute value of sum of negative weights

# 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	-7.4519%	9.6278%	13.1758%	-1.2650%	0.0000%	13.4986%	0.0000%	8.0891%	0.0000%	0.0000%	...	10.5861%	0.0000%	-0.0000%	-7.0711%	0.4849%	8.3073%	0.5676%	-14.2119%	4.9502%	0.0000%

1 rows × 25 columns

2.2 Plotting portfolio composition (in absolute values)¶

In [4]:

# 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 Calculate efficient frontier¶

In [5]:

points = 50 # Number of points of the frontier

frontier = port.efficient_frontier(model=model, rm=rm, points=points, rf=rf, hist=hist)

display(frontier.T.head())

	APA	BA	BAX	BMY	CMCSA	CNP	CPB	DE	HPQ	JCI	...	NI	PCAR	PSA	SEE	T	TGT	TMO	TXT	VZ	ZION
0	-0.4255%	0.3940%	6.7334%	4.5411%	2.6268%	7.4370%	2.9970%	0.7996%	-1.9263%	3.3470%	...	11.3536%	-1.4055%	14.7448%	0.5034%	6.5274%	4.3629%	-1.0414%	-0.0721%	8.2062%	0.0197%
1	-2.7563%	3.5594%	9.0748%	1.2802%	2.2703%	10.2967%	2.0656%	3.1161%	-2.3452%	2.5651%	...	12.4810%	-0.4610%	9.5486%	-2.9418%	6.5478%	5.9027%	0.2749%	-6.0506%	7.9061%	-0.2858%
2	-3.7498%	4.9086%	10.0728%	-0.1100%	2.1184%	11.5157%	1.6687%	4.1033%	-2.5253%	2.2319%	...	12.9618%	-0.0574%	7.3342%	-4.4107%	6.5569%	6.5591%	0.8365%	-8.5989%	7.7780%	-0.4142%
3	-4.5311%	5.9694%	10.8574%	-1.2030%	1.9990%	12.4741%	1.3566%	4.8797%	-2.6640%	1.9696%	...	13.3396%	0.2586%	5.5921%	-5.5650%	6.5634%	7.0751%	1.2777%	-10.6023%	7.6776%	-0.5179%
4	-5.2434%	6.8737%	11.5503%	-1.9816%	1.8439%	13.2574%	0.9830%	5.5489%	-2.4593%	1.5561%	...	13.7203%	0.3028%	3.7262%	-6.4013%	6.3258%	7.5125%	1.5731%	-12.0778%	7.5075%	-0.0000%

5 rows × 25 columns

In [6]:

# Plotting the efficient frontier

label = 'Max Risk Adjusted Return Portfolio' # Title of point
mu = port.mu # Expected returns
cov = port.cov # Covariance matrix
returns = port.returns # Returns of the assets

ax = rp.plot_frontier(w_frontier=frontier, mu=mu, cov=cov, returns=returns, rm=rm,
                      rf=rf, alpha=0.05, cmap='viridis', w=w, label=label,
                      marker='*', s=16, c='r', height=6, width=10, ax=None)

In [7]:

# Plotting efficient frontier composition
# This chart doesn't work well will short weights and leverage

ax = rp.plot_frontier_area(w_frontier=frontier, cmap="tab20", height=6, width=10, ax=None)

3. Estimating Mean Variance Portfolios with Leverage and Short Weights¶

3.1 Calculating the portfolio that maximizes Sharpe ratio.¶

In [8]:

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

# 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)

# Configuring short weights options

port.sht = True # Allows to use Short Weights
port.uppersht = 0.3 # Maximum absolute value of individual negative weights
port.upperlng = 1.3 # Maximum value of individual positive weights
port.budgetsht = 0.3 # Maximum absolute value of sum of negative weights

# Configuring leverage
port.budget = 1.3 # Sum of all weights

# 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	-8.8386%	11.6055%	16.5865%	-0.0000%	0.0000%	16.4661%	0.0000%	9.4146%	0.0000%	0.0000%	...	13.7573%	0.0000%	-0.0000%	-6.2643%	0.0000%	10.4658%	0.0000%	-14.8971%	6.6789%	0.0000%

1 rows × 25 columns

3.2 Plotting portfolio composition¶

In [9]:

# 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)

3.3 Calculate efficient frontier¶

In [10]:

points = 50 # Number of points of the frontier

frontier = port.efficient_frontier(model=model, rm=rm, points=points, rf=rf, hist=hist)

display(frontier.T.head())

	APA	BA	BAX	BMY	CMCSA	CNP	CPB	DE	HPQ	JCI	...	NI	PCAR	PSA	SEE	T	TGT	TMO	TXT	VZ	ZION
0	-0.5531%	0.5123%	8.7533%	5.9034%	3.4148%	9.6681%	3.8962%	1.0395%	-2.5042%	4.3511%	...	14.7597%	-1.8272%	19.1682%	0.6544%	8.4856%	5.6717%	-1.3538%	-0.0937%	10.6680%	0.0256%
1	-3.4202%	4.4057%	11.6333%	1.8922%	2.9764%	13.1857%	2.7505%	3.8887%	-3.0192%	3.3892%	...	16.1466%	-0.6651%	12.7765%	-3.5834%	8.5107%	7.5658%	0.2657%	-7.4472%	10.2990%	-0.3498%
2	-4.6388%	6.0605%	12.8574%	0.1872%	2.7901%	14.6808%	2.2636%	5.0998%	-3.2383%	2.9804%	...	16.7360%	-0.1713%	10.0599%	-5.3845%	8.5214%	8.3708%	0.9542%	-10.5728%	10.1420%	-0.5096%
3	-5.6217%	7.3514%	13.8285%	-1.0510%	2.6134%	15.8252%	1.8199%	6.0501%	-3.2126%	2.5434%	...	17.2412%	0.0692%	7.7063%	-6.7037%	8.3760%	8.9970%	1.4414%	-12.8728%	9.9648%	-0.1755%
4	-6.5148%	8.3621%	14.6498%	-1.2365%	2.1169%	16.6169%	0.9094%	6.7160%	-1.6184%	1.2602%	...	17.7018%	0.0000%	4.0384%	-6.9788%	7.2424%	9.4882%	1.4281%	-13.6515%	9.6093%	0.0000%

5 rows × 25 columns

In [11]:

# Plotting the efficient frontier

label = 'Max Risk Adjusted Return Portfolio' # Title of point
mu = port.mu # Expected returns
cov = port.cov # Covariance matrix
returns = port.returns # Returns of the assets

ax = rp.plot_frontier(w_frontier=frontier, mu=mu, cov=cov, returns=returns, rm=rm,
                      rf=rf, alpha=0.05, cmap='viridis', w=w, label=label,
                      marker='*', s=16, c='r', height=6, width=10, ax=None)

In [12]:

# Plotting efficient frontier composition
# This chart doesn't work well will short weights and leverage

ax = rp.plot_frontier_area(w_frontier=frontier, cmap="tab20", height=6, width=10, ax=None)

3. Estimating Mean Risk Portfolios with Leverage and Short Weights¶

In this part I will calculate optimal portfolios for several risk measures allowing Leverage and Short Weights. First I'm going to calculate the portfolio that maximizes risk adjusted return when CVaR is the risk measure, then I'm going to calculate the portfolios that maximize the risk adjusted return for all available risk measures.

3.1 Calculating the portfolio that maximizes Return/CVaR ratio.¶

In [13]:

rm = 'CVaR' # Risk measure

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	-7.8924%	0.0000%	19.3944%	-0.0000%	0.0000%	17.3216%	0.0000%	11.1497%	-0.0000%	-0.0000%	...	13.7696%	0.0000%	-0.0000%	-6.6619%	0.0000%	16.2182%	6.7777%	-15.4456%	10.3496%	0.0000%

1 rows × 25 columns

3.2 Plotting portfolio composition¶

In [14]:

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

3.3 Calculate efficient frontier¶

In [15]:

points = 50 # Number of points of the frontier

frontier = port.efficient_frontier(model=model, rm=rm, points=points, rf=rf, hist=hist)

display(frontier.T.head())

	APA	BA	BAX	BMY	CMCSA	CNP	CPB	DE	HPQ	JCI	...	NI	PCAR	PSA	SEE	T	TGT	TMO	TXT	VZ	ZION
0	1.8342%	0.7830%	2.0355%	9.6251%	0.0000%	3.1290%	8.4910%	-6.7987%	-19.2906%	11.1534%	...	11.9926%	5.5712%	19.4224%	1.9219%	9.4922%	8.0510%	-0.0000%	-3.2409%	24.3155%	-0.6699%
1	-2.5848%	1.1783%	7.1347%	4.2101%	-0.0000%	4.1823%	8.7607%	3.5851%	-14.8009%	4.1409%	...	9.6288%	4.8534%	17.8373%	-7.5913%	3.8923%	11.4037%	4.3931%	-5.0230%	22.4948%	0.0000%
2	-3.4395%	0.0000%	5.9264%	0.0000%	0.0000%	9.7684%	3.9293%	8.0762%	-12.0715%	5.8465%	...	9.6966%	3.0184%	14.6773%	-6.9885%	0.3784%	13.1392%	2.6852%	-7.5005%	24.0032%	0.0000%
3	-4.3667%	0.0000%	7.9893%	0.0000%	0.0000%	17.4982%	0.0000%	8.5019%	-9.6541%	2.7543%	...	10.0505%	0.0000%	11.0660%	-9.2572%	0.2073%	15.1826%	1.4811%	-6.7220%	22.0835%	0.0000%
4	-5.5466%	3.7188%	7.9819%	-0.0000%	0.0000%	27.6275%	0.0000%	5.5998%	-5.1615%	0.0000%	...	6.0290%	0.0000%	5.6016%	-10.6301%	0.0000%	13.9002%	0.0743%	-8.6618%	22.9280%	0.0000%

5 rows × 25 columns

In [16]:

label = 'Max Risk Adjusted Return Portfolio' # Title of point

ax = rp.plot_frontier(w_frontier=frontier, mu=mu, cov=cov, returns=returns, rm=rm,
                      rf=rf, alpha=0.05, cmap='viridis', w=w, label=label,
                      marker='*', s=16, c='r', height=6, width=10, ax=None)

In [17]:

# Plotting efficient frontier composition
# This chart doesn't work well will short weights and leverage

ax = rp.plot_frontier_area(w_frontier=frontier, cmap="tab20", height=6, width=10, ax=None)

3.4 Calculate Optimal Portfolios for Several Risk Measures¶

In [18]:

# 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.
# 'WR': Worst Realization (Minimax)
# 'MDD': Maximum Drawdown of uncompounded cumulative returns (Calmar Ratio).
# 'ADD': Average Drawdown of uncompounded cumulative returns.
# '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', 'WR', 'MDD', 'ADD', 'CDaR', 'UCI', 'EDaR']

w_s = pd.DataFrame([])

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

In [19]:

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

Out[19]:

	MV	MAD	MSV	FLPM	SLPM	CVaR	EVaR	WR	MDD	ADD	CDaR	UCI	EDaR
APA	-8.84%	-8.95%	-8.69%	-6.96%	-8.88%	-7.89%	-17.38%	-17.43%	-23.06%	-2.32%	-11.34%	-7.13%	-18.96%
BA	11.61%	11.79%	11.32%	13.67%	11.29%	0.00%	5.84%	0.00%	15.81%	10.80%	11.12%	10.08%	9.96%
BAX	16.59%	15.32%	14.44%	12.46%	14.52%	19.39%	9.27%	6.89%	38.26%	19.54%	11.48%	16.90%	12.66%
BMY	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	0.00%	0.00%	-0.00%	-2.37%	-3.89%	-3.86%	-5.12%
CMCSA	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	-0.00%	-6.51%	-1.43%	-5.05%	-0.00%	-0.00%
CNP	16.47%	15.08%	20.25%	13.52%	21.15%	17.32%	36.05%	28.73%	42.04%	15.91%	37.88%	27.15%	44.15%
CPB	0.00%	-0.00%	-0.00%	-0.00%	-0.00%	0.00%	4.96%	14.05%	-0.00%	0.00%	-0.00%	-0.00%	-0.00%
DE	9.41%	5.06%	6.81%	6.25%	6.86%	11.15%	0.00%	0.00%	0.00%	5.66%	5.06%	4.47%	4.42%
HPQ	0.00%	0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.21%	-5.27%	-2.86%	-0.00%
JCI	0.00%	0.00%	-0.00%	0.00%	-0.00%	-0.00%	0.00%	-0.00%	-0.00%	0.00%	-0.00%	-0.00%	-0.00%
JPM	22.20%	28.37%	21.33%	30.73%	20.34%	9.40%	10.51%	0.00%	0.00%	9.66%	0.00%	4.47%	0.00%
LUV	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%
MMC	31.01%	25.11%	31.60%	22.44%	32.13%	33.20%	33.66%	32.15%	38.26%	24.78%	24.00%	24.99%	27.37%
MO	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-7.41%	-0.44%	-1.03%	-0.54%	-2.04%	-5.37%
MSFT	21.82%	25.86%	26.73%	25.88%	26.78%	22.42%	37.77%	32.08%	16.29%	43.75%	49.28%	49.69%	51.53%
NI	13.76%	13.48%	11.43%	16.38%	11.03%	13.77%	0.00%	0.00%	5.42%	6.06%	3.55%	3.05%	3.38%
PCAR	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	17.67%	-0.00%	0.00%	0.00%	0.00%	0.00%
PSA	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	-0.00%	0.00%	0.00%	-0.00%	-0.00%	0.00%
SEE	-6.26%	-5.93%	-6.61%	-6.19%	-6.78%	-6.66%	-8.12%	-0.00%	-0.00%	-6.94%	-0.00%	-1.86%	0.00%
T	0.00%	7.03%	0.00%	6.00%	0.00%	0.00%	0.00%	-0.00%	-0.00%	1.03%	0.00%	0.00%	0.00%
TGT	10.47%	9.14%	12.78%	7.49%	13.06%	16.22%	21.94%	28.42%	0.00%	0.64%	0.00%	0.00%	0.25%
TMO	0.00%	0.50%	0.00%	0.04%	0.00%	6.78%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
TXT	-14.90%	-15.12%	-14.70%	-16.85%	-14.34%	-15.45%	-4.50%	-5.16%	-0.00%	-15.71%	-3.91%	-12.25%	-0.54%
VZ	6.68%	3.26%	3.30%	5.15%	2.84%	10.35%	0.00%	-0.00%	3.91%	16.61%	17.64%	19.21%	6.27%
ZION	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	-0.00%	0.00%	5.55%	-0.00%	0.00%	0.00%

In [20]:

import matplotlib.pyplot as plt

# Plotting a comparison of assets weights for each portfolio

fig = plt.gcf()
fig.set_figwidth(14)
fig.set_figheight(6)
ax = fig.subplots(nrows=1, ncols=1)

w_s.plot.bar(ax=ax)

Out[20]:

<Axes: >