DOW30 monthly#
Example of long-only portfolio among DOW-30 components.
Monthly rebalance, backtest spans from the start of data of the components of the current index (in the 60s), the other stocks enter the backtest as times goes on. It ends today.
This uses an explicit loop to create
cvxportfolio.MultiPeriodOptimization
policies with a grid of values for the risk term multiplier
and the transaction cost term multiplier. (We don’t use the
holding cost term because the portfolio is long-only.)
All result objects are collected, and then the one with largest Sharpe ratio, and the one with largest growth rate, are shown.
Finally, we show the effect of using symbolic hyper-parameters,
cvxportfolio.Gamma, as multipliers of the risk and transaction
cost terms. We can optimize on those explicitely, by finding the values
that maximize some back-test metric (in this case, profit).
Running the full example involves solving many (~100) back-tests, it takes a few minutes to half an hour or longer depending on how fast your computer is and how many processors it has. (Each back-test occupies one processor.)
import matplotlib.pyplot as plt
import numpy as np
import cvxportfolio as cvx
# we have up-to-date components of a few market indexes in the
# universes.py example script
from .universes import DOW30
# we use monthly resampling to make the example run faster
sim = cvx.StockMarketSimulator(DOW30, trading_frequency='monthly')
def make_policy(gamma_trade, gamma_risk):
"""Build MPO policy given risk and trans. cost multipliers.
:param gamma_trade: Transaction cost multiplier.
:type gamma_trade: float or int
:param gamma_risk: Risk model multiplier.
:type gamma_risk: float or int
:return: Multi-period optimization policy with given
hyper-parameter values.
:rtype: cvxportfolio.Policy
"""
return cvx.MultiPeriodOptimization(cvx.ReturnsForecast()
- gamma_risk * cvx.FactorModelCovariance(num_factors=10)
- gamma_trade * cvx.StocksTransactionCost(),
[cvx.LongOnly(), cvx.LeverageLimit(1)],
planning_horizon=6, solver='ECOS')
# define combinations of hyper-parameters
keys = [(gamma_trade, gamma_risk)
for gamma_trade in np.array(range(10))/10
for gamma_risk in [.5, 1, 2, 5, 10]]
# define many policies and back-test them in parallel
ress = sim.backtest_many([make_policy(*key) for key in keys])
# pick the result with the largest Sharpe ratio
print('\n\nLARGEST SHARPE RATIO')
idx = np.argmax([el.sharpe_ratio for el in ress])
print('gamma_trade and gamma_risk')
print(keys[idx])
print('result')
print(ress[idx])
largest_sharpe_figure = ress[idx].plot()
# pick the result with the largest growth rate (i.e., largest profit)
print('\n\nLARGEST GROWTH RATE')
idx = np.argmax([el.growth_rates.mean() for el in ress])
print('gamma_trade and gamma_risk')
print(keys[idx])
print('result')
print(ress[idx])
largest_growth_figure = ress[idx].plot()
# also try uniform allocation, for comparison
print('\n\nUNIFORM (1/N) ALLOCATION FOR COMPARISON')
result_uniform = sim.backtest(cvx.Uniform())
print('result_uniform')
print(result_uniform)
figure_uniform = result_uniform.plot()
# finally, run automatic hyper-parameter optimization
print('\n\nHYPER-PARAMETER OPTIMIZATION')
policy = cvx.MultiPeriodOptimization(cvx.ReturnsForecast()
- cvx.Gamma() * cvx.FactorModelCovariance(num_factors=10)
- cvx.Gamma() * cvx.StocksTransactionCost(),
[cvx.LongOnly(), cvx.LeverageLimit(1)],
planning_horizon=6, solver='ECOS')
sim.optimize_hyperparameters(policy, objective='profit')
result_hyperparameter_optimized = sim.backtest(policy)
print('result_hyperparameter_optimized')
print(result_hyperparameter_optimized)
hyp_optimized_figure = result_hyperparameter_optimized.plot()
This is the output printed to screen when executing this script. You can see many statistics of the back-tests.
Updating data..............................
LARGEST SHARPE RATIO
gamma_trade and gamma_risk
(0.9, 5)
result
###########################################################
Universe size 31
Initial timestamp 1963-02-01 14:30:00
Final timestamp 2024-03-01 14:30:00
Number of periods 734
Initial value (USDOLLAR) 1.000e+06
Final value (USDOLLAR) 1.972e+09
Profit (USDOLLAR) 1.971e+09
Avg. return (annualized) 13.1%
Volatility (annualized) 11.5%
Avg. excess return (annualized) 8.4%
Avg. active return (annualized) 8.4%
Excess volatility (annualized) 11.5%
Active volatility (annualized) 11.5%
Avg. growth rate (annualized) 12.4%
Avg. excess growth rate (annualized) 7.7%
Avg. active growth rate (annualized) 7.7%
Avg. StocksTransactionCost 2bp
Max. StocksTransactionCost 153bp
Avg. StocksHoldingCost 0bp
Max. StocksHoldingCost 0bp
Sharpe ratio 0.73
Information ratio 0.73
Avg. drawdown -4.6%
Min. drawdown -39.5%
Avg. leverage 55.8%
Max. leverage 100.1%
Avg. turnover 1.5%
Max. turnover 34.2%
Avg. policy time 0.040s
Avg. simulator time 0.008s
Of which: market data 0.001s
Total time 35.338s
###########################################################
LARGEST GROWTH RATE
gamma_trade and gamma_risk
(0.3, 1)
result
###########################################################
Universe size 31
Initial timestamp 1963-02-01 14:30:00
Final timestamp 2024-03-01 14:30:00
Number of periods 734
Initial value (USDOLLAR) 1.000e+06
Final value (USDOLLAR) 1.360e+11
Profit (USDOLLAR) 1.360e+11
Avg. return (annualized) 24.5%
Volatility (annualized) 31.5%
Avg. excess return (annualized) 19.7%
Avg. active return (annualized) 19.7%
Excess volatility (annualized) 31.6%
Active volatility (annualized) 31.6%
Avg. growth rate (annualized) 19.4%
Avg. excess growth rate (annualized) 14.6%
Avg. active growth rate (annualized) 14.6%
Avg. StocksTransactionCost 12bp
Max. StocksTransactionCost 1198bp
Avg. StocksHoldingCost 0bp
Max. StocksHoldingCost 0bp
Sharpe ratio 0.63
Information ratio 0.63
Avg. drawdown -25.7%
Min. drawdown -81.3%
Avg. leverage 97.7%
Max. leverage 112.2%
Avg. turnover 2.7%
Max. turnover 85.8%
Avg. policy time 0.048s
Avg. simulator time 0.009s
Of which: market data 0.001s
Total time 41.593s
###########################################################
UNIFORM (1/N) ALLOCATION FOR COMPARISON
result_uniform
###########################################################
Universe size 31
Initial timestamp 1963-02-01 14:30:00
Final timestamp 2024-03-01 14:30:00
Number of periods 734
Initial value (USDOLLAR) 1.000e+06
Final value (USDOLLAR) 8.997e+09
Profit (USDOLLAR) 8.996e+09
Avg. return (annualized) 16.4%
Volatility (annualized) 16.9%
Avg. excess return (annualized) 11.7%
Excess volatility (annualized) 17.0%
Avg. growth rate (annualized) 14.9%
Avg. excess growth rate (annualized) 10.2%
Avg. StocksTransactionCost 6bp
Max. StocksTransactionCost 360bp
Avg. StocksHoldingCost 0bp
Max. StocksHoldingCost 0bp
Sharpe ratio 0.69
Avg. drawdown -5.5%
Min. drawdown -51.9%
Avg. leverage 99.9%
Max. leverage 103.6%
Avg. turnover 2.6%
Max. turnover 50.0%
Avg. policy time 0.000s
Avg. simulator time 0.005s
Of which: market data 0.001s
Total time 3.395s
###########################################################
HYPER-PARAMETER OPTIMIZATION
iteration 0
Current objective:
98290861668.7877
iteration 1
Current objective:
104498474911.47737
iteration 2
Current objective:
111143662042.72948
iteration 3
Current objective:
118265870300.22061
iteration 4
Current objective:
122625251613.47884
iteration 5
Current objective:
126843647987.58827
iteration 6
Current objective:
130775820171.06282
iteration 7
Current objective:
134763415937.55232
iteration 8
Current objective:
138648657008.04605
iteration 9
Current objective:
142616756158.97928
iteration 10
Current objective:
146451509882.4869
iteration 11
Current objective:
150426864277.33624
iteration 12
Current objective:
154489826957.43265
iteration 13
Current objective:
158227019575.06552
iteration 14
Current objective:
161400378727.53326
iteration 15
Current objective:
163922145513.48956
iteration 16
Current objective:
165526213503.99875
iteration 17
Current objective:
165577391667.23886
result_hyperparameter_optimized
###########################################################
Universe size 31
Initial timestamp 1963-02-01 14:30:00
Final timestamp 2024-03-01 14:30:00
Number of periods 734
Initial value (USDOLLAR) 1.000e+06
Final value (USDOLLAR) 1.656e+11
Profit (USDOLLAR) 1.656e+11
Avg. return (annualized) 25.8%
Volatility (annualized) 34.7%
Avg. excess return (annualized) 21.1%
Avg. active return (annualized) 21.1%
Excess volatility (annualized) 34.7%
Active volatility (annualized) 34.7%
Avg. growth rate (annualized) 19.7%
Avg. excess growth rate (annualized) 15.0%
Avg. active growth rate (annualized) 15.0%
Avg. StocksTransactionCost 14bp
Max. StocksTransactionCost 1491bp
Avg. StocksHoldingCost 0bp
Max. StocksHoldingCost 0bp
Sharpe ratio 0.61
Information ratio 0.61
Avg. drawdown -27.6%
Min. drawdown -85.4%
Avg. leverage 98.6%
Max. leverage 115.5%
Avg. turnover 2.7%
Max. turnover 87.4%
Avg. policy time 0.039s
Avg. simulator time 0.006s
Of which: market data 0.001s
Total time 32.714s
###########################################################
And these are the figure that are plotted.
The result of the cvxportfolio.MultiPeriodOptimization policy
that has the largest out-of-sample Sharpe ratio:
This figure is made by the cvxportfolio.result.BacktestResult.plot() method.#
The result of the cvxportfolio.MultiPeriodOptimization policy
that has the largest out-of-sample growth rate:
This figure is made by the cvxportfolio.result.BacktestResult.plot() method.#
The result of the cvxportfolio.Uniform policy, which allocates equal
weight to all non-cash assets:
This figure is made by the cvxportfolio.result.BacktestResult.plot() method.#
Finally, the result of the cvxportfolio.MultiPeriodOptimization policy
obtained by automatic hyper-parameter optimization to have largest profit:
This figure is made by the cvxportfolio.result.BacktestResult.plot() method.#