Hello World Example¶
This is a simple example of Cvxportfolio’s capabilities.
A multi-period optimization policy, with default forecasts and simple choice of objective terms and constraints, is compared to a uniform (1/n) allocation for a certain selection of stocks and time period.
The results are printed and plotted using the default methods.
import cvxportfolio as cvx
# risk aversion parameter (Chapter 4.2)
# chosen to match resulting volatility with the
# uniform portfolio (for illustrative purpose)
GAMMA = 2.5
# covariance forecast error risk parameter (Chapter 4.3)
# this can help regularize a noisy covariance estimate
KAPPA = 0.05
objective = cvx.ReturnsForecast() - GAMMA * (
cvx.FullCovariance() + KAPPA * cvx.RiskForecastError()
) - cvx.StocksTransactionCost()
constraints = [cvx.LeverageLimit(3)]
policy = cvx.MultiPeriodOptimization(
objective, constraints, planning_horizon=2)
simulator = cvx.StockMarketSimulator(
['AAPL', 'AMZN', 'UBER', 'ZM', 'CVX', 'TSLA', 'GM', 'ABNB', 'CTAS',
'GOOG'])
results = simulator.backtest_many(
[policy, cvx.Uniform()], start_time='2020-01-01')
# print multi-period result
print("\n# MULTI-PERIOD OPTIMIZATION\n")
print(results[0])
# print uniform allocation result
print("\n# UNIFORM ALLOCATION:\n")
print(results[1])
# plot value and weights of the portfolio in time for MPO
mpo_figure = results[0].plot()
# plot value and weights of the portfolio in time for uniform
uniform_figure = results[1].plot()
This is the output printed to screen when executing this script. You can see many statistics of the back-tests. The timestamps of the back-test are the open times of the New York stock market (9.30am New York time) expressed in UTC.
Updating data..........
# MULTI-PERIOD OPTIMIZATION
#################################################################
Universe size 11
Initial timestamp 2020-01-02 14:30:00+00:00
Final timestamp 2024-03-18 13:30:00+00:00
Number of periods 1059
Initial value (USDOLLAR) 1.000e+06
Final value (USDOLLAR) 3.126e+06
Profit (USDOLLAR) 2.126e+06
Avg. return (annualized) 33.0%
Volatility (annualized) 34.4%
Avg. excess return (annualized) 31.1%
Avg. active return (annualized) 31.1%
Excess volatility (annualized) 34.4%
Active volatility (annualized) 34.4%
Avg. growth rate (annualized) 27.1%
Avg. excess growth rate (annualized) 25.2%
Avg. active growth rate (annualized) 25.2%
Avg. StocksTransactionCost 0bp
Max. StocksTransactionCost 2bp
Avg. StocksHoldingCost 1bp
Max. StocksHoldingCost 3bp
Sharpe ratio 0.90
Information ratio 0.90
Avg. drawdown -14.4%
Min. drawdown -43.1%
Avg. leverage 154.7%
Max. leverage 246.5%
Avg. turnover 0.7%
Max. turnover 31.1%
Avg. policy time 0.008s
Avg. simulator time 0.005s
Of which: market data 0.001s
Total time 14.134s
#################################################################
# UNIFORM ALLOCATION:
#################################################################
Universe size 11
Initial timestamp 2020-01-02 14:30:00+00:00
Final timestamp 2024-03-18 13:30:00+00:00
Number of periods 1059
Initial value (USDOLLAR) 1.000e+06
Final value (USDOLLAR) 2.401e+06
Profit (USDOLLAR) 1.401e+06
Avg. return (annualized) 25.8%
Volatility (annualized) 31.2%
Avg. excess return (annualized) 23.8%
Excess volatility (annualized) 31.2%
Avg. growth rate (annualized) 20.9%
Avg. excess growth rate (annualized) 18.9%
Avg. StocksTransactionCost 0bp
Max. StocksTransactionCost 3bp
Avg. StocksHoldingCost 0bp
Max. StocksHoldingCost 0bp
Sharpe ratio 0.76
Avg. drawdown -12.6%
Min. drawdown -39.7%
Avg. leverage 99.9%
Max. leverage 100.0%
Avg. turnover 0.8%
Max. turnover 50.0%
Avg. policy time 0.001s
Avg. simulator time 0.005s
Of which: market data 0.001s
Total time 6.367s
#################################################################
And these are the figure that are plotted.
The result of the cvxportfolio.MultiPeriodOptimization policy:
This figure is made by the cvxportfolio.result.BacktestResult.plot() method.¶
And 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.¶