Skip to content

Integrations

PortfolioOptimizer integrates nicely with various third-party libraries.

PyPortfolioOpt

PyPortfolioOpt is a library that implements portfolio optimization methods, including classical efficient frontier techniques and Black-Litterman allocation, as well as more recent developments in the field like shrinkage and Hierarchical Risk Parity, along with some novel experimental features like exponentially-weighted covariance matrices.

PyPortfolioOpt implements a range of optimization methods that are very easy to use. The optimization procedure consists of several distinct steps (some of them may be skipped depending on the optimizer):

  • Calculate the expected returns (mostly located in pfopt.expected_returns)
  • Calculate the covariance matrix (mostly located in pfopt.risk_models)
  • Initialize and set up an optimizer (mostly located in pypfopt.efficient_frontier, with the base class located in pypfopt.base_optimizer) including objectives, constraints, and target
  • Run the optimizer to get the weights
  • Convert the weights into a discrete allocation (optional)

For example, let's perform the mean-variance optimization (MVO) for maximum Sharpe:

>>> from pypfopt.expected_returns import mean_historical_return
>>> from pypfopt.risk_models import CovarianceShrinkage
>>> from pypfopt.efficient_frontier import EfficientFrontier

>>> expected_returns = mean_historical_return(data.get("Close"))
>>> cov_matrix = CovarianceShrinkage(data.get("Close")).ledoit_wolf()
>>> optimizer = EfficientFrontier(expected_returns, cov_matrix)
>>> weights = optimizer.max_sharpe()
>>> weights
OrderedDict([('ADAUSDT', 0.1166001117223088),
             ('BNBUSDT', 0.0),
             ('BTCUSDT', 0.0),
             ('ETHUSDT', 0.8833998882776911),
             ('XRPUSDT', 0.0)])

Parsing

Thanks to an outstanding work done by @robertmartin8, the entire codebase of PyPortfolioOpt (with a few exceptions) has consistent argument and function namings, such that we can build a semantic web of functions acting as inputs to other functions. Why this is important? Because the user just needs to provide the target function (let's say, EfficientFrontier.max_sharpe), and we can programmatically figure out the entire call stack having the pricing data alone! And if the user passes any additional keyword arguments, we can check which functions from the stack accept those arguments and automatically pass them.

For the example above, the web looks like this:

flowchart TD;
    id1["User"]
    id2["mean_historical_return"]
    id3["CovarianceShrinkage.ledoit_wolf"]
    id4["EfficientFrontier"]

    id1 -->|"prices"| id2;
    id1 -->|"prices"| id3;
    id2 -->|"expected_returns"| id4;
    id3 -->|"cov_matrix"| id4;

(Reload the page if the diagram doesn't show up)

And here comes vectorbt into play. First, it implements a function resolve_pypfopt_func_kwargs that takes an arbitrary PyPortfolioOpt function, and resolves its arguments. Whenever an argument passed by the user has been matched with an argument in the function's signature, it marks this argument to be passed to the function. Let's try it out on expected returns:

>>> from vectorbtpro.portfolio.pfopt.base import resolve_pypfopt_func_kwargs

>>> vbt.phelp(mean_historical_return)  # (1)!
mean_historical_return(
    prices,
    returns_data=False,
    compounding=True,
    frequency=252,
    log_returns=False
):
    Calculate annualised mean (daily) historical return from input (daily) asset prices.
    Use ``compounding`` to toggle between the default geometric mean (CAGR) and the
    arithmetic mean.

>>> print(vbt.prettify(resolve_pypfopt_func_kwargs(
...     mean_historical_return, 
...     prices=data.get("Close"),  # (2)!
...     freq="1h",  # (3)!
...     year_freq="365d",
...     other_arg=100  # (4)!
... )))
{
    'prices': <pandas.core.frame.DataFrame object at 0x7f9428052c50 of shape (8767, 5)>,
    'returns_data': False,
    'compounding': True,
    'frequency': 8760.0,
    'log_returns': False
}
  1. Get an idea what arguments does the function accept
  2. Can be found in the signature - will be passed
  3. Translates freq and year_freq into frequency (number of time periods in a year) - will be passed
  4. Cannot be found in the signature - will be ignored

And now let's run it on EfficientFrontier:

>>> print(vbt.prettify(resolve_pypfopt_func_kwargs(
...     EfficientFrontier, 
...     prices=data.get("Close")
... )))
{
    'expected_returns': <pandas.core.series.Series object at 0x7f9479927128 of shape (5,)>,
    'cov_matrix': <pandas.core.frame.DataFrame object at 0x7f94280528d0 of shape (5, 5)>,
    'weight_bounds': (
        0,
        1
    ),
    'solver': None,
    'verbose': False,
    'solver_options': None
}

We see that vectorbt magically resolved arguments expected_returns and cov_matrix using resolve_pypfopt_expected_returns and resolve_pypfopt_cov_matrix respectively. If we provided those two arguments manually, vectorbt would use them right away. We can also provide those arguments as strings to change the function with which they are generated:

>>> print(vbt.prettify(resolve_pypfopt_func_kwargs(
...     EfficientFrontier, 
...     prices=data.get("Close"),
...     expected_returns="ema_historical_return",
...     cov_matrix="sample_cov"
... )))
{
    'expected_returns': <pandas.core.series.Series object at 0x7f9428044cf8 of shape (5,)>,
    'cov_matrix': <pandas.core.frame.DataFrame object at 0x7f942805bf60 of shape (5, 5)>,
    'weight_bounds': (
        0,
        1
    ),
    'solver': None,
    'verbose': False,
    'solver_options': None
}

Auto-optimization

Knowing how to parse and resolve function arguments, vectorbt implements a function pypfopt_optimize, which takes user requirements and translates them into function calls. The usage of this function cannot be easier!

>>> vbt.pypfopt_optimize(prices=data.get("Close"))
{'ADAUSDT': 0.1166,
 'BNBUSDT': 0.0,
 'BTCUSDT': 0.0,
 'ETHUSDT': 0.8834,
 'XRPUSDT': 0.0}

In short, pypfopt_optimize first resolves the optimizer using resolve_pypfopt_optimizer, which, in turn, triggers a waterfall of argument resolutions by parsing arguments, including the calculation of the expected returns and the risk model quantifying asset risk. Then, it adds objectives and constraints to the optimizer instance. Finally, it calls the target metric method (such as max_sharpe) or custom convex/non-convex objective using the same parsing procedure as we did above. If wanted, it can also translate continuous weights into discrete ones using DiscreteAllocation.

Since multiple PyPortfolioOpt functions can require the same argument that has to be pre-computed yet, pypfopt_optimize deploys a built-in caching mechanism. Additionally, if any of the arguments weren't used, it throws a warning (which can be mitigated by setting silence_warnings to True) stating that an argument wasn't required by any function in the call stack.

Below, we will demonstrate various optimizations done both using PyPortfolioOpt and vectorbt. Optimizing a long/short portfolio to minimise total variance:

>>> S = CovarianceShrinkage(data.get("Close")).ledoit_wolf()
>>> ef = EfficientFrontier(None, S, weight_bounds=(-1, 1))
>>> ef.min_volatility()
>>> weights = ef.clean_weights()
>>> weights
OrderedDict([('ADAUSDT', -0.01118),
             ('BNBUSDT', 0.09695),
             ('BTCUSDT', 0.9624),
             ('ETHUSDT', -0.10516),
             ('XRPUSDT', 0.05699)])

>>> vbt.pypfopt_optimize(  # (1)!
...     prices=data.get("Close"),
...     expected_returns=None,
...     weight_bounds=(-1, 1),
...     target="min_volatility"
... )
{'ADAUSDT': -0.01118,
 'BNBUSDT': 0.09695,
 'BTCUSDT': 0.9624,
 'ETHUSDT': -0.10516,
 'XRPUSDT': 0.05699}
  1. CovarianceShrinkage.ledoit_wolf and EfficientFrontier are used by default

Optimizing a portfolio to maximise the Sharpe ratio, subject to direction constraints:

directions = ["long", "long", "long", "short", "short"]
direction_mapper = dict(zip(data.symbols, directions))

>>> from pypfopt.expected_returns import capm_return

>>> mu = capm_return(data.get("Close"))
>>> S = CovarianceShrinkage(data.get("Close")).ledoit_wolf()
>>> ef = EfficientFrontier(mu, S, weight_bounds=(-1, 1))
>>> for symbol, direction in direction_mapper.items():
...     idx = data.symbols.index(symbol)
...     if direction == "long":
...         ef.add_constraint(lambda w, _idx=idx: w[_idx] >= 0)
...     if direction == "short":
...         ef.add_constraint(lambda w, _idx=idx: w[_idx] <= 0)
>>> ef.max_sharpe()
>>> weights = ef.clean_weights()
>>> weights
OrderedDict([('BTCUSDT', 0.26614),
             ('ETHUSDT', 0.433),
             ('BNBUSDT', 0.30086),
             ('XRPUSDT', 0.0),
             ('ADAUSDT', 0.0)])

>>> constraints = []
>>> for symbol, direction in direction_mapper.items():
...     idx = data.symbols.index(symbol)
...     if direction == "long":
...         constraints.append(lambda w, _idx=idx: w[_idx] >= 0)
...     if direction == "short":
...         constraints.append(lambda w, _idx=idx: w[_idx] <= 0)
>>> vbt.pypfopt_optimize(  
...     prices=data.get("Close"),
...     expected_returns="capm_return",
...     cov_matrix="ledoit_wolf",
...     target="max_sharpe",
...     weight_bounds=(-1, 1),
...     constraints=constraints,
... )
{'BTCUSDT': 0.26614,
 'ETHUSDT': 0.433,
 'BNBUSDT': 0.30086,
 'XRPUSDT': 0.0,
 'ADAUSDT': 0.0}

Optimizing a portfolio to maximise the Sharpe ratio, subject to sector constraints:

>>> sector_mapper = {
...     "ADAUSDT": "DeFi",
...     "BNBUSDT": "DeFi",
...     "BTCUSDT": "Payment",
...     "ETHUSDT": "DeFi",
...     "XRPUSDT": "Payment"
... }
>>> sector_lower = {
...     "DeFi": 0.75
... }
>>> sector_upper = {}

>>> mu = capm_return(data.get("Close"))
>>> S = CovarianceShrinkage(data.get("Close")).ledoit_wolf()
>>> ef = EfficientFrontier(mu, S)
>>> ef.add_sector_constraints(sector_mapper, sector_lower, sector_upper)
>>> adausdt_index = ef.tickers.index("ADAUSDT")
>>> ef.add_constraint(lambda w: w[adausdt_index] == 0.10)
>>> ef.max_sharpe()
>>> weights = ef.clean_weights()
>>> weights
OrderedDict([('ADAUSDT', 0.1),
             ('BNBUSDT', 0.2772),
             ('BTCUSDT', 0.0524),
             ('ETHUSDT', 0.3728),
             ('XRPUSDT', 0.1976)])

>>> adausdt_index = list(sector_mapper.keys()).index("ADAUSDT")
>>> vbt.pypfopt_optimize(  # (1)!
...     prices=data.get("Close"),
...     expected_returns="capm_return",
...     sector_mapper=sector_mapper,
...     sector_lower=sector_lower,
...     sector_upper=sector_upper,
...     constraints=[lambda w: w[adausdt_index] == 0.10]
... )
{'ADAUSDT': 0.1,
 'BNBUSDT': 0.2772,
 'BTCUSDT': 0.0524,
 'ETHUSDT': 0.3728,
 'XRPUSDT': 0.1976}
  1. CovarianceShrinkage.ledoit_wolf, EfficientFrontier, and EfficientFrontier.max_sharpe are used by default

Optimizing a portfolio to maximise return for a given risk, subject to sector constraints, with an L2 regularisation objective:

>>> from pypfopt.objective_functions import L2_reg

>>> mu = capm_return(data.get("Close"))
>>> S = CovarianceShrinkage(data.get("Close")).ledoit_wolf()
>>> ef = EfficientFrontier(mu, S)
>>> ef.add_sector_constraints(sector_mapper, sector_lower, sector_upper)
>>> ef.add_objective(L2_reg, gamma=0.1)
>>> ef.efficient_risk(0.15)
>>> weights = ef.clean_weights()
>>> weights
OrderedDict([('ADAUSDT', 0.26004),
             ('BNBUSDT', 0.24466),
             ('BTCUSDT', 0.10778),
             ('ETHUSDT', 0.2453),
             ('XRPUSDT', 0.14222)])

>>> vbt.pypfopt_optimize(  # (1)!
...     prices=data.get("Close"),
...     expected_returns="capm_return",
...     sector_mapper=sector_mapper,
...     sector_lower=sector_lower,
...     sector_upper=sector_upper,
...     objectives=["L2_reg"],  # (2)!
...     gamma=0.1,  # (3)!
...     target="efficient_risk",
...     target_volatility=0.15  # (4)!
... )
{'ADAUSDT': 0.26004,
 'BNBUSDT': 0.24466,
 'BTCUSDT': 0.10778,
 'ETHUSDT': 0.2453,
 'XRPUSDT': 0.14222}
  1. CovarianceShrinkage.ledoit_wolf and EfficientFrontier are used by default
  2. Objective can be provided as an attribute of the pypfopt.objective_functions module
  3. Gets recognized as an argument of the objective function
  4. Gets recognized as an argument of the target metric method

Optimizing along the mean-semivariance frontier:

>>> from pypfopt import EfficientSemivariance
>>> from pypfopt.expected_returns import returns_from_prices

>>> mu = capm_return(data.get("Close"))
>>> returns = returns_from_prices(data.get("Close"))
>>> returns = returns.dropna()
>>> es = EfficientSemivariance(mu, returns)
>>> es.efficient_return(0.01)
>>> weights = es.clean_weights()
>>> weights
OrderedDict([('ADAUSDT', 0.0),
             ('BNBUSDT', 0.0),
             ('BTCUSDT', 1.0),
             ('ETHUSDT', 0.0),
             ('XRPUSDT', 0.0)])

>>> vbt.pypfopt_optimize(
...     prices=data.get("Close"),
...     expected_returns="capm_return",
...     optimizer="efficient_semivariance",  # (1)!
...     target="efficient_return",
...     target_return=0.01
... )
{'ADAUSDT': 0.0, 'BNBUSDT': 0.0, 'BTCUSDT': 1, 'ETHUSDT': 0.0, 'XRPUSDT': 0.0}
  1. The second argument of EfficientSemivariance is returns, which is recognized as such by vectorbt and converted from prices automatically

Minimizing transaction costs:

>>> initial_weights = np.array([1 / len(data.symbols)] * len(data.symbols))

>>> from pypfopt.objective_functions import transaction_cost

>>> mu = mean_historical_return(data.get("Close"))
>>> S = CovarianceShrinkage(data.get("Close")).ledoit_wolf()
>>> ef = EfficientFrontier(mu, S)
>>> ef.add_objective(transaction_cost, w_prev=initial_weights, k=0.001)
>>> ef.add_objective(L2_reg, gamma=0.05)
>>> ef.min_volatility()
>>> weights = ef.clean_weights()
>>> weights
OrderedDict([('ADAUSDT', 0.16025),
             ('BNBUSDT', 0.2),
             ('BTCUSDT', 0.27241),
             ('ETHUSDT', 0.2),
             ('XRPUSDT', 0.16734)])

>>> vbt.pypfopt_optimize(  # (1)!
...     prices=data.get("Close"),
...     objectives=["transaction_cost", "L2_reg"],
...     w_prev=initial_weights, 
...     k=0.001,
...     gamma=0.05,
...     target="min_volatility"
... )
{'ADAUSDT': 0.16025,
 'BNBUSDT': 0.2,
 'BTCUSDT': 0.27241,
 'ETHUSDT': 0.2,
 'XRPUSDT': 0.16734}
  1. mean_historical_return, CovarianceShrinkage.ledoit_wolf, and EfficientFrontier are used by default

Custom convex objective:

>>> import cvxpy as cp

>>> def logarithmic_barrier_objective(w, cov_matrix, k=0.1):
...     log_sum = cp.sum(cp.log(w))
...     var = cp.quad_form(w, cov_matrix)
...     return var - k * log_sum

>>> mu = mean_historical_return(data.get("Close"))
>>> S = CovarianceShrinkage(data.get("Close")).ledoit_wolf()
>>> ef = EfficientFrontier(mu, S, weight_bounds=(0.01, 0.3))
>>> ef.convex_objective(logarithmic_barrier_objective, cov_matrix=S, k=0.001)
>>> weights = ef.clean_weights()
>>> weights
OrderedDict([('ADAUSDT', 0.12214),
             ('BNBUSDT', 0.22175),
             ('BTCUSDT', 0.3),
             ('ETHUSDT', 0.21855),
             ('XRPUSDT', 0.13756)])

>>> vbt.pypfopt_optimize(  # (1)!
...     prices=data.get("Close"),
...     weight_bounds=(0.01, 0.3),
...     k=0.001,
...     target=logarithmic_barrier_objective  # (2)!
... )
{'ADAUSDT': 0.12214,
 'BNBUSDT': 0.22175,
 'BTCUSDT': 0.3,
 'ETHUSDT': 0.21855,
 'XRPUSDT': 0.13756}
  1. mean_historical_return, CovarianceShrinkage.ledoit_wolf, and EfficientFrontier are used by default
  2. The second argument of logarithmic_barrier_objective is cov_matrix, which is recognized as such by vectorbt and calculated automatically (or retrieved from cache)

Custom non-convex objective:

>>> def deviation_risk_parity(w, cov_matrix):
...     cov_matrix = np.asarray(cov_matrix)
...     n = cov_matrix.shape[0]
...     rp = (w * (cov_matrix @ w)) / cp.quad_form(w, cov_matrix)
...     return cp.sum_squares(rp - 1 / n).value

>>> mu = mean_historical_return(data.get("Close"))
>>> S = CovarianceShrinkage(data.get("Close")).ledoit_wolf()
>>> ef = EfficientFrontier(mu, S)
>>> ef.nonconvex_objective(deviation_risk_parity, ef.cov_matrix)
>>> weights = ef.clean_weights()
>>> weights
OrderedDict([('ADAUSDT', 0.17421),
             ('BNBUSDT', 0.19933),
             ('BTCUSDT', 0.2515),
             ('ETHUSDT', 0.1981),
             ('XRPUSDT', 0.17686)])

>>> vbt.pypfopt_optimize(  # (1)!
...     prices=data.get("Close"),
...     target=deviation_risk_parity,  # (2)!
...     target_is_convex=False
... )
{'ADAUSDT': 0.17421,
 'BNBUSDT': 0.19933,
 'BTCUSDT': 0.2515,
 'ETHUSDT': 0.1981,
 'XRPUSDT': 0.17686}
  1. mean_historical_return, CovarianceShrinkage.ledoit_wolf, and EfficientFrontier are used by default
  2. The second argument of deviation_risk_parity is cov_matrix, which is recognized as such by vectorbt and calculated automatically (or retrieved from cache)

Black-Litterman Allocation (read more):

>>> sp500_data = vbt.YFData.pull(
...     "^GSPC", 
...     start=data.wrapper.index[0], 
...     end=data.wrapper.index[-1]
... )
>>> market_caps = data.get("Close") * data.get("Volume")
>>> viewdict = {
...     "ADAUSDT": 0.20, 
...     "BNBUSDT": -0.30, 
...     "BTCUSDT": 0, 
...     "ETHUSDT": -0.2, 
...     "XRPUSDT": 0.15
... }

>>> from pypfopt.black_litterman import (
...     market_implied_risk_aversion,
...     market_implied_prior_returns,
...     BlackLittermanModel
... )

>>> S = CovarianceShrinkage(data.get("Close")).ledoit_wolf()
>>> delta = market_implied_risk_aversion(sp500_data.get("Close"))
>>> prior = market_implied_prior_returns(market_caps.iloc[-1], delta, S)
>>> bl = BlackLittermanModel(S, pi=prior, absolute_views=viewdict)
>>> rets = bl.bl_returns()
>>> ef = EfficientFrontier(rets, S)
>>> ef.min_volatility()
>>> weights = ef.clean_weights()
>>> weights
OrderedDict([('ADAUSDT', 0.0),
             ('BNBUSDT', 0.06743),
             ('BTCUSDT', 0.89462),
             ('ETHUSDT', 0.0),
             ('XRPUSDT', 0.03795)])

>>> vbt.pypfopt_optimize(  # (1)!
...     prices=data.get("Close"),
...     expected_returns="bl_returns",  # (2)!
...     market_prices=sp500_data.get("Close"),
...     market_caps=market_caps.iloc[-1],
...     absolute_views=viewdict,
...     target="min_volatility"
... )
{'ADAUSDT': 0.0,
 'BNBUSDT': 0.06743,
 'BTCUSDT': 0.89462,
 'ETHUSDT': 0.0,
 'XRPUSDT': 0.03795}
  1. mean_historical_return and EfficientFrontier are used by default
  2. BlackLittermanModel, delta, prior, and bl_returns are all resolved automatically

Hierarchical Risk Parity (read more):

>>> from pypfopt import HRPOpt

>>> rets = returns_from_prices(data.get("Close"))
>>> hrp = HRPOpt(rets)
>>> hrp.optimize()
>>> weights = hrp.clean_weights()
>>> weights
OrderedDict([('ADAUSDT', 0.19415),
             ('BNBUSDT', 0.24834),
             ('BTCUSDT', 0.22827),
             ('ETHUSDT', 0.15217),
             ('XRPUSDT', 0.17707)])

>>> vbt.pypfopt_optimize(
...     prices=data.get("Close"),  # (1)!
...     optimizer="hrp",
...     target="optimize"
... )
{'ADAUSDT': 0.19415,
 'BNBUSDT': 0.24834,
 'BTCUSDT': 0.22827,
 'ETHUSDT': 0.15217,
 'XRPUSDT': 0.17707}
  1. Returns are recognized as such by vectorbt and converted from prices automatically

Argument groups

In cases where two functions require an argument with the same name but you want to pass different values to them, pass the argument as an instance of pfopt_func_dict where keys should be functions or their names, and values should be different argument values:

>>> vbt.pypfopt_optimize(  
...     prices=data.get("Close"),
...     expected_returns="bl_returns",  
...     market_prices=sp500_data.get("Close"),
...     market_caps=market_caps.iloc[-1],
...     absolute_views=viewdict,
...     target="min_volatility",
...     cov_matrix=vbt.pfopt_func_dict({
...         "EfficientFrontier": "sample_cov",  # (1)!
...         "_def": "ledoit_wolf"  # (2)!
...     })
... )
{'ADAUSDT': 0.0,
 'BNBUSDT': 0.05013,
 'BTCUSDT': 0.91912,
 'ETHUSDT': 0.0,
 'XRPUSDT': 0.03075}
  1. Calculate the annualised sample covariance matrix for the EfficientFrontier class
  2. Calculate the Ledoit-Wolf shrinkage estimate for every other function

Periodically

So, why does vectorbt implement a special parser for PyPortfolioOpt instead of using the original, modularly-built API of the library?

Having a single function that rules them all makes it much easier to use as an optimization function. For example, vectorbt uses sensible defaults for expected returns and other variables, and knows exactly where those variables should be used. In addition, being able to pass arbitrary keyword arguments and letting vectorbt distribute them over functions enables easier testing of multiple argument combinations using groups.

Let's demonstrate this by using PortfolioOptimizer.from_pypfopt, which uses pypfopt_optimize as optimize_func. Optimize for the maximum Sharpe in the previous week:

>>> pfo = vbt.PortfolioOptimizer.from_pypfopt(
...     prices=data.get("Close"),
...     every="W"
... )

>>> pfo.plot().show()

And here's how easy it's to test multiple combinations of the argument target:

>>> pfo = vbt.PortfolioOptimizer.from_pypfopt(
...     prices=data.get("Close"),
...     every="W",
...     target=vbt.Param([
...         "max_sharpe", 
...         "min_volatility", 
...         "max_quadratic_utility"
...     ])
... )

>>> pfo.plot(column="min_volatility").show()  # (1)!
  1. Only one group can be plotted. Note that column here means a group since every PortfolioOptimizer instance is always grouped

Group 3/3

>>> pf = pfo.simulate(data, freq="1h")

>>> pf.sharpe_ratio
target
max_sharpe               2.779042
min_volatility           1.862926
max_quadratic_utility    2.352667
Name: sharpe_ratio, dtype: float64

We see that optimizing for the maximum Sharpe also yields the highest out-of-sample Sharpe. Great!

Manually

We can also wrap the pypfopt_optimize function manually, for example, to do some data preprocessing or weight postprocessing:

>>> def optimize_func(prices, index_slice, **kwargs):
...     period_prices = prices.iloc[index_slice]
...     return vbt.pypfopt_optimize(prices=period_prices, **kwargs)

>>> pfo = vbt.PortfolioOptimizer.from_optimize_func(
...     data.symbol_wrapper,
...     optimize_func,
...     prices=data.get("Close"),
...     index_slice=vbt.Rep("index_slice"),
...     every="W"
... )

Riskfolio-Lib

Riskfolio-Lib is a library for making quantitative strategic asset allocation or portfolio optimization in Python made in Peru 🇵🇪. Its objective is to help students, academics and practitioners to build investment portfolios based on mathematically complex models with low effort. It is built on top of cvxpy and closely integrated with pandas data structures.

Similarly to PyPortfolioOpt, Riskfolio-Lib also implements a range of portfolio optimization tools. A common optimization procedure consists of the following steps:

  • Load price data and convert it into returns
  • Create and set up a new portfolio (usually with the suffix Portfolio)
  • Depending on the model selected, run one or more methods (usually with the suffix stats) that pre-calculate various statistics required by the optimization method
  • Run the optimization method (usually with the suffix optimization) to get the weights

For example, let's perform the mean-variance optimization (MVO) for maximum Sharpe:

>>> import riskfolio as rp

>>> returns = data.get("Close").vbt.to_returns()

>>> port = rp.Portfolio(returns=returns)
>>> port.assets_stats(
...     method_mu="hist",
...     method_cov="hist",
...     d=0.94
... )
>>> w = port.optimization(
...     model="Classic",
...     rm="MV",
...     obj="Sharpe",
...     rf=0,
...     l=0,
...     hist=True
... )
>>> w.T
          ADAUSDT       BNBUSDT   BTCUSDT   ETHUSDT       XRPUSDT
weights  0.207779  1.043621e-08  0.336897  0.455323  3.650466e-09

Hint

Why doesn't assets_stats return anything? Because it calculates mu and cov and overrides the portfolio attributes port.mu and port.cov in place.

Parsing

Using the way above to produce a vector of weights from vectors of returns is great, but dividing the optimization procedure into a set of different function calls makes it harder to parameterize. What we need is just one function that can express an arbitrary Riskfolio-Lib setup, preferably defined using keyword arguments alone. To make one function out of many, we need to know the inputs of each function, the outputs, and how those functions play together. Thanks to the consistent naming of arguments and functions in Riskfolio-Lib (kudos to @dcajasn!), but also to the entire collection of tutorials, we can crystallize out the order of function calls depending on the optimization task.

For example, the optimization method Portfolio.optimization with the model "Classic" would require the statistic method Portfolio.assets_stats to be called first. The model "FM" would require the statistic methods Portfolio.assets_stats and Portfolio.factors_stats to be called. If the user also provided constraints, then we would additionally need to pre-process them by the respective constraints function.

Let's say we've established the call stack, how do we distribute arguments over the functions? We can read the signature of each function:

>>> from vectorbtpro.utils.parsing import get_func_arg_names

>>> get_func_arg_names(port.assets_stats)
['method_mu', 'method_cov', 'd']

If the user passes an argument called method_mu, it should be passed to this function and to any other function listing this argument as it mostly like means the same thing. To resolve the arguments that need to be passed to the respective Riskfolio-Lib function, there is a convenient function resolve_riskfolio_func_kwargs:

>>> from vectorbtpro.portfolio.pfopt.base import resolve_riskfolio_func_kwargs

>>> resolve_riskfolio_func_kwargs(
...     port.assets_stats,
...     method_mu="hist",
...     method_cov="hist",
...     model="Classic"
... )
{'method_mu': 'hist', 'method_cov': 'hist'}

In a case where any of the arguments need to be overridden for one particular function only, we can provide func_kwargs dictionary with functions as keys and keyword arguments as values:

>>> resolve_riskfolio_func_kwargs(
...     port.assets_stats,
...     method_mu="hist",
...     method_cov="hist",
...     model="Classic",
...     func_kwargs=dict(
...         assets_stats=dict(method_mu="ewma1"),
...         optimization=dict(model="BL")
...     )
... )
{'method_mu': 'ewma1', 'method_cov': 'hist'}

This way, we can let vectorbt distribute the arguments, but still reserve the possibility of doing this manually using func_kwargs.

Auto-optimization

Knowing how to parse and resolve function arguments, vectorbt once again implements a function that can take a single set of keyword arguments and translate them into an optimization procedure - riskfolio_optimize. This function is as easy to use as the one for PyPortfolioOpt!

>>> vbt.riskfolio_optimize(returns)
{'ADAUSDT': 0.20777948652846492,
 'BNBUSDT': 1.0435918170753283e-08,
 'BTCUSDT': 0.33689720861500716,
 'ETHUSDT': 0.45532329077024425,
 'XRPUSDT': 3.6503655112892327e-09}

Under the hood, it first resolves the portfolio class by reading the argument port_cls, and then creates a new portfolio instance by passing any keyword arguments that match the signature of its constructor method __init__. After this, it determines the optimization method by reading the argument opt_method, which is "optimization" by default. Knowing the optimization method and the model (provided via the argument model), it can figure out which statistic methods prior to the optimization should be executed and in what order. The names of those statistic methods are saved in stats_methods, unless they are already provided by the user. The next step is the resolution of any asset classes, constraints, and views, and translating them into keyword arguments that can be consumed by the methods that follow in the call stack. For instance, asset classes are pre-processed using the function resolve_asset_classes, which allows the user to pass asset_classes using a range of convenient formats otherwise not supported by Riskfolio-Lib. Having all keyword arguments ready, the function executes the statistic methods (if any), and finally, the optimization method. It then returns the weights as a dictionary with the columns (i.e., asset names) from the returns array as keys.

Below, we will demonstrate various optimizations done both using Riskfolio-Lib and vectorbt. Ulcer Index Portfolio Optimization for Mean Risk (notebook):

>>> port = rp.Portfolio(returns=returns)
>>> port.assets_stats(
...     method_mu="hist", 
...     method_cov="hist", 
...     d=0.94
... )
>>> w = port.optimization(
...     model="Classic", 
...     rm="UCI", 
...     obj="Sharpe", 
...     rf=0, 
...     l=0, 
...     hist=True
... )
>>> w.T
              ADAUSDT       BNBUSDT  BTCUSDT  ETHUSDT       XRPUSDT
weights  4.421983e-11  1.922731e-11   0.8343   0.1657  9.143250e-11

>>> vbt.riskfolio_optimize(
...     returns,
...     method_mu="hist", 
...     method_cov="hist", 
...     d=0.94,
...     model="Classic", 
...     rm="UCI", 
...     obj="Sharpe", 
...     rf=0, 
...     l=0, 
...     hist=True
... )
{'ADAUSDT': 4.4219828299615346e-11,
 'BNBUSDT': 1.9227309961407513e-11,
 'BTCUSDT': 0.8342998038068898,
 'ETHUSDT': 0.16570019603823058,
 'XRPUSDT': 9.143250192538338e-11}

Worst Case Mean Variance Portfolio Optimization using box and elliptical uncertainty sets (notebook):

>>> port = rp.Portfolio(returns=returns)
>>> port.assets_stats(
...     method_mu="hist", 
...     method_cov="hist", 
...     d=0.94
... )
>>> port.wc_stats(
...     box="s", 
...     ellip="s", 
...     q=0.05, 
...     n_sim=3000, 
...     window=3, 
...     dmu=0.1, 
...     dcov=0.1, 
...     seed=0
... )
>>> w = port.wc_optimization(
...     obj="Sharpe", 
...     rf=0, 
...     l=0, 
...     Umu="box", 
...     Ucov="box"
... )
>>> w.T
              ADAUSDT       BNBUSDT   BTCUSDT   ETHUSDT       XRPUSDT
weights  8.434620e-11  4.298850e-11  0.385894  0.614106  4.185089e-11

>>> vbt.riskfolio_optimize(
...     returns,
...     opt_method="wc",  # (1)!
...     method_mu="hist", 
...     method_cov="hist", 
...     box="s", 
...     ellip="s", 
...     q=0.05, 
...     n_sim=3000, 
...     window=3, 
...     dmu=0.1, 
...     dcov=0.1, 
...     seed=0,
...     obj="Sharpe", 
...     rf=0, 
...     l=0, 
...     Umu="box", 
...     Ucov="box"
... )
{'ADAUSDT': 8.434620227152581e-11,
 'BNBUSDT': 4.2988498616065945e-11,
 'BTCUSDT': 0.38589404919778153,
 'ETHUSDT': 0.6141059506330329,
 'XRPUSDT': 4.185089189555317e-11}
  1. Use the worst-case optimization method
>>> vbt.riskfolio_optimize(
...     returns,
...     func_kwargs=dict(  # (1)!
...         assets_stats=dict(
...             opt_method="wc",
...             method_mu="hist", 
...             method_cov="hist"
...         ),
...         wc_stats=dict(
...             box="s", 
...             ellip="s", 
...             q=0.05, 
...             n_sim=3000, 
...             window=3, 
...             dmu=0.1, 
...             dcov=0.1, 
...             seed=0
...         ),
...         wc_optimization=dict(
...             obj="Sharpe", 
...             rf=0, 
...             l=0, 
...             Umu="box", 
...             Ucov="box"
...         )
...     )
... )
{'ADAUSDT': 8.434620227152581e-11,
 'BNBUSDT': 4.2988498616065945e-11,
 'BTCUSDT': 0.38589404919778153,
 'ETHUSDT': 0.6141059506330329,
 'XRPUSDT': 4.185089189555317e-11}
  1. Functions listed as keys must come in the order as they should be called. Everything ending with stats will be interpreted as a statistic method (one or multiple). Everything ending with optimization will be interpreted as an optimization function (only one).

Mean Variance Portfolio with Short Weights (notebook):

>>> port = rp.Portfolio(returns=returns)
>>> port.sht = True
>>> port.uppersht = 0.3
>>> port.upperlng = 1.3
>>> port.budget = 1.0
>>> port.assets_stats(
...     method_mu="hist", 
...     method_cov="hist", 
...     d=0.94
... )
>>> w = port.optimization(
...     model="Classic", 
...     rm="MV", 
...     obj="Sharpe", 
...     rf=0, 
...     l=0, 
...     hist=True
... )
>>> w.T
          ADAUSDT       BNBUSDT   BTCUSDT   ETHUSDT   XRPUSDT
weights  0.295482 -2.109934e-07  0.456143  0.548375 -0.299999

>>> vbt.riskfolio_optimize(
...     returns,
...     sht=True,
...     uppersht=0.3,
...     upperlng=1.3,
...     budget=1.0,
...     method_mu="hist", 
...     method_cov="hist", 
...     d=0.94,
...     rm="MV", 
...     obj="Sharpe", 
...     rf=0, 
...     l=0, 
...     hist=True
... )
{'ADAUSDT': 0.2954820993653493,
 'BNBUSDT': -2.1099344275128538e-07,
 'BTCUSDT': 0.45614303697962627,
 'ETHUSDT': 0.5483745379125106,
 'XRPUSDT': -0.2999994632634474}

Constraints on Assets (notebook):

>>> port = rp.Portfolio(returns=returns)
>>> port.assets_stats(
...     method_mu="hist", 
...     method_cov="hist",
...     d=0.94
... )
>>> asset_classes = {"Assets": returns.columns.tolist()}
>>> asset_classes = pd.DataFrame(asset_classes)
>>> constraints = {  # (1)!
...     "Disabled": [False, False],
...     "Type": ["All Assets", "Assets"],
...     "Set": ["", ""],
...     "Position": ["", "BTCUSDT"],
...     "Sign": [">=", "<="],
...     'Weight': [0.1, 0.15],
...     "Type Relative": ["", ""],
...     "Relative Set": ["", ""],
...     "Relative": ["", ""],
...     "Factor": ["", ""],
... }
>>> constraints = pd.DataFrame(constraints)
>>> A, B = rp.assets_constraints(constraints, asset_classes)
>>> port.ainequality = A
>>> port.binequality = B
>>> w = port.optimization(
...     model="Classic",
...     rm="MV",
...     obj="Sharpe",
...     rf=0,
...     l=0,
...     hist=True
... )
>>> w.T
          ADAUSDT  BNBUSDT  BTCUSDT   ETHUSDT  XRPUSDT
weights  0.181443      0.1     0.15  0.468557      0.1
  1. Eeach asset must have a weight of at least 10%, BTCUSDT must have a weight of at most 15%
>>> vbt.riskfolio_optimize(
...     returns,
...     method_mu="hist", 
...     method_cov="hist", 
...     constraints=[{  # (1)!
...         "Type": "All Assets",
...         "Sign": ">=",
...         "Weight": 0.1
...     }, {
...         "Type": "Assets",
...         "Position": "BTCUSDT",
...         "Sign": "<=",
...         "Weight": 0.15
...     }],
...     d=0.94,
...     rm="MV", 
...     obj="Sharpe", 
...     rf=0, 
...     l=0, 
...     hist=True
... )
{'ADAUSDT': 0.181442978888792,
 'BNBUSDT': 0.10000000609450148,
 'BTCUSDT': 0.1499998352568763,
 'ETHUSDT': 0.4685571774444982,
 'XRPUSDT': 0.10000000231533206}
  1. No need to construct an entire DataFrame, vectorbt will do it for us! Also, no need to provide asset_classes, they will be taken from the columns.

Constraints on Asset Classes (notebook):

>>> tags = [
...     "Smart contracts",
...     "Smart contracts",
...     "Payments",
...     "Smart contracts",
...     "Payments"
... ]

>>> port = rp.Portfolio(returns=returns)
>>> port.assets_stats(
...     method_mu="hist", 
...     method_cov="hist",
...     d=0.94
... )
>>> asset_classes = {
...     "Assets": returns.columns.tolist(),
...     "Tags": tags
... }
>>> asset_classes = pd.DataFrame(asset_classes)
>>> constraints = {  # (1)!
...     "Disabled": [False],
...     "Type": ["Classes"],
...     "Set": ["Tags"],
...     "Position": ["Smart contracts"],
...     "Sign": [">="],
...     'Weight': [0.8],
...     "Type Relative": [""],
...     "Relative Set": [""],
...     "Relative": [""],
...     "Factor": [""],
... }
>>> constraints = pd.DataFrame(constraints)
>>> A, B = rp.assets_constraints(constraints, asset_classes)
>>> port.ainequality = A
>>> port.binequality = B
>>> w = port.optimization(
...     model="Classic",
...     rm="MV",
...     obj="Sharpe",
...     rf=0,
...     l=0,
...     hist=True
... )
>>> w.T
          ADAUSDT       BNBUSDT  BTCUSDT   ETHUSDT       XRPUSDT
weights  0.227839  5.856725e-10      0.2  0.572161  1.852774e-10
  1. Sum of all weights in the class "Smart contracts" of the set "Tags" must be at least 80%
>>> vbt.riskfolio_optimize(
...     returns,
...     method_mu="hist", 
...     method_cov="hist", 
...     asset_classes={"Tags": tags},
...     constraints=[{
...         "Type": "Classes",
...         "Set": "Tags",
...         "Position": "Smart contracts",
...         "Sign": ">=",
...         "Weight": 0.8
...     }],
...     d=0.94,
...     rm="MV", 
...     obj="Sharpe", 
...     rf=0, 
...     l=0, 
...     hist=True
... )
{'ADAUSDT': 0.22783907021563807,
 'BNBUSDT': 5.856745345006487e-10,
 'BTCUSDT': 0.19999999471503008,
 'ETHUSDT': 0.5721609342983793,
 'XRPUSDT': 1.852779892852209e-10}

Nested Clustered Optimization (NCO) (notebook):

>>> port = rp.HCPortfolio(returns=returns)
>>> w = port.optimization(
...     model="NCO",
...     codependence="pearson",
...     covariance="hist",
...     obj="MinRisk",
...     rm="MV",
...     rf=0,
...     l=2,
...     linkage="ward",
...     max_k=10,
...     leaf_order=True
... )
>>> w.T
              ADAUSDT  BNBUSDT   BTCUSDT       ETHUSDT   XRPUSDT
weights  6.402583e-09  0.05898  0.911545  3.331509e-09  0.029475

>>> vbt.riskfolio_optimize(
...     returns,
...     port_cls="HCPortfolio",  # (1)!
...     model="NCO",
...     codependence="pearson",
...     covariance="hist",
...     obj="MinRisk",
...     rm="MV",
...     rf=0,
...     l=2,
...     linkage="ward",
...     max_k=10,
...     leaf_order=True
... )
{'ADAUSDT': 6.402581338827853e-09,
 'BNBUSDT': 0.05897978986842499,
 'BTCUSDT': 0.9115447868616637,
 'ETHUSDT': 3.3315084935084894e-09,
 'XRPUSDT': 0.029475413535821407}
  1. Specify the name of the portfolio class

Note

If you're getting the message "The problem doesn't have a solution with actual input parameters" when using the "MOSEK" solver, make sure to install and activate MOSEK. Also, you can try out "ECOS".

Periodically

As mentioned earlier, having one function that rules them all is not only easier to operate with, but its main purpose is to be parameterized and used in rebalancing with PortfolioOptimizer. In particular, the optimization function above is used by the method PortfolioOptimizer.from_riskfolio, which calls it periodically. Let's demonstrate its power by optimizing for the maximum Sharpe in the previous week:

>>> pfo = vbt.PortfolioOptimizer.from_riskfolio(
...     returns=returns,
...     every="W"
... )

>>> pfo.plot().show()

What about parameters? We can wrap any (also nested) argument with Param to test multiple parameter combinations. Let's test various maximum BTCUSDT weights to see if constraints are working properly:

>>> pfo = vbt.PortfolioOptimizer.from_riskfolio(
...     returns=returns,
...     constraints=[{
...         "Type": "Assets",
...         "Position": "BTCUSDT",
...         "Sign": "<=",
...         "Weight": vbt.Param([0.1, 0.2, 0.3], name="BTCUSDT_maxw")  # (1)!
...     }],
...     every="W",
...     param_search_kwargs=dict(incl_types=list)  # (2)!
... )
  1. Parameters can be defined in arbitrary nested structures
  2. But for VBT to search for parameters in nested structures, we need to whitelist them first

Group 3/3

>>> pfo.allocations.groupby("BTCUSDT_maxw").max()
symbol        ADAUSDT  BNBUSDT  BTCUSDT  ETHUSDT  XRPUSDT
BTCUSDT_maxw                                             
0.1               1.0      1.0      0.1      1.0      1.0
0.2               1.0      1.0      0.2      1.0      1.0
0.3               1.0      1.0      0.3      1.0      1.0

Works flawlessly 👌

Universal portfolios

Note

To install this package, first install vectorbtpro and then universal-portfolios, not them together. Since its dependency versions are quite strict, you may want to ignore its dependencies altogether by running pip install -U universal-portfolios --no-deps.

The purpose of Universal Portfolios is to put together different Online Portfolio Selection (OLPS) algorithms and provide unified tools for their analysis.

In contrast to PyPortfolioOpt, where weights are generated based on a specific range in time, the purpose of OLPS is to choose portfolio weights in every period to maximize its final wealth. That is, the generated weights have always the shape of the original array.

Let's take a look at the uniform allocation (UCRP):

>>> from universal import tools, algos

>>> with vbt.WarningsFiltered():  # (1)!
...     algo = algos.CRP()
...     algo_result = algo.run(data.get("Close"))

>>> algo_result.weights
symbol                     ADAUSDT  BNBUSDT  BTCUSDT  ETHUSDT  XRPUSDT  CASH
Open time                                                                   
2020-01-01 00:00:00+00:00      0.2      0.2      0.2      0.2      0.2   0.0
2020-01-01 01:00:00+00:00      0.2      0.2      0.2      0.2      0.2   0.0
2020-01-01 02:00:00+00:00      0.2      0.2      0.2      0.2      0.2   0.0
...                            ...      ...      ...      ...      ...   ...
2020-12-31 21:00:00+00:00      0.2      0.2      0.2      0.2      0.2   0.0
2020-12-31 22:00:00+00:00      0.2      0.2      0.2      0.2      0.2   0.0
2020-12-31 23:00:00+00:00      0.2      0.2      0.2      0.2      0.2   0.0

[8767 rows x 6 columns]
  1. You may see some deprecation warnings from Pandas, prepend this line to ignore them

As we see, Universal Portfolios has generated and allocated weights at each single timestamp, which is pretty unrealistic because rebalancing that frequently is unsustainable in practice, unless the frequency of data is low. Additionally, iterating over this amount of data with this library is usually quite slow.

To account for this, we should downsample the pricing array to a longer time frame, and then upsample back to the original index. Let's try this out on the DynamicCRP algorithm by downsampling to the daily frequency first:

>>> with vbt.WarningsFiltered():
...     algo = algos.DynamicCRP(
...         n=30, 
...         min_history=7, 
...         metric='sharpe', 
...         alpha=0.01
...     )
...     algo_result = algo.run(data.get("Close").resample("D").last())
...     down_weights = algo_result.weights

>>> down_weights
symbol                          ADAUSDT       BNBUSDT   BTCUSDT       ETHUSDT  \
Open time                                                                       
2020-01-01 00:00:00+00:00  2.000000e-01  2.000000e-01  0.200000  2.000000e-01   
2020-01-02 00:00:00+00:00  2.000000e-01  2.000000e-01  0.200000  2.000000e-01   
2020-01-03 00:00:00+00:00  2.000000e-01  2.000000e-01  0.200000  2.000000e-01   
...                                 ...           ...       ...           ...   
2020-12-29 00:00:00+00:00  8.475716e-09  8.176270e-09  0.664594  8.274986e-09   
2020-12-30 00:00:00+00:00  0.000000e+00  0.000000e+00  0.656068  0.000000e+00   
2020-12-31 00:00:00+00:00  0.000000e+00  0.000000e+00  0.655105  0.000000e+00   

symbol                          XRPUSDT  
Open time                                
2020-01-01 00:00:00+00:00  2.000000e-01  
2020-01-02 00:00:00+00:00  2.000000e-01  
2020-01-03 00:00:00+00:00  2.000000e-01  
...                                 ...  
2020-12-29 00:00:00+00:00  9.004152e-09  
2020-12-30 00:00:00+00:00  0.000000e+00  
2020-12-31 00:00:00+00:00  0.000000e+00  

[366 rows x 5 columns]

Notice how the calculation still takes a considerable amount of time, even by reducing the total number of re-allocation timestamps by 24 times.

Let's bring the weights back to the original time frame:

>>> weights = down_weights.vbt.realign(
...     data.wrapper.index,
...     freq="1h",
...     source_rbound=True,  # (1)!
...     target_rbound=True,
...     ffill=False  # (2)!
... )
>>> weights
symbol                     ADAUSDT  BNBUSDT   BTCUSDT  ETHUSDT  XRPUSDT
Open time                                                              
2020-01-01 00:00:00+00:00      NaN      NaN       NaN      NaN      NaN
2020-01-01 01:00:00+00:00      NaN      NaN       NaN      NaN      NaN
2020-01-01 02:00:00+00:00      NaN      NaN       NaN      NaN      NaN
...                            ...      ...       ...      ...      ...
2020-12-31 21:00:00+00:00      NaN      NaN       NaN      NaN      NaN
2020-12-31 22:00:00+00:00      NaN      NaN       NaN      NaN      NaN
2020-12-31 23:00:00+00:00      0.0      0.0  0.655105      0.0      0.0

[8766 rows x 5 columns]
  1. We're working with the close price, thus use the right bound of each bar
  2. Do not forward-fill to avoid rebalancing at each timestamp

This array can now be used in simulation.

To simplify the workflow introduced above, vectorbt implements a class method PortfolioOptimizer.from_universal_algo, which triggers the entire simulation with Universal Portfolios and, after done, picks the allocations at specific dates from the resulting DataFrame. By default, it picks the timestamps of non-NA, non-repeating weights. The method itself takes the algorithm (algo) and the pricing data (S). The former can take many value types: from the name or instance of the algorithm class (must be a subclass of universal.algo.Algo), to the actual result of the algorithm (of type universal.result.AlgoResult).

Let's run the same algorithm as above, but now using PortfolioOptimizer. We will also test multiple value combinations for n:

>>> with vbt.WarningsFiltered():
...     down_pfo = vbt.PortfolioOptimizer.from_universal_algo(
...         "DynamicCRP",
...         data.get("Close").resample("D").last(),
...         n=vbt.Param([7, 14, 30, 90]), 
...         min_history=7, 
...         metric='sharpe', 
...         alpha=0.01
...     )

>>> down_pfo.plot(column=90).show()

Group 4/4

We can then upsample the optimizer back to the original time frame by constructing an instance of Resampler and passing it to PortfolioOptimizer.resample:

>>> resampler = vbt.Resampler(
...     down_pfo.wrapper.index, 
...     data.wrapper.index, 
...     target_freq="1h"
... )
>>> pfo = down_pfo.resample(resampler)

Note

An allocation at the end of a daily bar will be placed at the end of the first hourly bar on that day, which may be undesired if the allocation uses any information from that daily bar. To account for this, calculate and use the right bounds of both indexes with Resampler.get_rbound_index.

And finally, use the new optimizer in a simulation:

>>> pf = pfo.simulate(data, freq="1h")

>>> pf.sharpe_ratio
n
7     2.913174
14    3.456085
30    3.276883
90    2.176654
Name: sharpe_ratio, dtype: float64

Custom algorithm

Let's create our own mean-reversion algorithm using Universal Portfolios. The idea is that badly performing stocks will revert to its mean and have higher returns than those above their mean.

>>> from universal.algo import Algo

>>> class MeanReversion(Algo):
...     PRICE_TYPE = 'log'
...     
...     def __init__(self, n):
...         self.n = n
...         super().__init__(min_history=n)
...     
...     def init_weights(self, cols):
...         return pd.Series(np.zeros(len(cols)), cols)
...     
...     def step(self, x, last_b, history):
...         ma = history.iloc[-self.n:].mean()
...         delta = x - ma
...         w = np.maximum(-delta, 0.)
...         return w / sum(w)

>>> with vbt.WarningsFiltered():
...     pfo = vbt.PortfolioOptimizer.from_universal_algo(
...         MeanReversion,
...         data.get("Close").resample("D").last(),  # (1)!
...         n=30,  # (2)!
...         every="W"  # (3)!
...     )

>>> pfo.plot().show()
  1. Data frequency is daily
  2. Window length (in days)
  3. Pick an allocation at the beginning of each week

Now it's your turn: create and implement a simple optimization strategy that would make sense in the real world - you'd be amazed how complex and interesting some strategies can become after starting with something really basic 🙂

Python code Notebook