Portfolio Optimization with Investment Bands API Reference

Plot investment bands and expected returns per asset.

Shows a horizontal bar for each asset's investment band, colored per asset. The expected log-return is annotated to the right of each bar.

Parameters:

• ax (Axes | None, default: None ) –

  Matplotlib axes to draw on. Creates a new figure if None.

Returns:

• Axes –

  The axes with the plot.

Return a human-readable description of the problem data.

Returns:

• str –

  String representation of the data including all parameters and per-asset investment bands and expected returns.

Create a PoIbtvData instance from explicit problem parameters.

Parameters:

• log_returns (list[float]) –

  Expected log-return per asset. Positive values indicate expected gains, negative values indicate expected losses.

• covariance_matrix (ndarray) –

  Symmetric positive semi-definite covariance matrix of shape (n_assets, n_assets). Entry [i,j] represents the covariance between asset i and asset j. Diagonal entries are variances.

• investment_bands (list[tuple[float, float]]) –

  (lower, upper) investment bounds per asset. Each allocation is constrained to [lower, upper]. Must have length n_assets.

• max_budget (float) –

  Maximum total budget across all assets: sum_i investment[i] <= max_budget.

• n_bits (int, default: 3 ) –

  Number of binary bits used to discretise each asset's allocation within its band. Higher values give finer resolution but increase the number of variables exponentially. Default: 3.

• risk_aversion (float, default: 1.0 ) –

  Risk aversion parameter lambda in the Markowitz objective: Higher values penalise variance more strongly. Default: 1.0.

Returns:

• PoIbtvData –

  A validated data instance ready for optimisation.

Raises:

• ValueError –

  If any of the following conditions are violated:

  • covariance_matrix is not square
  • covariance_matrix shape does not match len(log_returns)
  • investment_bands length does not match len(log_returns)
  • Any lower bound exceeds its upper bound
  • max_budget is not positive
  • n_bits is not positive
  • risk_aversion is not positive

Examples:

>>> import numpy as np
>>> data = PoIbtvData.from_values(
...     log_returns=[0.05, 0.08, 0.03],
...     covariance_matrix=np.array(
...         [
...             [0.04, 0.01, 0.005],
...             [0.01, 0.09, 0.02],
...             [0.005, 0.02, 0.03],
...         ]
...     ),
...     investment_bands=[(0.1, 0.5), (0.1, 0.4), (0.1, 0.6)],
...     max_budget=1.0,
...     n_bits=3,
...     risk_aversion=1.0,
... )

Generate a random PO-IBTV instance.

Creates a random portfolio problem with plausible return and covariance structure. Investment bands are sampled uniformly, and the covariance matrix is constructed to be positive semi-definite.

Parameters:

• n_assets (int, default: 3 ) –

  Number of assets, by default 3.

• n_bits (int, default: 3 ) –

  Number of binary bits per asset for discretisation, by default 3.

• risk_aversion (float, default: 1.0 ) –

  Risk aversion parameter lambda controlling the trade-off between expected return and variance. Default: 1.0.

• seed (int | None, default: None ) –

  Random seed for reproducibility, by default None.

Returns:

• PoIbtvData –

  A randomly generated data instance.

Examples:

>>> data = PoIbtvData.generate_random(n_assets=4, n_bits=3, seed=42)

Format the formulation as a string.

Parameters:

• data (PoIbtvData) –

  The problem data.

Returns:

• str –

  String representation of the formulation.

Formulate PO-IBTV as an optimization model.

Expands the continuous Markowitz objective fully into binary variables by substituting the discretised investment expression. The resulting objective contains linear and quadratic terms in x[i,q].

Parameters:

• data (PoIbtvData) –

  The problem data containing returns, covariance, bands, and parameters.

Returns:

• Model –

  A Luna optimization model representing the investment band portfolio problem.

Extract solution from solver result.

Reconstructs the continuous allocation per asset from the binary variables and computes portfolio return, volatility, and validity.

Parameters:

• solution (Solution) –

  The solution containing variable assignments.

• data (PoIbtvData) –

  The original problem data.

Returns:

• PoIbtvSolution –

  A structured solution object with: - allocations: continuous allocation per asset - portfolio_return: expected return of the portfolio - portfolio_volatility: standard deviation of the portfolio - is_valid: whether investment bands and budget are satisfied

Raises:

• NoSolutionFoundError –

  If the solver did not find a solution.

Plot the portfolio allocation against investment bands.

Mirrors the data plot layout: horizontal bars show the investment bands (background) with the selected allocation overlaid as a marker, making it easy to see where each allocation falls within its band.

Parameters:

• data (PoIbtvData) –

  The original problem data containing investment bands.

• ax (Axes | None, default: None ) –

  Matplotlib axes to draw on. Creates a new figure if None.

Returns:

• Axes –

  The axes with the plot.

Return a string describing the PO-IBTV solution.

Generate random PO-IBTV instances.

Parameters:

• min_assets (int, default: 2 ) –

  Minimum number of assets per instance (default: 2).

• max_assets (int, default: 5 ) –

  Maximum number of assets per instance (default: 5).

• n_bits (int, default: 3 ) –

  Number of binary bits per asset (default: 3).

• num_instances (int, default: 1 ) –

  Number of instances per asset count (default: 1).

• seed (int | None, default: None ) –

  Random seed for reproducibility (default: None).

Returns:

• PoIbtvCollection –

  Collection containing generated instances.