Metadata-Version: 2.4
Name: cvxcla
Version: 1.8.0
Summary: Critical line algorithm for the efficient frontier
Project-URL: Homepage, https://github.com/cvxgrp/cvxcla
Project-URL: Repository, https://github.com/cvxgrp/cvxcla
Author-email: Thomas Schmelzer <thomas.schmelzer@gmail.com>, Philipp Schiele <pschiele@stanford.edu>
License-Expression: MIT
License-File: LICENSE
Classifier: License :: OSI Approved :: MIT License
Classifier: Programming Language :: Python :: 3.11
Classifier: Programming Language :: Python :: 3.12
Classifier: Programming Language :: Python :: 3.13
Requires-Python: >=3.11
Requires-Dist: numpy>=2.0.0
Requires-Dist: scipy>=1.11
Provides-Extra: plot
Requires-Dist: kaleido==1.3.0; extra == 'plot'
Requires-Dist: plotly>=6.0.1; extra == 'plot'
Description-Content-Type: text/markdown

<div align="center" markdown="1">

# 📈 [cvxcla](https://www.cvxgrp.org/cvxcla) - Critical Line Algorithm for Portfolio Optimization

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---

**Quick Links:**
[📖 Documentation](https://www.cvxgrp.org/cvxcla) •
[🐛 Report Bug](https://github.com/cvxgrp/cvxcla/issues) •
[💡 Request Feature](https://github.com/cvxgrp/cvxcla/issues) •
[💬 Discussions](https://github.com/cvxgrp/cvxcla/discussions)

---

</div>

## 📋 Overview

`cvxcla` is a Python package that implements the Critical Line Algorithm (CLA)
for portfolio optimization.
The CLA efficiently computes the entire efficient frontier for portfolio optimization
problems with linear constraints and bounds on the weights.

The Critical Line Algorithm was introduced by Harry Markowitz
in [The Optimization of Quadratic Functions Subject to Linear Constraints](https://www.rand.org/pubs/research_memoranda/RM1438.html)
and further described in his book [Portfolio Selection](https://www.wiley.com/en-us/Portfolio+Selection%3A+Efficient+Diversification+of+Investments%2C+2nd+Edition-p-9781557861085).

The algorithm is based on the observation that the efficient frontier
is a piecewise linear function when expected return is plotted against
expected variance. The CLA computes the turning points (corners)
of the efficient frontier, allowing for efficient representation of the entire frontier.

I gave the plenary talk at [EQD's Singapore conference](https://tschm.github.io/eqd_markowitz/PresentationEQDweb.pdf).

## 🧮 Why the Algorithm Works

The Markowitz problem is a quadratic program parametrized by a return target λ:

```
min  wᵀΣw - λ · μᵀw
s.t. Aw = b,  Gw ≤ h,  lb ≤ w ≤ ub
```

where `Aw = b` are linear equalities (the budget, sector/factor neutrality, …) and
`Gw ≤ h` are linear inequalities (group or sector exposure caps; a `≥` floor is the
negated row). As λ sweeps from ∞ (maximize return) down to 0 (minimize variance), the solution
traces the entire efficient frontier. The key insight is that **between consecutive
events, the optimal weights are a linear function of λ**:

```
w(λ) = α + λ · β
```

This holds because the KKT optimality conditions are linear in λ whenever the active
set — which assets sit at their bounds — is fixed. The algorithm exploits this in
three steps:

1. **Start** at λ = ∞, where the portfolio concentrates on the highest-return asset
   within bounds
   ([`init_algo`](https://github.com/cvxgrp/cvxcla/blob/main/src/cvxcla/first.py)).

2. **Solve** the KKT system for the current active set to find α and β by
   block elimination, then decrease λ until one of two events occurs
   (main loop in [`cla.py`](https://github.com/cvxgrp/cvxcla/blob/main/src/cvxcla/cla.py)):
   - a **free** asset hits its bound (leaves the free set), or
   - a **blocked** asset's KKT multiplier changes sign (enters the free set).

   General inequality rows `Gw ≤ h` add the row analogue of these two events: an
   inactive row becomes binding when its slack reaches zero, and an active row is
   released when its multiplier reaches zero. An active row is carried through the
   same block-eliminated solve as an extra equality row, so the structure is
   preserved.

3. **Update** the active set (exactly one asset or constraint row changes status) and
   repeat until λ ≤ 0.

Because only one coordinate changes per step and each step requires only a single
linear solve, the algorithm traces the full frontier cheaply and exactly — no
approximation needed.

## ✨ Features

- Efficient computation of the entire efficient frontier
- Fluent builder API — `CLA.problem(mean, cov).long_only().budget().trace()` — as a
  readable alternative to the explicit constructor
- Box bounds on every weight, plus general linear **equality** constraints
  `Aw = b` (budget, dollar-neutral, sector/factor neutrality) and general linear
  **inequality** constraints `Gw ≤ h` (group or sector exposure caps)
- Factor covariance backend: exact frontiers for diagonal-plus-low-rank
  covariances (factor models, RMT-cleaned matrices) in O(nk) memory via the
  Woodbury identity
- Visualization of the efficient frontier using Plotly
- Computation of the maximum Sharpe ratio portfolio
- Fully tested and documented codebase

## 🚀 Installation

### Using pip

```bash
pip install cvxcla
```

To include plotting support (Plotly and Kaleido):

```bash
pip install cvxcla[plot]
```

### Development Setup

To set up a development environment:

1. Clone the repository:

    ```bash
    git clone https://github.com/cvxgrp/cvxcla.git
    cd cvxcla
    ```

2. Create a virtual environment and install dependencies:

    ```bash
    make install
    ```

This will:

- Install the uv package manager
- Create a Python 3.12 virtual environment
- Install all dependencies from pyproject.toml

## 🔧 Usage

Here's a simple example of how to use `cvxcla` to compute the efficient frontier:

```python
import numpy as np
# Set a seed for reproducibility
np.random.seed(42)
from cvxcla import CLA

# Define your portfolio problem
n = 10  # Number of assets
mean = np.random.randn(n)  # Expected returns
cov = np.random.randn(n, n)
covariance = cov @ cov.T  # Covariance matrix
lower_bounds = np.zeros(n)  # No short selling
upper_bounds = np.ones(n)  # No leverage

# Create a CLA instance
cla = CLA(
    mean = mean,
    covariance = covariance,
    lower_bounds = lower_bounds,
    upper_bounds = upper_bounds,
    a = np.ones((1, n)),  # Fully invested constraint
    b = np.ones(1)
)

# Access the efficient frontier
frontier = cla.frontier

# Get the maximum Sharpe ratio portfolio
max_sharpe_ratio, max_sharpe_weights = frontier.max_sharpe
print(f"Maximum Sharpe ratio: {max_sharpe_ratio:.6f}")
# Print first few weights to avoid long output
print(f"First 3 weights: {max_sharpe_weights[:3]}")

```

```result
Maximum Sharpe ratio: 2.946979
First 3 weights: [0.         0.         0.08509841]
```

The same problem reads more declaratively through the fluent builder, reached via
`CLA.problem(...)`. Each step maps onto one constructor argument, and the terminal
`.trace()` returns the identical `CLA`:

```python
# Same fully-invested, long-only problem as above, assembled fluently.
built = CLA.problem(mean, covariance).long_only().budget().trace()

# Pure sugar over the constructor: it returns the identical frontier.
assert built.frontier.max_sharpe[0] == cla.frontier.max_sharpe[0]
```

`.bounds`, `.equality`, and `.inequality` add general bounds and constraints, as in
the examples below.

For visualization, you can plot the efficient frontier:

```python
# Plot the efficient frontier
fig = frontier.plot(volatility=True)
fig.show()
```

### Group and sector constraints

Pass `g` and `h` to add general inequality rows `Gw ≤ h` on top of the box bounds and
the budget. For example, to cap the combined weight of the first three assets (a
sector) at 40%:

```python
import numpy as np
from cvxcla import CLA

n = 10
rng = np.random.default_rng(42)
mean = rng.standard_normal(n)
factor = rng.standard_normal((n, n))
covariance = factor @ factor.T  # symmetric positive definite

# sum of the first three weights ≤ 0.40
g = np.zeros((1, n))
g[0, :3] = 1.0
h = np.array([0.40])

cla = CLA(
    mean=mean,
    covariance=covariance,
    lower_bounds=np.zeros(n),
    upper_bounds=np.full(n, 0.35),
    a=np.ones((1, n)),  # fully invested
    b=np.ones(1),
    g=g,                # inequality matrix  G  (p x n)
    h=h,                # inequality vector  h  (p,)
)

# every turning point now satisfies the sector cap
assert all(tp.weights[:3].sum() <= 0.40 + cla.tol for tp in cla.turning_points)
```

`g`/`h` default to `None`, so omitting them recovers the equality-only problem
unchanged. Stack multiple rows in `g` for several caps at once, and express a `≥`
floor by negating a row (`-Gw ≤ -h`).

### Factor models at scale

For diagonal-plus-low-rank covariances (factor risk models, eigenvalue-clipped
covariances) pass a `FactorCovariance` instead of a dense matrix; the algorithm
then never forms an n-by-n matrix:

```python
import numpy as np
from cvxcla import CLA, FactorCovariance

rng = np.random.default_rng(42)
n, k = 10_000, 50
covariance = FactorCovariance(
    d=rng.uniform(0.1, 0.5, n),      # idiosyncratic variances
    u=rng.standard_normal((n, k)),   # factor loadings
    delta=rng.uniform(0.5, 2.0, k),  # factor variances, (k,) or (k, k)
)
```

See the [factor backend documentation](https://www.cvxgrp.org/cvxcla/factor/)
for the protocol, the math, and benchmarks against the dense path.

## 🧪 Testing

Run the test suite with:

```bash
make test
```

or directly via pytest:

```bash
uv run pytest
```

## 🧹 Code Quality

Format and lint the code with:

```bash
make fmt
```

## 📖 Documentation

- [Online Documentation](https://www.cvxgrp.org/cvxcla/book)
- [API Reference](https://www.cvxgrp.org/cvxcla/pdoc/)

## 👥 Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

1. Fork the repository
2. Create your feature branch (`git checkout -b feature/amazing-feature`)
3. Run the tests to make sure everything works (`make test`)
4. Format your code (`make fmt`)
5. Commit your changes (`git commit -m 'Add some amazing feature'`)
6. Push to the branch (`git push origin feature/amazing-feature`)
7. Open a Pull Request

## 📄 License

This project is licensed under the MIT License - see the [LICENSE](LICENSE)
file for details.

## 🔍 Related Projects

- [PyCLA](https://github.com/phschiele/PyCLA) by Philipp Schiele - A
previous implementation of the Critical Line Algorithm in Python.

- [CLA](https://github.com/mdengler/cla) by Martin Dengler - The
original implementation by David Bailey and Marcos Lopez de Prado.
