Factor Pricing Model Risk Model

Package to build risk model for factor pricing model. For further details, please refer to the documentation

Installation

Install this via pip (or your favourite package manager):

pip install factor-pricing-model-risk-model

Usage

The library contains the pipelines to build the risk model. You can run the pipelines interactively in Jupyter Notebook.

import fpm_risk_model

Objective

The project provides frameworks to create multi-factor risk model on an "enterprise-like" level.

The target audiences are researchers, developers and fund management looking for flexibility in creating risk models.

Examples

For end-to-end examples, please refer to examples for the below notebooks

• Cryptocurrency Statistical Risk Model

• NumPy Backend Engine

• Empirical Analysis of Alpha Sizing Rules in Cryptocurrency

Features

Basically, there are three major features provided in the library

• Factor risk model creation
• Covariance estimator
• Tracking risk model accuracy

Factor risk model

The factor risk model is created by fitting instrument returns (which could be weekly, daily, or even higher granularity) and other related parameters into the model, and its products are factor exposures, factor returns, factor covariance, and residual returns (idiosyncratic returns).

For example, to create a simple statistical PCA risk model,

from fpm_risk_model.statistics import PCA

risk_model = PCA(n_components=5)
risk_model.fit(X=returns)

# Get fitted factor exposures
risk_model.factor_exposures

Then, the risk model can be transformed by the returns of a larger homogeneous universe.

risk_model.transform(y=model_returns)

For further details, please refer to the section in the documentation.

Covariance estimation

Currently, covariance estimation is supported in factor risk model, and the estimation depends on the fitted results.

For example, a risk model transformed by model universe returns can derive the pairwise covariance and correlation for the model universe.

risk_model.transform(y=model_returns)

cov = risk_model.cov()
corr = risk_model.corr()

Alternatively, covariance estimator CovarianceEstimator (or RollingCovarianceEstimator in a rolling basis) provides advanced features, including covariance shrinkage and variance adjustment. The following shrinkage methods are supported

• Constant
• Ledoit Wolf shrinkage (Q3 2023)
• Oracle Approximating shrinkage (Q3 2023)

For example, to construct a rolling covariance estimator with constant shrinkage delta 0.2,

from fpm_risk_model import RollingCovarianceEstimator

estimator = RollingCovarianceEstimator(
  rolling_risk_model,
  shrinkage_method="constant",
  delta=0.2
)

then the covariance can be computed with the rolling risk model and volatilities with better forecasting accuracy

estimator.cov(volatility=another_estimated_vol)

For further details, please refer to the section in the documentation.

Tracking risk model accuracy

The library also focuses on the predictability interpretation of the risk model, and provides a few benchmarks to examine the following metrics

• Bias
• Value at Risk (VaR)

For example, to examine the bias statistics of a risk model regarding an equally weighted portfolio (of which its weights are denoted as weights), pass the instrument observed returns (denoted as returns), and either a rolling risk model (to compute the volatility forecast) or a time series of volatility forecasts.

from fpm_risk_model.accuracy import compute_bias_statistics
compute_bias_statistics(
  X=returns,
  weights=weights,
  window=window
  ...
)

Roadmap

The following major features will be enhanced

• Factor exposures computation from factor returns (Q3 2023)
• Shrinking covariance (Q3 2023)
• Multi-asset class factor model (Q4 2023)
• Fundamental type risk model (Q4 2023)

Contribution

All levels of contributions are welcomed. Please refer to the contributing section for development and release guidelines.