Factor Risk Model¶

A factor risk model is a statistical model that is used to quantify the risk of an investment or portfolio. It takes into account one or more risk factors, or variables that are known to affect the risk of the investment. The model aims to identify the factors that contribute to risk and to measure their impact on the investment’s return.

Description¶

A factor risk model describes the instrument / portfolio returns \(R\) by factor exposures \(B\), factor returns \(F\) and residual returns (sometimes named as idiosyncratic returns) \(U\).

\[ R = BF + U \]

Therefore, a factor risk model object contains the following attributes

Factor returns: The time series of factor returns, in dimension of (T, n)
Factor covariance: The covariance of the factors derived from the factor returns, in dimension of (n, n)
Factor exposures: The exposure of the instrument / portfolio on each factor, in dimension of (n, N)
Residual returns: The residual returns specific for each instrument / portfolio, in dimension of (T, N)

where T, N and n are the number of timeframes, instruments and factors.

Transform¶

Transformation allows the risk model to be expanded from estimation universe to model universe.

Transformation requires passing the instrument returns of the model universe in

Same length and granularity of time series
Homogeneity

and the factor returns to examine their exposures and residual returns.

One usage is to transform the trained risk model to a bigger universe

risk_model.fit(estimation_returns)

transformed_risk_model = risk_model.transform(model_returns)

Another usage is to combine the factor returns from risk models derived from different methodologies, e.g. statistical and fundamental, and then transform into a more generic risk model.

For example, model1 and model2 contain the statistical and fundamental factors respectively. To combine them and then transform into a new risk model

import pandas as pd

from fpm_risk_model import FactorRiskModel

risk_model = FactorRiskModel(
    factor_returns=pd.concat([model1.factor_returns, model2.factor_returns])
)
risk_model.transform(returns)

The transformed risk model is always updated in place. To retain the original risk model, please always use copy as a backup.

Module¶

class fpm_risk_model.factor_risk_model.FactorRiskModel(factor_exposures: Optional[ndarray] = None, factor_returns: Optional[ndarray] = None, residual_returns: Optional[ndarray] = None, **kwargs)¶

Factor Risk Model.

The class is an abstract class to fit the factor risk model.

The factor risk model contains the data attribute factor_exposures, factors and residual_returns.

The factor exposures are the exposures of each instrument to the specified factors.

The factor returns are returns among the date / time series for each factor.

The residual returns are the idiosyncratic returns of the instruments regarding the specified factor exposures and returns.

__init__(factor_exposures: Optional[ndarray] = None, factor_returns: Optional[ndarray] = None, residual_returns: Optional[ndarray] = None, **kwargs)¶

Constructor

Parameters¶

factor_exposuresndarray: Factor exposures of the factor risk model.
factors_returnsndarray: Factor returns of the factor risk model.
residual_returnsndarray: Residual returns of the factor risk model.

property factor_exposures: ndarray¶

Return the factor exposures.

Return¶

ndarray: Matrix in dimension (n, N) where N is the number of instruments and n is the number of factors.

property factor_returns: ndarray¶

Return the factor returns.

Return¶

ndarray: Matrix in dimension (T, n) where n is the number of factors and T is the number of time frames.

property residual_returns: ndarray¶

Return the residual returns.

Return¶

ndarray: Matrix in dimension (T, N) where N is the number of instruments and T is the number of time frames.

fit(X: ndarray, weights: Optional[ndarray] = None) → object¶

Fit the model.

Parameters¶

Xndarray: Input array of shape (T, N) where N is the number of instruments and T is the number of timeframes.
weights: Optional[ndarray]: Weights array of shape (N,) where N is the number of instruments.

copy() → object¶

Copy the model.

Returns¶

object: Copy of the model.

specific_variances(weights=None, ddof=1) → ndarray¶

Get specific variances.

Parameters¶

ddofint: Degrees of freedom.

Returns¶

ndarray: Specific variances of the instruments.

transform(y: ndarray, regressor: Optional[object] = None) → object¶

Transform the factor risk model.

The method is used to transform the factor risk model by passing another set of returns. Most of the time, the factor risk model is fitted by the estimation universe, and then transformed by the model universe.

Parameters¶

yndarray: The instrument returns.
regressorobject, default=None: Regressor to transform the input y into factor exposures. If None, the regressor is set to the default WLS.

Returns¶

ndarray: The transformed factor risk model.

cov(halflife: Optional[float] = None, ddof=1) → ndarray¶

Get the covariance matrix.

Parameters¶

halflifeOptional[float]: Half life in applying the exponential weighting on factor returns for computing the factor covariance matrix. If None is passed, no exponential weighting is applied.

Returns¶

numpy.ndarray: A square pairwise covariance matrix which its diagonal entries are the variances.

write_directory(path: str, format='parquet', **kwargs)¶

Write the factor risk model to directory.

Parameters¶

path: str: Destination path.
format: str: Supported formats. Default is “parquet”. Options are “csv”, “parquet” and “hdf”.
**kwargs: dict: Optional keyword arguments for the write operation.

classmethod read_directory(path: str, format: str = 'parquet', **kwargs)¶

Read model from specified directory.

Parameters¶

path: str: Directory to read model from.
format: str: Supported formats. Default is “parquet”. Options are “csv”, “parquet” and “hdf”.
**kwargs: dict: Optional keyword arguments for the write operation.