Stochastic Discount Factor

StochasticDiscountFactorModel is a separate model family because the native object is not a latent factor with a premium forecast. The native object is a weight-based pricing-kernel proxy.

The implementation follows the phase-aware adversarial design of Chen, Pelger, and Zhu (2021): learn a pricing kernel that is disciplined by the most informative test-asset moments rather than only by reconstruction or covariance fit.

What The Model Estimates

The model is built around a no-arbitrage objective and returns:

• asset_weights
• optional realized sdf_values
• checkpoint-aware phase history

The public extracted state is:

• StochasticDiscountFactorState

Why It Is Separate From Latent Factors

Latent-factor models estimate:

• exposures
• factor realizations
• then expected returns through beta × premium

The stochastic discount factor family instead estimates a traded pricing object directly. It is closer to:

• a weight-learning model
• a no-arbitrage estimator
• a direct portfolio construction mechanism

That is why it lives under:

• ml4t.models.stochastic_discount_factor

instead of under latent_factors.

Training Phases

The model is phase-aware:

1. unconditional SDF training
2. moment network fitting
3. conditional SDF refinement

Key config fields:

• n_epochs_unc
• n_epochs_moment
• n_epochs_cond
• checkpoint_epochs
• default_checkpoint

For the beta-head side:

• beta_n_epochs
• beta_checkpoint_epochs
• beta_default_checkpoint

Native Output

The native output mode is:

• weights

That is enforced by the current model implementation. If you want expected-return-style projections, use an explicit downstream mapper rather than treating expected returns as the primary estimation target.

Optional Return Mapping

Current helpers include:

• LinearStochasticDiscountFactorReturnMapper
• StochasticDiscountFactorBetaNetworkHead

These are downstream transformations. They do not change the fact that the core estimator is weight-native.

The beta-network head is useful when you need an expected-return-like object for comparison with latent-factor studies, ranking experiments, or downstream backtests that expect asset predictions. It should still be documented as a secondary mapping, not as the primary SDF target.

Typical Workflow

from ml4t.models import CrossSectionBatch, StochasticDiscountFactorConfig, StochasticDiscountFactorModel

model = StochasticDiscountFactorModel(
    StochasticDiscountFactorConfig(
        checkpoint_epochs=(256, 512, 768, 1024, 1280),
        default_checkpoint=1280,
    )
)

fit_summary = model.fit(batch)
state = model.extract(batch)

Practical Interpretation

There are two common uses:

1. Trade The Weight Output Directly

Use the extracted asset weights as a cross-sectional allocation signal, subject to:

• leverage normalization
• caps
• liquidity filters
• turnover controls

2. Use A Beta-Or Return-Projection Head

If you need asset-level expected-return-like quantities for a downstream ranking or comparison study, use an explicit projection helper and document that it is a secondary object.

Checkpoints

Because the structural horizon is long, this family should usually use:

• explicit sparse checkpoint_epochs

rather than dense interval checkpointing.

That keeps:

• extraction cost manageable
• beta-head retraining manageable
• model provenance easier to interpret

For that reason, the recommended default is sparse explicit checkpoint_epochs, not dense interval checkpointing.