Estimación adversarial del factor de descuento estocástico para secciones transversales de opciones

# 11d_stochastic_discount_factor.py


```py
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# %% [markdown]
# # Option analytics: pricing the cross-section instead of describing it
#
# The three notebooks before this one share a shape. Estimate exposures, estimate factor returns,
# multiply. [`11a_pca`](11a_pca.ipynb) took the exposures from the return panel,
# [`11b_ipca`](11b_ipca.ipynb) made them a linear function of the characteristics, and
# [`11c_conditional_autoencoder`](11c_conditional_autoencoder.ipynb) made that function a network.
# All three answer the question *how does this cross-section move together*.
#
# **The stochastic discount factor asks a different question, and the answer is not a factor
# structure.** It asks what single random variable, multiplied into every asset's return, would make
# them all price correctly - which is what no-arbitrage says must exist. Estimating that object
# directly means there is no factor-return history to hand to a forecaster afterwards, so the
# two-stage shape is not simplified here, it is absent.
#
# **It is fitted adversarially, which is why the epoch schedule looks unlike its siblings'.** One
# network proposes the discount factor; a second network constructs the portfolio that the first one
# prices worst. Training alternates: the discount factor improves against the current adversary, the
# adversary improves against the current discount factor. The configuration therefore declares three
# separate budgets rather than one `n_epochs`, and the published checkpoint numbers are epochs of
# two different phases packed onto one axis - section 1 sets out how.
#
# **It is also the only member of this family that reads anything outside the cross-section.** The
# adapter resolves a macro panel for `sdf` and for no other model, so the state variables the
# discount factor is conditioned on include the macro environment as well as each stock's own option
# surface.
#
# **Learning objectives.** By the end of this notebook you will be able to:
#
# - State what a stochastic discount factor is estimating, and why that is not a factor model.
# - Explain what makes the training adversarial and what the three declared budgets do.
# - Read a checkpoint column that packs two training phases onto one axis, where an unconditional
#   epoch is published as itself and a conditional epoch as the unconditional budget plus itself.
# - Say why the states the library picked by reading the validation split are computed and then
#   discarded rather than published, and what would go wrong if one of them reached the population.
#
# **Book reference**: Chapter 14, Section 14.6 (the stochastic discount factor and the adversarial
# estimator of Chen, Pelger and Zhu, 2021). Chapter 6, Section 6.7 (Search accounting and run
# logging) introduces the run log this notebook writes into.
#
# **Prerequisites**: [`03_financial_features`](03_financial_features.ipynb) and
# [`04_model_based_features`](04_model_based_features.ipynb) have written the feature matrices,
# [`05_evaluation`](05_evaluation.ipynb) has established the walk-forward folds, and
# [`11_latent_factors`](11_latent_factors.ipynb) introduces the family and says which of its five
# members each notebook publishes.
#
# **What it writes**: one training run per label and one complete validation prediction set per
# label and checkpoint, in `run_log/registry.db` and under `run_log/training/` and
# `run_log/predictions/`, grouped under a population named for this model. The family splits across
# five notebooks, so each publishes its own population rather than one shared one.
# [`13_model_analysis`](13_model_analysis.ipynb) compares them against the other families and
# [`14_backtest`](14_backtest.ipynb) selects on validation backtest Sharpe. **Selection happens
# there, not here.**

# %%
"""Fit the declared option-analytics SDF population on the walk-forward folds."""

import plotly.graph_objects as go
import polars as pl

from case_studies.research import (
    declared_labels,
    load_model_configs,
    model_requests,
    open_study,
    plan_models,
    planned_model_plan,
    primary_label,
    run_model_population,
)
from utils.style import COLORS, show_plotly_with_alt

# %% tags=["parameters"]
LABELS: list[str] = []
EXECUTION_TIER = "canonical"
WORKSPACE: str = ""
PREVIEW_REDUCTIONS: dict = {}
POPULATION_NAME = ""
SUPERSEDES_POPULATION: str = ""
DEVICE: str = ""

MODEL_NAME = "sdf"

# %%
study = open_study(
    "sp500_equity_option_analytics",
    execution_tier=EXECUTION_TIER,
    workspace=WORKSPACE or None,
    entry_point="11d_stochastic_discount_factor",
)

# %% [markdown]
# ## 1. Which labels, and what the configuration says
#
# Every label whose training menu declares `latent_factors:` is fitted, and the cell below reads
# which those are rather than this sentence asserting a count that would go stale the moment a
# sixth label declared the family. What the names mean is the part prose has to supply:
# `fwd_ret_5d` is the stock's total return over the five trading days after the decision date,
# `fwd_ret_10d` the same over ten, and `fwd_ret_risk_adj_5d` the five-day return divided by a
# measure of its own dispersion. A `fwd_dir_*` classification label declaring only linear and
# gradient boosting is absent here rather than dropped.

# %%
declared_labels(study, "latent_factors")

# %% [markdown]
# ### Three budgets, and one checkpoint axis across two phases
#
# `case_studies/config/sdf/sdf.yaml` declares `n_epochs_unc: 256`, `n_epochs_moment: 64` and
# `n_epochs_cond: 1024`. Training runs in phases: an unconditional phase in which the discount
# factor is fitted against the whole cross-section, a moment phase in which the adversary is fitted,
# and a conditional phase in which the discount factor is refitted with the state variables
# available to it. `checkpoint_epochs: [256, 512, 768, 1024]` is applied **within each phase**.
#
# The published checkpoint number is a single integer across both phases, so the library offsets
# the conditional phase by the unconditional budget when it labels a checkpoint: conditional epoch
# *e* is published as `256 + e`. The unconditional phase is
# only 256 epochs long, so exactly one scheduled checkpoint falls inside it.
#
# **The library also keeps four states per fit that are not epochs, and none of them is published.**
# It captures, in each phase, the state with the lowest validation loss and the state with the
# highest validation Sharpe. The same labelling maps those onto zero and the negative integers so
# that two training phases fit on one axis, but the schedule that decides what gets
# registered is built from the physical epochs alone, so the four are computed and discarded. Section
# 5 says why that is the right disposal and why the axis they were packed onto is still a trap.
#
# `config/setup.yaml` restates `checkpoint_epochs` under `modeling.latent_factors.model_kwargs.sdf`
# along with `beta_checkpoint_epochs` and `beta_default_checkpoint`, which govern the separate head
# that turns the fitted discount factor into a per-stock signal.

# %%
configs = load_model_configs(
    study,
    "latent_factors",
    labels=LABELS or None,
    config_names=[MODEL_NAME],
)
configs

# %% [markdown]
# `LABELS` narrows what is fitted, and a narrowed run declares a different set of members than the
# canonical population does. A population is immutable once written, so such a run must publish
# under its own name: on a fresh workspace it would otherwise register an incomplete snapshot under
# the canonical one, and where the full population already exists the registry refuses it.
#
# The comparison is against this model's own declared rows rather than the whole `latent_factors`
# catalog. The family is split across five notebooks and each publishes one model, so the complete
# catalog is five times what this one publishes, and comparing against it would report every
# canonical run as narrowed.

# %%
declared = load_model_configs(study, "latent_factors", config_names=[MODEL_NAME])
if set(configs.get_column("label")) != set(declared.get_column("label")) and not POPULATION_NAME:
    raise ValueError(
        f"this run fits {configs.height} of the {declared.height} declared labels, so it cannot "
        "publish the canonical population; pass POPULATION_NAME to give it its own"
    )

# %% [markdown]
# ### The device, and the one input that comes from outside the cross-section
#
# `config/setup.yaml` declares the latent-factor family on CUDA. That declaration exists because the
# device sits inside the hashed computation rather than beside it as provenance: with no value
# declared, the library falls back to whichever device the machine happens to have, and the training
# identity becomes a property of the host. [`11a_pca`](11a_pca.ipynb) and
# [`11b_ipca`](11b_ipca.ipynb) override it to `cpu` because their runners take no device at all;
# this one is a torch model trained on the declared device, so it passes no override.
#
# The adapter resolves a macro panel for `sdf` and refuses it for every other latent model
# when the adapter resolves the request. Those macro values are hashed into the
# request alongside the characteristics, so a run whose macro panel differs is a different training
# identity rather than the same model on slightly different inputs.
#
# A machine without a card cannot run the declared device at all, and the library refuses to
# substitute one: the latent-factor runtime raises when CUDA is declared and unavailable rather
# than falling back to the CPU, because a silent fallback changes what was fitted. `DEVICE` names the
# device such a run fits on. It travels with `POPULATION_NAME`, because the device it names is
# inside the training identity: the run computes a different member set and has to publish under
# its own name rather than into the population the declaration describes.

# %%
overrides: dict = {"device": DEVICE} if DEVICE else {}
print(f"training device: {DEVICE or 'the family declaration in config/setup.yaml (cuda)'}")
print("macro context: resolved by the adapter for sdf, and hashed into the request")

# %% [markdown]
# ## 2. Binding the declarations to the data
#
# A menu entry names an estimator, a factor count and three epoch budgets. It does not say which
# feature columns exist today, where the walk-forward folds fall, or which symbol-date pairs have
# both a return and a label. **Planning** works all of that out - and every training and prediction
# identity with it - without fitting anything. Four things to check:
#
# - **`feature_count` and `eligible_rows` agree across the rows.** A row that differs is a label
#   measured on a different sample from its neighbours. They differ *between* labels, because a
#   ten-day forward window runs out earlier than a five-day one.
# - **`folds` is the same everywhere**, and equals the number of walk-forward splits
#   [`05_evaluation`](05_evaluation.ipynb) established.
# - **`validation_start` and `validation_end` bracket the development sample**, with none of the
#   held-out 2021 tail visible.
# - **`checkpoints` is larger than the four entries `checkpoint_epochs` declares**, because both
#   training phases draw from that one list and the conditional phase's epochs are published offset
#   by the unconditional budget. Read it here rather than inferring it from the configuration.

# %%
requests = model_requests(
    study,
    configs,
    execution_tier=EXECUTION_TIER,
    overrides=overrides,
    preview_reductions=PREVIEW_REDUCTIONS,
)
plan = plan_models(study, requests=requests)

planned_model_plan(plan).select(
    "label",
    "config_name",
    "task",
    "feature_count",
    "eligible_rows",
    "folds",
    "checkpoints",
    "validation_start",
    "validation_end",
)

# %% [markdown]
# The plan is also where a short population is visible. A run that fitted fewer labels than the
# menu declares would still print an IC table and still register its rows; what it would not do is
# announce the gap.

# %%
planned_pairs = {(member.label, member.config_name) for member in plan.members}
requested_pairs = set(zip(configs["label"], configs["config_name"], strict=True))
if planned_pairs != requested_pairs:
    raise RuntimeError(
        "the plan does not match the loaded SDF menu; "
        f"missing {sorted(requested_pairs - planned_pairs)}, "
        f"unexpected {sorted(planned_pairs - requested_pairs)}"
    )
print(f"{len(requested_pairs)} label-configuration pairs")
print(f"{len(plan.expected_training_hashes)} training identities")
print(f"{len(plan.expected_prediction_hashes)} validation prediction sets")

# %% [markdown]
# ## 3. Fitting the population
#
# `run_model_population` runs every planned request. For one request it walks the folds, and on
# each one:
#
# 1. fits the discount-factor network on the training window against a fixed set of instruments -
#    the unconditional phase,
# 2. fits the adversary network to find the portfolio the current discount factor misprices worst -
#    the moment phase,
# 3. refits the discount factor against that adversary, with the state variables and the macro panel
#    available to it - the conditional phase, capturing a state whenever the schedule says so,
# 4. fits a separate head that maps the fitted discount factor onto a per-stock signal, and applies
#    it to the validation window's characteristics.
#
# Step 4 is what makes the output comparable with the other four notebooks at all. The discount
# factor itself is a portfolio weight, not a return forecast; the head is what turns it into a
# number that can be ranked against a forward return. That translation is a modelling choice on top
# of the estimator, and it is the reason an SDF row and a PCA row can sit in the same table.
#
# **This notebook passes the plan rather than resolved requests, and on this family that changes
# what the plan table can show rather than how the fitting is ordered.** The linear, boosted and
# TabM adapters each provide a batch runner that prepares one fold set for several configurations;
# the latent-factor adapter provides none, so every request is fitted on its own whichever path is
# taken. There would be nothing to share in any case: this notebook publishes one model against
# three labels, and each label is a different set of rows. What passing the plan costs is
# `eligible_entities`, which needs the eligibility keys themselves; `eligible_rows` above moves
# whenever the universe does, so the check that column existed for is still made.
#
# **What the call publishes is a population**: a named, immutable list of the prediction sets it
# will produce, written down before the first fit. Afterwards every member must exist and be
# complete, which is what makes the downstream comparison well defined.


# %%
def catalog_labels(execution) -> int:
    """Number of distinct labels the execution published, read from its catalog rows."""
    return execution.catalog_rows.get_column("label").n_unique()


population_name = POPULATION_NAME or f"sp500_equity_option_analytics-{MODEL_NAME}-validation-v1"
execution, population = run_model_population(
    study, plan, population_name=population_name, supersedes=SUPERSEDES_POPULATION or None
)

# No per-fold counts: this family's runner reports none, and two zeros would read as a failed fit.
print(f"{len(execution.runs)} training runs across {catalog_labels(execution)} labels")
print(f"population {population.name}: {len(population.members)} prediction sets")

# %% [markdown]
# `reused` is not zero on a second run. Every identity is re-derived from the inputs, the registry
# already holds the matching rows, and the runner returns the stored result rather than fitting
# again - so re-running this notebook unchanged costs the time it takes to read the data.
#
# ### Running configurations of your own
#
# The published run log is read-only. To add runs, open the study against a workspace, which holds
# its own registry and artifacts and reads the same labels and features:
#
# ```python
# study = open_study("sp500_equity_option_analytics", workspace="~/ml4t-experiments")
# configs = load_model_configs(
#     study, "latent_factors", labels=["fwd_ret_5d"], config_names=["sdf"]
# )
# requests = model_requests(study, configs)
# plan = plan_models(study, requests=requests)
# execution, population = run_model_population(study, plan, population_name="my-sdf-v1")
# ```
#
# To change the budgets or the checkpoint schedule for your own run, edit
# `case_studies/config/sdf/sdf.yaml`, or declare the value under
# `modeling.latent_factors.model_kwargs.sdf` in `config/setup.yaml` to override the preset for this
# case study alone - which is what this case study already does for `checkpoint_epochs`. Note which
# of those you want: the preset is shared by every case study that declares `sdf`, so editing it
# moves the training identity of all of them. Either way the result registers as a new row beside
# the old one rather than replacing it.
# [`RUN_LOG.md`](../RUN_LOG.md#running-your-own-configurations) covers the rest.

# %% [markdown]
# ## 4. What came out
#
# One row per label and checkpoint. The **information coefficient** is the rank correlation, on one
# validation date, between the stocks ordered by the model's prediction and the stocks ordered by
# the return they went on to earn.
#
# `ic_mean` aggregates that **over folds, not over days**: each fold's own mean IC is computed and
# those are averaged with equal weight (`latent_factors/cv.py`, and the convention is stated in
# `registry/metrics.py`). With folds of unequal length the fold mean and the pooled daily mean are
# different numbers, and this column is the first.
#
# `ic_n_days` is how many validation dates produced a defined correlation, and it decides which rows
# are comparable with each other. `auc_scored_against` says what the AUC column was scored against:
# a regression row has no classes of its own and is scored as a ranking signal against a declared
# direction sibling, so `fwd_ret_5d` is scored against `fwd_dir_5d` and `fwd_ret_10d` against
# `fwd_dir_10d`. `fwd_ret_risk_adj_5d` declares no sibling and carries no AUC; null there means not
# computed, not zero.
#
# Every published `checkpoint_value` has to be a positive epoch, and the cell below refuses the
# catalog if one is not. The four validation-chosen states are packed onto zero and the negative
# integers, so a non-positive value here would mean one of them reached the registry - and it would
# then compete, on validation IC and later on validation Sharpe, against epochs that were not chosen
# by reading that split.
#
# **That guard is an invariant check on this population, not a test of what a checkpoint is.** It is
# safe here only because this catalog holds one family, whose schedule is positive epochs by
# construction. Section 5 forbids the same expression anywhere a population spans families, and the
# reason is the same fact that makes it safe here: zero means different things to different
# estimators.
#
# The published catalog is checked against the population planned before fitting rather than against
# its own row count, because a run that lost a member would otherwise report a shorter table and
# nothing else.

# %% tags=["results"]
catalog = execution.catalog_rows.select(
    "config_name",
    "label",
    "task",
    "complete",
    "checkpoint_kind",
    "checkpoint_value",
    "ic_mean",
    "ic_std",
    "ic_t",
    "ic_n_days",
    "auc_mean_daily",
    pl.col("direction_label").alias("auc_scored_against"),
    "n_folds",
    "training_hash",
    "prediction_hash",
).sort("label", "checkpoint_value")

if catalog.filter(pl.col("checkpoint_value") <= 0).height:
    raise RuntimeError("a validation-chosen SDF state reached the published population")

if set(catalog.get_column("prediction_hash")) != set(plan.expected_prediction_hashes):
    raise RuntimeError("the published catalog differs from the population planned before fitting")
if catalog.filter(~pl.col("complete")).height:
    raise RuntimeError("a partial SDF prediction set cannot pass to backtesting")
if catalog.select("label", "config_name", "checkpoint_value").n_unique() != catalog.height:
    raise RuntimeError("each label and checkpoint must identify one prediction set")

primary = primary_label(study)
present = sorted(set(catalog.get_column("label")))
# The primary label leads when it was fitted. A subset run that leaves it out orders by whichever
# label it did fit rather than by one that is not there.
ordered_labels = [label for label in [primary] if label in present] + [
    label for label in present if label != primary
]
print(f"{catalog.height} candidate models across {len(ordered_labels)} labels")
catalog.select(
    "label",
    "checkpoint_value",
    "ic_mean",
    "ic_std",
    "ic_t",
    "ic_n_days",
    "auc_mean_daily",
    "auc_scored_against",
)

# %% [markdown]
# ### Where the schedule went
#
# One line per label, against the published epoch number. `ic_t` in the table above is a Newey-West
# HAC statistic on the daily IC series; it is a diagnostic and not a selection rule, because the
# series is short, overlapping multi-day returns make successive days dependent, and the folds have
# been read many times over by the time a case study reaches this notebook. The shared axis keeps
# the distance between labels readable instead of each panel filling itself.

# %%
fig = go.Figure()
for label in ordered_labels:
    rows = catalog.filter(pl.col("label") == label).sort("checkpoint_value")
    fig.add_trace(
        go.Scatter(
            x=rows.get_column("checkpoint_value").to_list(),
            y=rows.get_column("ic_mean").to_list(),
            mode="lines+markers",
            name=label,
            line=dict(color=COLORS["blue"] if label == primary else COLORS["recede"]),
            marker=dict(color=COLORS["blue"] if label == primary else COLORS["recede"]),
        )
    )
fig.add_hline(y=0, line_width=1, line_dash="dash", line_color=COLORS["neutral"])
fig.update_yaxes(title_text="Mean IC (validation)")
fig.update_xaxes(title_text="Published checkpoint (unconditional epochs, then 256 + conditional)")
fig.update_layout(
    title="An adversarial fit does not settle onto one stopping point",
    height=460,
    width=880,
    margin=dict(t=90),
)
# The span of each line is a fact about the frame, so the alt text counts it rather than asserting
# a shape the next run may not reproduce.
spans = "; ".join(
    f"{row['label']} spans {row['lo']:+.4f} to {row['hi']:+.4f}"
    for row in catalog.group_by("label")
    .agg(lo=pl.col("ic_mean").min(), hi=pl.col("ic_mean").max())
    .sort("label")
    .iter_rows(named=True)
)
show_plotly_with_alt(
    fig,
    "Line chart of mean validation information coefficient against the published checkpoint number, "
    "one line per label on one axis, the primary target in dark navy "
    f"and the two variants in light slate, with a dashed zero line. Counted from the frame: {spans}.",
)

# %% [markdown]
# ## 5. What to notice
#
# **This is the one notebook in the family that is not estimating a factor structure**, so its row in
# [`13_model_analysis`](13_model_analysis.ipynb) is not comparable with its siblings' in the way
# theirs are with each other. PCA, IPCA and the conditional autoencoder differ by one map and
# nothing else. This differs in what is being estimated, and the head that turns a discount factor
# into a per-stock signal is an extra modelling choice sitting between the estimator and the IC.
#
# **The four states the library chose by reading validation are not in the population, and that is
# the point.** An entry whose definition is "the epoch where validation Sharpe was highest", entered
# into a contest judged on validation Sharpe, wins by construction - and the number it wins with is
# a maximum over many attempts reported as a single result. If it won, that configuration is what
# would be replayed on the holdout, which is read once. The schedule that decides what gets
# registered is built from the physical epochs alone, so this cannot happen, and the guard in
# section 3 fails the catalog rather than trusting that it stayed true.
#
# **The axis those states were packed onto is still a trap, and the sign of `checkpoint_value` is
# not a safe test.** Flattening two training phases onto one integer puts one validation-chosen
# state on `0` - the same value IPCA legitimately publishes for its single
# fit. A `< 0` filter would keep the most dangerous of the four and a `<= 0` filter would throw away
# a sibling's only checkpoint. Anything that needs to identify a checkpoint's kind reads the
# library's named constants, never the arithmetic.
#
# **An adversarial objective has no single stopping point to find.** Two networks improve against
# each other, so a plateau in one is not a plateau in the system, and the epoch chart is where that
# shows: a schedule that wanders is what this class of estimator does, not evidence that the fit
# failed. That is also why the library offers best-validation states at all, and why using them
# needs the caveat above rather than a shrug.
#
# **The macro panel is the only outside information in this family, and it is hashed.** Nothing else
# here reads a series that is not the cross-section's own. If the macro panel is rebuilt, this
# model's training identity moves and its four siblings' do not, which is worth knowing before
# concluding that SDF has drifted relative to them.
#
# **Known limitations.** Two folds, one of them validating on 2020, a year in which the
# cross-section co-moved unlike any other in the sample - which bears on a pricing-kernel estimator
# at least as much as on a factor model. The factor count, the three budgets and the network shapes
# are declared rather than chosen, and nothing here tests whether other settings would order the
# cross-section better; that would be a search, and a search over validation IC is what this
# notebook is arranged to avoid. The IC carries no adjustment for the serial dependence overlapping
# multi-day returns create, so it is a ranking diagnostic rather than a test. Adversarial training
# is stochastic and the two networks can trade places between runs, so reproducing the identity does
# not reproduce the third decimal place. And nothing in this path makes a convergence determination:
# the fit runs its declared budgets and stops, so a run that had not settled would publish looking
# exactly like one that had.
#
# **Next**: [`11e_supervised_autoencoder`](11e_supervised_autoencoder.ipynb) returns to the
# autoencoder of [`11c`](11c_conditional_autoencoder.ipynb) and adds the one thing every model in
# this family has so far been denied - the forward return itself, in the objective.

```