基于模型预测的等权期权策略回测

# 12_backtest.py


```py
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# %% [markdown]
# # S&P 500 Options: Equal-Weight Baseline Backtests
#
# Every model fitted in `06_linear` through `09b_patchtst` produced a set of predicted
# decision-date returns. This notebook turns each of those prediction sets into a traded
# strategy and measures what it earned, so that the families can be compared on money
# rather than on rank correlation.
#
# The strategy is the same for all of them, which is what makes the comparison fair. On each
# weekly decision date it ranks the predicted return, keeps the highest-scoring symbols,
# restricts them to the liquid option universe, and sells one at-the-money straddle - a call
# and a put at the same strike and expiration - on each, equally weighted. Each straddle is
# held to expiration and settled in cash at intrinsic value, with the underlying delta measured
# at every session close and hedged when it breaches its threshold. Only the number of symbols
# held varies across requests.
#
# The run publishes a named, immutable population of backtest results. `13_portfolio_management`
# and `15_costs` resolve that population by name and build on it, and `18_strategy_analysis` is
# where the results are ranked and interpreted.
#
# **Learning objectives**
#
# - Turn a registered prediction set into an exact set of option contracts to trade, and check
#   that the interval traded is the interval the prediction was scored over.
# - Read a concentration grid out of the case study's configuration rather than choosing one.
# - Publish a set of backtests as a named population whose membership is fixed before the first
#   backtest runs, so that a later comparison cannot quietly gain or lose a member.
#
# **Book reference**: Chapter 16
#
# **Prerequisites**: the complete official prediction populations published by `06_linear`,
# `07_gbm`, `08_tabular_dl` and the three sequence notebooks.

# %%
"""Execute the complete S&P 500 options equal-weight baseline population."""

import plotly.express as px
import polars as pl

from case_studies.research import supersedes_for_run
from case_studies.sp500_options.research_workflow import (
    ALL_LABELS,
    official_prediction_catalog,
    open_study,
    option_decision_dates,
    option_trade_calendar,
    preview_prediction_candidates,
    run_official_backtest_requests,
    strategy_request_frame,
)
from case_studies.utils.backtest_loaders import load_backtest_prices_for
from case_studies.utils.sweep_config import get_top_k_values_for, get_universe_filters_for
from utils.style import COLORS, show_plotly_with_alt

CASE_STUDY = "sp500_options"
PRIMARY_LABEL = "ret_to_expiry"
BASELINE_POPULATION = "sp500-options-baseline-validation-v1"
MODEL_POPULATIONS = (
    "sp500-options-linear-validation-v1",
    "sp500-options-gbm-validation-v1",
    "sp500-options-tabular-dl-validation-v1",
    "sp500-options-sequence-validation-v1",
)

# %% tags=["parameters"]
EXECUTION_TIER = "canonical"
WORKSPACE: str = ""
PREVIEW_LABELS: list[str] = []
PREVIEW_MAX_PREDICTIONS = 0

# The baseline population is immutable under its name, so a run whose members have moved has to
# say which generation it retires. Anything upstream that changes a backtest identity moves them:
# here it was the corrected settlement in `02_labels`, which moved every training identity and so
# every prediction the requests below resolve. Empty for a first snapshot.
SUPERSEDES_BASELINE_POPULATION: str = ""

# %% [markdown]
# ## Which predictions are traded
#
# A population is a named list of prediction sets, written into the registry by the notebook
# that fitted them and immutable afterwards. Resolving the four populations by name - rather
# than querying the registry for whatever it happens to hold - is what makes this run
# reproducible: a prediction set that arrived later cannot join the comparison, and one that
# was expected and is missing raises instead of shrinking the population silently.
#
# A preview run has no populations to resolve, because preview results never enter one. It
# names the label it trades and how many of that label's configurations to take, and
# `preview_prediction_candidates` selects them from what the preview model stages registered
# in the same workspace. Naming them by hash instead would tie the run to the machine that
# produced them, because a hash is a property of the run and nothing can declare one ahead
# of time.

# %%
study = open_study(execution_tier=EXECUTION_TIER, workspace=WORKSPACE or None)
if EXECUTION_TIER == "canonical":
    if PREVIEW_LABELS or PREVIEW_MAX_PREDICTIONS:
        raise ValueError("canonical execution cannot declare preview reductions")
    predictions = official_prediction_catalog(study, MODEL_POPULATIONS)
elif EXECUTION_TIER == "preview":
    if not WORKSPACE or not PREVIEW_LABELS or PREVIEW_MAX_PREDICTIONS < 1:
        raise ValueError(
            "preview execution requires WORKSPACE, PREVIEW_LABELS and PREVIEW_MAX_PREDICTIONS"
        )
    unknown = sorted(set(PREVIEW_LABELS) - set(ALL_LABELS))
    if unknown:
        raise ValueError(f"preview labels this case study does not declare: {unknown}")
    predictions = preview_prediction_candidates(
        study, labels=PREVIEW_LABELS, limit=PREVIEW_MAX_PREDICTIONS
    )
else:
    raise ValueError(f"unsupported execution tier: {EXECUTION_TIER!r}")
if predictions.filter(~pl.col("complete")).height:
    raise RuntimeError("baseline requests contain incomplete predictions")

# %% [markdown]
# Each model family contributes one prediction set per configuration and per saved checkpoint,
# so the table below counts what the four populations hold rather than listing them.

# %% tags=["results"]
population_summary = (
    predictions.group_by("family")
    .agg(
        configurations=pl.col("config_name").n_unique(),
        checkpoints_per_configuration=(pl.len() / pl.col("config_name").n_unique()).round(1),
        prediction_sets=pl.len(),
    )
    .sort("family")
)
population_summary

# %% [markdown]
# ## The interval the strategy trades
#
# A backtest is only meaningful if the interval it trades is the interval the prediction was
# scored over. Here the two are tied together by construction, and the table below states the
# convention each date follows:
#
# - **Decision date** - the last session of the week present in the prediction set, whose close
#   is the last piece of information the model is allowed to use. That is a Friday whenever the
#   set reaches one, and the session before it otherwise. The prediction is scored on this date.
# - **Entry date** - the next session's close, where the straddle is actually sold. Nothing
#   trades at the price that produced the signal.
#
# The fill is a close rather than the next open because this chain has no open. The AlgoSeek
# option data is one end-of-session quote per contract per day - `LastBidPrice`, `LastAskPrice`,
# `LastMidPrice` - and carries no open, high or low, so a next-open fill is not a convention this
# case study declined to adopt but a price that does not exist in its data. Worth stating plainly,
# because a one-session delay to the next close is also the more conservative choice and reads
# like one: a reader who assumes it was chosen for conservatism would also assume it could be
# relaxed, and here it cannot be. `execution_delay: next_session_close` in `config/setup.yaml`
# records the same fact for the engine, which resolves it to the `next_bar` execution mode.
# - **Expiration** - where the position is closed, in cash, at the intrinsic value of the two
#   legs. Cash settlement is not a trade, so a contract that reaches expiration pays no exit-side
#   option spread. A contract whose quote history ends before its expiration date does not reach
#   it: the engine buys that position back at the last quoted ask and charges the exit spread and
#   commission, because that is the same trade at the same price a round-trip exit would pay.
#
# The net delta of the straddle is measured at every session close in between, and the underlying
# hedge is traded only when that delta breaches its threshold, so the price series the backtest
# marks against is the daily underlying close over exactly the entry-to-expiration window.
#
# The schedule comes from the predictions being traded, because that is where the engine reads it
# from: `weekly_friday` is the last session present in each week of a prediction set, so a set that
# does not reach a Friday enters on that week's Thursday. The contract artifact carries every
# session, and the sessions no prediction set reaches are ones nothing enters on.
#
# The universe filter below is applied first, for the same reason. It is a semi-join against the
# price rows, so a decision date it empties is a date the engine does not rank on, and that too
# can move a week's last session earlier.

# %%
prices = load_backtest_prices_for(CASE_STUDY, PRIMARY_LABEL, split="validation")
universe_filters = get_universe_filters_for(CASE_STUDY)
if universe_filters != ["liquid"]:
    raise ValueError(f"the canonical option universe must be liquid alone, got {universe_filters}")
decision_dates = option_decision_dates(
    study,
    predictions.get_column("prediction_hash"),
    prices=prices,
    signal={"universe_filter": universe_filters[0]},
)
trade_calendar = option_trade_calendar(decision_dates)
sessions = prices.get_column("timestamp").cast(pl.Date).unique().sort().to_frame("session")
# A straddle entered near the end of the window expires after the last priced session, so the
# holding period is measured over the candidates that open and expire inside it.
holding = (
    trade_calendar.join(
        sessions.with_row_index("entry_session").rename({"session": "entry_date"}),
        on="entry_date",
        how="inner",
    )
    .join(
        sessions.with_row_index("exit_session").rename({"session": "expiration"}),
        on="expiration",
        how="inner",
    )
    .with_columns((pl.col("exit_session") - pl.col("entry_session") + 1).alias("sessions_held"))
)
if holding.is_empty():
    raise RuntimeError("no candidate straddle resolves to sessions in the validation calendar")
if holding.filter(pl.col("sessions_held") < 2).height:
    raise RuntimeError("a candidate straddle expires on the session it is entered")

# %% [markdown]
# Read the figure for the spread rather than the centre: a strategy whose holding period is
# fixed by an expiration calendar rather than by a chosen horizon will trade some intervals
# considerably longer than others, and the cost of a day of gamma exposure is paid over each of
# them.

# %%
holding_figure = px.histogram(
    holding.select("sessions_held"),
    x="sessions_held",
    nbins=int(holding.get_column("sessions_held").max()),
    color_discrete_sequence=[COLORS["blue"]],
)
holding_figure.update_layout(
    title="Sessions from entry to expiration across candidate straddles",
    height=420,
    width=900,
    bargap=0.05,
    margin=dict(t=70),
)
holding_figure.update_xaxes(title_text="Trading sessions held")
holding_figure.update_yaxes(title_text="Candidate straddles")
show_plotly_with_alt(
    holding_figure,
    "Histogram of the number of trading sessions each candidate straddle is held from entry "
    "to expiration, over the validation period.",
)

# %% [markdown]
# ## How many symbols to hold
#
# `top_k` is the number of symbols the strategy is short a straddle on at any one decision
# date. It is the only field that varies across the requests below, and it trades diversification
# against liquidity: a small `top_k` concentrates the portfolio in the names the model scores
# highest, a large one dilutes the signal across names it ranks less confidently. The grid comes
# from `config/setup.yaml`, so the notebook demonstrates the sweep rather than choosing it.
#
# The universe filter is a separate restriction and is not swept here. `setup.yaml` pins the
# canonical strategy to the liquid subset - the fifth of the option surface with the tightest
# quoted half-spread on each decision date - because the round-trip cost on the full surface
# consumes the premium the strategy collects. `15_costs` is where the full surface is priced
# against the liquid one.

# %%
n_symbols = prices.get_column("symbol").n_unique()
top_k_values = get_top_k_values_for(CASE_STUDY, PRIMARY_LABEL, n_symbols)
if not top_k_values:
    raise ValueError(
        f"backtest.sweep.top_k_grid[{PRIMARY_LABEL!r}] declares no value below the "
        f"{n_symbols} symbols quoted in the validation universe"
    )
print(f"Universe: {n_symbols} symbols quoted, restricted to the liquid subset each date")
print(f"Concentration grid: {top_k_values} symbols held per decision date")

# %% [markdown]
# ## The requests
#
# One request per prediction set and concentration. Each carries the signal in full - the
# ranking method, how many symbols to keep, the universe restriction - so the request, and not
# an ambient default, is what determines the strategy that runs. Holding to expiration is
# enforced downstream: a request that declares an earlier exit is rejected rather than executed.

# %%
request_rows = []
for row in predictions.iter_rows(named=True):
    for top_k in top_k_values:
        request_rows.append(
            {
                "request_name": f"{row['prediction_hash']}-top{top_k}-liquid",
                "prediction_hash": row["prediction_hash"],
                "label": row["label"],
                "top_k": top_k,
                "signal": {
                    "method": "equal_weight_top_k",
                    "top_k": top_k,
                    "direction": "long_only",
                    "long_short": False,
                    "universe_filter": "liquid",
                },
                "allocation": None,
                "risk": None,
                "costs": None,
                "chapter": "ch16",
            }
        )
requests = strategy_request_frame(request_rows)
print(f"{requests.height} requests: {predictions.height} prediction sets x {len(top_k_values)} k")

# %% [markdown]
# ## Execute
#
# Every request resolves its predictions to exact option contracts and publishes that resolution
# as a decision artifact before any accounting happens, so what was traded is recorded
# independently of what it earned. The engine then values the paired legs daily at their
# midpoint, settles them at intrinsic value, carries the hedge position between sessions, and
# charges the entry-side option spread plus the underlying hedge spread on each session the hedge
# actually trades.
#
# In a canonical run the population's membership is computed and written before the first
# backtest executes. An interrupted run therefore resumes into the same population instead of
# publishing a shorter one.

# %%
execution = run_official_backtest_requests(
    study,
    requests,
    population_name=BASELINE_POPULATION if EXECUTION_TIER == "canonical" else None,
    supersedes=supersedes_for_run(
        study,
        population_name=BASELINE_POPULATION,
        declared=SUPERSEDES_BASELINE_POPULATION or None,
        execution_tier=EXECUTION_TIER,
    ),
)
catalog = execution.catalog_rows.sort("request_name")
if catalog.height != requests.height or catalog.filter(~pl.col("complete")).height:
    raise RuntimeError("baseline execution did not publish every declared request")

# %% [markdown]
# ## What the run produced
#
# The Sharpe ratios below are the raw outcome of the sweep. They are not ranked here and no
# configuration is preferred: choosing one needs the uncertainty around each estimate and the
# count of configurations searched, which `18_strategy_analysis` computes.

# %%
published = (
    study.backtests.table(include_preview=EXECUTION_TIER == "preview")
    .filter(pl.col("backtest_hash").is_in(catalog.get_column("backtest_hash").to_list()))
    .select("family", "config_name", "sharpe", "backtest_hash")
    .join(catalog.select("request_name", "backtest_hash"), on="backtest_hash", how="inner")
    .join(requests.select("request_name", "top_k"), on="request_name", how="inner")
    .drop("request_name")
)
if published.height != catalog.height or published.get_column("sharpe").null_count():
    raise RuntimeError("the published baseline population is missing rows or Sharpe metrics")

# %% tags=["results"]
baseline_spread = (
    published.group_by("family", "top_k")
    .agg(
        backtests=pl.len(),
        sharpe_median=pl.col("sharpe").median(),
        sharpe_min=pl.col("sharpe").min(),
        sharpe_max=pl.col("sharpe").max(),
    )
    .sort("family", "top_k")
)
baseline_spread

# %%
sharpe_figure = px.strip(
    published.with_columns(concentration=pl.col("top_k").cast(pl.String)).sort("family", "top_k"),
    x="sharpe",
    y="family",
    color="concentration",
    hover_data=["config_name", "backtest_hash"],
    color_discrete_sequence=[COLORS["blue"], COLORS["amber"], COLORS["copper"]],
)
sharpe_figure.add_vline(x=0, line_width=1, line_dash="dash", line_color=COLORS["neutral"])
sharpe_figure.update_layout(
    title="Validation Sharpe of the equal-weight baseline, by family and concentration",
    height=520,
    width=1000,
    margin=dict(t=70),
    legend_title_text="symbols held",
)
sharpe_figure.update_xaxes(title_text="Validation Sharpe")
sharpe_figure.update_yaxes(title_text="Model family")
show_plotly_with_alt(
    sharpe_figure,
    "Strip plot of validation Sharpe for every equal-weight baseline backtest, one row per "
    "model family, coloured by the number of symbols held per decision date.",
)

# %% [markdown]
# ## Key takeaways
#
# - A prediction set becomes a strategy only once it is resolved to specific contracts on
#   specific dates; that resolution is published as its own artifact so the trades are on record
#   separately from their returns.
# - Fixing the population before execution is what lets a later notebook say it compared
#   everything: membership cannot grow with a stray re-run or shrink with a failed one.
# - The concentration grid is the only degree of freedom exercised here. Allocation weights,
#   cost assumptions and risk overlays are each varied in their own notebook, so that a
#   difference between two results can be attributed to one field.
#
# **Known limitations**: every result is a validation-period estimate with no interval attached,
# so nothing here supports a statement about which family or concentration is better. The
# liquid-universe restriction is a modelling assumption inherited from the configuration, and
# its cost is quantified in `15_costs` rather than tested here.

```