S&P 500のショートストラドル：満期保有リターンと取引コスト

# Case Study: S&P 500 Options (Straddles)


# Case Study: S&P 500 Options (Straddles)

This case study trades options directly rather than using options as side information for an equity model. It is built around the central finding of O'Donovan and Yu (2024, *A Transaction Cost Perspective on Option Anomalies*): of 24 widely-cited single-name option-return predictors, 17 generate significant gross long-short returns, but none survive realistic transaction costs in the standard one-month delta-hedged framing. Option spreads are large enough that a strategy entering and exiting at quoted bid-ask prices pays the spread twice; for ATM single-name straddles the round-trip cost is typically a sizable fraction of the premium itself.

The pipeline adopts the **hold-to-maturity (HTM) mitigation** as its primary modeling target, following the first of three cost-mitigation strategies in O'Donovan and Yu. Each position is a short ATM straddle on an S&P 500 constituent, written on the last available session of each ISO week and held to expiry. This schedule uses Thursday when Friday is a market holiday. Daily delta hedging captures the variance risk premium while the option leg accrues to intrinsic value at expiration. There is no exit-side option trade, so the round-trip option spread becomes a one-sided entry cost. The `ret_to_expiry` label measures the strategy's per-position return and is the registry's only strategy label. Four legacy forward-return variants remain outside the strategy pipeline because their interpretation does not match the HTM engine. Equity-style bps-of-notional accounting understates option spread cost by one to two orders of magnitude.

The teaching point is methodological: equity-style bps-of-notional cost models are structurally mismatched with option premium returns. The case study supplies a worked example of switching to a premium-denominated cost framework as the cost mitigation itself, and quantifying what survives.

## At a Glance

| Property | Value |
|----------|-------|
| Asset Class | S&P 500 equity options (ATM straddles) |
| Frequency | Weekly last-available-session entry, daily delta hedge during hold |
| Universe | S&P 500 constituents with listed options |
| History | 2017–2021 |
| Primary Label | `ret_to_expiry` (HTM short straddle, ~30-day DTE) |
| CV Folds | 2 (single-window, expanding) |
| Cost Model | HTM daily-MTM with full per-leg accounting (entry-side option spread + daily underlying hedge spread; no exit-leg option trade) |

## Backtest engines

All `ret_to_expiry` backtests dispatch through the **HTM cohort engine** (`_htm_backtest.py` to `_run_htm_daily_mtm`). Weekly last-available-session entry with about 30 days to expiry puts up to **5 concurrent cohorts** per underlying at any time. Each cohort carries a short straddle plus a daily-rebalanced delta hedge. Cohort capital is 1/N_ROLL, and portfolio P&L is the weighted sum of per-cohort daily MTM. The shared `ml4t-backtest` engine assumes one position per symbol with continuous reallocation and does not model overlap, paired option and hedge legs, or daily option-premium MTM.

The cost-mitigation cascade (O'Donovan & Yu 2024) is encoded in the `strategy.signal.universe_filter` spec field: `None` runs on the full S&P 500 ATM straddle surface (rung 2 in O'Donovan & Yu's framing), `'liquid'` restricts to the per-rebalance bottom-quintile half-spread subset (rung 3). The canonical sweep is pinned to `'liquid'` (`setup.yaml::backtest.sweep.universe_filter`), since the full surface does not survive round-trip costs; the `'full'` vs `'liquid'` contrast is retained in the Ch18 HTM cost cascade as a narrative comparison only, not as a rank-1 candidate.

## Pipeline

| Stage | Notebook | Chapter | Description | Writes |
|-------|----------|---------|-------------|--------|
| Setup | [`01_feasibility_analysis`](01_feasibility_analysis.ipynb) | Ch6 | Universe breadth, round-trip cost against premium, premium persistence, fold structure | Nothing |
| Labels | [`02_labels`](02_labels.ipynb) | Ch7 | HTM short-straddle return + delta-hedged and raw forward variants | Five parquets in `labels/` — `ret_to_expiry` plus the 5- and 10-session forward returns and their delta-hedged counterparts — each with a `.digest.json` sidecar. Cross-validation folds come from `config/setup.yaml` |
| Features | [`03_financial_features`](03_financial_features.ipynb) | Ch8 | VRP, IV surface, skew, term structure, and Greeks features | `features/financial.parquet` |
| Temporal | [`04_model_based_features`](04_model_based_features.ipynb) | Ch9 | Walk-forward GJR-GARCH volatility + particle-filtered stochastic volatility | `features/model_based.parquet` |
| Evaluation | [`05_evaluation`](05_evaluation.ipynb) | Ch7–9 | IC diagnostics on the engineered feature set | `evaluation/triage_ledger.parquet`, `evaluation/ic_timeseries.parquet` |
| Linear | [`06_linear`](06_linear.ipynb) | Ch11 | Ridge / Lasso / Elastic Net on each label | Training runs and prediction sets in `run_log/registry.db`; coefficients under `run_log/training/{hash}/`, scores under `run_log/predictions/{hash}/` |
| GBM | [`07_gbm`](07_gbm.ipynb) | Ch12 | LightGBM regression and classification on each label | Training runs and prediction sets; boosters, `learning_curves.parquet`, and `feature_importance.parquet` under `run_log/training/{hash}/` (this case study has its own artifact writer and does not emit `fold_metrics.parquet`) |
| Tabular DL | [`08_tabular_dl`](08_tabular_dl.ipynb) | Ch12 | TabM rank-1 adapter MLP on the options feature matrix | Training runs and prediction sets; checkpoints under `run_log/training/tabular_dl/` |
| Deep Learning | [`09_deep_learning`](09_deep_learning.ipynb) | Ch13 | Index notebook for sequence models | Nothing - it reads the registry |
| LSTM | [`09a_lstm`](09a_lstm.ipynb) | Ch13 | Sequential gating over daily options features | Training runs and prediction sets; checkpoints under `run_log/training/deep_learning/` |
| PatchTST | [`09b_patchtst`](09b_patchtst.ipynb) | Ch13 | Multi-scale patch attention on options dynamics | Training runs and prediction sets; checkpoints under `run_log/training/deep_learning/` |
| Causal DML | [`10_causal_dml`](10_causal_dml.ipynb) | Ch15 | Treatment effect of VRP on delta-hedged returns | A row in the registry's `causal_runs` |
| Model Analysis | [`11_model_analysis`](11_model_analysis.ipynb) | — | Cross-model IC comparison and fold stability diagnostics | Nothing - it reads the registry |
| Backtest | [`12_backtest`](12_backtest.ipynb) | Ch16 | HTM dispatch with multi-cohort daily-MTM aggregation | One backtest run per prediction set and entry scheme; `daily_returns.parquet`, `weights.parquet`, and `spec.json` under `run_log/backtest/{hash}/` (the vectorized path produces no trade or fill ledger) |
| Portfolio | [`13_portfolio_management`](13_portfolio_management.ipynb) | Ch17 | Long-short straddle allocation with margin constraints | One backtest run per allocation method, same artifact layout |
| Risk | [`14_risk_management`](14_risk_management.ipynb) | Ch19 | Proves the risk-overlay boundary: the option path refuses a target-weight overlay | Nothing - the comparison stays in the notebook |
| Costs | [`15_costs`](15_costs.ipynb) | Ch18 | HTM cost-sensitivity grid in % of premium across families and universes | `evaluation/htm_cost_sensitivity.parquet`, plus one registered backtest run per cost cell with `daily_returns.parquet` and `spec.json` under `run_log/backtest/{hash}/` (the grid is aggregated inline rather than through `run_backtest()`, so there are no weights) |
| Holdout Predictions | [`16_holdout_predictions`](16_holdout_predictions.ipynb) | Ch20 | Refits the selected configuration over the holdout interval under a training identity of its own | One training run and one `split='holdout'` prediction set |
| Holdout Backtest | [`17_holdout_backtest`](17_holdout_backtest.ipynb) | Ch20 | Writes straddles from those predictions with the carrier's own signal and allocator | One backtest run at `stage='holdout'`, its decision artifact, and the population `sp500_options-holdout-ret_to_expiry` |
| Strategy Analysis | [`18_strategy_analysis`](18_strategy_analysis.ipynb) | Ch20 | End-to-end strategy assessment with paired-bootstrap holdout closure | `results/strategy_assessment.json`. The tear sheet is gated on a `trades.parquet` the vectorized HTM backtester does not emit, so it is skipped |
| Appendix | [`90_ic_diagnostic`](90_ic_diagnostic.ipynb) | — | Signal-attribution deep dive outside the main pipeline | Nothing - it reads the registry |

## Key Results

A negative-result case on the HTM primary label `ret_to_expiry`. The cross-stage validation rank-1 is `deep_learning / patchtst` with an HRP overlay on the top-5 cross-section of the cost-feasible liquid universe. A cohort is entered on the last available session of each ISO week - Friday, or Thursday when Friday is a holiday - and held to expiry, where it is cash-settled: the HTM engine takes no market exit and pays no exit spread, so `decision.exit_time` in `setup.yaml` describes the label's horizon and not an early exit the backtest performs. Every number below is read from `run_log/registry.db` by [`18_strategy_analysis`](18_strategy_analysis.ipynb); the carrier is resolved there rather than pinned here, because a name written into prose agrees with the registry only until the next rebuild.

**Signal direction.** The carrier's daily IC is +0.0128 [-0.0112, +0.0368] over 478 validation dates (HAC lag 34, t=1.047, p=0.296), positive on 55.4% of them. The interval straddles zero, and the prediction and strategy evidence agree that validation does not establish an edge.

**Validation performance.** Validation Sharpe is -0.2461 [-1.5461, +1.1682] over 473 daily periods, with maximum drawdown -0.7606 driven by a single 225-day episode that begins 2019-07-22, bottoms 2020-06-11 and never recovers inside the window. Across the two validation folds the backtest spans, Sharpe ranges [-0.553, +0.174] with a standard deviation of 0.514, so the point estimate is not distinguishable from fold-to-fold noise. Every one of the 2,358 equal-weight baseline backtests on this label is negative - 786 prediction sets, three concentration arms each. Restricted to the 262 prediction sets with complete fold coverage, which is what the search-risk statistics rank, the 786 rows have mean Sharpe -1.012, median -1.030 and P90 -0.809, and the best of them is -0.481 (`gbm / default_mse`); the best baseline anywhere on the label is -0.311, also gbm. By family the medians are -1.046 (deep_learning, n=540), -1.060 (tabular_dl, 216), -1.074 (gbm, 1,350) and -1.269 (linear, 252). The 60 allocation-stage rows run from -0.8952 to the carrier's -0.2461, which is the best anywhere on the label. The carrier's own 60-variant allocation cohort deflates to DSR_ER -0.0230 (p=0.743). PBO has only two combinations, below the ten-combination reporting threshold.

**Holdout closure.** The carrier was refitted over the holdout interval by [`16_holdout_predictions`](16_holdout_predictions.ipynb) - a training identity of its own, covering a CV interval that ends a full option cycle before the window opens - and traded by [`17_holdout_backtest`](17_holdout_backtest.ipynb). Holdout Sharpe is +0.5622 over 247 sessions. The holdout-minus-validation difference is +0.8083 [-1.5299, +3.2209] (p=0.494) and straddles zero: one year of weekly straddle cohorts is too few independent observations to separate a strategy that turned around from one that had an ordinary year. Against the equal-weight holdout universe (Sharpe +2.7137) the difference is -1.9853 [-3.9036, -0.0619] (p=0.046), which excludes zero on the negative side - over the holdout year the strategy underperforms simply holding the universe it selects from. The holdout never enters selection.

**Friction floor.** The HTM cost grid contains 32 rows across four model families, two universes, and four fractions of the quoted half-spread. Every row is negative, from -0.24 at the lowest fraction to -1.66 at the full spread, and Sharpe falls monotonically in the fraction paid within every family and universe. Premium-denominated option spreads remain the binding constraint.

The printed book records the production environment its results were computed in. This README reports the corrected living-code registry, including the holiday-aware weekly schedule and current model cohort. Hardware and library differences can cause small numerical variation, while the no-edge conclusion should remain stable.

## Running

Run from the repository root with the project environment. The pipeline requires the materialized AlgoSeek S&P 500 options straddles and matching daily underlying bars under `ML4T_DATA_PATH`. Missing licensed data fails at the loader boundary.

Notebooks 09a and 09b require explicit CUDA. On an RTX 3090, the accepted full runs took about 12 minutes for LSTM and 67 minutes for PatchTST. Other notebooks use the stored registry and artifacts when available. Do not replace a skipped long model with a CPU run; retain the accepted artifact or document the skip.

```bash
# From repo root
uv run python case_studies/sp500_options/01_feasibility_analysis.py
uv run python case_studies/sp500_options/02_labels.py
uv run python case_studies/sp500_options/03_financial_features.py
uv run python case_studies/sp500_options/04_model_based_features.py
uv run python case_studies/sp500_options/05_evaluation.py
uv run python case_studies/sp500_options/06_linear.py
uv run python case_studies/sp500_options/07_gbm.py
uv run python case_studies/sp500_options/08_tabular_dl.py
uv run python case_studies/sp500_options/09_deep_learning.py
uv run python case_studies/sp500_options/09a_lstm.py
uv run python case_studies/sp500_options/09b_patchtst.py
uv run python case_studies/sp500_options/10_causal_dml.py
uv run python case_studies/sp500_options/11_model_analysis.py
uv run python case_studies/sp500_options/12_backtest.py
uv run python case_studies/sp500_options/13_portfolio_management.py
uv run python case_studies/sp500_options/14_risk_management.py
uv run python case_studies/sp500_options/15_costs.py
uv run python case_studies/sp500_options/16_holdout_predictions.py
uv run python case_studies/sp500_options/17_holdout_backtest.py
uv run python case_studies/sp500_options/18_strategy_analysis.py
uv run python case_studies/sp500_options/90_ic_diagnostic.py
```

## Run Log

Model training runs, predictions, and backtest results are tracked in a content-addressed registry under `run_log/registry.db`.