Conventional Binomial MSM Forecast-Driven Volatility Targeting

Strategy Card

Conventional Binomial MSM Forecast-Driven Volatility Targeting — strategy card

Spec ID: spec-msm-forecast-volatility-targeting-liquid-us-equities-etfs-1787691749 · Generated: 2026-08-26 01:15 UTC

Cluster: Volatility Targeting · Sub Cluster: Msm Forecast Inverse-Volatility Overlay

One-line description

The strategy holds SPY long with exposure scaled from a one-day-ahead binomial Markov-switching multifractal volatility forecast. It targets 12% annualized portfolio volatility and exits when forecast SPY volatility exceeds 35%.

Why this trade exists

Equity volatility clusters and evolves across multiple persistence horizons. A binomial MSM represents this behavior through latent volatility multipliers with heterogeneous switching rates, potentially producing a more responsive conditional-variance forecast than a static volatility estimate.

The trading overlay seeks to stabilize risk rather than predict return direction: exposure falls when forecast volatility rises and increases when forecast volatility falls, subject to gross-exposure and position caps. Because the universe contains only SPY, the forecast controls market exposure rather than allocating risk across assets.

Algorithm

[code omitted from public view] The occupation-sector filter is analysis-only and never generates portfolio weights.

Parameters

Param	Value	Notes
Universe	SPY ETF	Fixed symbol SPY&US&ETF; GSPC is not traded
Direction	Long-only	Exposure ranges from cash to the applicable cap
Data and return	Daily adjusted close; log(close_t/close_{t-1})	Close is assumed split- and dividend-adjusted
Signal / rebalance	Daily at close	Information through date t forecasts t+1; market-on-close convention
Backtest window	2020-01-01 to 2024-07-01	Daily bars
MSM states	Binomial, conventional full-state filter	Sector filter is analysis-only
Candidate orders	k ∈ {2,3,4,5,6}	Re-estimated and selected by minimum BIC
BIC	-2*ell_k + 3*ln(T_est)	Three fitted parameters: m_0, sigma, and b
Slowest switch probability	gamma_k = 1/756	Remaining gamma_l values follow Eq. (10)
Return drift	mu_t = 0	Strategy-layer implementation choice
Forecast horizon	1 trading day	Full-state posterior is propagated to t+1
Annualization	252	Volatility is multiplied by sqrt(252)
Volatility target	12% annualized	Scaler is min(1.5, 0.12/v_port)
High-volatility gate	35% annualized	Desired exposure becomes zero above the threshold
Portfolio covariance	Diagonal approximation	v_port = sqrt(sum_i((u_i*v_i)^2)); immaterial cross-covariance for one asset
Position / gross cap	1.5 / 1.5	A single SPY position may use the full gross cap
Maximum leverage guard	4.0	Gross and position caps bind first under stated rules
Calibration history	Expanding window	The implementation indicates expansion because no rolling window is specified; warm-up details are not supplied
Explicit trading charge	5 bps per side	Applied to traded notional on buys and sells
Platform costs	$0.004/share; $1 minimum; 1% maximum commission; 0 bps slippage	Cost configuration accompanying the backtest

Look-ahead audit

#	Concern	Status
1	Close-derived signal execution	Pass — the signal uses data through date t and trades at that date's close under the platform's market-on-close convention
2	Future returns entering MSM calibration	Pass if implemented as specified — each calibration must contain observations dated no later than t
3	BIC model selection leakage	Pass if implemented as specified — candidate models are compared only on the contemporaneous calibration sample
4	Corporate-action information	Assumption — the supplied close is treated as split- and dividend-adjusted; no synthetic or forward-filled execution prices are permitted
5	Fundamental release timing	Not applicable — the strategy uses no earnings, filings, transcripts, or other fundamental data
6	Missing execution prices	Pass — orders are skipped when the required close is missing or non-finite

Caveats / known limitations

• The production MLE specification does not impose the binomial domain 1 < m_0 < 2. It can therefore admit m_0 >= 2, making the second multiplier 2-m_0 <= 0 and invalidating the square root and Gaussian variance in Eqs. (9), (16), and (17); the paper's likelihood and filtering results then do not describe the forecast being traded.
• Initial component or full-state probabilities are not specified. Because the likelihood, BIC selection, posterior, and variance forecast depend on initialization, the fitted strategy is not uniquely defined and the paper's fitted-model results cannot identify this implementation.
• The specification does not fully define the calibration sample, warm-up, or derivative-free optimization procedure. Although the implementation indicates an expanding window, T_est and the solution of the non-concave MLE remain implementation-dependent, preventing a direct reproduction of the paper's calibration results.
• Trading always uses the conventional full-state filter and dynamically selects k by BIC. The paper's sector-filter O(k^2) runtime advantage and its fixed-k likelihood, marginal-error, MAP-agreement, orbit-TV, and recovery results in Tables 4 and 5 do not characterize production trading.
• The strategy trades SPY rather than GSPC, fixes gamma_k=1/756, and sets mu_t=0. These deviations invalidate direct use of the paper's GSPC timing benchmark, Eq. (14) calibration-dependent likelihood and QLIKE results, and any results requiring nonzero or time-varying drift.
• The 12% annualized volatility target, 35% exit gate, 1.5 gross cap, and inverse-volatility overlay are strategy-layer additions. The paper's filtering and runtime tables do not establish this strategy's return, Sharpe ratio, drawdown, turnover, or target-volatility accuracy.
• This portfolio backtest does not test the predicted filter-complexity reduction, synthetic exactness discrepancies, orbit-level total variation, MAP agreement, recovery accuracy, or symmetry-induced regularization; no comparator-level forecast or runtime diagnostics are included in the reported outputs.
• Results are concentrated in one ETF and include 1,069 trades, making them sensitive to SPY regime behavior, MSM calibration stability, the adjusted-close assumption, and the stated transaction-cost implementation.

Results

From 2020-01-01 through 2024-07-01, the SPY overlay returned 54.55% with a 0.90 Sharpe ratio, 1.21 Sortino ratio, and 13.52% annualized volatility. Realized volatility exceeded the 12% target, while maximum drawdown reached 20.21%. The run recorded a 3.08 profit factor, an 80.55% win rate, and 1,069 trades; these outcomes describe this single-asset implementation and do not validate the MSM forecast against the listed filter comparators.

Run diagnostics

Recomputed here from the run's stored daily returns, because every annualized figure in the table above is derived from the LENGTH of that array (years = n / 252). Only total return and max drawdown do not depend on the row count, so when the recomputed and stored values differ by a common factor, those two are the numbers to trust.

Check	From the run's own returns	Note
Daily-return rows	1,131	1.00x the 1,134 trading days in 2020-01-01..2024-07-01
Distinct dates	1,131	one row per date
Date span	2020-01-02 .. 2024-07-01
Sum of daily returns	54.55%	matches the reported total return
Sharpe from these rows	0.90	stored 0.90
Volatility from these rows	13.52%	stored 13.52%
Max drawdown from these rows	-20.21%	stored -20.21%
CAGR from these rows	10.19%	stored 10.19%

Backtest metrics snapshot

Metric	Value
Total Return	54.55%
Sharpe	0.90
Sortino	1.21
Calmar	0.50
Max Drawdown	-20.21%
Volatility	13.52%
Beta vs SPY	0.46
Win Rate	80.55%
Profit Factor	3.08
Total Trades	1069
Symbols	1 (SPY)