Strategy Card

Covariance-Regret Dual Tilt Allocation on Liquid US Large-Cap Equities — strategy card

Spec ID: spec-covariance-regret-dual-tilt-us-largecap-1785694276 · Generated: 2026-08-02 18:47 UTC

Cluster: Risk Allocation · Sub Cluster: Covariance-Regret Dual Tilt

One-line description

Allocates weekly across 200 liquid US large-cap stocks using a minimum-variance anchor plus covariance-weighted recent-return tilts. The two active directions implement opposite gradient signs: an alpha/momentum sleeve and a regret/contrarian sleeve, then project weights into long-only, capped, volatility-targeted constraints.

Why this trade exists

The strategy is motivated by a covariance-regret framing in which the sensitivity of a linear allocation rule to cross-sectional return/cost covariance is proportional to the covariance matrix. A minimum-variance portfolio is used as the budget-constrained anchor, while recent demeaned returns are transformed by the rolling covariance matrix to emphasize assets whose recent relative moves align with broad covariance structure.

Economically, the alpha-maximizing direction behaves like covariance-weighted momentum, while the opposite sign is intended to behave like covariance-weighted mean reversion. The projection layer turns the theoretical gradient tilt into a tradable long-only portfolio with single-name caps, turnover limits, transaction costs, and volatility targeting.

Algorithm

[code omitted from public view]

Parameters

Param	Value	Notes
Universe	Top 200 US stocks	Yearly capitalization screen; ADRs excluded; daily close prices used.
Backtest window	2020-01-01 to 2025-10-08	Daily bars, weekly rebalancing on the last available trading day.
Anchor	Minimum variance	w_MVP = Sigma^-1 1 / (1' Sigma^-1 1).
Covariance lookback	252 trading days	Rolling daily return covariance; minimum history 252 days.
Covariance stabilization	5% diagonal shrinkage; eigenvalue floor 1e-6	Used to stabilize a 200-name covariance inversion.
Recent-return signal	20 trading days	Mean recent return minus rolling 252-day mean return.
Step size	eta = 1 / spectral_norm(Sigma_hat)	Recomputed each rebalance.
Active tilts	+eta Sigma x_t and -eta Sigma x_t	Alpha-maximizing and regret-minimizing sleeves.
Rebalance frequency	Weekly	Signals measured through the rebalance close and executed at that close.
Constraints	Long-only, max 10% per name	Budget projection with residual cash when volatility scaling reduces exposure.
Volatility target	10% annualized ex-ante	Risky weights scaled down toward cash if projected volatility exceeds target; no gross leverage above 1.0 in implementation.
Turnover cap	25% one-way per rebalance	Euclidean projection toward prior weights when cap is exceeded.
Trading cost	5 bps per dollar traded	Strategy-level transaction cost model.
Brokerage assumptions	$0.004/share, $1 min/order, max 1% commission	No additional slippage bps in the supplied cost block.

Look-ahead audit

#	Concern	Status
1	Signal/execution timing	Signals use data available through the rebalance close and execute at that same close via market-on-close convention.
2	Same-day open execution	No same-day open execution is specified for close-derived signals.
3	Rolling return and covariance windows	Covariance, mean return, and recent-return features are computed from historical close-to-close returns up to the rebalance date.
4	Universe selection	Universe uses a yearly capitalization screen with rebalance_year; researchers should confirm the source table is point-in-time for that year.
5	Missing prices	Required close prices are not fabricated; affected symbol orders are skipped.
6	Fundamental data latency	No earnings, filings, transcripts, or other event-time fundamentals are used.

Caveats / known limitations

• The 200-name covariance inversion is economically fragile: near-duplicate share classes such as GOOG/GOOGL with r=0.9969 and BRK-A/BRK-B make the minimum-variance anchor depend materially on the 5% diagonal shrinkage and 1e-6 eigenvalue floor, so the paper's clean positive-definite MVP result does not describe the traded allocation.
• The covariance sample is thin for the dimension: 252 observations for 200 assets gives N/d about 1.26, far below the paper's stated sample-complexity scale of d ln d, so Eq. 13/17/18-style positive-definite and convergence assumptions are not reliable for this backtest.
• The sign mapping between cost-space theory and return-space implementation is suspect: the spec applies -eta Sigma_r x_t to demeaned returns for the sleeve labeled regret-minimizing, which may invert the intended cost-space descent direction; the alpha and regret labels should therefore be interpreted cautiously.
• The executed method is a one-step projected trading heuristic rather than the paper's full convergence procedure; the declared deviations invalidate the return-targeted efficient-frontier interpretation, Algorithm 8.1 convergence-to-tolerance reading, Eq. 17/18/19/21 convergence or stochastic bounds, Eq. 20 high-probability gradient-estimation guarantee, and the rank-1 regret-optimal tilt-to-target result.
• Several predicted properties are analytic rather than directly tested by the aggregate backtest metrics: covariance-regret sign by sleeve, high-covariance pair sensitivity, condition-number-driven convergence behavior, and turnover-constrained regret-cost scaling require sleeve-level diagnostics not shown in the appended metrics.
• The universe contains some non-US-domiciled or cross-listed large-cap names despite the US stock screen, so the portfolio is not a pure US operating-company exposure set.
• Performance is measured over a single 2020-2025 regime with no walk-forward split; the period includes extreme COVID, mega-cap growth, AI, and rate-cycle effects.
• Trade count is high at 16,431 trades, so realized performance remains sensitive to fill quality, borrow/corporate-action handling, taxes, and capacity even with large-cap names.

Results

The backtest produced a positive total return of 94.68% with Sharpe 0.79, Sortino 1.19, and profit factor 1.99 over 2020-01-01 to 2025-10-08. Risk was material: realized volatility was 20.90% and max drawdown reached -25.11%, which is high relative to the 10% ex-ante volatility target and suggests realized risk control was imperfect during this sample.

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	1,450	1.00x the 1,454 trading days in 2020-01-01..2025-10-08
Distinct dates	1,450	one row per date
Date span	2020-01-02 .. 2025-10-08
Sum of daily returns	94.68%	matches the reported total return
Sharpe from these rows	0.79	stored 0.79
Volatility from these rows	20.90%	stored 20.90%
Max drawdown from these rows	-25.11%	stored -25.11%
CAGR from these rows	12.28%	stored 12.28%

Backtest metrics snapshot

Metric	Value
Total Return	94.68%
Sharpe	0.79
Sortino	1.19
Calmar	0.49
Max Drawdown	-25.11%
Volatility	20.90%
Win Rate	56.69%
Profit Factor	1.99
Total Trades	16431
Symbols	200 (AAPL, ABBV, ABNB, ABT, ACN, ADBE, ADI, ADP, ADSK, AJG, +190 more)