Monthly MNTS and ICA Tempered-Stable EVaR-Deviation Tail-Risk Parity

Strategy Card

Monthly MNTS and ICA Tempered-Stable EVaR-Deviation Tail-Risk Parity — strategy card

Spec ID: spec-multi-asset-evar-deviation-tail-risk-parity-us-etfs-1789135350 · Generated: 2026-09-11 15:20 UTC

Cluster: Risk Parity · Sub Cluster: Tempered-Stable Tail-Risk Contribution Parity

One-line description

Each month, the strategy fits a multivariate normal tempered-stable model to 12 months of daily ETF returns and allocates capital so centered EVaR Euler contributions are as equal as constraints permit. It trades the long-only, fully invested target at the next session's close.

Why this trade exists

Volatility parity treats symmetric second moments as a complete description of risk. Multi-asset returns can instead exhibit skewness, heavy tails, and nonlinear dependence, causing covariance-based allocations to understate assets' contributions during adverse states.

Centered entropic value-at-risk (EVaR deviation) uses the fitted moment-generating function to measure tail dispersion while removing expected-return estimates, which are particularly noisy over a 12-month window. Equalizing its Euler contributions seeks diversification by modeled tail-risk contribution rather than by capital or volatility alone. Tempered-stable distributions provide finite, weight-dependent MGF domains while accommodating heavier and asymmetric tails.

Algorithm

[code omitted from public view] Only MNTS_EVaR_DEVIATION_ERC is funded; ICA, inverse-risk, raw-EVaR, CVaR, Gaussian, and equal-weight variants are diagnostics or benchmarks.

Parameters

Param	Value	Notes
Executed variant	MNTS_EVaR_DEVIATION_ERC	Single funded portfolio
Tail probability / confidence	0.05 / 0.95	Centered EVaR deviation
Distribution	Joint MNTS	Parameters fitted once per rebalance and fixed across candidate weights and perturbations
ERC target	DEVaRC_{eta,i}(w) = D_eta^c(w)/N	Squared contribution residuals are minimized when constraints prevent equality
Derivative	Central finite differences	Unconstrained coordinate perturbations; h = 1e-5
MGF domain	Recomputed for every candidate and perturbation	A finite active endpoint is evaluated when applicable
Lookback	12 months of daily log returns	Full history required through the month-end signal close
Rebalance / holding period	Monthly / 1 month	Signal on the last trading session of each calendar month
Execution	Next trading session close; 1-session lag	Existing positions remain in place through the signal date
Constraints	Long-only, fully invested	Minimum weight 0; weights sum to 1
Maximum position	10%	Platform concentration constraint; may prevent exact ERC equality
Maximum leverage	4.0 safety limit	A long-only, fully invested target ordinarily has gross leverage 1.0
Universe	AGG, EFA, GLD, TIP, VNQ, VTI, VWO, XLB, XLC, XLE, XLF, XLI, XLK, XLP, XLU, XLV, XLY	17 US-listed ETFs; pooled multi-asset and sector universe
Backtest window	2020-01-01..2024-07-01	Daily bars
Commissions	$0.0040 per share, minimum $1.00 per order, capped at 1.00% of trade value	Charged per fill by the results module; all metrics are net of them
Slippage	0 bps — not applied	Not an omission — MOC (market-on-close) fills at the auction print the backtest uses
Costs not modelled	short borrow fees / rebate, margin financing on leverage, market impact, exchange/regulatory/clearing pass-through fees, taxes	Excluded deliberately, not unknown
Minimum notional order limit	$0.0	No platform minimum notional threshold
Not modelled	short borrow fees / rebate; margin financing on leverage; market impact; exchange/regulatory/clearing pass-through fees; taxes	The portfolio is long-only and ordinarily unlevered, making borrow and financing inapplicable under normal operation

Look-ahead audit

#	Concern	Status
1	Rolling-window information cutoff	✓ The 12-month return matrix includes only closes available on or before the month-end signal date.
2	Signal and execution ordering	✓ The signal is formed at month-end close and executed at the next trading session's close.
3	Parameter leakage across candidate weights	✓ MNTS parameters are fitted once per rebalance and held fixed during optimization and finite differences.
4	Weight-dependent MGF domain	✓ The admissible endpoint is recalculated for every candidate and positive or negative perturbation.
5	Transaction costs	✓ commissions $0.0040/share (min $1.00/order); slippage 0 bps — not applied
6	Universe selection and survivorship	⚠ The fixed ETF list and full-history requirement can favor instruments surviving and remaining liquid through the test period.

Caveats / known limitations

• The specification designates 25 bps as the conservative primary cost path even though the source paper evaluates 0, 5, 10, and 25 bps symmetrically and does not identify 25 bps as primary. Consequently, that designation and any paper-relative conclusion based on it are implementation choices; the reported platform metrics here are net of the separately charged per-fill commissions.
• Signals formed at month-end close execute at the next session's close rather than the paper's unspecified timing. This changes portfolio return paths and prevents exact reproduction of the paper's Tables 2–6 performance statistics.
• Turnover is drift-adjusted one-way turnover, calculated as one half of absolute target-versus-pretrade weight changes. The paper's turnover figures and transaction-cost-adjusted Sharpe comparisons in Tables 3–6 are therefore not guaranteed to match.
• ICA diagnostics use FastICA, an implementation choice not specified by the paper. All paper-reported ICA+NTS and ICA+CTS weights, contributions, turnover, drawdown, Sharpe differences, and significance results are not directly reproducible, although the funded strategy uses joint MNTS rather than ICA.
• The strategy pools cross-asset and sector ETFs and omits XLRE while retaining VNQ. The paper's universe-specific weights and all associated Sharpe, drawdown, turnover, cost, and significance results do not describe this traded portfolio.
• The mandatory 10% position cap changes the paper-form feasible set and can make exact EVaR-deviation contribution equality impossible; the optimizer then returns the minimum-residual constrained solution.
• This single executed-variant run does not report benchmark or diagnostic return series, so it cannot test the paper's claimed Sharpe differences, Gaussian EVaR/volatility identity, raw-versus-centered similarity, or matched EVaR-versus-CVaR comparisons. The 2020–2024 pooled sample is also different from the paper's samples.
• Market impact, exchange/regulatory/clearing pass-through fees, and taxes are excluded. These can reduce realizable returns despite the charged commissions; short-borrow and leverage-financing costs are ordinarily inapplicable to this long-only, fully invested book.

Results

Over 2020-01-01 through 2024-07-01, the commission-net backtest returned 58.68% with a 0.66 Sharpe ratio, 19.86% annualized volatility, and a -22.29% maximum drawdown. The Sortino ratio was 0.72, Calmar ratio 0.49, and beta versus SPY 0.46. The run recorded 422 trades, a 93.39% win rate, and an 11.85 profit factor, but the absence of supplied benchmark and matched-variant metrics prevents attributing performance to tempered-stable EVaR parity rather than the sample's broad asset exposures.

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	58.68%	matches the reported total return
Sharpe from these rows	0.66	stored 0.66
Volatility from these rows	19.86%	stored 19.86%
Max drawdown from these rows	-22.29%	stored -22.29%
CAGR from these rows	10.84%	stored 10.84%

Backtest metrics snapshot

Metric	Value
Total Return	58.68%
Sharpe	0.66
Sortino	0.72
Calmar	0.49
Max Drawdown	-22.29%
Volatility	19.86%
Beta vs SPY	0.46
Win Rate	93.39%
Profit Factor	11.85
Total Trades	422
Symbols	17 (AGG, EFA, GLD, TIP, VNQ, VTI, VWO, XLB, XLC, XLE, +7 more)