# STRATUM — Systematic Index Architecture Document: STX-METH-001 | Revision: 0.3 | Status: concept research draft STRATUM is a fictional concept platform. This document describes authored specifications and simplified demonstrators, not an issued index, managed portfolio, market-data product or execution service. All coefficients, correlations and index paths are illustrative. ## 1. Implementation map Implemented: synthetic index path diagnostics; parameterized deterministic scenario P&L; fixed-covariance volatility attribution; Gaussian loss scales; cost reconciliation; scenario sensitivity grid; JSON export; searchable definitions. Research specifications only: live data qualification; signal normalization; state estimation; optimization; scheduled rebalancing; exception governance. None of these are operating market services. ## 2. Index specifications ### STX–M / Multi-Strategy Blend directional and non-directional research sleeves within a transparent capital allocation. - Signal: Composite trend score with volatility and basis overlays - Weights: Strategic 60 / 25 / 15 capital allocation - Review: Monthly review; hypothetical 5 pp drift band - Risk control: 14% annual volatility review level - Universe: Liquid directional proxies, options overlays, and cash–futures relationships - Failure conditions: Trend reversal, correlations converging during stress, or offsetting sleeves failing together. - Implementation boundary: Weights are fixed illustrations. The dashboard does not implement signal estimation or scheduled rebalancing. ### STX–V / Volatility Carry Study option-related premia while explicitly separating carry from stress convexity. - Signal: Implied-versus-realized volatility spread, skew and term structure - Weights: Strategic 15 / 70 / 15 capital allocation - Review: Weekly exposure review; daily stress observation proposed - Risk control: Vega and negative-convexity concentration review - Universe: Hypothetical option spreads, hedges and collateral sleeves - Failure conditions: Gap moves, volatility repricing, skew changes and rising hedge costs can overwhelm carry. - Implementation boundary: The scenario model uses invented return proxies, not option quotes, a volatility surface, or a pricing engine. ### STX–B / Relative Value Isolate the economics of relative-price relationships, financing and convergence. - Signal: Annualized basis, financing spread and convergence horizon - Weights: Strategic 10 / 15 / 75 capital allocation - Review: Monthly reset; funding and roll-event review proposed - Risk control: Basis divergence and liquidity concentration review - Universe: Hypothetical spot–derivative pairs and cash-management exposures - Failure conditions: Basis can widen, funding can reprice, and liquidity can disappear before convergence. - Implementation boundary: No venue data, execution access or hedge matching is connected. This allocation is not a claim of market neutrality. ## 3. Research architecture ### 01 / Data qualification A proposed eligibility layer rejects stale observations, incomplete contract histories and inconsistent timestamps before a signal is constructed. Formula: eligible = freshness ∩ depth ∩ continuity Inputs: Reference prices · Contract terms · Funding curves Outputs: Eligible universe + exclusion register Parameters: Draft gates: 252 observations; 20-session liquidity window; instrument-specific quote age. Status: Design specification ### 02 / Signal normalization Normalize signals with an explicit scale estimator, cap outliers and preserve the distinction between a missing observation and a neutral signal. Formula: zᵢ = clip((xᵢ − median(x)) / scale(x), −3, 3) Inputs: Trend · Carry · Basis · Liquidity measures Outputs: Comparable factor scores + coverage flags Parameters: Draft: robust scale; ±3 score cap; missing data excluded before allocation. Status: Design specification ### 03 / State conditioning A proposed state vector conditions a strategic allocation on market structure. A state label expresses a model assumption, not a verified market regime. Formula: sₜ = f(trend, vol, dispersion, funding) Inputs: Factor scores + covariance assumptions Outputs: Conditional allocation proposal Parameters: Research states: expansion; compression; risk-off; dislocation. Status: Design specification ### 04 / Constraint projection A research objective balances covariance risk, signal preference and a turnover penalty. The displayed prototype uses user-set weights rather than solving this optimization. Formula: min ½wᵀΣw − λsᵀw + κ‖w − w₀‖₁ Inputs: Scores · Risk budgets · Exposure constraints Outputs: Proposed weights + constraint diagnostics Parameters: Concept constraints: nonnegative sleeve weights; total 100%; gross exposure 0.5–2.0×. Status: Specification; sliders implemented ### 05 / Scenario accounting The interactive risk console calculates a deterministic shock outcome and a separate covariance-based loss scale. These are deliberately distinct models. Formula: ΔNAV = Σ sleeve P&L − funding − fees − execution Inputs: Weights · Shocks · Horizon · Cost assumptions Outputs: P&L attribution + sensitivity grid + model export Parameters: Invented sleeve coefficients; 252-session year; fixed covariance; no calibration. Status: Interactive demonstrator ## 4. Scenario model and units Let C be starting capital, L gross exposure, w capital weights summing to 1, s spot return as a decimal, v the change in implied volatility in percentage points, b basis widening in basis points, and T holding sessions / 252. These quantities are user inputs except for the authored response coefficients. - Trend return proxy: rT = 0.85s + 0.10s² - Volatility return proxy: rV = 0.07T − 0.004v − 0.70s² - Basis return proxy: rB = 0.05T − 0.35b / 10,000 - Gross sleeve P&L: C × L × Σ(wi × ri) - Funding: C × max(L−1,0) × annual funding rate × T - Management expense: C × annual fee in bps / 10,000 × T - Execution expense: C × L × one-time cost in bps / 10,000 - Net P&L: gross sleeve P&L less all modeled costs - Ending capital: C + net P&L Terminal shocks are applied once, regardless of holding horizon. Only carry, annual costs and Gaussian horizon risk scale with time. Unallocated capital below 1.0× exposure earns zero interest. Execution is charged once, not at each hypothetical rebalance. Annual volatility assumptions: Trend 20%, Volatility 14%, Basis 8%. Correlations: Trend/Volatility 0.15; Trend/Basis −0.10; Volatility/Basis 0.30. These are fixed, assigned constants, not fitted observations. - Covariance Σij = σi × σj × ρij - Portfolio annual volatility = L × sqrt(wᵀΣw) - Volatility contribution i = L × wi × (Σw)i / sqrt(wᵀΣw) - Horizon volatility = annual volatility × sqrt(T) - Gaussian 95% VaR = C × 1.64485362695 × horizon volatility - Gaussian 97.5% ES = C × 2.33780279220 × horizon volatility Gaussian metrics assume zero mean, fixed covariance and square-root-of-time scaling. The deterministic shock P&L is a separate proxy model and is not assigned a probability. These are not regulatory capital calculations. The 14% annual-volatility and 1.50× gross-exposure thresholds are illustrative review triggers, not safety guarantees. The model does not include stochastic path simulation, real options Greeks, volatility-surface calibration, dynamic hedging, taxes, market impact, settlement, margin calls, liquidation, defaults or automatic rebalancing. ## 5. Synthetic path diagnostics Each selected homepage horizon contains 65 positive index levels, defining 64 evenly spaced illustrative return intervals. Endpoints are manually chosen. Simple interval returns are computed from adjacent levels. Annualized sample volatility is sample standard deviation of those returns multiplied by sqrt(64 / horizon in years). Maximum drawdown is the most negative level / previous running peak − 1. Positive-interval share counts strictly positive interval returns. No output is a backtest or historical statistic. ## 6. Control domains ### M-01 / Universe & observation policy Define the observation calendar, eligible instruments and data hierarchy before evaluation. A production design would distinguish exchange closes, composite marks and stale observations. The STRATUM demonstrator has no market-data feed: every path and coefficient is synthetic. ### M-02 / Return convention & index continuity State price return, total return or excess return explicitly. Define the base level, treatment of distributions and handling of contract events. The homepage uses a synthetic base of 1,000 with manually set endpoint changes; it is not a replicable benchmark calculation. ### M-03 / Reconstitution versus rebalancing Reconstitution changes the eligible set. Rebalancing changes weights within that set. A proposed rulebook would separately document review frequency, observation cutoff, execution window and effective date, including holidays and disrupted markets. ### M-04 / Drift bands, turnover & hysteresis A draft 5-percentage-point weight drift band is a research trigger, not an active instruction. Hysteresis means using different entry and exit thresholds to reduce repeated switching. Any evaluation would account for execution costs and the trade-off between precision and turnover. ### M-05 / Volatility scaling & exposure limits Volatility scaling adjusts gross exposure against a risk estimate and an exposure cap. Estimation windows, smoothing and lag create trade-offs. A target is not a ceiling on realized loss. This site implements adjustable gross exposure and threshold diagnostics, not an automatic volatility-control strategy. ### M-06 / Collateral, financing & liquidity A production policy would specify eligible collateral, haircuts, margin timing and financing conventions. The model here charges simple funding only on exposure above 1.0× capital and assumes idle capital earns zero. It does not simulate margin calls, liquidation, defaults or settlement. ### M-07 / Model changes & exception handling A proposed change process records rationale, model differences, validation results and effective dates. Historical results should never be silently restated. This concept has no external administrator, independent committee, audited history or licensed index product. ### M-08 / Replication & investability boundaries A calculated index is distinct from a tradable portfolio. Position rounding, contract multipliers, position limits, slippage, borrow availability and taxes can create differences. No illustration on this site establishes implementation feasibility or capacity. ## 7. Research notes ### RN–001 / Capital weights are not risk weights. A 60% capital allocation does not automatically represent 60% of portfolio volatility. Covariance determines how an exposure interacts with the rest of the portfolio. #### Risk contribution For portfolio volatility σ = √(wᵀΣw), the volatility contribution of sleeve i is wᵢ(Σw)ᵢ / σ. Contributions can differ substantially from capital weights, and a diversifying sleeve may have a negative contribution. The console calculates these quantities from its assumed covariance matrix. #### Practical implication Assess marginal exposure alongside standalone volatility. Changing the correlation assumptions can alter the diversification argument even if each individual allocation is unchanged. Fixed assumptions are useful for a transparent demonstration, not evidence of future dependence. #### Boundary No covariance estimator, optimizer or market calibration is connected. All annual sleeve volatilities and correlations in this prototype are assigned constants. ### RN–002 / The carry–convexity trade-off. Carry accrues through time, while adverse repricing can occur abruptly. A useful specification separates these mechanisms instead of treating a return stream as a single number. #### Local sensitivities Delta, gamma, vega and theta describe different local price sensitivities. They depend on the instrument, units and valuation point. A local approximation can deteriorate during a large move or a changing volatility surface. #### The demonstrator The volatility sleeve combines a 7% annual carry assumption with a linear volatility shock and a negative quadratic spot term. These are authored return proxies, not measured Greeks or an option valuation. #### Stress design Test simultaneous price and volatility changes, not just one isolated shock. Financing and execution costs should remain visible when a strategy appears profitable before costs. ### RN–003 / A threshold is not the tail. A loss quantile describes a threshold. Expected shortfall describes the average loss beyond a tail threshold. Both depend on the model and the horizon. #### Separate definitions At a given confidence level, value-at-risk is a loss quantile. Expected shortfall averages losses in the worse tail. Two portfolios can share a quantile while having very different outcomes beyond it. #### This implementation The console reports 95% Gaussian VaR and 97.5% Gaussian ES under zero mean and fixed covariance. It uses 1.64485 and 2.33780 times horizon volatility respectively. These are differently configured loss scales, not a regulatory capital calculation. #### Failure modes Normality and square-root-of-time scaling exclude important features such as jumps, persistent volatility, changing correlations and forced liquidation. The separately defined stress P&L is not calibrated to either confidence level. ### RN–004 / Rebalancing is an economic assumption. An allocation rule needs a trading convention. Observation time, execution time and transaction costs can materially change the meaning of an index result. #### The clock Specify when information is available, when a decision is made, and when a trade is assumed to occur. An index should not assume execution at a price that was unavailable after the signal was observed. #### The cost of precision Tighter drift bands may improve alignment to target weights while increasing turnover. A transparent study shows gross return, execution expense and financing separately instead of hiding them in a net series. #### Research status The site documents proposed review and drift policies but does not run a rebalancing engine. Its synthetic index paths and scenario console are separate demonstration surfaces. ## 8. Technical lexicon **Basis:** The difference between related spot and derivative prices. Sign and annualization conventions must be stated. **Basis point:** One hundredth of one percentage point: 100 bps equals 1%. **Carry:** A return component associated with holding an exposure over time, conditional on pricing and financing assumptions. **Convexity:** Curvature in the relationship between a position value and a risk factor. A linear approximation omits this effect. **Covariance:** A measure of joint variation. Portfolio variance is computed from both individual variances and cross-covariances. **Delta:** The local first derivative of an instrument value with respect to its underlying price. **Gamma:** The local rate of change of delta with the underlying price; a second-order sensitivity. **Vega:** Local sensitivity to implied volatility, with the quoted volatility unit specified. **Theta:** Sensitivity to the passage of time under a specified convention. Its sign and units depend on the position. **Gross exposure:** Total absolute exposure relative to capital. In this long-only sleeve model, it is the user-selected multiplier L. **Excess return:** A return convention expressed relative to a specified financing or reference component. It is not a synonym for outperformance. **Maximum drawdown:** The largest peak-to-subsequent-trough decline in the observed series. It says nothing about unobserved paths. **Value-at-risk:** A model-dependent loss quantile for a stated horizon and confidence level, not a maximum possible loss. **Expected shortfall:** The mean loss in the tail beyond a stated confidence threshold, given a specified loss distribution. **Risk contribution:** A component attribution of a chosen risk measure, such as each sleeve’s contribution to portfolio volatility. **Turnover:** The magnitude of portfolio changes under a specified convention. One-way and two-way definitions differ. **Reconstitution:** A change to the index membership or eligible set, distinct from changing the weights of existing members. **Hysteresis:** Different entry and exit conditions intended to reduce frequent state switching near a threshold. **Liquidity horizon:** An assumed period needed to exit or hedge a position. It may lengthen in stressed markets. **Model risk:** The possibility that a result is wrong or misleading because its assumptions, estimates, implementation or usage are inadequate. ## 9. Background references These sources explain general concepts only. They do not validate the STRATUM coefficients, endorse this concept, or supply its synthetic data. - [CME Group · Options premium and the Greeks](https://www.cmegroup.com/education/courses/option-greeks/options-the-greeks-options-premium-and-the-greeks) — Background on interacting option sensitivities. - [MSCI · Index methodology resources](https://www.msci.com/indexes/index-resources/index-methodology) — Examples of published index rulebooks and policy documents. - [BIS · Market risk framework explainer](https://www.bis.org/bcbs/publ/d457_note.pdf) — Background on VaR, expected shortfall and liquidity horizons. No investments are offered, no funds are accepted, and no orders are executed.