Strategy Specific Vs Shared Risk Budget Allocation

When to Use

Use this skill when a multi-strategy book runs two limits per strategy and needs to know which one is binding. Policing risk only at the strategy level ignores diversification and punishes good hedges; policing it only at the portfolio level lets one volatile strategy quietly consume the fund's whole risk capacity.

Strategy-specific limit — standalone volatility. $\sigma_i = \sqrt{\Sigma_{ii}}$, annualized. A property of the strategy's own return series. Correlation-blind by construction.
Shared limit — component risk contribution. The strategy's share of portfolio volatility once correlation is accounted for, by Euler allocation:

$$\sigma_p = \sqrt{w^{\mathsf T}\Sigma w}, \qquad \text{MCR}_i = \frac{(\Sigma w)_i}{\sigma_p}, \qquad \text{RC}_i = w_i,\text{MCR}_i, \qquad c_i = \frac{\text{RC}_i}{\sigma_p}$$

$\sigma_p$ is homogeneous of degree 1 in $w$, so Euler's theorem gives $\sum_i \text{RC}_i = \sigma_p$ exactly, with no residual (Tasche 2008). Because parametric VaR is a fixed multiple of $\sigma_p$, $c_i$ is also the Component VaR share: $\text{Component VaR}_i = c_i \times \text{VaR}_p$.

Terminology. $c_i$ is the Component VaR share. It is not CVaR. In the risk literature CVaR means Conditional Value-at-Risk (Expected Shortfall) — a tail-average loss measure this engine does not compute. Never label these outputs "CVaR" in a risk report.

When NOT to Use

As a tail-risk or drawdown budget. Equal volatility contribution is not equal tail contribution. A short-gamma or carry strategy contributes little volatility right up to the point it contributes all of the loss. The reported figure is a Gaussian, zero-mean parametric VaR — it says nothing about losses beyond the quantile. Pair with kill-switch-and-drawdown-circuit-breakers and tail-correlation-between-strategies-under-stress.
As a monitoring limit at the default horizon. var_horizon_days defaults to 252 (one year) to match the annualized volatility reported alongside it. That is the most aggressive possible use of the square-root-of-time rule, which systematically underestimates risk under jump diffusion, worsening with horizon and confidence level (Danielsson & Zigrand 2006). For any figure compared against an intraday or daily limit, set var_horizon_days=1.
Without a trustworthy $\Sigma$. Every number is a function of the caller's covariance matrix. The engine does not estimate it, does not know it is stale, and does not know correlations converge under stress. A book balanced on a calm-period $\Sigma$ is not balanced in the drawdown the budget existed for. See cross-strategy-correlation-monitoring.
To clear a standalone volatility breach by reallocating capital. $\sigma_i$ is read from the covariance diagonal and is invariant to capital weights — see the Workflow decision point below.
As a rebalancing scheduler or optimizer. No turnover, transaction-cost, or weight-bound awareness; the audit is recomputed from scratch each call. Whether a reallocation is worth paying for is rebalancing-frequency-optimization-cost-vs-drift. To solve for balanced weights rather than audit given ones, use risk-parity-allocation-across-strategies.

Prerequisites

One StrategyRiskBudgetSpec per strategy: strategy_id (unique, non-empty), target_capital_usd, max_standalone_volatility_pct, max_shared_risk_contribution_pct. All three numbers must be finite and strictly positive — limits are given in percent, so 15.0 means 15%.
An $N \times N$ covariance matrix of daily strategy returns: finite, symmetric, and positive definite. It is annualized internally by $\sqrt{252}$; override trading_days_per_year if $\Sigma$ was estimated on a different calendar (NSE ~250, crypto 365). If $\Sigma$ is already annualized, pass trading_days_per_year=1 and var_horizon_days=1 — otherwise it is annualized twice and every figure is ~15.9× too large. Nothing in the numbers reveals this, so the unit convention is the caller's responsibility.
strategy_ids_order listing every registered strategy_id exactly once, in the row/column order of $\Sigma$.

Workflow

Validate $\Sigma$ before computing anything. Check shape, finiteness, symmetry, and positive definiteness (smallest eigenvalue relative to the largest — a reciprocal condition-number floor).
- Decision point — reject a bad matrix, never repair it. port_vol = sqrt(max(1e-8, w'Σw)) is the tempting one-liner and it is the most dangerous line in a risk engine: an implied correlation of 5.0 becomes a plausible-looking portfolio volatility, the Euler identity still sums to 100%, and the audit passes. A negative diagonal is worse — $\sqrt{\Sigma_{ii}}$ is NaN, and NaN > limit is False, so every standalone breach silently disappears.
- Decision point — test the eigenvalue relatively, not against zero. Two perfectly correlated strategies leave a smallest eigenvalue around $10^{-20}$, not exactly $0$.
Validate strategy_ids_order as a permutation of the registered specs. An omitted id drops that strategy's capital from the portfolio and under-reports total risk; a duplicate id counts one strategy's capital twice. Both are silent without an explicit check — raise on either.
Compute portfolio volatility and VaR. $\sigma_p = \sqrt{w^{\mathsf T}\Sigma w}$ with $w_i$ the capital weights; $\text{VaR}_{95%} = \text{Capital} \times \sigma_p \times \sqrt{H} \times 1.645$ for a horizon of $H$ trading days. Record $H$ alongside the number — an unlabelled "95% VaR" is ambiguous by a factor of $\sqrt{252} \approx 15.9$.
Decompose by Euler allocation: $\text{MCR}_i$, $\text{RC}_i$, and the share $c_i$.
- Decision point — the Euler identity check is a degeneracy detector, not a model check. $\sum_i c_i = 1$ holds algebraically whenever $\sigma_p$ is computed exactly, so is_euler_decomposition_valid = True proves only that no NaN propagated and $\sigma_p$ was not floored. It is not evidence the covariance matrix is sound.
Audit both tiers independently. Compare $\sigma_i$ against max_standalone_volatility_pct and $c_i$ against max_shared_risk_contribution_pct, strictly (>), so a strategy sitting exactly on its limit is compliant. Report the two flags separately: a strong hedge can be the loudest standalone offender while contributing negative portfolio risk.
- Decision point — also check the budgets are jointly satisfiable. Shares always sum to 100%, so if the declared max_shared_risk_contribution_pct values sum to less than 100 no allocation can ever satisfy them all. That is a policy error, not a breach.
Produce the two adjustment factors, and do not confuse them.
- shared_budget_capital_factor — multiply target capital by this. Solve for it; do not divide. Component risk share is not linear in the capital weight (roughly quadratic for a dominant strategy, and scaling one strategy renormalizes every other weight), and it is not even monotone when the strategy is a strong hedge. The engine bisects on the exact share function and returns the conservative lower bracket, so the result lands at or under budget.
- standalone_delever_factor — de-lever the strategy's positions, not its capital line. $\text{limit}/\sigma_i$ is a target for the strategy's own risk-taking. Re-running this engine with reduced capital reports the identical standalone breach forever, because $\sigma_i$ comes from the covariance diagonal. A standalone breach is a gate on the strategy, not something the allocator can fix.
- Decision point — factors are computed one strategy at a time, holding the others fixed. Applying several simultaneously does not land them all on budget. Re-run the engine and iterate until breached_strategies is empty.
Emit PortfolioRiskBudgetAllocationReport and deploy capital only once breached_strategies is empty and budgets_feasible is true.

Full procedure: see references/workflows.md. Standards reference: see references/standards.md. Printable pre-flight checklist: see assets/checklist.md.

Common Pitfalls

Calling the recommended factor budget / actual. The single most consequential bug in this skill's history. On a 70/30 book with $\Sigma = [[4\times10^{-4}, 2\times10^{-5}], [2\times10^{-5}, 10^{-4}]]$, the dominant strategy holds 93.81% of portfolio risk. Against a 40% budget the naive ratio is $40/93.81 = 0.4264$, and applying it leaves the strategy at 77.6% — still nearly double its budget, while the report claims the breach is remediated. The solved factor is 0.1714.
Trying to fix a standalone volatility breach with capital. $\sigma_i = \sqrt{\Sigma_{ii}}$ does not depend on $w$. Halve the strategy's capital and the reported standalone volatility is unchanged, so the breach never clears and the remediation loop never terminates.
Cutting a high-volatility strategy that is the book's best diversifier. Standalone volatility ignores correlation entirely. A hedge can breach its standalone limit while contributing a negative component risk share; removing it raises portfolio risk. Always read both flags before acting on either.
Flooring the portfolio variance. max(w'Σw, 1e-8) converts an indefinite covariance matrix into a plausible volatility and a passing audit — and the Euler identity still sums to 100%, so the self-check does not catch it.
Letting a NaN through. One NaN in $\Sigma$ makes $\sigma_i$ NaN, and NaN > limit is False. Every standalone limit then passes and the strategy appears compliant. Non-finite input must raise.
Reading an unlabelled "95% VaR" as a daily number. At the default 252-day horizon the figure is roughly 15.9× the one-day equivalent. A 95% VaR of 30% of capital is unremarkable for a year and alarming for a day. Always carry var_horizon_days with the number.
Trusting $\sqrt{T}$ scaling to a one-year horizon. The square-root-of-time rule systematically underestimates risk under jump diffusion, and the underestimation worsens with the horizon and the confidence level (Danielsson & Zigrand 2006). The annual figure is a capital-planning number, not a risk limit.
Abbreviating Component VaR as "CVaR". CVaR is Conditional Value-at-Risk / Expected Shortfall everywhere else in the literature. The collision turns a volatility-share report into an apparent tail-loss report.
Setting shared budgets that sum to less than 100%. Component shares always sum to 100%, so such a budget set is unsatisfiable by construction and will show a permanent breach somewhere in the book.
Omitting a live strategy from strategy_ids_order. Without validation its capital vanishes from the denominator and total portfolio risk is under-reported while every individual share looks fine.
Rebalancing on a stale $\Sigma$. Correlations converge under stress; a calm-period covariance understates exactly the co-movement the shared budget exists to cap.

Verification

Instantiate StrategySpecificVsSharedRiskBudgetEngine on a 50/50 book with daily $\Sigma = [[10^{-4}, 2\times10^{-5}], [2\times10^{-5}, 4\times10^{-4}]]$. By hand: $\Sigma w = [6\times10^{-5},, 2.1\times10^{-4}]$, $w^{\mathsf T}\Sigma w = 1.35\times10^{-4}$, so the component shares are the exact rationals $2/9 = 22.22%$ and $7/9 = 77.78%$ $\implies$ verify is_euler_decomposition_valid = True, the two shares, and $\sum_i \text{RC}_i = \sigma_p$.
Standalone volatilities from the diagonal alone: $\sqrt{10^{-4}}\sqrt{252}\times100 = 15.87%$ and $\sqrt{4\times10^{-4}}\sqrt{252}\times100 = 31.75%$.
Adjustment-factor regression (the test that fails against the old budget / actual behavior): on the 70/30 concentrated book, the dominant strategy's share is 93.81% against a 40% budget; verify the returned shared_budget_capital_factor is strictly below the naive 0.4264, that re-running with capital scaled by it leaves the share $\leq 40%$ and breached_strategies empty, and that the naive ratio would instead leave it above 70%.
Verify a hedge with $\Sigma = [[4\times10^{-4}, -1.8\times10^{-4}], [-1.8\times10^{-4}, 10^{-4}]]$ breaches its standalone limit while its component share is negative and its shared budget is not breached.
Verify $\sigma_i$ is unchanged when the strategy's capital is halved, and that a strategy sitting exactly on its limit is not flagged.
Verify the 252-day VaR equals $\sqrt{252}$ times the one-day VaR and that var_horizon_days is reported.
Negative checks — each must raise ValueError: covariance matrix of the wrong shape, one-dimensional, non-numeric, containing NaN or infinity, asymmetric, with a negative or zero diagonal entry, indefinite, or singular through perfect correlation; strategy_ids_order that is empty, omits a registered strategy, repeats one, or names an unknown one; a spec with non-positive or non-finite capital or limits, or an empty strategy_id; duplicate specs; and a non-positive or non-finite confidence_level_z, trading_days_per_year, or var_horizon_days.
Run python -m unittest discover -s skills/strategy-specific-vs-shared-risk-budget-allocation/scripts.

Strategy Specific Vs Shared Risk Budget Allocation

When to Use

When NOT to Use

Prerequisites

Workflow

Common Pitfalls

Verification

Hands off to 10

Handed off from 2

When to Use

When NOT to Use

Prerequisites

Workflow

Common Pitfalls

Verification

Related Skills

Hands off to 10

Handed off from 2