Portfolio‑Level Sizing: Correlation‑Adjusted Lots and Risk Budgeting Across Strategies

Introduction — Why portfolio‑level sizing matters

Position sizing is usually taught at the trade level (risk X% of equity per trade), but traders and fund managers running multiple strategies need a portfolio view: correlations and covariance across strategies can make individually‑sized trades produce unacceptable portfolio concentration or over‑exposure. A robust portfolio‑level sizing framework explicitly converts strategy signals or nominal lots into allocations that reflect volatility, correlation and an overall risk budget.

In practice, this means sizing not by capital alone but by contribution to portfolio risk. That approach reduces tail concentration, makes drawdowns more predictable and aligns position sizes to target overall volatility or drawdown limits. Basic position‑sizing principles remain relevant, but they must be extended to account for cross‑strategy interaction.

Core concepts: covariance, marginal contribution and risk budgets

At the portfolio level the key object is the covariance matrix Σ of strategy returns (or instrument returns aggregated at strategy level). Portfolio volatility σP for weight vector w is σP = sqrt(wᵀ Σ w). The incremental effect of a small change in a strategy weight is captured by the Marginal Contribution to Risk (MCR):

∂σP/∂w_i = σ_{iP} / σP

where σ_{iP} is the covariance between strategy i and the portfolio. Marginal and percentage contributions (MCR and PCR) let you see which strategies dominate total risk and which provide diversification. These measures are the building blocks of risk budgeting — allocating a pre‑set share of total portfolio risk to each strategy or factor.

Risk Parity and Equal Risk Contribution (ERC) are special cases: instead of equal capital weights, you target equal risk contribution across components. That idea is useful when you want no single strategy to be the dominant source of volatility in your book.

From theory to practice: a step‑by‑step implementation

1. Define the ‘strategy return’ series: For each algo/strategy, build a return time series at a consistent frequency (daily or per‑trade P&L aggregated to a common cadence). Use net-of-cost returns if possible.
2. Estimate covariance robustly: Compute Σ using a lookback that balances responsiveness with stability (e.g., 6–12 months for many FX/crypto strategies). Consider shrinkage or robust estimators, and monitor regime changes.
3. Choose your risk budget: Decide target total portfolio volatility (or expected drawdown) and how it will be split — by strategy, factor, or manager. Targets can be equal risk, tiered (core vs opportunistic), or alpha‑weighted.
4. Compute MCR and PCR: Calculate marginal and percentage contributions to identify overweighted risk sources and candidates for scaling down.
5. Translate weights to lot sizes: Convert target weights back into instrument/lot sizes via each strategy’s risk per nominal unit (e.g., ATR, dollar stop loss, or historical volatility per lot). Apply minimum increment and execution constraints.
6. Apply drawdown gates and volatility caps: Add equity gates or per‑strategy caps so sizing responds to realized drawdowns, desynchronization risk and liquidity constraints.

Example: if Strategy A has high volatility but low correlation to the book, it may be allowed a larger nominal size because its PCR is small; conversely Strategy B with modest volatility but very high correlation to other strategies should be reduced because it contributes a larger share of portfolio risk.

For modern systematic portfolios, algorithmic solvers (convex optimizers, mirror‑descent variants) can directly solve for weights that meet non‑linear risk budgets and constraints—these methods are increasingly used in academic and practitioner implementations.

Sizing heuristics, hybrids and practical caveats

Pure Kelly or full geometric‑growth sizing often produces sizes that are impractically large and unstable in multi‑strategy books because Kelly does not by itself penalize correlation concentration. Hybrid methods combine Kelly‑like edge estimation with volatility caps, correlation adjustments and explicit risk budgets to get better drawdown control. Recent research and practitioner notes show hybrid approaches outperform blind Kelly when applied to option selling or volatility strategies in noisy, regime‑shifting markets.

Operational considerations:

• Re‑estimate covariances frequently enough to catch regime shifts but not so frequently that estimates are dominated by noise.
• Stress‑test with bootstraps and Monte Carlo to understand worst‑case simultaneous drawdowns across strategies.
• Monitor realized vs expected percentage contributions and set automated alarms or equity gates when contributions deviate meaningfully.
• Account for execution friction, margin cross‑effects, and correlated tail risk (liquidity or funding squeezes) that covariance alone may understate.

Finally, maintain a governance loop: periodic backtests, walk‑forwards and live monitoring to ensure the risk budget approach remains calibrated to market dynamics.