Who this is for — Anyone checking whether many positions genuinely distribute risk or reproduce the same exposure under different names.
Diversification is the process of combining weights, sensitivities and dependencies with the objective of reducing portfolio concentration. The result depends on exposures, data and the scenario considered: it does not guarantee that no source will dominate under every condition. Counting instruments, strategies or accounts does not measure the achieved effect.
In the linear volatility case:
σₚ² = ∑ᵢ (wᵢ² × σᵢ²) + 2 × ∑ᵢ<ⱼ (wᵢ × wⱼ × σᵢ × σⱼ × ρᵢⱼ)The cross terms explain why two portfolios holding the same instruments at different weights can have different risk. The formula alone does not capture nonlinearities, liquidity, default, jumps or tail dependence.
Look through the labels
| Dimension | Control question |
|---|---|
| Name / issuer | do several instruments depend on the same entity? |
| Sector and geography | do revenues, funding or regulation react to the same shock? |
| Market factor | do equity beta, rates, credit, volatility or currency dominate? |
| Strategy | do different signals create similar positions at the same time? |
| Liquidity | do exits require the same market or time window? |
| Counterparty and custody | are capital and collateral concentrated at one entity? |
Five long equities are not “one trade” by definition: they may reduce idiosyncratic risk while retaining strong common market or sector exposure. Likewise, trend, mean reversion and market-neutral labels do not create diversification automatically. Measure them after weights, leverage, costs and behaviour in adverse scenarios.
A verifiable process
- Choose the unit: market value, beta, delta, DV01, volatility or scenario loss.
- Look through to actual instruments, issuers, currencies, factors and counterparties.
- Calculate weights and contributions at the same date and over the same scope.
- Estimate dependence on aligned returns and test sensitivity to window and regime.
- Apply common scenarios and liquidity constraints; low average correlation is not enough.
- Set concentration limits for the mandate rather than adopting universal thresholds.
Ex-ante risk reduction is an estimate. New data, weight changes, leverage and market moves can quickly transform portfolio structure. Diversification therefore requires monitoring and reconciliation, not permanent asset labels.
Common mistake — Calling a second position a “hedge” merely because it belongs to another asset class. A hedge needs a defined economic relation and size, and may add basis, liquidity and counterparty risk.
Sources
- Harry Markowitz, Portfolio Selection, The Journal of Finance (1952) — foundation of covariance-based portfolio selection rather than simple security counts.
- Basel Committee on Banking Supervision, Supervisory framework for measuring and controlling large exposures — BCBS 283 — prudential treatment of concentrations to individual counterparties and connected groups; a banking standard, not a universal trader limit.
- Basel Committee on Banking Supervision, Principles for effective risk data aggregation and risk reporting — BCBS 239 — completeness, accuracy and adaptability needed to aggregate exposures and concentrations.
- U.S. Securities and Exchange Commission, Division of Economic and Risk Analysis, Use of Derivatives by Registered Investment Companies — why equal notionals across derivatives and asset classes do not imply comparable risks.