Concentration risk

Concentration risk is the vulnerability created when a material share of exposure or potential loss depends on a small number of elements or on a common characteristic. A concentration may be visible, such as one large position, or hidden inside a look-through analysis: different instruments may depend on the same issuer, factor, sector, country, model, broker or exit market.

There is no single number called “concentration.” The answer changes with the selected lens: market value, notional, delta, DV01, scenario loss, contribution to volatility, Expected Shortfall, collateral or liquidation capacity. A complete diagnosis always states the object, unit, scope, valuation date and aggregation rule.

Concentration is not simply the opposite of diversification. Diversification describes a process and its effect; concentration analysis locates where the portfolio may be dominated. A portfolio can be spread across issuers and concentrated in equity beta, or balanced by volatility while remaining concentrated at one counterparty.

Where concentration can hide

Classification requires look-through. Holding a stock, an ETF that owns it and a structured product linked to it creates three rows, but not three independent sources. Likewise, a long and a short position may reduce net exposure while leaving gross exposure, basis risk, liquidity and dependence on the same infrastructure at high levels.

Descriptive weight measures

If xᵢ are non-negative, homogeneous exposures over one scope, they can be normalized into shares:

Three common diagnostics are the largest share, the sum of the largest k shares and the Herfindahl-Hirschman Index applied to the shares:

The effective number equals n when n shares are equal and approaches one as a single share dominates. It does not measure correlation, liquidity or tail loss. With shorts, derivatives or negative risk contributions, normalization needs a different convention, such as gross exposure with long and short books shown separately. Using signed values without disclosure can create offsets that hide the true scale.

Neither HHI nor the effective number supplies a universal threshold. Values depend on the universe, category granularity and chosen metric. Grouping by individual security, corporate group or sector gives different results.

Risk and scenario concentration

Capital weights do not reveal who determines portfolio risk. For a differentiable, homogeneous measure, risk contribution attributes the total to its components. Highly uneven contribution shares signal concentration in that selected measure. The conclusion is model-dependent: concentration in volatility is not the same as concentration in Expected Shortfall or liquidation loss.

Contributions may also be negative when a position offsets part of the risk. In that case, mechanically applying HHI to contribution shares is ambiguous. Show signed contributions, absolute contributions, diversification benefit and results with and without the hedge.

Scenarios provide another view. Under each coherent shock, revalue the portfolio and identify which positions, factors or counterparties generate the loss. A small position in ordinary conditions may dominate a gap, default or volatility scenario. Concentration control therefore cannot end with a historical covariance matrix.

Reproducible example

Four non-negative exposures have shares of 40%, 30%, 20% and 10%. The largest share is 40%, the top two add to 70%, and:

This calculation describes dispersion across four shares. If the first two companies depend on the same industry and currency, however, look-through reveals a 70% common exposure. If the fourth position is an option with a convex payoff, its 10% market value does not summarize its scenario loss. None of these values is an operating limit by itself.

Control process

1. Reconcile positions, funds, derivatives, collateral and counterparties at the same valuation time.
2. Define stable taxonomies for connected groups, sectors, countries, factors and venues.
3. Calculate concentration in several coherent units: capital, gross exposure, sensitivity and risk.
4. Apply look-through and inspect offsets between long and short positions.
5. Add price, default, liquidity and margin-call scenarios.
6. Tie limits and escalation to the mandate, capacity and applicable rules.
7. Monitor weight drift, changing dependencies and data quality.

The Basel large-exposures framework sets thresholds relative to Tier 1 capital for banks and defined counterparties. It is useful evidence for measurement, connectedness and escalation; it does not permit those percentages to be transferred to a retail account, fund or strategy without the same regulatory scope.

Sources

• Basel Committee on Banking Supervision, LEX10 — Definitions and application — current rationale, scope and definitions for the prudential large-exposures framework.
• Basel Committee on Banking Supervision, LEX20 — Requirements — limits and reporting requirements for banks within the framework’s scope.
• Basel Committee on Banking Supervision, SRP32 — Credit risk — forms of concentration, common factors, policies, measurement and control.
• Basel Committee on Banking Supervision, Studies on credit risk concentration — Working Paper No 15 — analytical distinction between name and sector concentration and methods of quantification.
• Office of the Comptroller of the Currency, Concentrations of Credit, Comptroller’s Handbook — identifying pools of exposure that share sensitivity to an economic or financial development.

Links

• Risk allocation and sensitivities
• Capital allocation
• Risk contribution
• Diversification
• Counterparty risk