Risk Limit

Definition

A Risk Limit is a general and widely used risk and portfolio management technique. It denotes one or more numerical thresholds defined in relation with specific risk exposures such as Credit Risk, Market Risk or Liquidity Risk exposures. Internal Risk Policy limits aim to contain the risk exposures undertaken by the organization below an acceptable level.

The overall orchestration of risk limits is usually done in the context of a Limit framework, which may be further part of a broader Risk Appetite framework. Risk limits are most widely used in Market Risk, Credit Risk and Liquidity Risk management, where quantitative metrics characterising risk exposures can be established with some certainty. Limits can be set at a variety of hierarchies, depending on the Risk Type: e.g. total, sectoral, regional, by business line, Single Obligor Exposure limits. Ideally those will for a consistent limit framework.

Note: Sometimes the concept of Risk-based Limit is introduced, aiming to distinguish limit systems that utilize additional (potentially Risk Model dependent parameters) from those that are based more directly on observables.

Relation with Eligibility Criteria

In the context of Portfolio Management risk limits are related to the concept of Portfolio Constraints or Eligibility Criteria which narrow the range of possible portfolio configurations by either completely forbidding or constraining certain configurations. Whereas such criteria do not permit any exposure in given categories (e.g. sub-investment grade, emerging markets, long-dated etc.) limits aim to capture and make concrete a non-zero risk appetite. Hence eligibility criteria can be thought of as "zero-level" limits

Structure

A risk limit is defined via:

• the applicable Risk Metric (e.g. notional amount, value-at-risk etc)
• the limit value expressed in terms of the risk metric (e.g. 10 mln, 1% of total risk etc.)
• the scope of its application (position, relation, desk, unit etc.)
• the entity responsible for conforming to the limit (trader, portfolio manager, business line etc)

Types

• Limits can be soft or hard depending on the tolerance / internal procedure followed in cases where the limit is exceeded. Soft limits aim to provide a structured way to escalate and approve the limit breach
• Limits can be absolute or relative in nature. Absolute limits will set a monetary value (e.g. 10 mln), whereas relative limits set a percentage of the relevant portfolio (e.g. 5% of exposure or capital etc)
• Limits can be uniform or customized. Uniform limits apply similarly across a portfolio or portfolios. Custom (bespoke) limits are more granular. For example the might be a specific limit set for each sector or even every counterparty / obligor

Examples

Credit Risk Management

In the context of Credit Risk management, risk limits can be classified into (at least) the following types:

• Exposure limits that constrain the individual or total amount of credit exposure in terms of e.g., loan balances, credit derivative notional amounts etc
• Tenor limits that constrain the individual or average maturity of the exposure / portfolio
• Credit Rating based limits that constrain the individual or average rating
• Expected Credit Loss based limits that take into account both Probability of Default and Loss Given Default of the exposures / portfolio
• Volatility, Value at Risk and/or Capital based limits that constrain the risk contribution of an exposure to unexpected losses, Risk Capital or Regulatory Capital consumption

Market Risk Management

In the context of Market Risk management, risk limits can be classified into (at least) the following types:

• Value-at-Risk Limits. These sensitivity limits are designed to restrict potential loss to an amount equal to a board-approved percentage of projected earnings or capital
• Loss Control Limits. Loss control limits require a specific management action if a defined level of loss is approached or breached.
• Tenor or Gap Limits. Tenor (maturity) or gap (repricing) limits are designed to reduce market risk by limiting the maturity and/or controlling the volume of transactions that matures or reprices in a given time period
• Notional or Volume Limits. Notional or volume limits are most effective for controlling operational capacity and, in some cases, liquidity risk. Notional limits may be very useful for highly illiquid instruments, such as emerging market issues for which the frequency and volatility of price changes render Value-at-risk limits less useful
• Options Limits. Limits specific to option exposure should be established for any entity with sizable option positions. Such limits should consider the sensitivity of positions to changes in delta, gamma, vega, theta, and rho.
• Product Concentration Limits. Product concentration limits may be useful to ensure that a concentration in any one product does not significantly increase the market risk of the portfolio as a whole.

Issues and Challenges

There is a large collection of potential pitfalls associated with the use of risk limits. We can group them roughly in two categories: immediate issues relating the fitness of the risk limits themselves and issues relating to how people respond to the presence of risk limits over time

Immediate Issues

• Absence of relevant limits. This can be due to the risk not being recognized, not being considered material or there being a lack of resources to measure / implement
• Wrong limits in the sense of either too loose or two restrictive, either by mistake or because of other factors.
• Outdated limit structure (not sufficiently adapted to evolving risk landscape)
• Unclear limits, e.g., too complex, or otherwise difficult to observe
• Limits that are not sufficiently sensitive to the risk the purport to cover

Behavioural Issues

• The limit becomes the target (a form of Anchoring Bias)
• Materiality buffers before a Limit Breach is declared, associated grace periods etc may be taken for granted
• Excessive reliance on automated Compliance

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