Market risk limits are the primary mechanism by which a bank controls the risk its trading desks take. Without limits, traders could accumulate positions of unlimited size, exposing the bank to losses that dwarf its capital base. The limit framework translates the board's risk appetite — an abstract statement about how much risk the bank is willing to run — into specific, measurable, operationally enforceable constraints on individual positions and portfolios. Understanding what limits exist, what they measure, and how breaches are handled is essential context for anyone working on or near a trading floor.

Value at Risk: The Headline Risk Measure

Value at Risk (VaR) is the most widely used summary statistic of market risk. It answers the question: what is the maximum loss the portfolio could suffer over a given time horizon at a given confidence level? A 99%, one-day VaR of £10 million means that, on 99 out of 100 days, the portfolio is not expected to lose more than £10 million. The 1% of days where losses exceed £10 million are the tail of the distribution.

For regulatory capital purposes under the pre-FRTB framework, the relevant VaR was 99%, 10-day: the maximum loss over 10 business days at the 99th percentile, scaled from a one-day measure by multiplying by the square root of 10 (under the assumption of independent daily returns). This 10-day 99% VaR formed the basis of the market risk capital charge for banks using the internal models approach.

VaR is computed using three main methods. The historical simulation method replays actual historical market moves against the current portfolio. The parametric (variance-covariance) method assumes returns are normally distributed and uses estimated volatilities and correlations. The Monte Carlo simulation method generates thousands of random market scenarios drawn from a statistical model of how risk factors move. Each method has its uses and its weaknesses; large banks typically use historical simulation as the primary method with Monte Carlo for complex products.

The Limitations of VaR

VaR's limitations are as important to understand as its definition. The most significant are:

Fat Tails

Financial return distributions are not normal — they have "fat tails", meaning extreme events occur more frequently than a normal distribution would predict. A 99% VaR calibrated to normal return history will systematically understate the true frequency of large losses. The 2008 crisis produced daily moves in many markets that were tens of standard deviations from the mean under the assumptions embedded in pre-crisis VaR models — events that were theoretically astronomically improbable under normality but happened in practice.

Procyclicality

VaR is calculated from historical data, typically using a rolling one to two year window. In calm market periods, historical volatility is low, and VaR produces low capital requirements — precisely when risk appetite is expanding and positions are growing. When market volatility spikes, historical data quickly incorporates the new volatility, VaR jumps, and capital requirements surge — at the worst possible moment, when reducing positions is most difficult. This procyclical behaviour amplified the 2008 crisis: banks were forced to deleverage by spiking VaR and capital requirements precisely when markets were most stressed.

Concentration and Correlation Risk

VaR does not tell you about the composition of the tail. A portfolio might have the same VaR whether the tail risk comes from a well-diversified set of small positions or from a single concentrated exposure. VaR also relies on historical correlation estimates that may break down in stress — correlations that are low in normal conditions often spike toward one in crises, as all risky assets fall simultaneously. A VaR model that does not capture this correlation stress will understate tail risk in precisely the scenarios where it matters most.

What VaR Does Not Measure

VaR says nothing about the magnitude of losses beyond the confidence threshold. A 99% 10-day VaR of £10 million means losses will exceed £10 million on 1% of 10-day periods — but it does not say by how much. Losses of £11 million and £500 million are both consistent with the same VaR figure. This is why Expected Shortfall (ES) — the average of losses beyond the VaR threshold — is a superior measure for capital purposes.

Expected Shortfall and FRTB

The FRTB replaced the 10-day 99% VaR with Expected Shortfall at 97.5% as the primary regulatory risk measure. At the 97.5% confidence level, ES captures the average of the worst 2.5% of outcomes — the tail of the distribution. ES is more conservative than VaR for most portfolios, more sensitive to the shape of the tail, and does not exhibit the same procyclicality (because the stress period requirement in FRTB anchors the ES to a historical stress period). For internal management purposes, many banks continue to use VaR alongside ES as a familiar reference point.

DV01 Limits

DV01 (Dollar Value of a 01, or sometimes called PV01) measures the sensitivity of a rates position to a one basis point (0.01%) move in interest rates. A rates trading desk with a DV01 of £500,000 per basis point will gain or lose £500,000 for every basis point move in the relevant rate. DV01 limits are set by tenor bucket — a limit on the DV01 at each point of the yield curve (2-year, 5-year, 10-year, 30-year) and on the overall aggregate — to control both outright rate risk and curve risk (the risk that different parts of the curve move by different amounts).

DV01 limits are the primary risk metric for rates desks. They are intuitive — a DV01 of £1 million per basis point is clearly more risk than £100,000 per basis point — and they translate directly into the P&L impact of a given market move. A trader who knows their DV01 and a reasonable expected daily rate move can quickly estimate their day's P&L risk.

Greeks Limits for Options Desks

Options desks face a richer risk landscape than linear positions. The key risk sensitivities — the Greeks — each require their own limits:

  • Delta: The sensitivity of the option price to the underlying asset price. A delta limit controls the net directional exposure of the options book.
  • Gamma: The sensitivity of delta to the underlying price — the rate of change of delta. High positive gamma means the book profits from large moves; high negative gamma (short gamma) means it loses from large moves and requires costly dynamic hedging.
  • Vega: The sensitivity to implied volatility. A long vega position profits from rising volatility; short vega profits from declining volatility. Vega limits are set by strike and expiry to control the volatility surface exposure.
  • Theta: The time decay of the option value. Theta limits ensure that the book is not accumulating excessive short-gamma, short-vega positions that will decay slowly in value but expose the bank to sudden large losses.

Stop-Loss Limits

Stop-loss limits are P&L-based limits: they specify the maximum loss a desk is permitted to incur before trading must be halted or positions must be reduced. A desk with a daily stop-loss of £5 million must immediately escalate to senior management if its daily loss reaches that level, and will typically be required to reduce risk. A monthly or annual stop-loss triggers a review of the desk's strategy and may result in position limits being cut.

Stop-loss limits are a backstop control — they catch the situation where a desk is losing money rapidly, regardless of whether any individual risk limit has been breached. A desk can technically be within all its DV01 and VaR limits while suffering large losses if the market moves are persistent and in one direction. Stop-loss limits provide the P&L-side protection that pure risk-factor limits do not.

The Limit Breach Process

When a limit is breached, the response depends on the severity and type of breach. All breaches must be reported to market risk and escalated within defined timeframes — typically same-day for significant breaches, immediate for material breaches. The desk head must provide an explanation of the breach and a plan to return within limits. Market risk will assess whether to grant a temporary excess (an approved breach) — usually only for minor breaches in unusual market conditions — or require immediate reduction. Persistent breaches, or breaches resulting from deliberate position-taking beyond limits, are serious governance failures that escalate to senior management and potentially to the board risk committee.

The governance framework specifies who has authority to approve temporary excesses at each level of severity. A minor DV01 breach might be approved by the head of market risk. A significant VaR breach at the desk level requires the CRO. A breach of a firm-level limit requires board risk committee notification. These approval authority matrices are documented in the market risk policy and are tested in regulatory reviews.