Market risk limits

RiskAtoms Bank's Markets desk has a one-day 99% VaR of £1.94m. Is that too much? The number alone cannot say. A limit can: it turns the board's risk appetite into a figure the desk checks before every trade, and a breach into a decision someone senior has to make. Most of a market risk manager's day is spent on limits.

L2.3.06: Limits and escalation covered the governance: hard and soft limits, temporary excesses and passive breaches. This lesson puts numbers on them. A market risk limit framework cascades down from the board's risk appetite: an overall stress loss the bank will accept from trading, then a VaR limit for each desk, then limits for each book and each risk factor.

Five families of limit

The desk VaR limit is £2.5m; the four book limits add up to £4.55m. That is not a mistake: books diversify each other (L3.2.13: Scaling and aggregating risk), so each book needs room for its own stand-alone VaR while the desk is held to the diversified total.

Today's dashboard

12 limits are green and 2 amber; nothing is in breach. The two ambers tell a story. The 10-year bucketA sensitivity measured for one point of the curve (here the 10-year rate) rather than for a parallel shift. DV01 is at 92%: the long gilt is the desk's largest single bet, and the same exposure made the gilt sell-off its worst stress scenario. The largest issuer in the corporate bond book, Issuer A (utility), sits exactly at its £20m limit, so the desk cannot buy more of it, however small its CS01. Amber is a warning, not a breach: the desk head sees it every morning and plans around it.

Stop-loss limits on the desk's history

Suppose the desk had two stop-loss rules: a daily loss above £3m triggers a review with the head of market risk, and a loss above £6m over the last 20 trading days forces a cut in positions. Run on the 750 days with today's positions, the daily rule fires on days 488 (−£4.98m) and 494 (−£3.44m). The rolling rule fires in 3 episodes:

The first episode follows the surprise rate rise on day 205, in otherwise calm markets: a run of modest losses added up. The worst 20 days end on day 532, at −£10.29m. A stop-loss acts only after the loss, but it limits how long a losing position can survive on hope.

Breaches and escalation

An active breachA breach caused by a trade the desk chose to do. comes from a trade; a passive breachA breach with no new trade: the market moved, a sensitivity changed or the risk model was recalibrated. from the market or the model. Suppose the risk team recalibrates the covariance matrix to the stressed spell (volatilities × 2.5, crisis correlations). The same positions now show a VaR of £4.72m, 189% of the limit. Nobody traded, but it is still a breach, and it goes up the same path:

A pre-trade checkChecking a proposed trade against every limit before it is done. runs every proposed trade through the limits before it is done. Pick each trade in turn. Notice which limit stops it: buying futures breaks the equity delta limit before the VaR limit; selling puts breaks only the stress limit; buying corporate bonds breaks only the issuer limit. Then shrink the size until the trade fits.

Since the 1996 Market Risk Amendment, a bank that uses its own VaR model for capital must show that the model is closely integrated into day-to-day risk management and used together with trading and exposure limits, and that an independent risk control unit oversees it. The current Basel text (MAR30) keeps the independent unit and its daily reports of exposures against trading limits, but asks only that the capital model share its core design with the models used to manage risk day to day. Supervisors also expect limits to be tied to a documented risk appetite approved by the board (L2.3.05: Risk appetite frameworks); how they review that, through Pillar 2, is in M4.9: Supervision, stress testing and disclosure. The capital rules for market risk are in M4.3: Market risk capital (FRTB) and CVA.

• Limits cascade from the board's risk appetite to desk VaR, book VaR, sensitivity, stress, stop-loss and concentration limits.
• Book VaR limits add up to more than the desk limit, because books diversify each other.
• Each family catches what the others miss: VaR limits alone would have allowed trades that sensitivity, stress and concentration limits stopped.
• A pre-trade check runs every proposed trade through every limit; the binding limit sets the largest trade that fits.
• Active and passive breaches are both reported and escalated; the response is a cut, a hedge or an approved temporary excess.

VaR limit

A cap on a desk's or book's VaR. It limits the overall size of the risk, after diversification.

Sensitivity limit

A cap on one sensitivity (equity delta, DV01, vega, CS01 and so on). It limits exposure to one factor, whatever the VaR model says.

Stress limit

A cap on the loss in the desk's agreed stress scenarios.

Stop-loss limit

A trigger on realised losses, daily or over a rolling period, that forces a review or a cut in positions.

Concentration limit

A cap on exposure to one issuer, one instrument or one market, measured in size rather than in risk.

Utilisation

A figure as a share of its limit. Here: green below 80%, amber from 80% to 100%, red (a breach) above 100%.

Active breach

A breach caused by a trade the desk chose to do.

Passive breach

A breach with no new trade: the market moved, a sensitivity changed or the risk model was recalibrated.

Bucket sensitivity

A sensitivity measured for one point of the curve (here the 10-year rate) rather than for a parallel shift.

Pre-trade check

Checking a proposed trade against every limit before it is done.