FINC6023 · Financial Risk Management
Liquidity Risk & Liquidity-Adjusted VaR
Liquidity Risk & Liquidity-Adjusted VaR splits liquidity into two flavours: trading liquidity (the price you realise on a forced or large sale differs from the mark-to-market) and funding liquidity (you run out of cash to roll over leverage). The headline calculation adds a liquidation cost to ordinary VaR: in normal markets LVaR = VaR + ½ Σ sᵢ wᵢ, where sᵢ is the proportional bid-offer spread. The catch the unit flags: LVaR is examinable but NOT on the provided formula sheet, so you must memorise it (and the stressed-market version).
What this chapter covers
- 01Trading liquidity vs funding liquidity
- 02Proportional bid-offer spread s = (offer − bid)/mid
- 03Normal-market LVaR = VaR + ½ Σ sᵢ wᵢ [OFF-SHEET — memorise]
- 04Stressed-market LVaR = VaR + ½ Σ (μᵢ + λσᵢ) wᵢ [OFF-SHEET]
- 05Optimal unwinding: market impact vs price risk trade-off
- 06Liquidity black holes, positive/negative feedback trading, the leverage-deleverage cycle
Liquidity-adjusted VaR in a normal market (off-sheet)
- 2 marksCompute the ordinary VaR first: VaR = W · z · σ = 400,000 × 2.326 × 0.02.
- 2 marksEvaluate: 400,000 × 0.02 = 8,000; 8,000 × 2.326 = $18,608.
- 2 marksCompute the liquidity add-on = ½ · s · W = ½ × 0.005 × 400,000 = $1,000.
- 1 markAdd them: LVaR = 18,608 + 1,000 = $19,608.
Key terms
- Trading vs funding liquidity
- Trading liquidity risk is that a large or forced sale realises a worse price than the mark-to-market; funding liquidity risk is that a leveraged firm cannot raise cash to meet obligations and is forced to deleverage.
- Proportional bid-offer spread
- s = (offer − bid)/mid, the round-trip transaction cost expressed as a fraction of the mid price. It is the input to the LVaR liquidity add-on.
- Liquidity-adjusted VaR (LVaR)
- Ordinary VaR plus the cost of unwinding: LVaR = VaR + ½ Σ sᵢ wᵢ in normal markets. It is OFF the provided formula sheet but examinable, so it must be memorised.
- Liquidity black hole
- A self-reinforcing spiral where falling prices trigger forced selling and deleveraging, which depresses prices further and dries up liquidity — illustrated by LTCM (1998) and flash crashes.
Liquidity Risk & Liquidity-Adjusted VaR FAQ
Is the LVaR formula on the exam formula sheet?
No — the unit flags that LVaR is one of the basic formulas that is NOT on the provided sheet, yet it IS examinable. You must memorise both the normal-market form (½ × spread × position) and the stressed-market form (replace the fixed spread with its mean plus a confidence multiple of its standard deviation).
Why is the add-on half the spread, not the whole spread?
Liquidating a position means crossing from the mid price to the bid (selling) — on average about half the quoted bid-offer spread. The ½ factor converts the round-trip proportional spread into the one-way liquidation cost.
How does the stressed-market LVaR differ?
In a crisis the spread itself widens and becomes uncertain. The stressed form replaces the fixed spread s with μ + λσ, where μ and σ are the mean and standard deviation of the spread and λ is a confidence multiplier — so the liquidity add-on grows precisely when markets are most fragile.
Exam move
Write the normal and stressed LVaR formulas from memory three times before the exam, since they are off-sheet. In a question, always compute ordinary VaR first, then layer the half-spread add-on on top.
