FINC6023 Chap.4 Liquidity Risk & Liquidity-Adjusted VaR
Liquidity Risk & Liquidity-Adjusted VaR
Liquidity Risk and Liquidity-Adjusted VaR distinguishes trading liquidity from funding liquidity. Trading liquidity concerns how quickly a position can be sold and how much its price moves during liquidation. Funding liquidity concerns the ability to meet cash obligations, margin calls, and collateral demands when they fall due.
The two can reinforce one another when a fall in asset prices triggers funding pressure and forced sales.
Ordinary market VaR assumes a frictionless exit at the quoted mid-price. Liquidity-adjusted VaR adds the expected cost of crossing the bid-offer spread. In normal conditions the add-on uses one half of the proportional spread multiplied by each position value.
A stressed version replaces a fixed spread with a high spread estimate built from the spread mean and volatility. The adjustment must use proportional spreads and consistent position units, otherwise an apparently small input error can change the answer by orders of magnitude.
Liquidation speed creates a trade-off.
Selling quickly reduces exposure to future price volatility but can create greater market impact and spread cost. Selling gradually reduces immediate impact but leaves the position exposed for longer.
Feedback trading, leverage, and common risk limits can turn this private choice into a liquidity black hole: many institutions try to sell together, prices fall, measured risk rises, and further sales are forced.
The available final paper includes a calculation multiple-choice item on liquidity-adjusted VaR.
A complete solution first calculates ordinary VaR, then adds the half-spread cost without applying the normal quantile to that cost. Conceptual questions can ask students to distinguish market, trading-liquidity, and funding-liquidity channels or to explain why liquidation assumptions become unreliable during stress.
What this chapter covers
- 01
Trading liquidity vs funding liquidity
- 02
Proportional bid-offer spread s = (offer − bid)/mid
- 03
Normal-market LVaR = VaR + ½ Σ sᵢ wᵢ [OFF-SHEET — memorise]
- 04
Stressed-market LVaR = VaR + ½ Σ (μᵢ + λσᵢ) wᵢ [OFF-SHEET]
- 05
Optimal unwinding: market impact vs price risk trade-off
- 06
Liquidity black holes, positive/negative feedback trading, the leverage-deleverage cycle
Worked example · free
Liquidity-adjusted VaR in a normal market (off-sheet)
- 2Compute the ordinary VaR first: VaR = W · z · σ = 400,000 × 2.326 × 0.02.
- 2Evaluate: 400,000 × 0.02 = 8,000; 8,000 × 2.326 = $18,608.
- 2Compute the liquidity add-on = ½ · s · W = ½ × 0.005 × 400,000 = $1,000.
- 1Add 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.
- Market impact
- Market impact is the adverse price movement caused by executing a trade, especially when the order is large relative to available depth or must be completed quickly.
- Funding liquidity
- Funding liquidity is the capacity to obtain cash or financing to meet obligations, margin calls, and collateral requirements as they become due.
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 long position means crossing from the mid price to the bid, which is about half the quoted bid-offer spread under the course convention. The one-half factor converts the round-trip proportional spread into a one-way liquidation cost. If the input is a dollar spread, divide by the midpoint before applying it to position value.
How does the stressed-market LVaR differ?
In a crisis the spread itself widens and becomes uncertain. The stressed form replaces fixed s with μ + λσ, using the spread's average as μ, its volatility as σ, and a confidence multiplier λ, so the liquidity add-on grows precisely when markets are most fragile.
How does liquidity-adjusted VaR appear on the final?
The available paper gives a position size, price, return volatility, and bid-offer spread, then asks for one-day liquidity-adjusted VaR. Calculate ordinary market VaR from the return volatility, convert the quoted spread to a proportional cost when necessary, add one half of the spread cost, and keep the two components separate.
Why can selling more slowly still be risky?
A slower sale can reduce market impact and spread cost, but the unsold position remains exposed to price changes for longer. Optimal liquidation balances execution cost against market risk. During stress, funding pressure may remove that choice and force rapid sales, which can widen spreads and deepen the price decline.
Exam move
Write the normal and stressed liquidity-adjusted VaR relationships from memory, then label every spread as a dollar amount or a proportion before calculating. If bid and offer prices are supplied, compute the midpoint and proportional spread explicitly.
Calculate ordinary market VaR first and keep it separate from the liquidation-cost add-on; the normal quantile belongs to the market-loss term, not to the deterministic half-spread. Use a two-line sanity check: a wider spread or larger position must increase the adjustment, and using the full spread instead of one half should be recognised as an overstatement under the course convention.
For conceptual revision, draw the feedback loop linking falling prices, margin pressure, forced sales, wider spreads, and further price declines. Contrast that process with funding liquidity, where the immediate question is whether cash obligations can be met.
Practise one timed multiple-choice calculation and one short explanation together, because the available final paper treats this topic as both arithmetic and classification.
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