What is Liquidity-Adjusted VaR (LVaR), and how do funding liquidity risk and market liquidity risk interact?

Liquidity risk is one of the most practically important topics in FRM Part II — the 2008 crisis and the March 2020 dash-for-cash both showed how devastating liquidity spirals can be. Let me untangle the two types and then show how LVaR works.

Two Types of Liquidity Risk:

1. Market Liquidity Risk (Asset Liquidity)

• The risk that you cannot sell an asset at its fair value without significant price impact.
• Drivers: bid-ask spread widening, reduced market depth, increased price volatility.
• Example: Redwood Capital holds $200M in high-yield corporate bonds. In normal markets, the bid-ask spread is 50 basis points. During a credit stress event, spreads blow out to 300+ bps, and the market can only absorb $10M per day without further pushing down prices.

2. Funding Liquidity Risk

• The risk that a firm cannot meet its cash obligations when due without incurring unacceptable losses.
• Drivers: inability to roll over short-term debt, margin calls exceeding available cash, depositor runs.
• Example: Silverlake Investment Partners funds its bond portfolio with 30-day commercial paper. If CP investors refuse to roll over, Silverlake must liquidate bonds at fire-sale prices to meet redemptions.

The Liquidity Spiral (How They Interact):

This is the critical concept for the exam:

1. Asset prices drop → margin calls trigger on leveraged positions (funding liquidity)
2. Forced selling to meet margins → further price drops and wider bid-ask spreads (market liquidity)
3. Wider spreads → larger mark-to-market losses → more margin calls
4. Repeat until the position is liquidated or external liquidity arrives

This positive feedback loop is why liquidity crises are self-reinforcing.

Liquidity-Adjusted VaR (LVaR):

Standard VaR assumes you can liquidate your entire portfolio at mid-market prices instantly. LVaR corrects for this unrealistic assumption.

Simple Exogenous Spread Approach:

$$\text{LVaR} = \text{VaR} + \text{Liquidity Cost}$$

$$\text{Liquidity Cost} = \frac{1}{2} \times (\bar{s} + z_\alpha \times \sigma_s) \times \text{Position Value}$$

Where:

• s-bar = mean bid-ask spread
• sigma_s = volatility of the bid-ask spread
• z_alpha = confidence level multiplier (2.33 for 99%)

Worked Example:

Redwood Capital's bond portfolio:

Step 1 — Stressed half-spread:

0.5 × (0.50% + 2.33 × 0.35%) = 0.5 × (0.50% + 0.816%) = 0.5 × 1.316% = 0.658%

Step 2 — Liquidity cost:

0.658% × $200M = $1,316,000

Step 3 — LVaR:

$8,500,000 + $1,316,000 = $9,816,000

The liquidity adjustment adds $1.3M (about 15%) to the standard VaR. In a severe stress scenario where spreads widen to 5x normal, this adjustment would be much larger.

Limitations of Simple LVaR:

• Treats liquidity cost as additive — doesn't capture the dynamic spiral effect.
• Assumes the entire position is liquidated at once — ignores the option to liquidate gradually.
• Doesn't account for endogenous liquidity — the price impact of your own selling.

Exam Tips:

1. Know the difference: market liquidity = ability to sell, funding liquidity = ability to pay.
2. The liquidity spiral connects both: forced selling (funding) worsens market liquidity, which triggers more forced selling.
3. Basel III introduced the LCR (Liquidity Coverage Ratio) and NSFR (Net Stable Funding Ratio) to address funding liquidity at the regulatory level.

For a comprehensive treatment of liquidity risk including LCR/NSFR calculations and exam-style case studies, explore AcadiFi's FRM Part II Liquidity Risk module.