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: | Parameter | Value | |---|---| | Portfolio value | $200M | | Standard 99% 10-day VaR | $8.5M | | Mean bid-ask spread (s-bar) | 0.50% | | Spread volatility (sigma_s) | 0.35% | | z at 99% | 2.33 | **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.