How does the bid-ask spread approach to liquidity-adjusted VaR work?

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AcadiFi · Accepted Answer

Liquidity-adjusted VaR (LVaR) augments market VaR with a cost-of-liquidation term driven by bid-ask spread volatility. The Bangia-Diebold-Schuermann-Stroughair (BDSS) formulation is the FRM standard: LVaR = VaR + 0.5·P·[μ_s + k·σ_s], where P is current mid price, μ_s is mean relative spread, σ_s is spread standard deviation, and k is the confidence-level scaling factor (e.g., 3 for a high percentile).

Example: Serapine Emerging Markets Fund holds a $5 million position in Brundell Telecom equity. Daily mid = $42, mean bid-ask relative spread μ_s = 0.80% (0.0080), spread stdev σ_s = 0.35% (0.0035), k = 2.33 for 99%. Liquidity add-on per share = 0.5·42·(0.0080 + 2.33·0.0035) = 0.5·42·0.01616 = $0.339. On 119,048 shares, add-on ≈ $40,365. Market VaR under normality with σ = 2.1% is $5M·2.33·0.021 = $244,650. Total LVaR = $285,015.

The 0.5 reflects that a round trip costs the full spread but only the half-spread is charged on liquidation. Some desks use the 'endogenous' liquidity approach (Almgren-Chriss) which accounts for market impact as a function of trade size. For FRM, memorize BDSS and know its limits: it assumes spread independent of size, which fails in crises when depth evaporates. Firms like Oakspur Risk combine BDSS with liquidity-horizon scaling for regulatory fundamental review of the trading book (FRTB) reporting.

How does the bid-ask spread approach to liquidity-adjusted VaR work?

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