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A realizable value ofa portfolio can be significantly different from a value based on mid-market rates. Even a partial sale may take time and expose the owner to market risks. The Liquidity-Adjusted Value-- at-Risk (La VaR) measure developed in this paper assumes that each asset is disposed of over a certain period with an impact on price that depends on the size of the position held. The liquidation horizon is a solution to a dynamic optimization that trades off the risk of protracted liquidation against the extent of the adverse price impact. [JEL: G1, G2, C4, D4]
Value-at-Risk (VaR) is used as a predictive measure of the dollar losses that a portfolio may suffer as a result of adverse movement of market rates and prices. It takes market prices as given, and ignores possible divergence of the realizable value from mid-market levels. It also ignores the market risks the portfolio holder is exposed to while the liquidation is in progress. These risks are of concern to financial institutions and regulators alike.
Jarrow and Subramanian (1997) offer a correction to VaR that depends on the means and variances of a liquidation discount and an execution lag function for each asset. The four additional parameters are not easy to estimate and may require a trader's intuition.
Bangia, Diebold, Schuermann, and Stroughan (1999a and b) limit the adjustment to VaR to exogenous liquidity defined as "common to all market players and unaffected by the actions of any one participant." It does not accommodate endogenous liquidity which "varies across market participant [and] is mainly driven by the size of the position." The Bangia et al. (1999a and b) correction to VaR is appropriate only for continuously traded markets such as currencies. For markets like US high yield, the input bid-ask spread is often not observed for any quote depth.
The Liquidity-Adjusted Value-at-Risk (LaVaR) statistic I develop takes into account both the costs and the risks associated with sale of a portfolio. The adjustment reflects optimal liquidation strategies for all assets in a given portfolio. These endogenously determined strategies reflect the best trade-off between the impact on realized prices and the additional exposure to market fluctuations a protracted liquidation of the portfolio may entail.
The LaVaR calculation is...