This paper proposes a practical framework for the quantification of Liquidity-adjusted Value at Risk ("L-VaR") incorporating the market liquidity of financial products. This framework incorporates the mechanism of the market impact caused by the investor's own dealings through adjusting Value-at-Risk according to the level of market liquidity and the scale of the investor's position. Specifically, the optimal execution strategy for liquidating the investor's entire position is first calculated taking the market impact into account. Then the maximum loss that may be incurred by price fluctuations under optimal execution strategy is calculated as L-VaR.
This paper presents a specific model providing a closed-form solution for calculating L-VaR, and examines whether this framework can be applied to the practices of financial risk management by calculating numerical examples. It also demonstrates that this L-VaR calculation framework may be applied under more general conditions, such as (1) when the market impact is uncertain, (2) when the investor's portfolio consists of multiple financial assets, and (3) when there is a non-linear relationship between the market impact and the trading volume.
Keywords: Liquidity risk; Value at risk; Market risk; Market impact; Optimal execution strategy; Optimal holding period
Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.