Liquidation discount—a novel application of ARFIMA–GARCH

Urgent liquidation of a large stock portfolio entails a liquidity cost—i.e., a “liquidation discount”. This is the market impact discount in value yielded by the immediate sale of the portfolio relative to its in-hand market value calculated from prevailing market prices. For any portfolio, the day-to-day liquidation discount “at risk” (i.e., the liquidation discount that would be suffered if liquidation were undertaken) is variable. This liquidation discount risk is additional to price risk and will be of concern to portfolio managers that may, at short notice, wish to convert substantial stockholdings to cash. We obtain daily time series of instantaneous log liquidation discount for variously sized portfolios of Australian stocks and determine that these time series are best modeled with an Autoregressive Fractionally Integrated Moving Average-Generalized Autoregressive Conditional Heteroskedasticity (ARFIMA–GARCH) process. We then formulate a liquidation discount-at-risk measure with which portfolio managers can budget for the future cost of portfolio liquidity for a chosen liquidation horizon and confidence level.