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An Analytical VaR Approach for Credit Portfolio with Liquidity Horizon and Portfolio Rebalancing

We provide an analytical VaR approach for the credit portfolio with liquidity horizon and the constant level of risk. Given any time horizon, a two period credit portfolio loss model is derived and, at the end of the first period, the portfolio is rebalanced to ensure a constant level risk of the portfolio as measured by the credit rating. The analytical solution of VaR is found by extending the granularity adjustment (GA) approximation. The orders of all error terms for two period loss model are also provided. The model is applied to IRC (IDR), with the liquidity horizon of each asset being six months. We show that, compared with the standard one-period ASRF model with and without GA, our analytical approach does behave better to achieve a comparable measure to IRC in capturing important risks such as concentration. We also show that, in the presence of liquidity horizon and portfolio rebalancing, the tail distributions of the credit portfolio losses are very different from that computed by the standard one-period model such as ASRF (with and without standard GA). The standard ASRF will always be aggressive at the 100 percentile but, depending on the credit quality of portfolio and percentile, it can be both conservative and aggresive for other percentiles.