VAR - Liquidity risk

CFA Level III Derivatives
#1

Sch book 4 LOS 27 i, pg 67

Liquidity is not considered in measuring VAR. Implicit in VAR is the assumption that positions can be sold at their trading or estimated market value. Thus, AR can give an inaccurate estimate of the true potential for loss. Estimating liquidity is difficult. For example, due to a statistical anomaly and in spite of large bid-ask spreads, some infrequently traded securities have low historical volatility. Even if historical volatility is accurate, the inability to quickly adjust a position can lead to increased losses not caught in the VAR measure

Not clear on the following:

  1. For example, due to a statistical anomaly and …

Which statistical anomaly is being referred here.

Kindly help

#2

I believe it is appraisal based pricing … where prices are known only when the item is appraised for being sold. hence volatility reduces.

additionally - the prices are usually between a buyer who wants the item badly and the seller who wants to get the items sold.