Analytical Bound on the Cost of Illiquidity for Equity Securities Subject to Sale Restrictions

We derive a theoretical upper bound for the cost of illiquidity to an undiversified investor whose entire wealth is committed to a single asset that is restricted from trading for a fixed time period. The analytical bound for the illiquidity discount is established using no-arbitrage principles and is applicable to a large class of models for asset price dynamics that admit option pricing functions with homogeneity of degree one with respect to the spot and strike prices. The model improves earlier bounds on restricted stock discounts established by Longstaff [1995a, b] without any loss of generality.