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

Abstract

In many situations, an investor can hold an asset that is traded in the market, but she is prohibited from selling it during some period. A private placement with a trading restriction is one example. How much more would the same stock be worth without the restriction? One solution in the literature suggests computing an upper bound as the value of a lookback put option, which would allow the stockholder to liquidate her position when the prohibition ends, at the most favorable price that could have been obtained at any point during the restriction period. Such an option would fully compensate a restricted investor with perfect foresight about the stock price path who would have known the exact best point at which to sell the restricted stock. But this leads to a very high and unrealistically loose upper bound under many conditions. In this article, Ghaidarov models the value of the trading restriction more realistically, as a forward-starting put option that would allow the investor to fix the exercise price at any point she chooses during the restriction period. Such an option can be priced at the beginning, but the holder would later choose the date within the period to liquidate the position (i.e., to fix the put strike equal to that day’s market price), without the benefit of knowing the subsequent path of stock prices. The resulting bounds on illiquidity discounts are much tighter and, as Ghaidarov shows, much closer to the way restricted stocks are priced in the market.