Locking in Value: An Alternative Approach to Measuring Illiquidity

Locking in Value: An Alternative Approach to Measuring Illiquidity

September 01, 2013


Investors holding shares in publicly traded companies face liquidity restrictions with respect to the sale of their shares for a variety of reasons. Examples of these types of situations may involve: (i) restricted shares purchased in a private placement transaction; (ii) restricted stock grants held by management team members; (iii) control securities held by company affiliates; (iv) stock subject to post-IPO lock-up restrictions; (v) restricted shares related to a merger or acquisition involving stock as consideration; or (vi) holding a large block of stock that can’t be sold quickly without depressing the market.

Valuation experts and the tax courts have long debated various frameworks for determining appropriate discounts to apply in situations where an asset may lack immediate liquidity. Analysts frequently use various terms interchangeably to describe this discount, including “marketability discount,” “blockage discount,” or “illiquidity discount.” The most commonly accepted and widely applied research for measuring marketability discounts is based on restricted stock studies, which analyze discounts observed in private placement transactions of restricted shares in public companies.

In general, private placements of restricted stock occur at a discount to the publicly traded price in order to compensate investors for (i) the inability to sell the stock over a pre-determined period of time (currently six months pursuant to the latest Securities and Exchange Commission (“SEC”) Rule 144 amendment) and (ii) the risk that the issuing company’s stock fluctuates relative to the price at which it was transacted during the applicable period of illiquidity. Restricted stock studies continue to provide compelling information given the ability to compare and contrast key attributes that impact the magnitude of discounts, such as effective holding period, stock price volatility, and block size, among other factors.

Other methods used to determine discounts include various quantitative models based on options theory. A put option method can be utilized to measure illiquidity discounts by estimating the cost of acquiring put options to hedge against market exposure risk by effectively protecting an investor from loss of value over the course of an estimated liquidation period.

This article explores an alternative approach for measuring the detriment associated with publicly traded stock that is subject to liquidity restrictions.


Consider a framework in which an owner of the subject restricted stock enters a series of transactions in order to: (i) eliminate all price-risk associated with the stock over the period of liquidity restriction by assembling a portfolio of stock options and (ii) obtain immediate liquidity by borrowing against the stock. We propose that the cost of executing this strategy can provide a meaningful indication as to an appropriate discount for lack of marketability relative to the freely traded price.

To illustrate, we analyzed a hypothetical scenario in which an investor owns 55,556 shares of stock in Pandora Media, Inc. (“Pandora”). As of the date of the composition of this article, Pandora’s stock traded at approximately $18.00 per share, giving the investor’s stock a market-implied value of $1.0 million. However, we have also assumed that the investor’s shares maintain certain liquidity restrictions whereby the investor cannot sell the stock for six months.

As outlined, it is possible for the investor to undertake a transaction today in which liquidity is achieved and all prospective price risk associated with the shares is eliminated. The details of this series of transactions are as follows.

Elimination of Price Risk

The key element to this analysis is the elimination of all prospective price risk, which can be achieved through the creation of a portfolio of stock options. Specifically, the investor could form a portfolio of stock options consisting of (i) the purchase of at-the-money (i.e., a strike price of $18.00) put options and (ii) the sale of at-the-money call options. The charts in Table 1 (above) depict the payoff functions for each of these options positions.

Additionally, in order to analyze the net cost of this portfolio of options, we examined the publicly traded price of Pandora call and put options. A summary of the cost of these options, as quoted by Charles Schwab & Co., Inc., as of the date of the composition of this article, is presented in Table 2. Note that the term of the options is equal to the investor’s period of liquidity restriction, or approximately six months.

Upon the formation of the options portfolio whereby put options are purchased and call options are sold, the investor will have effectively locked in liquidity at $18.00 per share at the expiration of the options in six months. Table 3 identifies all possible scenarios of stock price movement and liquidity for the investor. In each scenario, the investor receives $18.00 cash in exchange for each share of Pandora stock at the expiration of the options, which is also the date that the liquidity restrictions lapse. Based on this analysis, the investor has eliminated both downside risk and upside potential achieving zero price risk and has guaranteed the ability to achieve liquidity at $18.00 per share in six months.

Transaction Execution

Now that we have established the manner in which the investor could eliminate price risk, we will analyze the execution of the transaction, which will incorporate the investor receiving “liquidity today” in addition to all related fees and expenses. This analysis is presented in Table 4.

Summary of Sources and Uses of Cash at Transaction Inception

  • First, the investor borrows the indicated level of funds either on margin or from a bank. The investor’s Pandora stock could serve as collateral for such a loan. In consideration of the market interest rate environment, we assumed the investor could borrow these funds at an interest rate of 8.0%.
  • Next, the investor purchases put options and sells call options in an amount equal to the number of Pandora shares. The net cost, which reflects the cost of the put options and the proceeds from selling the call options, is funded by the loan discussed previously.
  • Next, the investor pays transaction fees associated with forming the options portfolio, which are assumed to be equal to 1.5% of the aggregate value of the put and call options. Transaction costs are also funded with the loan.
  • Finally, the investor receives the remaining cash proceeds from the loan. This consideration represents the investor’s “liquidity today.”

Summary of Sources and Uses of Cash After Six Months

  • After six months, the investor receives cash equal to $18.00 per share in conjunction with the options strategy discussed previously. Again, the investor has locked in this value and there is no risk of receiving less or more than the indicated $18.00 per share, or $1.0 million.
  • Finally, the investor repays the principal amount of the loan as well as accrued interest.


Indicated Discount for Lack of Marketability

As presented in Table 4, the indicated liquidity received at time zero represents a 5.4% discount to the face value of the investor’s stock of $1.0 million. Overall, contingent on the liquidity of publicly traded stock options and the availability of a loan at the assumed rate, this series of transactions could be undertaken by any holder of public stock with liquidity restrictions in order to receive cash proceeds today while retaining no additional price risk. Based thereon, the cost of executing this transaction provides a meaningful indication with respect to the appropriate discount for lack of marketability for the shares.

Longer Holding Period Restrictions

As illustrated in Table 5, we have also applied this framework to scenarios involving longer holding periods. It is not surprising that the resulting discount increases with holding period, which is consistent with other empirical evidence regarding discounts for lack of marketability. We do recognize, however, that the stock options contemplated in this analysis with longer terms may not have comparable liquidity to stock options with shorter terms. As a result, an investor looking to execute this strategy over a longer term may have to work with a specialized broker of such securities.


Overall, the discounts for lack of marketability observed in this analysis are comparable to those generally indicated by restricted stock studies and other quantitative models. There are strengths and weaknesses associated with every study. In the instant case, we recognize that there are certain limitations associated with the ability of an investor to execute the transactions referenced herein, such as the liquidity of long-term stock options, and the ability to borrow funds at the assumed rate. Nevertheless, this model serves as another tool that valuation analysts can use. In particular, this model accounts for several key factors that should be considered in estimating a discount for lack of marketability, such as expected holding period, risk, volatility, and dividends. Using a combination of empirical data and testing the indications with quantitative methods can provide compelling evidence for estimating valuation discounts.