Quantifying Lack of Marketability Discounts of Employee Stock Options

It is well known that the cost of expensing employee stock options (ESOs) through the income statement is enormous, representing an aggregate additional expense for firms amounting to billions of dollars. Traditional option pricing methods clearly overstate the value of ESOs. Since the ESO’s cost to the employer depends not only on the variables contained in option pricing models but also on the interrelationship of these factors unique to ESOs, the traditional option pricing models will overstate the value of an ESO unless adjustments are made to the valuation model to account for the unique issues associated with ESOs. Specifically, the exercise policy of the employee, the contingent nature of ESOs, and the lack of an organized exchange to buy and sell ESOs must be considered. Black-Scholes not fully applicable to ESOs While the underlying assumptions of the Black-Scholes option-pricing model – the most widely used method – approximate the characteristics of publicly traded stock options, they do not parallel the structure of ESOs. For example, the Black-Scholes option-pricing model assumes the use of a European option. European exercise terms dictate that the option can only be exercised on its expiration date. In contrast, the exercise term for an American-style option, including a vested ESO, allow the option to be exercised at any time during its life. Consequently, American options are more valuable due to their greater flexibility. The issue of an option being American or European may not be significant for publicly traded stock options, because they are easily traded and generally short-term in duration, however, it is an important issue for ESOs. It is common for ESOs to be exercised well before their maturities given the linkage between continuing employment and exercise of the stock option manifested by the long-term nature of ESOs, and the concentration of personal wealth represented by options for many executives. Black-Scholes also assumes that markets are efficient, that the stock and option markets are liquid, and that the option’s owner can immediately convert the option into cash. However, no exchange exists where ESOs can be traded. Clearly, the marketplace for ESOs is inefficient and completely illiquid absent the employee converting the option to cash by selling it back to the issuing company. Third, Black-Scholes assumes that there are no transaction costs and no taxes. However, the tax effect of ESOs is a very important consideration for the executive. While there are other stock option pricing models available, each alternative contains the same fundamental assumptions. While the Black-Scholes option-pricing model provides a fair value estimate for publicly traded options, unfortunately it is unable to capture many of the nuances incumbent on ESOs. There are many significant differences between ESOs and publicly traded options. ESOs are more complex than standard exchange traded call options. Standard exchange-traded options can quickly be bought and sold and converted into cash. Conversely, an ESO’s maturity can be as long as 10 years, and frequently there is more than one date that must be considered when analyzing an ESO, including the grant date and the vesting date. Furthermore, even after the employee exercises the ESO, the shares delivered to the employee may be restricted and may not be able to be sold for a specified period of time. ESOs also can be classified into either a fixed ESO or a performance ESO. Fixed ESOs have parameters that specify the exercise price and number of shares associated with each option, and are not subject to change. Performance ESOs contain conditions or outcomes that affect the number of shares or the exercise price associated with the ESO. For example, the number of shares that an employee is entitled to receive may be greater if the firm achieves a certain level of earnings per share or return on equity. Adjustments needed for ESO pricing Furthermore, the original logic behind Black-Scholes does not apply to ESOs since employees cannot trade the ESO freely and may exercise it early given job changes or wealth diversification reasons. Therefore, the mismatch between the characteristics of ESOs and the assumptions underlying the Black-Scholes options pricing model will lead to inaccurate ESO valuations unless the option pricing models results are adjusted for a lack of liquidity. It is intuitive that the value of an ESO should be less than the value generated by Black-Scholes, but how much less? As a market does not exist to trade ESOs, it is impossible to quantify an ESO’s value degradation due to its lack of marketability. For more than 40 years it has been empirically shown that, all other factors being equal, a lack of marketability diminishes the value of a security versus an otherwise identical security that is readily marketable. Unfortunately, the studies on the illiquidity of a security have addressed common stock rather than stock options. A significant moment in the development of stock options occurred in the early 1900s when the Put and Call Brokers and Dealers Association (PCBDA) was formed. PCBDA members arranged transactions between those wanting to buy and those wanting to sell options. The PCBDA was an over-the-counter stock option exchange which existed for about 70 years until the creation of the Chicago Board of Options Exchange (CBOE) in 1973. Information was available for long periods of time for the PCBDA. The PCBDA dealers advertised in major financial newspapers their selling prices for various stock options on a wide variety of large-cap stocks. The ads included the name of the firm on which the call option was written, the firm’s stock price, the option’s exercise price, and the option’s maturity. Given these data, we were able to quantify how illiquidity effects the value of a stock option. Our study compared published asking prices of stock options traded on the PCBDA to prices generated via Black-Scholes. This comparison yielded a proxy for the illiquidity discount of an ESO. We gathered weekly ads from The Wall Street Journal of a representative over-the-counter put and call dealer for eight years prior to the opening of the CBOE – March 1965 to March 1973. Our data included all of the dealer’s weekly call option asking prices, each option’s exercise price, and maturity dates. We also obtained yields from the Federal Reserve Bulletin for the Treasury bills which corresponded to each of the option’s maturities. This information was merged with the Center for Research in Security Prices (CRSP) data files to obtain company share price and dividend histories. When completed, the data set consisted of approximately 5,700 option observations. We then calculated the Black-Scholes option value for each of those 5,700 advertised options. Next we compared the asking price of the over-the-counter stock option to the theoretical Black-Scholes price. The comparison results led us to conclude that the illiquidity discount from the theoretical price for in-the-money call options was 22% while the illiquidity discount for the asking price of out-of-the-money call options to their theoretical price approximately 45%. Given that ESOs restrict the right to sell the option to a third party and contain provisions that are contingent upon company performance, we believe that an ESO is of less value than a stock option that can be freely traded in a public market. Unambiguously, an illiquidity factor should be considered as part of the ESO valuation process. Based on our research, we believe that discounts ranging from at least 22% to 45% should be applied to an option-pricing model used to generate prices for ESOs, with the specific discount value being determined by the option’s maturity and intrinsic value. The results of our empirical study suggest that the fair value of the ESO may be much less than the Black-Scholes value of the option. We believe that our results represent the minimum discount for lack of marketability that inures to illiquid ESOs. The reason is that our data were gathered from an illiquid market that nevertheless did have an infrastructure of approximately 25 dealers making an option market and advertising prices. However, no such market or infrastructure exists for many stock options granted to employees. As a result, the illiquidity discount for stock options traded outside of any organized infrastructure, such as ESOs, will exceed the illiquidity discounts identified in our analysis. Lawrence M. Levine is Director-Corporate Finance Services at American Express Tax & Business Services Inc. Carl F. Luft, Ph.D., is Associate Professor of Finance at DePaul University.