A Note On Stock Trading Models - SLCG Securities Litigation

A Note On Stock Trading Models Craig J. McCann, Ph.D., C.F.A., © 2001 Damage awards in securities class action lawsuits depend on the total number of damaged shares and on the damage per share. Damaged shares are shares bought when the stock price was artificially high due to material omissions or misrepresentations and held until the mispricing is reduced or eliminated. It is difficult to determine the exact number of damaged shares because some shares purchased at artificially high prices are sold while prices are still artificially high; these shares are “re-traded.” The earliest and simplest trading model, the Proportional Trader Model (“PTM”), was developed by plaintiffs’ experts. The PTM assumes that each share is equally likely to trade on

any given day. Other experts have developed two classes of models—Multiple Trader Models (‘MTMs”) and Accelerated Trader Models (“ATMs”). MTMs allocate trading and shareholdings to at least two types of investors and apply the PTM to each type. ATMs assume that shares that have already traded during a class period are more likely to trade than shares that have not yet traded. The amount of re-trading estimated by MTMs and ATMs is controlled by the choice of a few critical parameter values. Published empirical research does not conclusively support one model type or one set of parameter assumptions. Figure 1 illustrates a simple class action lawsuit covering a period of 3 days during which the share price was $1 .00 above its true value because of material misrepresentations. The difference between the market price and the true value of a share is commonly referred to as “inflation.” There were 100,000 shares available to trade and 10,000 shares traded each day. If none of the shares bought during the class period are re-traded until after the class period, aggregate damages equal $30,000. Investors paid $1.00 per share too much for the first day’s 10.000 shares purchased, the second day’s 10,000 shares purchased and the third day’s 10,000 shares purchased—and lost $1.00 on the fourth day when the fraud was disclosed, The $30,000 estimate derived by assuming no shares bought during the class period are resold during the class period is the upper bound on damages. At the other extreme, if all 10,000 shares bought each day are re-traded the next day, aggregate damages are only $10,000. Investors who paid too much for the first day’s 10,000 shares and the second day’s 10,000 shares would not be damaged since they sold their purchases on the next day at the same inflation. Only purchasers of the third day’s 10,000 shares are damaged, since inflation declined from $1.00 to $0 per share before they could sell their purchases. The $10,000 estimate derived by assuming all shares bought during the class period are resold the next day is the lower bound on damages. It’s the Re-trading That Matters As our simple example illustrates, the greater the amount of re-trading assumed, the lower the resulting damage estimate, i.e., from $30,000 for a 0% re-trading assumption to $10,000 for a 100% re-trading assumption. Proportional Trader Model The Proportional Trader Model (“PTM”) assumes that each share available to...

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