Estimating class size without the shareholder register
Axiom Forensics is often engaged by firms seeking to investigate the merits of commencing proceedings in relation to shareholder class actions.
In addition to undertaking work on the quantum of claims (including by way of preparing indicative Event Study analysis), a relevant consideration prior to investing significant resources into commencing proceedings is to gain an understanding of the size of any potential class and, therefore, the quantum of any potential recovery.
Whilst noting that class size can only be conclusively determined with a copy of the shareholder register, in the absence of a copy of the shareholder register Axiom applies three models to estimate class size and, therefore, to assist in evaluating the economic merits of potential claims.
In this article we set out an overview of these models.
Estimation models considered
In this article we provide a brief overview of the following class estimation models:
- The institutional shareholder model (Institutional Model);
- The Single-Trader model (ST Model); and
- The Multi-Sector, Multi-Trader model (MS-MT Model).
To varying degrees, these estimation models rely on data which includes:
- The number of issued shares;
- The volume of shares traded;
- Institutional shareholdings;
- The number of shares held by ‘insiders’ (who are typically excluded when considering the potential class);
- Short positions;
- The frequency of trading by category of investor; and
- The breakdown of ownership by category of investor.
This information is obtainable from a combination of the company, ASIC (in respect of short positions) and external data providers (Axiom uses S&P Capital IQ).
The data that is required is typically at the commencement, conclusion and (in respect of trading activity) across the ‘relevant period’, being the period in which the share price is said to have been affected by the claimed non-disclosure.
The estimation models that we apply have varying degrees of sophistication, ranging from the Institutional Model at the low end to the MS-MT Model at the high end, with the degree of confidence regarding class estimates generally increasing as sophistication is added.
We set out an overview of each of the estimation models in turn.
1. Institutional shareholder inference model
With limited data it is possible to estimate a potential class by analysing the movement in the shareholdings of large/institutional shareholders.
The Institutional Model applied by Axiom produces an estimate of specific identified institutional shareholder class members (which occurs via Stage 1, discussed below) which can then be extrapolated across the share register as a whole (which occurs in Stage 2), resulting in an estimate of the number of shares that form part of a potential class.
Stage 1 – estimating the increase for institutional shareholders
By obtaining listings of institutional / large shareholders at the commencement and completion of the ‘relevant period’ we can calculate the net increase in shares held; this net increase representing those shares that were purchased in an environment where it is claimed that non-disclosure resulted in (typically) an inflated share price.
As this figure represents the potential class in respect of identified institutional shareholders, it only reflects a subset of shareholders in the company and, therefore, only a subset of the potential class.
Stage 2 – extrapolation to the share register
Adopting the net increase observed for identified institutional shareholders, we then extrapolate this to the share register as a whole, in so doing deriving an estimate of the net increase in shares in respect of all shareholders in the company, not merely institutional shareholders.
By way of example, assume:
- A company has 10,000 outstanding shares;
- Institutional shareholdings in the company at the commencement of the period were 4,000 shares; and
- Institutional shareholdings in the company at the conclusion of the relevant period were 5,000 shares.
In this simplified scenario, Stage 1 of the Institutional Model calculates a net increase in the shareholdings of the identified institutional shareholders of 1,000 shares.
Under Stage 2, we assume that the relationship observed for institutional shareholders applies to all shareholders, and estimate a total class size of 250 shares, which is calculated as:
- Total issued shares divided by institutional shares at the commencement of the relevant period (10,000 / 4,000);
- Multiplied by the net increase for identified institutional shareholders (1,000);
- Equals an estimated class size of 2,500 shares.
The Institutional Model is a simple model that can be applied quickly with no more data required than that which is publically available.
Whilst Stage 1 of the calculation results in a sound estimate of potential institutional shareholder class members, it is often the case that institutional shareholders may not participate in a class action. In addition, if the analysis is restricted to institutional shareholders, a funder may not gain comfort that the prospective class size is large enough to warrant an investment.
Whilst Stage 2 of the Institutional Model will produce a higher class estimate (by virtue that it is being applied across the share register), the extrapolation to all shareholders in Stage 2 necessarily assumes that the observed rate of increase in ownership observed for institutional shareholders applies to all shareholders. This may not be a sound assumption.
In the remainder of this article, we address two more sophisticated models that can be applied in estimating class size. In so doing, we note that the ST Model and the MS-MT Model are estimation models that are applied widely in securities litigation both in the United States and Australia.
2. Single Trader Model
The ST Model and MS-MT Model are what are described as ‘decay’ models, the object of which is to calculate the number of shares acquired on a particular day that would continue to be held at the conclusion of the ‘relevant period’.
It is only those shares that were acquired during the ‘relevant period’ and that continue to be held at the conclusion of the ‘relevant period’ (being shares that were, therefore, acquired at an inflated price) that form the class of shares in respect of which a loss may have been suffered.
The difference between the ST Model and the MS-MT Model relates to the assumptions that impact the calculation of the rate at which shares acquired are assumed to be sold over the ‘relevant period’ (that is, the rate of ‘decay’).
The ST Model builds on the Institutional Model by incorporating:
- Short positions in the company; and
- Insider purchases and sales,
the result of which is an estimate of the daily purchases and sales across the ‘relevant period’.
The ST Model assumes that all tradeable shares are equally likely to trade. Once combined with an estimate of the number of shares that are able to be traded on each day of the ‘relevant period’, the percentage of shares assumed to be retained at the conclusion of the ‘relevant period’ is calculated.
By way of example, assume:
- Total issued shares of 10,000
- Daily sales of 1,000 shares (10% of issued volume);
- A three day ‘relevant period’; and
- Shares traded over the ‘relevant period’ are thus 3,000.
Applying the assumption that all shares are as likely to trade as each other, the number of shares purchased over the ‘relevant period’ that are retained at the conclusion of the ‘relevant period’ are 2,710 shares, calculated as:
- Shares acquired on Day 1: 1,000 x 90% retention (Day 2) x 90% retention (Day 3) = 810 shares retained; plus
- Shares acquired on Day 2: 1,000 x 90% retention (Day 2) equals 900 shares retained; plus
- Shares acquired on Day 3: 1,000 shares retained
In this simple illustration, 2,710 shares of the 3,000 shares traded over the ‘relevant period’ remain held at the conclusion of the relevant period. It is these ‘held’ shares that form the class of shareholders who acquired their shares at an inflated price and claim to have suffered a loss because those shares continued to be held at the conclusion of the ‘relevant period’.
3. Multi-Sector, Multi-Trader Model
The MS-MT Model applies the basic framework of the ST Model but adds empirical assumptions regarding the trading behaviour of different categories of shareholders.
In particular, the MS-MT Model separates trading activity between ‘high activity’ and ‘low activity’ shareholders, with the frequency of trading by each category of shareholder based on empirical research.
Given that ‘high activity’ shareholders trade in and out of shares more quickly than ‘low activity’ shareholders, the inclusion of this additional element in the MS-MT Model results in an estimated class size that is lower than that which is estimated under the ST Model.
Using another simplified example, the effect of the inclusion of ‘high frequency’ and ‘low frequency’ shareholders is illustrated as follows:
- Total issued shares of 10,000, of which:
- High activity shareholders account for 20% of shares; and
- Low activity shareholders account for 80% of shares
- Daily sales of 1,000 shares (10% of issued volume), of which:
- High activity shareholders account for 80% of volume; and
- Low activity shareholders account for 20% of volume
- A three day ‘relevant period’; and
- Shares traded over the ‘relevant period’ are thus 3,000;
In this example, of total shares traded of 3,000, the number of shares purchased over the ‘relevant period’ that are retained at the conclusion of the ‘relevant period’ are 2,200 shares, calculated as:
- High activity traders (1,952 shares retained):
- Shares acquired on Day 1: 800 x 80% retention (Day 2) x 80% retention (Day 3) = 512 shares retained; plus
- Shares acquired on Day 2: 800 x 80% retention (Day 2) equals 640 shares retained; plus
- Shares acquired on Day 3: 800 shares retained
- Low activity traders (248 shares retained):
- Shares acquired on Day 1: 200 x 20% retention (Day 2) x 20% retention (Day 3) = 8 shares retained; plus
- Shares acquired on Day 2: 200 x 20% retention (Day 2) equals 40 shares retained; plus
- Shares acquired on Day 3: 200 shares retained
Under the MS-MT Model, therefore, 2,200 shares of the 3,000 shares traded over the ‘relevant period’ are assumed to remain held at the conclusion of the ‘relevant period’ and, as such, are assumed to form part of the class.
The lower estimate relative to the ST Model is attributed to the different trading characteristics introduced in respect of ‘high activity’ and low activity’ shareholders – a factor that is not present in the ST Model.
Application to IPO based class actions
The above examples have been prepared based on shares traded and held over a ‘relevant period’ and therefore relate to claims in respect of shares acquired on-market where the market price is said to have been influenced by the claimed non-disclosure.
The class estimation models can be adapted so that they are applied in circumstances in which the claim relates to shares acquired in an initial public offering.
In these circumstances, the class size is estimated by reference to a calculation of the percentage of shares retained at the end of the period (which is informed by the daily rate of purchases / intra-day trading and the trading characteristics of ‘high activity’ and ‘low activity’ shareholders) multiplied by the shares issued/acquired under the IPO.
Estimating the size of a potential class in a shareholder class action can be an important step in determining whether to proceed with conducting further investigation into the merits of commencing proceedings.
Whilst the size of the class can be determined conclusively only with a copy of the shareholder register, the class estimation models that we have addressed represent a method for estimating the potential class size in the absence of the shareholder register and therefore a means of gaining a degree of comfort that the class size is sufficiently large to justify an investment of time and resources in pursuing potential actions.
 For simplicity of this example, we assume there is no intra-day trading. In the typical application of the MS-MT Model, intra-day trading is removed.