The pricing of contributing shares : a contingent claims approach

Dunlop, Ian Arthur. (1990). The pricing of contributing shares : a contingent claims approach PhD Thesis, School of Business, The University of Queensland.

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Author Dunlop, Ian Arthur.
Thesis Title The pricing of contributing shares : a contingent claims approach
School, Centre or Institute School of Business
Institution The University of Queensland
Publication date 1990
Thesis type PhD Thesis
Total pages 223
Language eng
Subjects 14 Economics
Formatted abstract A number of Australian public companies use contributing or partly-paid shares as a source of finance for their operations. Contributing shares are shares for which the full subscription price has not yet been paid by the shareholder. Thus, at some future date, the company can call upon shareholders to pay the difference between the current paid up amount of the shares and the full subscription price. This amount can be called in total, or in a number of smaller payments.

Contingent Claim Analysis is appropriate for determining the price of a security whose payoffs depend upon the prices of one or more other securities. A contributing share can be classified as a contingent claim security as the payoffs depend upon the price of a fully paid share issued by the same firm. Further, in the case of no liability firms, shareholders have the option of not paying calls and forfeiting their shares. Such forfeited shares are auctioned by the firm and any funds remaining after expenses and calls have been paid are refunded, pro rata, to the defaulting shareholders.

The use of contributing shares appears to be almost unique to Australia. A search of computer data bases found no literature on the pricing of this type of security. It is the primary aim of this thesis to extend contingent claim analysis to the pricing of contributing shares.

To do this rational boundary pricing conditions between fully paid and contributing shares are developed. The rational boundary pricing conditions are dividend into two groups:
- dominance boundary conditions, which are independent of a firm's policy of calling unpaid subscription amounts;
- call dependent boundary conditions, which, depend on a firm's call policy by definition.

From the empirical tests of the above boundary conditions, it is concluded that:
- dominance boundaries are rarely violated;
- firms generally appear to be adopting call policies with respect to contributing shares which are either indeterminate or contributing share value maximizing.

Six models of the pricing of contributing shares are developed. Three of these are stochastic models based on contingent claims analysis. The other three are simple non-stochastic models.

All six models were tested empirically. Based on these tests the ranking of models, in order of proportion of variance explained, and using both contemporaneous and historical parameter estimates, is:
- stochastic dual probability of call model; - stochastic single probability of call model;
- simple constant probability of call model;
- called model.

The other two models tested were the never called and the alternative stochastic models. Based on the results, these models were not considered worth ranking.

In a number of cases the four ranked models all give the same proportion of variance explained. This is due to one or both of the following causes:
- when the probability of call is very high all of the ranked models reduce to the called model;
- when a contributing share is almost paid to full par value the stochastic component of the models is small and may not be detected by the methods employed.

As a result of comparisons of the above four ranked models it is recommended that the following two models be used to forecast contributing share prices. The models are:
- stochastic single probability of call model; - called model.

The called model is appropriate when either:
- there is a very high probability of a call to full par value; or
- a contributing share is almost paid to full par value.

In all other cases the stochastic single probability of call model is appropriate. It is suggested that this model be employed as:
- it is simpler to use than the stochastic dual probability of call model, which is possibly over specified;
- the proportion of variance explained is almost the same as that for the stochastic dual probability of call model.

Keyword Stocks -- Prices -- Mathematical models.
Corporations -- Finance -- Mathematical models.
Securities -- Mathematical models.

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