The Demutualisation of AMP Society: An Example of the Valuation of Collars Comprising Asian Options.

1. Introduction

A number of Australian mutual organisations have recently been demutualised and restructured as public companies. The most notable of these organisations include: National Mutual (listed in October 1996), Colonial Mutual (listed in May 1997) and AMP Society (listed in June 1998). In the case of AMP Society, a collar comprising average, or Asian, options formed part of the financial structure of the demutualisation process.

Collars are generally discussed in the context of interest rate derivatives, where a variable-rate borrower or lender seeks to place a limit on both the maximum interest rate, the cap, and the minimum interest rate, the floor, that will be charged pursuant to the loan agreement. These securities are valued relatively easily using techniques such as Black's (1976) forward option pricing model. However, where the options comprising the collar are Asian options, the valuation of the collar is more complex. This paper uses the demutualisation of AMP Society to provide an examination of the valuation of such a collar.

On 20 November 1997, at an extraordinary general meeting held for AMP Society members, 98.3% of votes were cast in favour of the demutualisation of Australia's largest insurance and funds management group. The new company, AMP Ltd, was created on 1 January 1998 and shares in the company were held in trust until its listing on the ASX. On 6 May 1998 the prospectus relating to the listing was issued to shareholders. Of particular interest to shareholders was the fact that, under the plan, they were provided with the opportunity to sell their allocation of shares to AMP Ltd and/or purchase a limited number of additional shares from the company. The device through which these transactions would occur was called the Facility.

The price that was to be paid for shares bought/sold through the Facility was to be determined by a formula that was predicated upon the price at which the share traded upon listing. Hence, policyholders were required to determine whether it would be advantageous for them to sell on-market or via the Facility, prior to their knowing what the Facility Price would be. The purpose of this paper is to analyse the circumstances under which the AMP shareholder would rationally choose to sell via the Facility rather than on-market.

2. The Facility

Policyholders who were entitled to receive shares through the demutualisation program had the opportunity to purchase additional shares and/or sell their allocation of shares through an off-market mechanism known as the Facility. Investors wishing to increase their shareholding were limited to applying for $1000 worth of additional shares, but there was no such restriction on the number of shares that could be sold through the Facility. Shareholders wanting to participate in the Facility were required to inform AMP by 5 pm on 3 June 1998. At the time that shareholders were required to convey their willingness to buy (sell) shares under the Facility, they were unaware of the price that they would pay (receive). Page 10 of the AMP prospectus set out the way in which the Facility Price would be set:

The Facility Price will be made up of:

* The Base Price--set by AMP Limited, following consultation with the Joint Lead Managers, after Institutions bid for Shares. It will be announced before stockmarket trading of Shares begins, plus

* 50% of the amount (if any) by which the Average Market Price of AMP Shares in the first five days of stockmarket trading after Listing is higher than the Base Price.

There is a limit on the Facility Price. It will not exceed the Base Price by more than 20%.

Therefore the price to be paid under the Facility may be described by the following equation:

(1) FP = max [BP, min[BP + 0.5 (AVG - BP), 1.2BP]]

where: FP = the Facility Price;

BP = the Base Price; and

AVG = the Average Market Price of AMP shares traded in the first five days following listing.

The relationship between the Average Share Price, the Base Price and the Facility Price is illustrated in figure 1. This diagram illustrates that the price received by shareholders electing to sell through the Facility could be viewed as being the payoff from positions held in options, with payoffs dependent upon the average price of AMP shares in the first five days of trading and the base price set by the company. Specifically, the party who takes a short position in the facility has an entitlement to sell an AMP share for 0.5AVG + 0.5BP and has a collar around this price by having a long position in an arithmetic average price put option with an exercise price of BP and a short position in an arithmetic average price call option with an exercise price of 1.2BP.

[Figure 1 ILLUSTRATION OMITTED]

Therefore, the valuation of the Facility requires the valuation of two arithmetic average price options,(1) While Ritchken, Sankarnsubramanian and Vijh (1990) and Turnbull and Wakeman (1991) have derived closed-form solutions for geometric average price options, Kemna and Vorst (1990) have demonstrated that it is impossible to derive an exact closed-form solution for arithmetic average price options, although various authors have derived analytic approximations that yield closed-form expressions (see Bouaziz, Briys & Crouhy 1994; Hansen & Jorgensen 1997; Milevsky & Posner 1998; Vorst 1996). Many numerical procedures, such as the standard binomial lattice approach, are also inappropriate for the valuation of such options, as these procedures only provide an option value when the payoff from the option is dependent on the value of the underlying asset at a point in time and not when it depends on the history of those values. A numerical procedure that can be readily applied to the valuation of Asian options is Monte Carlo simulation. As the payoff from the Facility is dependent upon the value of AMP shares traded in the first five days of listing, Monte Carlo simulation will be employed to simulate the path of the share's price during this period. In order to capture the uncertainty associated with the initial price at which AMP shares first trade upon listing, we assume that a policyholder's belief as to this price can be characterised by a lognormal distribution with a mean of [P.sub.0] and a standard deviation of [[Sigma].sub.1][P.sub.0]. Thus, the first price is simulated by randomly selecting a value from a lognormal distribution with a mean of [P.sub.0] and a standard deviation of [[Sigma].sub.1][P.sub.0]. The sequence of subsequent AMP share prices in the first five days is then generated using the expression;

(2) [P.sub.t] = [P.sub.t-1] + r.[Delta]t.[P.sub.t-1] + [[Sigma].sub.2].[Epsilon][square root of [Delta]t]

where: [P.sub.t] = the value of the AMP share at time t;

r = the continuous risk-free rate of interest;

[[Sigma].sub.2] = the annualised standard deviation of AMP share returns in the five-day post-listing period;

[Epsilon] = a random number drawn from the standard normal distribution; and

[Delta]t = the proportion of a year between each price simulated in the second stage of the Monte Carlo procedure.(2)

An arithmetic average of each of the simulated share prices was then calculated. This average share price was then subjected to the payoff conditions contained in equation 1, and the Facility Payoff (FP) was calculated. In order to ensure that the Estimated Facility Payoff (EFP) is within acceptable bounds of accuracy, 100000 simulations were performed with the antithetic variable technique of variance reduction being utilised.(3) The payoff from the facility was then estimated as:(4)

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The purpose of this paper is to identify the different conditions under which the AMP shareholder would rationally have chosen to sell via the Facility rather than sell on-market.

3. Parameter Estimates

The valuation of the Facility requires the specification of values for five parameters; the Base Price (BP), the initial price ([P.sub.0]), the standard deviation of the estimate of the initial market price of the AMP share (0.1), the annualised standard deviation of AMP share returns in the five-day post-listing period ([[Sigma].sub.2]) and the risk-free rate of return (r).

3.1 Base Price (BP)

As at 3 June, the date by which policyholders were required to make a decision with regard to their participation in the Facility, the market was unaware of what the Base Price would be. The Base Price would be determined by institutional bidding for shares in a book-building exercise that was to take place between 9 June and 12 June and the number of policy-holders electing to purchase $1000 worth of additional shares. The AMP prospectus supplied an indicative range of values for the Base Price as being between $12.50 and $16. For the purpose of calculating the Facility payoff, this paper will utilise the Base Price of $16 that was finally set. To the extent that we have chosen the upper limit of the indicative Base Price range, our results will overstate the ex-ante value of the Facility

3.2 Price Upon Listing [P.sub.0]

The primary variable to be accounted for by policyholders when considering whether or not to sell through the Facility, is the opportunity cost associated with making this election. The opportunity cost being the price forgone if the policyholder had instead chosen to sell immediately on-market. In order to get a sense of the market's expectation as to the initial price upon listing, a review was undertaken of all issues of The Australian Financial Review from 8 October 1997 (the date on which the initial explanatory memorandum detailing the proposed demutualisation and listing of AMP was released) to 3 June 1998. All forecasts of an initial listing price were noted and details of these are contained in table 1.

Table 1 Forecasts of AMP Share Price Upon Listing

    Date                 Page     Forecast

8 October 1997            20      $8.81 to $10.37
14 October 1997           56      At least $10
4 December 1997           60      $14 to $15
27 February 1998          49      $11 to $14
4 May 1998                19      $18 to $20
7 May 1998                A1      Up to $20
7 May 1998                A2      $12.50 to $16
7 May 1998                A2      Up to $18
7 May 1998                A2      $15
7 May 1998                A2      Significantly higher than $13
7 May 1998                A2      $17 to $18
7 May 1998                A3      $17
7 May 1998                A3      $15
7 May 1998                A4      $11.10 to $19.75
7 May 1998                64      $15.90
7 May 1998                64      $18.05
13 May 1998               32      Higher end of Base Range
23-24 May 1998            34      Up to $16.50

Note: Forecasts included in Table One comprise all those forecasts provided in The Australian Financial Review from 8 October 1998 (the date on which the initial explanatory memorandum detailing the proposed demutualisation and listing of AMP Society was released) to 3 June 1998 (the date by which shareholders wanting to participate in the Facility were required to inform AMP).

As can be seen from table 1, there was some uncertainty associated with the expected listing value of AMP shares with forecasts in the month preceding 3 June ranging from $11.10 to $20. The average of this sample of forecasts, utilising the mid-point of the two extreme forecasts when an interval is given and the extreme forecast when only one limit of an interval is supplied, is $16.47 and the median is $16.25. The suitability of this sample of forecasts as a proxy for market-wide sentiment may be open to question for a number of reasons. Firstly, the small sample size problem is further exacerbated by the fact that most of the forecasts are quoted from unnamed analysts, therefore it is unclear whether any forecasts have been mistakenly counted more than once. A related issue is the question of whether the forecasts are independent of each other as there may exist a motivation for analysts not to be seen to have a different opinion to their colleagues. Having outlined some of the possible problems associated with our measure of the market's expectations of values for [P.sub.0], this paper will analyse the difference between the value of the Facility and the on-market price ([P.sub.0]) for a range of values for [P.sub.0] ranging from $11 to $20.

Another possible advantage associated with selling shares through the Facility as opposed to trading through the Australian Stock Exchange is the ability to avoid brokerage costs and stamp duty. This issue is easily resolved, however, by recognising that there were brokers that openly advertised that they would process AMP sell-orders commission-free and would, where the shareholder sold a minimum of 50 000 shares, pay any stamp duty levied on the transaction.(5)

3.3 Standard Deviation of the Estimate of the Initial Market Price of the AMP Share ([[Sigma].sub.1])

The standard deviation that is required in order to simulate the price at which AMP shares first trade is a measure of the uncertainty associated with the estimate of [P.sub.0]. Table 1 detailed a range of estimates of the expected price of AMP shares upon listing. The standard deviation of the forecast estimates, utilising the mid-point of the two extreme forecasts when an interval is given and the extreme forecast when only one limit of an interval is supplied, is approximately 12%. The dispersion of the forecast estimates may understate the level of uncertainty for two main reasons. As outlined in the previous section, it is unclear whether forecasts have been inadvertently counted more than once and furthermore, whether or not the clustering of forecasts may reflect a desire by analysts not to stand out from their colleagues. Another problem with the approach of trying to ascertain the level of uncertainty inherent in the market from a sample of genuine and imputed point estimates is that this may give a false sense of certainty to the sample under consideration. Bearing in mind these and other obvious limitations of this approach, such as the rather small and selective sample size, a range of standard deviations relating to the estimate of the initial market price for AMP shares will be utilised. The range to be considered will be from 0% to 60% in 10% increments.

3.4 The Annualised Standard Deviation of AMP Share Returns in the Five-Day Post-Listing Period ([[Sigma].sub.2])

The standard deviation that needs to be incorporated into equation 2 is the annualised standard deviation of AMP share returns return over the first five-day's of listing. This variable is a measure of the volatility of share returns in the immediate post-listing period. A number of Australian studies have analysed the behaviour of share prices in the IPO aftermarket. How, Izan and Monroe (1995) in their analysis of 340 Australian IPOs listed between 1980 and 1990, document an average standard deviation of returns in the first twenty trading days after listing, excluding the initial return, of 4.07%. This corresponds to an annualised figure of 14.39%. Lee, Taylor and Walter (1996) examine 266 Australian IPOs listed between 1976 and 1989. They calculate that the average standard deviation of returns in the twelve months following listing, excluding the initial return, is 15.11%. Recognising the possible error introduced by using an average of historical volatilities relating to past IPOs as a proxy for the volatility of returns relating to a future IPO, and the expected insensitivity of the results to differing values of [[Sigma].sub.2], analysis will be undertaken using the following three estimates of volatility; 0%, 15% and 30% p.a.

3.5 Risk-Free Rate of Return (r)

Due to the assumption of risk neutrality made when valuing options, the growth rate to be used in equation 2 is the risk-free rate of return. As at 3 June 1998, the RBA 11 am cash rate was 5.00% pa and, moreover, it had not deviated from this value by more than 0.03% pa in the preceding month. Therefore, for the purposes of the simulation, a value of 5.00% pa will be used as a proxy for the risk-free rate of return.(6)

4. Analysis and Results

The analysis will be undertaken in two stages. First, the value of the Facility will be estimated under various assumptions relating to parameter estimates. The second stage will answer the question; under what conditions would policyholders choose to sell their share entitlement through the Facility rather than on-market? In attempting to answer this question, the paper will examine the effect of the various parameter estimates on the policyholder's decision.

Table 2 provides values of the Facility across a range of values for [P.sub.0], [[Sigma].sub.1] and [[Sigma].sub.2]. The relationship between Facility value and [P.sub.0], for different values of [[Sigma].sub.1], assuming [[Sigma].sub.2] = 15%, is represented diagrammatically in figure 2. The value of the Facility is fairly insensitive to the annualised standard deviation of AMP share returns in the five-day post-listing period ([[Sigma].sub.2]). The notable exception to this is when the put option is at-the-money and there is no uncertainty associated with the estimate of the initial market value (i.e. [P.sub.0] = $16 and [[Sigma].sub.1] = 0%).

Table 2 Simulation Results: Facility Value(*)

                       Panel A: [[Sigma].sub.2]=0%

[P.sub.0]          $11     $12     $13     $14     $15
[[Sigma].sub.1]

0%                16.00   16.00   16.00   16.00   16.00
10%               16.00   16.00   16.00   16.03   16.12
20%               16.01   16.05   16.11   16.22   16.38
30%               16.09   16.16   16.27   16.40   16.57
40%               16.18   16.28   16.40   16.53   16.68
50%               16.27   16.37   16.49   16.61   16.74
60%               16.34   16.44   16.54   16.65   16.77

                       Panel B: [[Sigma].sub.2]=15%

[P.sub.0]          $11     $12     $13     $14     $15
[[Sigma].sub.1]

0%                16.00   16.00   16.00   16.00   16.00
10%               16.00   16.00   16.00   16.03   16.12
20%               16.01   16.04   16.11   16.22   16.38
30%               16.09   16.16   16.27   16.40   16.57
40%               16.18   16.28   16.40   16.53   16.68
50%               16.27   16.37   16.49   16.61   16.74
60%               16.33   16.44   16.54   16.65   16.77

                       Panel C: [[Sigma].sub.2]=30%

[P.sub.0]          $11     $12     $13     $14     $15
[[Sigma].sub.1]

0%                16.00   16.00   16.00   16.00   16.00
10%               16.00   16.00   16.01   16.03   16.13
20%               16.02   16.04   16.11   16.22   16.38
30%               16.09   16.16   16.27   16.41   16.57
40%               16.19   16.28   16.40   16.53   16.68
50%               16.27   16.37   16.49   16.61   16.74
60%               16.34   16.43   16.54   16.65   16.77

                       Panel A: [[Sigma].sub.2]=0%

[P.sub.0]          $16     $17     $18     $19     $20
[[Sigma].sub.1]

0%                16.00   16.50   17.00   17.50   18.00
10%               16.32   16.64   17.05   17.50   17.94
20%               16.60   16.86   17.15   17.45   17.75
30%               16.76   16.97   17.18   17.40   17.61
40%               16.84   17.01   17.18   17.35   17.51
50%               16.88   17.02   17.16   17.29   17.43
60%               16.89   17.01   17.13   17.24   17.36

                      Panel B: [[Sigma].sub.2]=15%

[P.sub.0]          $16     $17     $18     $19     $20
[[Sigma].sub.1]

0%                16.03   16.50   17.00   17.50   18.00
10%               16.32   16.64   17.05   17.49   17.94
20%               16.60   16.86   17.15   17.45   17.75
30%               16.76   16.97   17.18   17.40   17.61
40%               16.84   17.01   17.18   17.35   17.51
50%               16.88   17.02   17.16   17.29   17.43
60%               16.89   17.01   17.13   17.24   17.36

                      Panel C: [[Sigma].sub.2]=30%

[P.sub.0]          $16     $17     $18     $19     $20
[[Sigma].sub.1]

0%                16.06   16.50   17.00   17.50   18.00
10%               16.33   16.64   17.05   17.49   17.94
20%               16.60   16.86   17.15   17.45   17.75
30%               16.76   16.97   17.18   17.40   17.61
40%               16.84   17.01   17.18   17.35   17.51
50%               16.88   17.02   17.16   17.29   17.43
60%               16.89   17.01   17.13   17.24   17.36

Note: (*) = the Facility values were derived using Monte Carlo simulation. For each value, 100 000 series were used. The antithetic variance technique was used to reduce the variance of the simulation results;

[[Sigma].sub.2] = the annualised standard deviation of AMP share returns in tile five-day post-listing period;

[P.sub.0] = the estimate of the initial market price of the AMP share; and

[[Sigma].sub.1] = the standard deviation of the estimate of the initial market price of the AMP share.

[Figure 2 ILLUSTRATION OMITTED]

Changes in the standard deviation of the estimate of the initial market price ([[Sigma].sub.1]) have a significant impact on the value of the Facility. For lower values of [P.sub.0] an increase in [[Sigma].sub.1] increases the value of the Facility whereas for higher values of [P.sub.0] an increase in the value of [[Sigma].sub.1] results in a decrease in the value of the Facility. These changes in the value of the Facility are linked to changes in the value of the put and call options. For lower values of [P.sub.0], the probability that the call option will be exercised is extremely low, and hence the increase in the value of the put outweighs the increase in the value of the call, resulting in a net increase in the value of the Facility. Conversely, for higher values of [P.sub.0] the probability that the put option will be exercised is negligible and hence the increase in the value of the call option exceeds the increase in the value of the put option, resulting in a net decrease in the value of the Facility.

The second stage of the analysis involves an examination of the conditions under which the policyholder would choose to sell via the Facility rather than on-market. Table 3 details the difference between the expected payoffs from these alternatives, whilst figure 3 provides a diagrammatic representation of panel B in table 3. Figure 3 indicates that a policyholder would always elect to sell through the Facility rather than on-market, if their best estimate of [P.sub.0] was less than or equal to $16. Similarly, if the policyholder's best estimate of [P.sub.0] was $18 or more, they would always elect to sell on-market. The decision made by investors whose best estimate of [P.sub.0] is less than or equal to $16 or greater than $18, is unchanged by the level of uncertainty associated with their estimate. In order to ascertain whether the level of uncertainty associated with the estimate of [P.sub.0] may affect the decision made by policyholders, values for [P.sub.0] between $16 and $18 are considered.

Table 3 Simulation Results: Facility Value(*) Less Estimated Share Value

                      Panel A: [[Sigma].sub.2]=0%

[P.sub.0]         $11     $12     $13     $14     $15
[[Sigma].sub.1]

0%                5.00   4.00    3.00    2.00    1.00
10%               5.00   4.00    3.00    2.03    1.12
20%               5.01   4.05    3.11    2.22    1.38
30%               5.09   4.16    3.27    2.40    1.57
40%               5.18   4.28    3.40    2.53    1.68
50%               5.27   4.37    3.49    2.61    1.74
60%               5.34   4.44    3.54    2.65    1.77

                      Panel B: [[Sigma].sub.2]=15%

[P.sub.0]         $11     $12     $13     $14     $15
[[Sigma].sub.1]

0%                5.00   4.00    3.00    2.00    1.00
10%               5.00   4.00    3.00    2.03    1.12
20%               5.01   4.04    3.11    2.22    1.38
30%               5.09   4.16    3.27    2.40    1.57
40%               5.18   4.28    3.40    2.53    1.68
50%               5.27   4.37    3.49    2.61    1.74
60%               5.33   4.44    3.54    2.65    1.77

                      Panel C: [[Sigma].sub.2]=30%

[P.sub.0]         $11     $12     $13     $14     $15
[[Sigma].sub.1]

0%                5.00   4.00    3.00    2.00    1.00
10%               5.00   4.00    3.01    2.03    1.13
20%               5.02   4.04    3.11    2.22    1.38
30%               5.09   4.16    3.27    2.41    1.57
40%               5.19   4.28    3.40    2.53    1.68
50%               5.27   4.37    3.49    2.61    1.74
60%               5.34   4.43    3.54    2.65    1.77

                       Panel A: [[Sigma].sub.2]=0%


[P.sub.0]         $16     $17     $18     $19     $20
[[Sigma].sub.1]

0%                0.00   -0.50   -1.00   -1.50   -2.00
10%               0.32   -0.36   -0.95   -1.50   -2.06
20%               0.60   -0.14   -0.85   -1.55   -2.25
30%               0.76   -0.03   -0.82   -1.60   -2.39
40%               0.84    0.01   -0.82   -1.65   -2.49
50%               0.88    0.02   -0.84   -1.71   -2.57
60%               0.89    0.01   -0.87   -1.76   -2.64

                      Panel B: [[Sigma].sub.2]=15%

[P.sub.0]         $16     $17     $18     $19     $20
[[Sigma].sub.1]

0%                0.03   -0.50   -1.00   -1.50   -2.00
10%               0.32   -0.36   -0.95   -1.51   -2.06
20%               0.60   -0.14   -0.85   -1.55   -2.25
30%               0.76   -0.03   -0.82   -1.60   -2.39
40%               0.84    0.01   -0.82   -1.65   -2.49
50%               0.88    2.00   -0.84   -1.71   -2.57
60%               0.89    0.01   -0.87   -1.76   -2.64

                      Panel C: [[Sigma].sub.2]=30%

[P.sub.0]         $16     $17     $18     $19     $20
[[Sigma].sub.1]

0%                0.06   -0.50   -1.00   -1.50   -2.00
10%               0.33   -0.36   -0.95   -1.51   -2.06
20%               0.60   -0.14   -0.85   -1.55   -2.25
30%               0.76   -0.03   -0.82   -1.60   -2.39
40%               0.84    0.01   -0.82   -1.65   -2.49
50%               0.88    0.02   -0.84   -1.71   -2.57
60%               0.89    0.01   -0.87   -1.76   -2.64

Note: (*) = The Facility values were derived using Monte Carlo simulation. For each value, 100 000 series were used. The antithetic variance technique was used to reduce the variance of the simulation results;

[[Sigma].sub.2] = the annualised standard deviation of AMP share returns in the five-day post-listing period;

[P.sub.0] = an estimate of the initial market price of the AMP share; and

[[Sigma].sub.1] = the standard deviation of the estimate of the initial market price of the AMP share.

[Figure 3 ILLUSTRATION OMITTED]

Table 4 and figure 4 demonstrate that for values of [P.sub.0] equal to or greater than $17.10, policyholders would always choose to sell on-market rather than through the Facility. For values of [P.sub.0] between $16.20 and $17, the decision made by policyholders would depend upon the level of uncertainty associated with their estimate of [P.sub.0]. For this range of values of [P.sub.0], as [[Sigma].sub.1] increases from zero there is initially a corresponding increase in the value of the put option component of the Facility. As [P.sub.0] increases, however, the increase in the value of the call option component that results from high levels of [[Sigma].sub.1], outweighs the increase in the value of the put option component. Hence, we note in both table 4 and figure 4 that the value of the Facility starts to decrease for high levels of [[Sigma].sub.1] results.

Table 4

Simulation Results: Facility Value(*) Less Estimated Share Value

                              [[Sigma].sub.2]=15%

[P.sub.0]         16.00   16.20   16.40   16.60   16.80   17.00
[[Sigma].sub.1]

0%                0.03    -0.09   -0.20   -0.30   -0.40   -0.50
10%               0.32     0.18    0.04   -0.10   -0.23   -0.36
20%               0.60     0.45    0.30    0.15    0.01   -0.14
30%               0.76     0.60    0.44    0.28    0.13   -0.03
40%               0.84     0.68    0.51    0.34    0.18    0.01
50%               0.88     0.71    0.53    0.36    0.19    0.02
60%               0.89     0.72    0.54    0.36    0.19    0.01

                           [[Sigma].sub.2]=15%

[P.sub.0]         17.20   17.40   17.60   17.80   18.00
[[Sigma].sub.1]

0%                -0.60   -0.70   -0.80   -0.90   -1.00
10%               -0.48   -0.60   -0.72   -0.84   -0.95
20%               -0.28   -0.42   -0.57   -0.71   -0.85
30%               -0.19   -0.35   -0.50   -0.66   -0.82
40%               -0.16   -0.32   -0.49   -0.66   -0.82
50%               -0.15   -0.33   -0.50   -0.67   -0.84
60%               -0.17   -0.34   -0.52   -0.70   -0.87

Note: (*) The Facility values were derived using Monte Carlo simulation. For each value, 100 000 series were used. The antithetic variance technique was used to reduce the variance of the simulation results;

[[Sigma].sub.2] = the annualised standard deviation of AMP share returns in the five-day post-listing period;

[p.sub.0] = an estimate of the initial market price of the AMP share; and

[[Sigma].sub.1] = the standard deviation of the estimate of the initial market price of the AMP share.

[Figure 4 ILLUSTRATION OMITTED]

5. What Occurred after 3 June 19987

By 5:00 pm on 3 June 1998, 200,000 of approximately 1.2 million shareholders, had informed AMP of their desire to sell a combined total of 149 million shares through the Facility. A further 375,000 policyholders elected to purchase an additional $1,000 worth of shares through the Facility.(7) A Base Price of $16 was announced by the company on 14 June 1998; the day before listing. AMP shares were listed for trading at noon on 15 June 1998 with the opening trade taking place at $35.998.(8) During the first day's trading, the highest price paid was $45, the lowest was $21.80 and the last trade took place at a price of $23 per share. In total there were 16,013 transactions in AMP shares at an average price of $24.75 for an average parcel of 2,234 shares. At the end of the first five days of trading, the volume-weighted average price paid for an AMP share was $21.93, suggesting that the Facility price would be approximately $18.97. However, page 15 of the prospectus contained a clause that allowed AMP to `withdraw, cancel or modify the Facility ...'. AMP exercised this right and declared that in calculating the five-day volume weighted average price, it would ignore the first ten minutes of trading, during which shares traded at a volume-weighted average price of $35.988, as trades during this period `did not reflect a normal market in its shares'.(9) After excluding these trades, the Facility price announced on 21 June 1998 was $18.706.

6. Conclusion

The Facility employed by AMP as part of its demutualisation comprised a collar with Asian options. This Facility would appear to have been priced such that policyholders would have preferred to sell through the Facility if their best estimate of the initial price for AMP shares was $16 or less. Similarly, if the policyholder's best estimate of the initial market price was greater than or equal to $17.10, there is a clear preference to sell on-market. Where the policyholders' estimate of the initial market price for AMP shares was between $16.10 and $17, their decision would be dependent upon the level of uncertainty associated with their estimate. Companies moving towards demutualisation need to recognise that disclosure of information during the demutualisation process may affect the proportion of shareholders taking up a Facility-type alternative.

(Date of receipt of final transcript: April, 2000. Accepted by Stephen Gray, Area Editor)

(1) For a discussion of the way in which a sell-financing portfolio consisting of investments in the underlying asset and risk-free bonds may be established to replicate the payoff from an Asian option see Ritchken, Sankarasubramanian and Vijh (1990, p. 1203 & 1993).

(2.) As the five-day post-listing period is divided into 1000 intervals, At is set at:

1/1000 x 5/365 = 1.3699 x [10.sup.-5]

(3) For a discussion of the antithetic Monte Carlo method, see Boyle (1977) and Rubinstein (1986).

(4) For ease of illustration, this paper will compare the Estimated Facility Payoff with the estimated initial market price, without allowing for the difference in time value associated with the receipt of the proceeds from the Facility and the sale on-market. Assuming a risk-free rate of return of 5% pa, this will overstate the relative value of the facility by approximately 0.07%.

(5.) For an example of such an offer, see the advertisement placed by BT Private Stockbroking in The Australian Financial Review, 2 June 1998, p 9.

(6.) Values of 0% pa and 10% pa were also used and the results wore virtually identical.

References

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(7.) Hoyle, S. and M. Carr, `AMP: Analysts query `low' $16 price', The Australian Financial Review, 15 June 1998, p. 21.

(8.) Information relating to the trading history of AMP shares in the post-listing period was obtained from the Bridge DFS IRESS database.

(9.) Hoyle, S., `As the dust settles, a fair price for all', The Australian Financial Review, 22 June 1998, p. 23.

Stephen A. Easton([dagger])

Sean M. Pinder([dagger])

([dagger]) Department of Accounting and Finance, University of Newcastle, Callaghan, NSW 2308. Email: [e-mail]

We are grateful to the two anonymous referees, seminar participants at the Australian Graduate School of Management, Macquarie University, Monash University and the University of Melbourne and conference participants at the 1999 British Accounting Association Annual Conference at the University of Glasgow for their helpful comments.