# Lack of diversification and the value of Maori fisheries assets.

1. Introduction

The year 1992 was a crucial one in New Zealand's recent history, as it was the year when the New Zealand Crown ('the Crown') began preparing a landmark settlement with Maori tribes ('iwi') over New Zealand's fisheries' assets. The settlement was historic in that it was the first between the two parties that affected all iwi (Waitangi Tribunal, 1992). The settlement was awarded to redress historic Treaty of Waitangi breaches relating to iwi's right to New Zealand fisheries. It began with the Crown's purchase of 50% of a company called Sealord Limited, but this investment represents only a portion of the settlement. Iwi were also to receive a substantial amount of fishing quota and other assets (Te Ohu Kaimoana, 2008).

Fishing for iwi is regarded as taonga. (1) The cultural significance of fishing has been recognised as part of the settlement. This was achieved by only allowing AFL sharese awarded to iwi to be owned by, and sold between, mandated iwi. Despite the lengths to which both the Crown and iwi went to arrive at a fair and cost effective settlement, this limitation on sale does result in a significant cost for iwi. The cost arises due to the widely understood notion that a rational, risk-averse investor requires a premium when their ability to diversify freely is reduced (Garvey, 2001).

If iwi added the fisheries assets to a well-diversified portfolio, the expected return calculated using the classical Capital Asset Pricing Model ('CAPM'), developed by Sharpe (1964) and Lintner (1965), would adequately compensate iwi for bearing solely market risk. The fisheries assets' value for iwi would then be equal to the fair market value) Fair market value provides a comparison in this scenario as it represents the value iwi would realise if they were able to sell their fisheries assets to investors in the wider investment community. Our analysis is founded on the notion that iwi, on mass, prior to receiving the fisheries assets, did not hold a well-diversified portfolio. By not holding a well-diversified portfolio, iwi are left exposed to all, or a component of, the fisheries assets' idiosyncratic risk. The idiosyncratic risk results in inefficient risk-bearing on the iwi's part, which means they must require a higher expected return than suggested by the CAPM and will discount the value of the fisheries assets below fair market value (Brickley & Dark, 1987).

Meulbroek (2001) addresses this restriction of the CAPM by developing a model, known as the opportunity cost approach, which estimates the expected return on an asset where limits exist on an individual's ability to diversify. In addition, the opportunity cost approach allows for estimation of the difference between the fair market value of an asset and the value a sub-optimally diversified investor places on the same asset.

The opportunity cost approach suggests that an undiversified investor requires a return that is as great as they would realise by leveraging up the market portfolio to achieve the same level of risk as their undiversified asset carries (Meulbroek, 2001). It follows that the required return for an undiversified investor is that which makes them indifferent between allocating their funds in the conventional Tobin (1958) fashion between the market portfolio and the risk-free rate or the undiversified asset. Put another way, an undiversified investor requires the same Sharpe (1994) ratio (4) from their undiversified asset as the market portfolio.

This methodology can be applied to the situation confronting iwi. Using Meulbroek's opportunity cost approach, we estimate the expected return on fisheries assets for iwi and the corresponding discount they place on the fisheries' assets relative to fair market value. Any discount below fair market value represents value lost on the settlement due to the restrictive sale condition. To illustrate the economic significance of this discount, assume a mandated iwi organisation wishes to sell their shares. If the purchaser must be another mandated iwi organisation, the purchaser experiences the same diversification limitations as the seller, and hence they will not be willing to pay the fair market value for the fisheries assets. This results in an economic loss in value for the selling iwi. (5) In this analysis, we make no attempt to adjust for the cultural significance of the fisheries assets in the valuation.

To quantify the extent of the value loss under Meulbroek's (2001) approach requires estimating the risk free rate, market risk premium, the systematic risk of the equity interest in fisheries assets, and total risk metrics. We provide illustrations of the value loss, based on our estimates and assumptions of the proportion of iwi wealth invested in 'restricted' fisheries assets. For iwi who have one quarter of their wealth so invested, we estimate that they would value their assets at between 70% and 84% of 'fair value', depending on what assumptions are made about the market risk premium and growth in future cash flows from these assets. Consequently (in this case) up to 30% of the settlement value is lost if mandated iwi are restricted to sell among themselves.

Section 2 details the background behind the fisheries settlement and the motivation for this paper. Section 3 presents a short literature review relating to the value implications of undiversified investments. Section 4 provides a description of the methodology employed to estimate the value lost for iwi through restricting their ability to diversify freely, section 5 provides parameter estimates, and section 6 presents the results. Section 7 provides a brief discussion of the results.

2. Background and motivation

Europeans began settling extensively in New Zealand during the 1830s. According to King (2003), fears of 'permanent anarchy' and 'depopulation as a result of tribal wars' (6) led to the British Government despatching William Hobson with instructions to take the constitutional steps necessary to establish a British colony. The result was a historic document between the Europeans and Maori called the Treaty of Waitangi (hereafter referred to as 'the Treaty'). The Treaty itself is written in both English and Maori and was supposed to represent the wishes of the British Crown and approximately 540 Maori rangatira (chiefs). From a British perspective, the Treaty was designed to establish British 'Sovereignty' in New Zealand. In return, the Queen (Victoria) guaranteed to Maori 'the full exclusive and undisturbed possession of their Lands and Estates Forests Fisheries and other properties ... so long as it is their wish and desire to retain the same in their possession.'

In the decades following the signing of the Treaty, fisheries in New Zealand evolved to become a prosperous and valuable national asset. Under the Treaty, the ownership rights of these fisheries vested with Maori. In the mid-1980s, a New Zealand Court ruled that the Crown had not done enough to protect Maori fishing rights as specified under the Treaty (Aotearoa Fisheries Limited (AFL), 2008). Following this decision, Maori were awarded a settlement of substantial value, now deemed to be worth about $750 million, $150 million of which was used to purchase a 50% holding in Sealord Limited (Hodgson, 2003; Waitangi Tribunal, 1992). Maori were also promised an increase to their ongoing allocation of fishing quota under the Quota Management System ('QMS'). The settlement awarded to iwi represented full consideration for all historical fishing claims. In return, Maori agreed:

to discontinue their current court actions relating to fisheries and to take no more proceedings, to endorse the quota management system and to support legislation to give effect to the settlement; and that this tribunal shall have no further say on commercial fishing matters. (Waitangi Tribunal, 1992, p. 1)

Beginning in 1992, coinciding with the purchase of Sealord, what turned out to be a 12-year project was undertaken to decide how the settlement was to be divided equitably among iwi. Its close was marked with the passing of The Maori Fisheries Act 2004 ('the Act'). Among other things, the resulting statute established the holding company AFL and its governing body, Te Ohu Kaimoana ('TOKM'). AFL has two classes of shares, voting shares and income shares. All voting shares of AFL are held by TOKM to give them sole discretion in appointing the directors of AFL. The Act also stipulates that 20% of the income shares of AFL are to be owned by TOKM with the remaining 80% to be held by local iwi. The income shares are divided among iwi according to the iwi's population (Te Ohu Kaimoana, 2008). In addition, iwi will continue to receive their fishing quota under the QMS. Iwi must satisfy certain criteria under the Act before they receive their fisheries asset entitlement. The AFL shares may only be sold to other mandated iwi and the fishing quota may only be sold after it has been held for a minimum of two years.

Despite the enactment taking 12 years to come to fruition, consequences for iwi remain. The sale restriction imposed under the Act results in at least some of the iwi fisheries assets being highly illiquid and potentially leaves iwi with a sub-optimally diversified investment portfolio. There is therefore an opportunity cost for iwi in holding these assets. If iwi retain the fisheries assets, they must require a higher expected return than a well diversified investor to compensate for bearing unnecessary idiosyncratic risk (Brickley & Dark, 1987).

Fisheries assets are often seen as risky. However, much of the risk associated with fishing is idiosyncratic. For example, the risk surrounding the availability of fish to catch, and the weather, is specific to one firm or one time, and can be diversified away by investors, leaving them to bear solely the market risk. Fisheries assets have low measures of systematic risk, or beta within the context of the CAPM. This results in fisheries assets having high total risk, comprising low market risk and high idiosyncratic risk.

Although this is a generalisation of a wider population of fisheries assets, it is expected to be no different for the iwi's fisheries assets. The high degree of idiosyncratic risk associated with fishing makes for an interesting application of Meulbroek's opportunity cost approach.

3. Literature review

The CAPM is arguably the most widely used model in finance. The model assumes inter alia that there are no restrictions on the assets that investors can buy and sell, and consequently the expected return of an asset reflects its contribution to the risk of the market portfolio. This is captured by the beta which measures the relative risk associated with holding an asset. There are times this conclusion appears unreasonable. Examples include executives who are locked into share ownership in the companies that employ them, employees whose pension funds invest in the shares of the company that employs them, venture capitalist partnerships, and owner-manager businesses. In the context of fisheries, as not all iwi can freely diversify, the CAPM would understate their expected return. As a result, there is a need for a model that could take into account the lack of diversification in determining the expected return.

This paper uses the same approach as in Meulbroek (2001). She points out that executive stock options have become the main tool in compensation committees' repertoire to align the interests of owners and managers. The use of equity based compensation, which cannot be divested or hedged against, leads to the executives being overly exposed to the affairs of the firm by having both their human capital and a portion of financial capital tied up in the firm. Consequently, there is a deadweight cost. This is represented by their stock options being worth less than the fair market value of the stock option.

Meulbroek (2001) takes this notion of the executive being overly exposed in their firm and uses it to calculate the true cost of awarding stock options to executives. By using the Sharpe ratio, Meulbroek (2001) is able to calculate the required return on an executive stock option that would make a fully undiversified executive indifferent between holding the stock option or the market portfolio levered up to achieve the same level of total risk. She concludes that the required returns on stock options based on the CAPM for a well-diversified investor and the required returns for fully or partly undiversified executives, based on the Sharpe ratio, differ substantially. The undiversified executive values the stock option at considerably less than a well-diversified investor due to the excess risk the undiversified executive is bearing.

Kerins, Smith and Smith (2004) calculate the cost of capital for venture capitalists and entrepreneurs. Their paper was motivated by the fact that an investor typically devotes large amounts of human and monetary capital into a venture, leaving them exposed to the total risk of the venture. Assuming various levels of wealth invested in a given venture, the authors calculate the required return for their partial diversification. They find that the required return for an undiversified venture capitalist or entrepreneur is substantially higher than for a well-diversified investor, and estimate, using conservative parameters, that this required return can fall within the range of two to four times higher. These results also clearly illustrate a positive relationship between the portion of the investor's wealth invested in the venture and the required return they demand. Accordingly, as the venture capitalist or entrepreneur becomes more diversified, their required return diminishes.

The same methodology can be applied to cooperative structures, whereby (for example) suppliers own the processing company that they supply. In New Zealand, this applies to the supply of liquid milk whereby dairy farmers own their processing companies, the largest one of which is Fonterra, New Zealand's largest corporate enterprise. The shares in Fonterra are owned by the farmers, proportional to the kilograms of milksolids (7) they provide to the firm. Implicitly, the farmers have an associated investment in Fonterra (Maher & Emanuel, 2005). In the past, the shares in Fonterra have not been able to be sold (or redeemed) and must be held by the farmer for the duration they wish to sell milksolids to Fonterra. This resulting lack of diversification is the focus of the paper by Maher and Emanuel (2005). They also use the work of Meulbroek (2001, 2005). Using variations to the market risk premium, the authors estimate the value loss to a fully undiversified farmer with a 20 year investment horizon to lie between 53% and 63% of the fair market value of their investment in Fonterra.

If investors are limited in their ability to diversify, arguably the CAPM understates investors' expected return. However Meulbroek's (2001) approach is not without criticism. Investors would not necessarily bear the same level of risk as an undiversified asset, even if their asset allowed them to be well diversified. In other words, investors who can diversify freely would not likely lever up the market portfolio to carry the same total risk as an undiversifiable asset. To assess the choices investors would actually make, it is important to consider an investor's utility function.

Garvey (2001) incorporates a typical investor's utility function to test the reasonableness of the opportunity cost approach. He finds that if investors are forced to allocate their remaining wealth in the market portfolio, the opportunity cost approach understates the required return on the undiversifiable asset. Fortunately, it is more reasonable to assume that investors can decide how to allocate their liquid wealth. Under this scenario, the opportunity cost approach provides a reasonable estimate of the required return on the undiversifiable asset. In addition, for very low levels of risk aversion, the opportunity cost approach can overstate the required return on the undiversifiable asset. However, the significance of this finding is minimal as this deviation only occurs at inconceivably low levels of risk aversion. Garvey (2001) therefore concludes that the opportunity cost approach provides a reasonable estimate of the required return on an undiversifiable asset without requiring prior knowledge about the individual investor's risk aversion.

4. Methodology

The analysis in this paper considers two broad cases. The first is where iwi only holds the fisheries assets, which means that iwi is 'fully undiversified'. The second is where iwi holds multiple assets, which we capture by assigning a weight to the fisheries asset, and the remaining weight to a market portfolio.

Following Meulbroek (2001) the expected return that compensates an undiversified investor will be given by the capital market line in equation (1).

[E.sup.u.sub.a] = [r.sub.f] + [[sigma].sub.a]/[[sigma].sub.m] ([E.sub.m] - [r.sub.f]) (1)

where [E.sup.u.sub.a] is the expected return on fisheries assets for fully undiversified iwi, [[sigma].sub.a] is the standard deviation of returns on fisheries assets, [[sigma].sub.m] is the standard deviation of returns on the market, [r.sub.f] the risk-free rate and [E.sub.m] is the expected market return.

On the other hand, a well-diversified investor will expect a return given by the CAPM. This is shown in equation (2).

[E.sub.a] = [r.sub.f] + [beta]([E.sub.m] - [r.sub.f]) (2)

where [E.sub.a] is the expected return on fisheries assets for a well diversified investor, and [beta] is the levered beta of the investment.

Figure 1 provides an illustration. The two expected rates of return can be used in a valuation model to create value ratios, which give the relative difference in value. This will be dealt with shortly.

In the situation where an investor is partially diversified, the investor will also require a return from the fisheries asset such that the portfolio return is equal to the return given by the capital market line, for the portfolio's degree of risk.

The portfolio risk is given by equation (3) below.

[[sigma].sup.2.sub.p] = [w.sup.2][[sigma].sup.2.sub.a] + [(1 - w).sup.2][[sigma].sup.2.sub.m] + 2w(1 - w) [[sigma].sub.am] (3)

where [[sigma].sup.2.sub.p] is the variance of the returns from the iwi's investment portfolio, w is the proportion of an iwi's investment portfolio held in fisheries assets, 1 - w is the remaining proportion of an iwi's investment portfolio, which is assumed to be held in the market portfolio, and [[sigma].sub.am] is the covariance between the returns on fisheries assets and the market.

[FIGURE 1 OMITTED]

The covariance between returns on fisheries assets and the market is given by

[[sigma].sub.am] = [[beta].sup.2.sub.m] (4)

Based on equation (3) we can now estimate the capital market line expected return for the degree of risk of the iwi's portfolio, [[sigma].sup.2.sub.p] . This is shown in equation (5) below.

[E.sup.*.sub.p] = [r.sub.f] + [[sigma].sub.p]/[[sigma].sub.m] ([E.sub.m] - [r.sub.f]) (5) Gm

Iwi will (expect to) receive returns from the proportion (w) that they have invested in fisheries, and the remainder (1 - w) that they have invested in the market portfolio. The expected return will need to be adequate to provide for the risk involved, and we know that this must be [E.sup.*.sub.p] in equation (5) above. This expected return will come from the market portfolio and an adequate return from the fisheries investment, which is [E.sup.*.sub.a]. This is shown in equation (6) below.

[E.sup.*.sub.p] = w[E.sup.*.sub.a] + (1 - w)[E.sub.m] (6)

If we set equation (5) equal to equation (6) we get

[r.sub.f] = [[sigma].sub.p]/[[sigma].sub.m] ([E.sub.m] - [r.sub.f]) = w[E.sup.*.sub.a] + (1 - w)[E.sub.m] (7)

Rearranging equation (7) gives

[E.sup.*.sub.a] = 1/w [[r.sub.f] + ([E.sub.m] - [r.sub.f]) [[sigma].sub.p]/[[sigma].sub.m] - (1 - w)[E.sub.m]] (8)

The intuition is that the required return on an investment in fisheries needs to be increased, the less well-diversified are iwi. A 'fully diversified' iwi will still hold an investment in fisheries assets but it would be relative to the market values of all investments as fisheries assets will be represented in the market portfolio. On the other hand if w is one, equation (8) gives the same expected return as equation (1).

The final step is to quantify the value iwi place on their investment in fisheries assets given the higher expected return they demand. To do this, value ratios are created, and to create value ratios a valuation model must be invoked. A dividend valuation model with constant growth is used. (8) The model is shown in equation (9) below.

V = [Div.sub.1]/(E - g) (9)

where E equals [E.sup.*.sub.a] if the investor is undiversified to some degree ([E.sup.u.sub.a] if fully undiversified), or [E.sub.a] (the expected return from the CAPM) if the investor is fully diversified, g is the expected annual growth rate in dividends (Div). V is equal to [V.sup.u.sub.a0] if the investor is fully or partially undiversified, and [V.sub.a0] is the 'fair market value' of the investment.

We can now calculate a value ratio, which is

[V.sup.u.sub.a0]/[V.sub.a0] = [E.sub.a] - g/[E.sup.*.sub.a] - g (10)

which gives a value that is a percentage of fair value, and this reflects the proportionate value that an undiversified (or partially undiversified) investor would assign to the shares, conditional on the degree to which that investor is not fully diversified. To create value ratios we need to assume that [Div.sub.1] and g are the same in the different scenarios. (9)

5. An illustration--required estimates

We use the only fisheries company listed on the New Zealand Stock Exchange, Sanford Limited ('Sanford'), as the benchmark company. Sanford has similar (10) operations to that of AFL and is devoted entirely to the harvesting, farming, processing, storage and marketing of seafood and aquaculture products. Sanford is allocated fishing quota, as are iwi, under New Zealand's quota management system. In terms of size, Sanford had (at the time of this research) a market capitalisation and total assets of roughly $400 million and $700 million respectively (NZX, 2008; Sanford Limited, 2007). AFL has no computable market (11) capitalisation but had total assets of around $400 million (Aotearoa Fisheries Limited, 2007).

The beta of Sanford's shares was estimated to be 0.65. (12) The levered beta needs to be un-levered using Sanford's debt-to-equity ratio. The debt-to-equity ratio of Sanford is 0.2913 based on Sanford's accounts at 30 September 2007.

The un-levered beta calculation is given by

[[beta].sub.U] = [[beta].sub.L]/[1 + Debt/Equity (1 - [T.sup.*])] (11)

where [[beta].sub.U] is the un-levered beta of Sanford, [[beta].sub.L] is the levered beta of Sanford, Debt/Equity is the actual debt-to-equity ratio of Sanford and [T.sup.*] is the imputation adjusted tax rate, which in New Zealand with its imputation tax system is assumed to equal zero. We estimate the un-levered beta of Sanford to be 0.50, and this becomes the proxy for the systematic risk of iwis' fisheries assets.

In order to estimate the risk-free rate in New Zealand, we take the average 5-year government bond rate. The 5-year yield is used to better reflect a long investment horizon of iwi holding their fisheries assets. Using this methodology, the average risk-free rate (at the time of this research) equates to approximately 6% per annum. (14)

Dimson, Marsh and Staunton (2006) study the market risk premium globally using 106 years of data from 17 countries. The authors report a geometric (arithmetic) worldwide equity market risk premium of 4 (5)%. These authors find this value is lower than widely accepted as the market risk premium is non-stationary over time. Further, historical market risk premiums (estimated using the methods of Dimson et al., 2006) overstate future market risk premiums due to historical returns being inflated by past re-pricings prompted by reductions in the market risk premium. There is also the confounding nature of a survivorship bias, which is likely to put upward pressure on historical market risk premiums. We therefore employ three different market risk premiums: 3%, 4% and 5%.

The analysis also requires estimates of the total volatility of the expected returns from fisheries assets, and the total volatility of the expected market return. We use the volatility of Sanford's share returns (adjusted for leverage) as an estimate of the former, and a historical estimate of share market index volatility as an estimate of the latter, calculated over the same period as Sanford's beta coefficient. Given the beta coefficient and these two standard deviations we can also compute the covariance [[sigma].sub.am].

6. Results

As mentioned in the previous section, three different market risk premia are used leading to three different CAPM and CML returns. The results are summarised in Table 1 for the case where w = 1. (15)

We use four weights for w in order to give a representative coverage of possible proportions of fisheries assets that a typical iwi may hold. The first and most obvious is that whereby iwi hold solely fisheries assets and is depicted by w equal to 1. The remaining three weights are 0.75, 0.50 and 0.25. For example, w equal to 0.50 implies 50% of iwi's investment portfolio is held in fisheries assets and the remaining 50% comprises the market portfolio.

Using the four w values, the results of equation (3) are contained in Panel A of Table 2.

From Table 2, when iwi hold solely fisheries assets, given by w equals 1, their portfolio standard deviation is that of the fisheries asset proxy. As the proportion of wealth held in fisheries assets declines relative to that held in a well diversified portfolio, the standard deviation of the total investment portfolio converges to that of the market.

From Table 2, Panel B we can see that, when w equals 1, the expected return for iwi on fisheries assets under the three market risk premiums is the same as was computed using the CML methodology from equation (1). Consistent with intuition, when the proportion of wealth held in fisheries assets declines so does the capital market line expected return, as the portfolio becomes less risky. When w equals 0 the expected return on the fisheries assets is the CAPM return. This is illustrated in Figure 2 for a market risk premium of 4%. The distance between the two lines gives the additional return required from the investment in fisheries. This is not the same as the difference between the CML return (for the portfolio level of risk) and the CAPM return. For example the difference at w = 0.50 between the CML required return and the CAPM required return is 1.79%. (16) This means that an additional 3.57% (1.79%/0.50) is required from the investment and it is these distances that are given in Figure 2.

Table 3 shows the relative values, conditional on assumptions about annual growth rates in dividends. The growth rates chosen are 0% to 3% per annum. It is difficult to determine across iwi what the extent of diversification is, although the annual accounts of the trading arms of some iwi are in the public domain (examples are Ngai Tahu and Tainui). (17) If we assume that (say) 25% of an iwi's assets are locked into fisheries, and the market risk premium is 4%, that the anticipated growth rate is 2% per annum and all the other assumptions hold and the estimates of the parameters are reasonable, then we can conclude that the value assigned to fisheries assets would be roughly 76% of fair market value. Under these assumptions, iwi collectively value the $750 million fisheries settlement at $573 million.

As can be seen from Table 3, holding w constant, a higher market risk premium leads to greater discrepancy between the two expected returns, which leads to lower value ratios for iwi, and, as the anticipated growth rate in dividends increases, the value discrepancy also increases.

[FIGURE 2 OMITTED]

7. Discussion and conclusion

If indeed the fisheries settlement has a fair market value of $750 million as reported, the value ratios in Table 3 illustrate that a portion of this settlement's value is lost to the New Zealand economy and more importantly, iwi.

There is a considerable divergence between an iwi's and a well-diversified investor's expected returns. Such divergence drives value losses for iwi. If this value is to be captured, iwi would need to be allowed to sell the fisheries assets to investors outside mandated iwi who will not discount the price of the fisheries assets due to diversification restrictions.

We have looked at one aspect of how the fisheries settlement has been structured and the implications this has had on the value for iwi. Practitioners and academics widely use and accept the CAPM. The model assumes the asset for which expected returns are being estimated is the market portfolio. Although some iwi may in fact be well diversified, it is possible that others are not. Consequently, if undiversified iwi hold onto their fisheries assets they were allocated under the Act, their required return is greater than that estimated by the CAPM due to idiosyncratic risk they must bear. Meulbroek (2001) argues their expected return is a point on the capital market line (as in equations (1) and (5)).

As expected, this research clearly shows that the disparity between the CAPM and CML expected returns is substantial. This disparity increases as the level of diversification decreases or a higher assumed market risk premium is used.

The Crown has committed a considerable sum of taxpayers' money to the fisheries settlement. Through restricting who can and cannot own the fisheries assets, a portion of the settlement's value is lost. Obviously this argument is dependent on invoking the capital market line, and the CAPM that is derived from it. In turn, this means invoking the assumptions of perfect capital markets and so on, which lie behind the derivations. No consideration is given of spiritual values associated with the ownership of fisheries assets. A response to this analysis from that perspective is that the analysis may be irrelevant. Nevertheless it should be understood.

Acknowledgements

The authors acknowledge the very helpful comments of three anonymous reviewers, and the editor.

DOI: 10.1080/00779951003614073

(Received 17 February 2009; final version received 4 September 2009)

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Notes

(1.) Taonga in Maori culture is regarded as a treasured thing, whether tangible or intangible. Such tangible examples include land, forestry and fisheries.

(2.) The motivation in this paper comes from the investment in Aotearoa Fisheries Limited, but by implication extends to other fisheries assets.

(3.) Fair market value is defined as "[t]he price at which an asset or service passes from a willing seller to a willing buyer. It is assumed that both the seller and buyer are rational and informed of any factors material to the transaction' (Scott & Stringfellow Inc, 2008).

(4.) The Sharpe ratio takes the (expected) return on the asset, subtracts the riskless rate, and divides the amount by the asset return's standard deviation.

(5.) As we show later in the paper, the extent of the loss in value is dependent on the level of diversification of an iwi's investment portfolio.

(6.) These terms were used by James Busby ('first British Resident in New Zealand') to the London Colonial Office. See King (2003, p. 155).

(7.) This is the solid content of the liquid milk supplied, and this is the basis on which payouts are made and shares are owned.

(8.) This is commonly called the Gordon growth model (Gordon, 1959).

(9.) In sum, we need to assume away any agency problems associated with different ownership, which may result in different internal operating strategies and behaviours.

(10.) Sanford is similar but not the same as AFL. For example Sanford is vertically integrated and fishes its own quota, rather than leasing the quota to other harvesters of fish. It is possible to get supplementary data on listed fishing companies from other countries. For example, there are fishing companies listed on the Australian, Japanese, Norwegian and Icelandic share markets. As the computational aspects of this paper are illustrative only, we have not used any of this supplementary information in this research.

(11.) The most recent annual report of Tainui Group Holdings Limited makes reference to a valuation of AFL 'as a whole'. A range of values is reported and the mid-point is $325 million. The most recent report (as at 30 June 2008) of Te Runanga-A-Iwi-O-Ngapuhi values their interest in AFL at $311.50 per share implying a total value of about $389 million, but this value is after taking into account restrictions on sale and inability of the investor to appoint directors. We do not use these valuations in this analysis, as the valuation reports are not in the public domain.

(12.) Using daily data over a two-year period prior to the valuation date.

(13.) This consists of $16.919m of bank overdraft and borrowings at call, and $130m of long term bank loans, divided by $504m of market value of equity.

(14.) This information is taken from Bloomberg Inc. Over the 2007-2008 period 5-year government stock yields vary from approximately 4.5% (end of 2008) to 7% (mid-2007). We have used 6% as an approximate (average) rate.

(15.) w = 1 assumes 100% of an iwi's wealth is invested in fisheries assets, or alternatively, iwi have no diversification.

(16.) The CAPM return with w = 0.50 is 9.01% and the CML required return is 10.79%. The additional portfolio return of 1.79% (rounded) needs to be loaded onto AFL's return in a setting where AFL is only half the portfolio. Hence the additional required return from AFL is 1.79%/0.50 = 3.57%.

(17.) Ngai Tabu for example is reasonably heavily invested in fishing (on our estimate between 20% and 25% of its assets are fisheries related). Ngapuhi appears to be heavily invested in fishing activity at June 2008--by our estimates about three-quarters of the trust's assets. Fourteen percent is represented by shares in AFL and 59% by quota.

Cameron Day (a) * and David Emanuel (b)

(a) Deloitte, Private Bag 115-033, Shortland Street, Auckland 1140, New Zealand; (b) Department of Accounting and Finance, The University of Auckland Business School, Private Bag 92019, Auckland 1142, New Zealand

* Corresponding author. Email: caday@deloitte.co.nz

The year 1992 was a crucial one in New Zealand's recent history, as it was the year when the New Zealand Crown ('the Crown') began preparing a landmark settlement with Maori tribes ('iwi') over New Zealand's fisheries' assets. The settlement was historic in that it was the first between the two parties that affected all iwi (Waitangi Tribunal, 1992). The settlement was awarded to redress historic Treaty of Waitangi breaches relating to iwi's right to New Zealand fisheries. It began with the Crown's purchase of 50% of a company called Sealord Limited, but this investment represents only a portion of the settlement. Iwi were also to receive a substantial amount of fishing quota and other assets (Te Ohu Kaimoana, 2008).

Fishing for iwi is regarded as taonga. (1) The cultural significance of fishing has been recognised as part of the settlement. This was achieved by only allowing AFL sharese awarded to iwi to be owned by, and sold between, mandated iwi. Despite the lengths to which both the Crown and iwi went to arrive at a fair and cost effective settlement, this limitation on sale does result in a significant cost for iwi. The cost arises due to the widely understood notion that a rational, risk-averse investor requires a premium when their ability to diversify freely is reduced (Garvey, 2001).

If iwi added the fisheries assets to a well-diversified portfolio, the expected return calculated using the classical Capital Asset Pricing Model ('CAPM'), developed by Sharpe (1964) and Lintner (1965), would adequately compensate iwi for bearing solely market risk. The fisheries assets' value for iwi would then be equal to the fair market value) Fair market value provides a comparison in this scenario as it represents the value iwi would realise if they were able to sell their fisheries assets to investors in the wider investment community. Our analysis is founded on the notion that iwi, on mass, prior to receiving the fisheries assets, did not hold a well-diversified portfolio. By not holding a well-diversified portfolio, iwi are left exposed to all, or a component of, the fisheries assets' idiosyncratic risk. The idiosyncratic risk results in inefficient risk-bearing on the iwi's part, which means they must require a higher expected return than suggested by the CAPM and will discount the value of the fisheries assets below fair market value (Brickley & Dark, 1987).

Meulbroek (2001) addresses this restriction of the CAPM by developing a model, known as the opportunity cost approach, which estimates the expected return on an asset where limits exist on an individual's ability to diversify. In addition, the opportunity cost approach allows for estimation of the difference between the fair market value of an asset and the value a sub-optimally diversified investor places on the same asset.

The opportunity cost approach suggests that an undiversified investor requires a return that is as great as they would realise by leveraging up the market portfolio to achieve the same level of risk as their undiversified asset carries (Meulbroek, 2001). It follows that the required return for an undiversified investor is that which makes them indifferent between allocating their funds in the conventional Tobin (1958) fashion between the market portfolio and the risk-free rate or the undiversified asset. Put another way, an undiversified investor requires the same Sharpe (1994) ratio (4) from their undiversified asset as the market portfolio.

This methodology can be applied to the situation confronting iwi. Using Meulbroek's opportunity cost approach, we estimate the expected return on fisheries assets for iwi and the corresponding discount they place on the fisheries' assets relative to fair market value. Any discount below fair market value represents value lost on the settlement due to the restrictive sale condition. To illustrate the economic significance of this discount, assume a mandated iwi organisation wishes to sell their shares. If the purchaser must be another mandated iwi organisation, the purchaser experiences the same diversification limitations as the seller, and hence they will not be willing to pay the fair market value for the fisheries assets. This results in an economic loss in value for the selling iwi. (5) In this analysis, we make no attempt to adjust for the cultural significance of the fisheries assets in the valuation.

To quantify the extent of the value loss under Meulbroek's (2001) approach requires estimating the risk free rate, market risk premium, the systematic risk of the equity interest in fisheries assets, and total risk metrics. We provide illustrations of the value loss, based on our estimates and assumptions of the proportion of iwi wealth invested in 'restricted' fisheries assets. For iwi who have one quarter of their wealth so invested, we estimate that they would value their assets at between 70% and 84% of 'fair value', depending on what assumptions are made about the market risk premium and growth in future cash flows from these assets. Consequently (in this case) up to 30% of the settlement value is lost if mandated iwi are restricted to sell among themselves.

Section 2 details the background behind the fisheries settlement and the motivation for this paper. Section 3 presents a short literature review relating to the value implications of undiversified investments. Section 4 provides a description of the methodology employed to estimate the value lost for iwi through restricting their ability to diversify freely, section 5 provides parameter estimates, and section 6 presents the results. Section 7 provides a brief discussion of the results.

2. Background and motivation

Europeans began settling extensively in New Zealand during the 1830s. According to King (2003), fears of 'permanent anarchy' and 'depopulation as a result of tribal wars' (6) led to the British Government despatching William Hobson with instructions to take the constitutional steps necessary to establish a British colony. The result was a historic document between the Europeans and Maori called the Treaty of Waitangi (hereafter referred to as 'the Treaty'). The Treaty itself is written in both English and Maori and was supposed to represent the wishes of the British Crown and approximately 540 Maori rangatira (chiefs). From a British perspective, the Treaty was designed to establish British 'Sovereignty' in New Zealand. In return, the Queen (Victoria) guaranteed to Maori 'the full exclusive and undisturbed possession of their Lands and Estates Forests Fisheries and other properties ... so long as it is their wish and desire to retain the same in their possession.'

In the decades following the signing of the Treaty, fisheries in New Zealand evolved to become a prosperous and valuable national asset. Under the Treaty, the ownership rights of these fisheries vested with Maori. In the mid-1980s, a New Zealand Court ruled that the Crown had not done enough to protect Maori fishing rights as specified under the Treaty (Aotearoa Fisheries Limited (AFL), 2008). Following this decision, Maori were awarded a settlement of substantial value, now deemed to be worth about $750 million, $150 million of which was used to purchase a 50% holding in Sealord Limited (Hodgson, 2003; Waitangi Tribunal, 1992). Maori were also promised an increase to their ongoing allocation of fishing quota under the Quota Management System ('QMS'). The settlement awarded to iwi represented full consideration for all historical fishing claims. In return, Maori agreed:

to discontinue their current court actions relating to fisheries and to take no more proceedings, to endorse the quota management system and to support legislation to give effect to the settlement; and that this tribunal shall have no further say on commercial fishing matters. (Waitangi Tribunal, 1992, p. 1)

Beginning in 1992, coinciding with the purchase of Sealord, what turned out to be a 12-year project was undertaken to decide how the settlement was to be divided equitably among iwi. Its close was marked with the passing of The Maori Fisheries Act 2004 ('the Act'). Among other things, the resulting statute established the holding company AFL and its governing body, Te Ohu Kaimoana ('TOKM'). AFL has two classes of shares, voting shares and income shares. All voting shares of AFL are held by TOKM to give them sole discretion in appointing the directors of AFL. The Act also stipulates that 20% of the income shares of AFL are to be owned by TOKM with the remaining 80% to be held by local iwi. The income shares are divided among iwi according to the iwi's population (Te Ohu Kaimoana, 2008). In addition, iwi will continue to receive their fishing quota under the QMS. Iwi must satisfy certain criteria under the Act before they receive their fisheries asset entitlement. The AFL shares may only be sold to other mandated iwi and the fishing quota may only be sold after it has been held for a minimum of two years.

Despite the enactment taking 12 years to come to fruition, consequences for iwi remain. The sale restriction imposed under the Act results in at least some of the iwi fisheries assets being highly illiquid and potentially leaves iwi with a sub-optimally diversified investment portfolio. There is therefore an opportunity cost for iwi in holding these assets. If iwi retain the fisheries assets, they must require a higher expected return than a well diversified investor to compensate for bearing unnecessary idiosyncratic risk (Brickley & Dark, 1987).

Fisheries assets are often seen as risky. However, much of the risk associated with fishing is idiosyncratic. For example, the risk surrounding the availability of fish to catch, and the weather, is specific to one firm or one time, and can be diversified away by investors, leaving them to bear solely the market risk. Fisheries assets have low measures of systematic risk, or beta within the context of the CAPM. This results in fisheries assets having high total risk, comprising low market risk and high idiosyncratic risk.

Although this is a generalisation of a wider population of fisheries assets, it is expected to be no different for the iwi's fisheries assets. The high degree of idiosyncratic risk associated with fishing makes for an interesting application of Meulbroek's opportunity cost approach.

3. Literature review

The CAPM is arguably the most widely used model in finance. The model assumes inter alia that there are no restrictions on the assets that investors can buy and sell, and consequently the expected return of an asset reflects its contribution to the risk of the market portfolio. This is captured by the beta which measures the relative risk associated with holding an asset. There are times this conclusion appears unreasonable. Examples include executives who are locked into share ownership in the companies that employ them, employees whose pension funds invest in the shares of the company that employs them, venture capitalist partnerships, and owner-manager businesses. In the context of fisheries, as not all iwi can freely diversify, the CAPM would understate their expected return. As a result, there is a need for a model that could take into account the lack of diversification in determining the expected return.

This paper uses the same approach as in Meulbroek (2001). She points out that executive stock options have become the main tool in compensation committees' repertoire to align the interests of owners and managers. The use of equity based compensation, which cannot be divested or hedged against, leads to the executives being overly exposed to the affairs of the firm by having both their human capital and a portion of financial capital tied up in the firm. Consequently, there is a deadweight cost. This is represented by their stock options being worth less than the fair market value of the stock option.

Meulbroek (2001) takes this notion of the executive being overly exposed in their firm and uses it to calculate the true cost of awarding stock options to executives. By using the Sharpe ratio, Meulbroek (2001) is able to calculate the required return on an executive stock option that would make a fully undiversified executive indifferent between holding the stock option or the market portfolio levered up to achieve the same level of total risk. She concludes that the required returns on stock options based on the CAPM for a well-diversified investor and the required returns for fully or partly undiversified executives, based on the Sharpe ratio, differ substantially. The undiversified executive values the stock option at considerably less than a well-diversified investor due to the excess risk the undiversified executive is bearing.

Kerins, Smith and Smith (2004) calculate the cost of capital for venture capitalists and entrepreneurs. Their paper was motivated by the fact that an investor typically devotes large amounts of human and monetary capital into a venture, leaving them exposed to the total risk of the venture. Assuming various levels of wealth invested in a given venture, the authors calculate the required return for their partial diversification. They find that the required return for an undiversified venture capitalist or entrepreneur is substantially higher than for a well-diversified investor, and estimate, using conservative parameters, that this required return can fall within the range of two to four times higher. These results also clearly illustrate a positive relationship between the portion of the investor's wealth invested in the venture and the required return they demand. Accordingly, as the venture capitalist or entrepreneur becomes more diversified, their required return diminishes.

The same methodology can be applied to cooperative structures, whereby (for example) suppliers own the processing company that they supply. In New Zealand, this applies to the supply of liquid milk whereby dairy farmers own their processing companies, the largest one of which is Fonterra, New Zealand's largest corporate enterprise. The shares in Fonterra are owned by the farmers, proportional to the kilograms of milksolids (7) they provide to the firm. Implicitly, the farmers have an associated investment in Fonterra (Maher & Emanuel, 2005). In the past, the shares in Fonterra have not been able to be sold (or redeemed) and must be held by the farmer for the duration they wish to sell milksolids to Fonterra. This resulting lack of diversification is the focus of the paper by Maher and Emanuel (2005). They also use the work of Meulbroek (2001, 2005). Using variations to the market risk premium, the authors estimate the value loss to a fully undiversified farmer with a 20 year investment horizon to lie between 53% and 63% of the fair market value of their investment in Fonterra.

If investors are limited in their ability to diversify, arguably the CAPM understates investors' expected return. However Meulbroek's (2001) approach is not without criticism. Investors would not necessarily bear the same level of risk as an undiversified asset, even if their asset allowed them to be well diversified. In other words, investors who can diversify freely would not likely lever up the market portfolio to carry the same total risk as an undiversifiable asset. To assess the choices investors would actually make, it is important to consider an investor's utility function.

Garvey (2001) incorporates a typical investor's utility function to test the reasonableness of the opportunity cost approach. He finds that if investors are forced to allocate their remaining wealth in the market portfolio, the opportunity cost approach understates the required return on the undiversifiable asset. Fortunately, it is more reasonable to assume that investors can decide how to allocate their liquid wealth. Under this scenario, the opportunity cost approach provides a reasonable estimate of the required return on the undiversifiable asset. In addition, for very low levels of risk aversion, the opportunity cost approach can overstate the required return on the undiversifiable asset. However, the significance of this finding is minimal as this deviation only occurs at inconceivably low levels of risk aversion. Garvey (2001) therefore concludes that the opportunity cost approach provides a reasonable estimate of the required return on an undiversifiable asset without requiring prior knowledge about the individual investor's risk aversion.

4. Methodology

The analysis in this paper considers two broad cases. The first is where iwi only holds the fisheries assets, which means that iwi is 'fully undiversified'. The second is where iwi holds multiple assets, which we capture by assigning a weight to the fisheries asset, and the remaining weight to a market portfolio.

Following Meulbroek (2001) the expected return that compensates an undiversified investor will be given by the capital market line in equation (1).

[E.sup.u.sub.a] = [r.sub.f] + [[sigma].sub.a]/[[sigma].sub.m] ([E.sub.m] - [r.sub.f]) (1)

where [E.sup.u.sub.a] is the expected return on fisheries assets for fully undiversified iwi, [[sigma].sub.a] is the standard deviation of returns on fisheries assets, [[sigma].sub.m] is the standard deviation of returns on the market, [r.sub.f] the risk-free rate and [E.sub.m] is the expected market return.

On the other hand, a well-diversified investor will expect a return given by the CAPM. This is shown in equation (2).

[E.sub.a] = [r.sub.f] + [beta]([E.sub.m] - [r.sub.f]) (2)

where [E.sub.a] is the expected return on fisheries assets for a well diversified investor, and [beta] is the levered beta of the investment.

Figure 1 provides an illustration. The two expected rates of return can be used in a valuation model to create value ratios, which give the relative difference in value. This will be dealt with shortly.

In the situation where an investor is partially diversified, the investor will also require a return from the fisheries asset such that the portfolio return is equal to the return given by the capital market line, for the portfolio's degree of risk.

The portfolio risk is given by equation (3) below.

[[sigma].sup.2.sub.p] = [w.sup.2][[sigma].sup.2.sub.a] + [(1 - w).sup.2][[sigma].sup.2.sub.m] + 2w(1 - w) [[sigma].sub.am] (3)

where [[sigma].sup.2.sub.p] is the variance of the returns from the iwi's investment portfolio, w is the proportion of an iwi's investment portfolio held in fisheries assets, 1 - w is the remaining proportion of an iwi's investment portfolio, which is assumed to be held in the market portfolio, and [[sigma].sub.am] is the covariance between the returns on fisheries assets and the market.

[FIGURE 1 OMITTED]

The covariance between returns on fisheries assets and the market is given by

[[sigma].sub.am] = [[beta].sup.2.sub.m] (4)

Based on equation (3) we can now estimate the capital market line expected return for the degree of risk of the iwi's portfolio, [[sigma].sup.2.sub.p] . This is shown in equation (5) below.

[E.sup.*.sub.p] = [r.sub.f] + [[sigma].sub.p]/[[sigma].sub.m] ([E.sub.m] - [r.sub.f]) (5) Gm

Iwi will (expect to) receive returns from the proportion (w) that they have invested in fisheries, and the remainder (1 - w) that they have invested in the market portfolio. The expected return will need to be adequate to provide for the risk involved, and we know that this must be [E.sup.*.sub.p] in equation (5) above. This expected return will come from the market portfolio and an adequate return from the fisheries investment, which is [E.sup.*.sub.a]. This is shown in equation (6) below.

[E.sup.*.sub.p] = w[E.sup.*.sub.a] + (1 - w)[E.sub.m] (6)

If we set equation (5) equal to equation (6) we get

[r.sub.f] = [[sigma].sub.p]/[[sigma].sub.m] ([E.sub.m] - [r.sub.f]) = w[E.sup.*.sub.a] + (1 - w)[E.sub.m] (7)

Rearranging equation (7) gives

[E.sup.*.sub.a] = 1/w [[r.sub.f] + ([E.sub.m] - [r.sub.f]) [[sigma].sub.p]/[[sigma].sub.m] - (1 - w)[E.sub.m]] (8)

The intuition is that the required return on an investment in fisheries needs to be increased, the less well-diversified are iwi. A 'fully diversified' iwi will still hold an investment in fisheries assets but it would be relative to the market values of all investments as fisheries assets will be represented in the market portfolio. On the other hand if w is one, equation (8) gives the same expected return as equation (1).

The final step is to quantify the value iwi place on their investment in fisheries assets given the higher expected return they demand. To do this, value ratios are created, and to create value ratios a valuation model must be invoked. A dividend valuation model with constant growth is used. (8) The model is shown in equation (9) below.

V = [Div.sub.1]/(E - g) (9)

where E equals [E.sup.*.sub.a] if the investor is undiversified to some degree ([E.sup.u.sub.a] if fully undiversified), or [E.sub.a] (the expected return from the CAPM) if the investor is fully diversified, g is the expected annual growth rate in dividends (Div). V is equal to [V.sup.u.sub.a0] if the investor is fully or partially undiversified, and [V.sub.a0] is the 'fair market value' of the investment.

We can now calculate a value ratio, which is

[V.sup.u.sub.a0]/[V.sub.a0] = [E.sub.a] - g/[E.sup.*.sub.a] - g (10)

which gives a value that is a percentage of fair value, and this reflects the proportionate value that an undiversified (or partially undiversified) investor would assign to the shares, conditional on the degree to which that investor is not fully diversified. To create value ratios we need to assume that [Div.sub.1] and g are the same in the different scenarios. (9)

5. An illustration--required estimates

We use the only fisheries company listed on the New Zealand Stock Exchange, Sanford Limited ('Sanford'), as the benchmark company. Sanford has similar (10) operations to that of AFL and is devoted entirely to the harvesting, farming, processing, storage and marketing of seafood and aquaculture products. Sanford is allocated fishing quota, as are iwi, under New Zealand's quota management system. In terms of size, Sanford had (at the time of this research) a market capitalisation and total assets of roughly $400 million and $700 million respectively (NZX, 2008; Sanford Limited, 2007). AFL has no computable market (11) capitalisation but had total assets of around $400 million (Aotearoa Fisheries Limited, 2007).

The beta of Sanford's shares was estimated to be 0.65. (12) The levered beta needs to be un-levered using Sanford's debt-to-equity ratio. The debt-to-equity ratio of Sanford is 0.2913 based on Sanford's accounts at 30 September 2007.

The un-levered beta calculation is given by

[[beta].sub.U] = [[beta].sub.L]/[1 + Debt/Equity (1 - [T.sup.*])] (11)

where [[beta].sub.U] is the un-levered beta of Sanford, [[beta].sub.L] is the levered beta of Sanford, Debt/Equity is the actual debt-to-equity ratio of Sanford and [T.sup.*] is the imputation adjusted tax rate, which in New Zealand with its imputation tax system is assumed to equal zero. We estimate the un-levered beta of Sanford to be 0.50, and this becomes the proxy for the systematic risk of iwis' fisheries assets.

In order to estimate the risk-free rate in New Zealand, we take the average 5-year government bond rate. The 5-year yield is used to better reflect a long investment horizon of iwi holding their fisheries assets. Using this methodology, the average risk-free rate (at the time of this research) equates to approximately 6% per annum. (14)

Dimson, Marsh and Staunton (2006) study the market risk premium globally using 106 years of data from 17 countries. The authors report a geometric (arithmetic) worldwide equity market risk premium of 4 (5)%. These authors find this value is lower than widely accepted as the market risk premium is non-stationary over time. Further, historical market risk premiums (estimated using the methods of Dimson et al., 2006) overstate future market risk premiums due to historical returns being inflated by past re-pricings prompted by reductions in the market risk premium. There is also the confounding nature of a survivorship bias, which is likely to put upward pressure on historical market risk premiums. We therefore employ three different market risk premiums: 3%, 4% and 5%.

The analysis also requires estimates of the total volatility of the expected returns from fisheries assets, and the total volatility of the expected market return. We use the volatility of Sanford's share returns (adjusted for leverage) as an estimate of the former, and a historical estimate of share market index volatility as an estimate of the latter, calculated over the same period as Sanford's beta coefficient. Given the beta coefficient and these two standard deviations we can also compute the covariance [[sigma].sub.am].

6. Results

As mentioned in the previous section, three different market risk premia are used leading to three different CAPM and CML returns. The results are summarised in Table 1 for the case where w = 1. (15)

We use four weights for w in order to give a representative coverage of possible proportions of fisheries assets that a typical iwi may hold. The first and most obvious is that whereby iwi hold solely fisheries assets and is depicted by w equal to 1. The remaining three weights are 0.75, 0.50 and 0.25. For example, w equal to 0.50 implies 50% of iwi's investment portfolio is held in fisheries assets and the remaining 50% comprises the market portfolio.

Using the four w values, the results of equation (3) are contained in Panel A of Table 2.

From Table 2, when iwi hold solely fisheries assets, given by w equals 1, their portfolio standard deviation is that of the fisheries asset proxy. As the proportion of wealth held in fisheries assets declines relative to that held in a well diversified portfolio, the standard deviation of the total investment portfolio converges to that of the market.

From Table 2, Panel B we can see that, when w equals 1, the expected return for iwi on fisheries assets under the three market risk premiums is the same as was computed using the CML methodology from equation (1). Consistent with intuition, when the proportion of wealth held in fisheries assets declines so does the capital market line expected return, as the portfolio becomes less risky. When w equals 0 the expected return on the fisheries assets is the CAPM return. This is illustrated in Figure 2 for a market risk premium of 4%. The distance between the two lines gives the additional return required from the investment in fisheries. This is not the same as the difference between the CML return (for the portfolio level of risk) and the CAPM return. For example the difference at w = 0.50 between the CML required return and the CAPM required return is 1.79%. (16) This means that an additional 3.57% (1.79%/0.50) is required from the investment and it is these distances that are given in Figure 2.

Table 3 shows the relative values, conditional on assumptions about annual growth rates in dividends. The growth rates chosen are 0% to 3% per annum. It is difficult to determine across iwi what the extent of diversification is, although the annual accounts of the trading arms of some iwi are in the public domain (examples are Ngai Tahu and Tainui). (17) If we assume that (say) 25% of an iwi's assets are locked into fisheries, and the market risk premium is 4%, that the anticipated growth rate is 2% per annum and all the other assumptions hold and the estimates of the parameters are reasonable, then we can conclude that the value assigned to fisheries assets would be roughly 76% of fair market value. Under these assumptions, iwi collectively value the $750 million fisheries settlement at $573 million.

As can be seen from Table 3, holding w constant, a higher market risk premium leads to greater discrepancy between the two expected returns, which leads to lower value ratios for iwi, and, as the anticipated growth rate in dividends increases, the value discrepancy also increases.

[FIGURE 2 OMITTED]

7. Discussion and conclusion

If indeed the fisheries settlement has a fair market value of $750 million as reported, the value ratios in Table 3 illustrate that a portion of this settlement's value is lost to the New Zealand economy and more importantly, iwi.

There is a considerable divergence between an iwi's and a well-diversified investor's expected returns. Such divergence drives value losses for iwi. If this value is to be captured, iwi would need to be allowed to sell the fisheries assets to investors outside mandated iwi who will not discount the price of the fisheries assets due to diversification restrictions.

We have looked at one aspect of how the fisheries settlement has been structured and the implications this has had on the value for iwi. Practitioners and academics widely use and accept the CAPM. The model assumes the asset for which expected returns are being estimated is the market portfolio. Although some iwi may in fact be well diversified, it is possible that others are not. Consequently, if undiversified iwi hold onto their fisheries assets they were allocated under the Act, their required return is greater than that estimated by the CAPM due to idiosyncratic risk they must bear. Meulbroek (2001) argues their expected return is a point on the capital market line (as in equations (1) and (5)).

As expected, this research clearly shows that the disparity between the CAPM and CML expected returns is substantial. This disparity increases as the level of diversification decreases or a higher assumed market risk premium is used.

The Crown has committed a considerable sum of taxpayers' money to the fisheries settlement. Through restricting who can and cannot own the fisheries assets, a portion of the settlement's value is lost. Obviously this argument is dependent on invoking the capital market line, and the CAPM that is derived from it. In turn, this means invoking the assumptions of perfect capital markets and so on, which lie behind the derivations. No consideration is given of spiritual values associated with the ownership of fisheries assets. A response to this analysis from that perspective is that the analysis may be irrelevant. Nevertheless it should be understood.

Acknowledgements

The authors acknowledge the very helpful comments of three anonymous reviewers, and the editor.

DOI: 10.1080/00779951003614073

(Received 17 February 2009; final version received 4 September 2009)

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Notes

(1.) Taonga in Maori culture is regarded as a treasured thing, whether tangible or intangible. Such tangible examples include land, forestry and fisheries.

(2.) The motivation in this paper comes from the investment in Aotearoa Fisheries Limited, but by implication extends to other fisheries assets.

(3.) Fair market value is defined as "[t]he price at which an asset or service passes from a willing seller to a willing buyer. It is assumed that both the seller and buyer are rational and informed of any factors material to the transaction' (Scott & Stringfellow Inc, 2008).

(4.) The Sharpe ratio takes the (expected) return on the asset, subtracts the riskless rate, and divides the amount by the asset return's standard deviation.

(5.) As we show later in the paper, the extent of the loss in value is dependent on the level of diversification of an iwi's investment portfolio.

(6.) These terms were used by James Busby ('first British Resident in New Zealand') to the London Colonial Office. See King (2003, p. 155).

(7.) This is the solid content of the liquid milk supplied, and this is the basis on which payouts are made and shares are owned.

(8.) This is commonly called the Gordon growth model (Gordon, 1959).

(9.) In sum, we need to assume away any agency problems associated with different ownership, which may result in different internal operating strategies and behaviours.

(10.) Sanford is similar but not the same as AFL. For example Sanford is vertically integrated and fishes its own quota, rather than leasing the quota to other harvesters of fish. It is possible to get supplementary data on listed fishing companies from other countries. For example, there are fishing companies listed on the Australian, Japanese, Norwegian and Icelandic share markets. As the computational aspects of this paper are illustrative only, we have not used any of this supplementary information in this research.

(11.) The most recent annual report of Tainui Group Holdings Limited makes reference to a valuation of AFL 'as a whole'. A range of values is reported and the mid-point is $325 million. The most recent report (as at 30 June 2008) of Te Runanga-A-Iwi-O-Ngapuhi values their interest in AFL at $311.50 per share implying a total value of about $389 million, but this value is after taking into account restrictions on sale and inability of the investor to appoint directors. We do not use these valuations in this analysis, as the valuation reports are not in the public domain.

(12.) Using daily data over a two-year period prior to the valuation date.

(13.) This consists of $16.919m of bank overdraft and borrowings at call, and $130m of long term bank loans, divided by $504m of market value of equity.

(14.) This information is taken from Bloomberg Inc. Over the 2007-2008 period 5-year government stock yields vary from approximately 4.5% (end of 2008) to 7% (mid-2007). We have used 6% as an approximate (average) rate.

(15.) w = 1 assumes 100% of an iwi's wealth is invested in fisheries assets, or alternatively, iwi have no diversification.

(16.) The CAPM return with w = 0.50 is 9.01% and the CML required return is 10.79%. The additional portfolio return of 1.79% (rounded) needs to be loaded onto AFL's return in a setting where AFL is only half the portfolio. Hence the additional required return from AFL is 1.79%/0.50 = 3.57%.

(17.) Ngai Tabu for example is reasonably heavily invested in fishing (on our estimate between 20% and 25% of its assets are fisheries related). Ngapuhi appears to be heavily invested in fishing activity at June 2008--by our estimates about three-quarters of the trust's assets. Fourteen percent is represented by shares in AFL and 59% by quota.

Cameron Day (a) * and David Emanuel (b)

(a) Deloitte, Private Bag 115-033, Shortland Street, Auckland 1140, New Zealand; (b) Department of Accounting and Finance, The University of Auckland Business School, Private Bag 92019, Auckland 1142, New Zealand

* Corresponding author. Email: caday@deloitte.co.nz

Table 1. CAPM and CML (w, = 1) calculations. Market risk premium 3.00% 4.00% 5.00% CAPM return 7.51% 8.01% 8.52% CML return 11.80% 13.73% 15.66% Table 2. (Panel A) Standard deviations of portfolios; (Panel B) Expected return on fisheries assets. Proportion of wealth invested in fisheries assets (w) 1.00 0.75 0.50 0.25 Panel A Standard deviation 20.91% 16.59% 12.96% 10.74% Panel B market risk premium = 3% Expected return 11.80% 11.13% 10.19% 8.91% market risk premium = 4% Expected return 13.73% 12.85% 11.58% 9.88% market risk premium = 5% Expected return 15.66% 14.56% 12.98% 10.85% Table 3. Value ratios. Expected growth rates in dividends Weights 0% 1% 2% 3% Value of fisheries assets as a percentage of fair market value (MRP is 3%) 100% 63.65% 60.29% 56.23% 51.26% 75% 67.44% 64.23% 60.32% 55.44% 50% 73.71% 70.85% 67.29% 62.74% 25% 84.31% 82.32% 79.76% 76.34% 0% 100.00% 100.00% 100.00% 100.00% Value of fisheries assets as a percentage of fair market value (MRP is 4%) 100% 58.36% 55.09% 51.26% 46.72% 75% 62.38% 59.20% 55.44% 50.91% 50% 69.17% 66.26% 62.74% 58.40% 25% 81.13% 79.00% 76.34% 72.90% 0% 100.00% 100.00% 100.00% 100.00% Value of fisheries assets as a percentage of fair market value (MRP is 5%) 100% 54.37% 51.26% 47.69% 43.56% 75% 58.50% 55.44% 51.89% 47.73% 50% 65.61% 62.74% 59.34% 55.27% 25% 78.52% 76.34% 73.66% 70.31% 0% 100.00% 100.00% 100.00% 100.00%

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Title Annotation: | RESEARCH ARTICLE |
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Author: | Day, Cameron; Emanuel, David |

Publication: | New Zealand Economic Papers |

Article Type: | Report |

Date: | Apr 1, 2010 |

Words: | 6445 |

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