The nine firms where the CEO is not on the board - Air New Zealand, Auckland International Airport, Contact Energy, Mighty River Power, NZX, Port of Tauranga, Restaurant Brands, TrustPower and Z Energy - are mainly in the energy, transport or infrastructure sectors.
The chief executive of Fonterra, the country's largest company, also doesn't have a board seat.
Under the traditional corporate governance structure shareholders appoint directors and approve their remuneration, while the directors choose the CEO, set the remuneration and monitor their performance.
The cycle is broken if the chief has board representation because he or she is not appointed to this position by shareholders and shareholders do not have the ability to approve the remuneration of executive directors.
Some boards believe it is very hard to monitor the performance of a chief executive who has a board seat while others believe a board cannot be fully effective if the CEO is not a director.
As a general rule entrepreneurial companies - Xero for example - will have at least one executive director while the well-established, process-driven firms will have no executive directors. The electricity sector is a good example of the latter group.
Although executives can be appointed to the board without shareholder approval there are exceptions to this rule.
At the recent AWF Group annual meeting shareholders were asked to approve the re-appointment of CEO Mike Huddleston to the board under clause 26 of the constitution.
Only one executive director is exempt from needing shareholder approval and managing director Simon Hull has this slot at AWF.
Finally there is the contentious issue of whether a chief executive should remain on the board as a non-executive director after retiring.
Many international corporate governance advisers believe former CEOs can dominate the board agenda and decisions, particularly as they may have appointed most of the management team and recruited many of the non-executive directors. Former chiefs can also restrain their successors from making big changes.
There is a widespread belief that chief executives should not remain on the board after they retire although this conviction does not apply to founder directors, which includes Bruce Plested at Mainfreight and Kevin Hickman at Ryman Healthcare.
Some of decisions regarding board composition can be confusing. For example, Maurice Prendergast stayed on the Pumpkin Patch board after he resigned but replacement CEO Neil Cowie was not appointed to it.
Did this contribute to Cowie's recent decision to leave the firm?
Former NZX chief executive Mark Weldon was on that board but Tim Bennett, his successor, is not.
DNZ Property Fund's annual meeting this week raised some of the issues that concern shareholders.
Many shareholders did not agree with the strategy to sell properties in low-growth regions and reinvest this money in the fast-growing Auckland market. Most of these disgruntled shareholders, who wanted the sale proceeds distributed as dividends, were encouraged to invest in DNZ by Money Managers, the controversial financial adviser.
A fundamental conflict between individual shareholders, who want higher dividends, and institutional investors, who want capital growth, is one of the main features of New Zealand shareholder meetings.
The fourth item on DNZ's agenda was a proposed increase in director fees. The resolution read: "That, with effect from the start of the financial year commencing on 1 April 2013, the company adopt a fee pool (being a monetary sum per annum payable to all directors taken together) pursuant to Listing Rule 3.5.1(a) of $375,000."
Listing Rule 3.5.1 is important in this regard because it states that each such resolution shall express directors' remuneration as either:
a) A monetary sum per annum payable to all directors of the issuer taken together, or
b) A monetary sum per annum payable to any person who from time to time holds office as a director of the issuer.
The rule goes on to state that "no resolution which increases the amount fixed pursuant to a previous resolution shall be approved at a general meeting of the issuer unless notice of the amount of increase has been given in the notice of meeting".
A surprising number of companies do not include the amount of the increase in the notice of meeting and have to send out a revised notice after this omission is pointed out to them.
South Port New Zealand was an example of this last year.
DNZ's notice of meeting covered this issue extremely well as it noted the total fee pool would be increased by $80,000, or 27.1 per cent, from $295,000 to $375,000. It also revealed the chairman's pay would rise from $100,000 to about $130,000 and non-executive directors from $65,000 to about $75,000.
There was no objection or discussion on DNZ's director fee increase. DNZ shareholders are far more interested in their dividend than director remuneration.
Chairman Tim Story called for a poll vote on all resolutions. The voting figures, which were released to the NZX, showed only 21,165 votes (0.12 per cent) were cast against his re-election as a director whereas 6,118,660 (5.33 per cent) voted against the directors' fee rise.
The lack of opposition to the fee increase at the meeting indicated that most of these negative votes were cast by shareholders who did not attend the DNZ meeting and voted by proxy.
A company chairman can decide to take a vote by either a show of hands or by poll. The poll method is becoming increasingly popular because it gives a more accurate indication of the shareholders' view. The poll figures should be disclosed to the NZX because this gives non-attending shareholders a better indication of the meeting's mood.
All resolutions at this week's Infratil meeting were decided by a show of hands, but the proxy voting numbers were released to the NZX.
The chairman can decide to hold a poll vote but a poll can also be demanded by
a) not less than five shareholders having the right to vote at the meeting
b) a shareholder or shareholders representing not less than 10 per cent of the total voting rights of all shareholders having the right to vote at the meeting; or
c) a shareholder or shareholder holding shares that confer a right to vote at the meeting and on which the aggregate amount paid is not less than 10 per cent of the total voting rights.
Poll votes are more transparent, particularly when the full voting figures are released to the NZX. It doesn't take much organisation for shareholders to call for poll voting.
Disclosure of interest; Brian Gaynor is an executive director of Milford Asset Management.