"The undersigned shareholders expect immediate and tangible confirmation of efforts to arrest the continued erosion of shareholder value," the letter to Miller said.
Should the NZX board continue to ignore shareholders in this regard ... the undersigned shareholders see little option but to effect change at the NZX board level."
The shareholders point out that NZX has shown little or no growth at a time when capital markets around the world have been very positive. Yet the NZX share price performance and total return is among the worst in the world for a listed stock exchange.
NZX's sharemarket value has declined from $322 million to $285m over the past five years while the ASX's market value has soared from A$7105m to A$11,476m over the same period.
At the same time the NZX has failed to attract new initial public offerings (IPOs) and has only 133 listed domestic companies compared with 140 five years ago, while the ASX has 2015 listed domestic companies compared with 1924 in late 2013.
Last week the NZX reported net profit of $11.6m in calendar 2018, down from $14.8m.
That was largely due to $3m of impairment charges NZX booked in selling its Farmers Weekly, AgriHQ and grain information businesses, which no longer sat comfortably within the stock market operator's plans to refocus on its core market business.
Operating earnings from continuing operations were flat at $27.3m.
Expenses from continuing operations increased 0.8 per cent to $40.2m.
The company's annual report showed 101 staff were paid more than $100,000 a year, including chief executive Mark Peterson who was paid just over $800,000 in 2018.
NZX unveiled its long-term strategy in late 2017, saying 2018 would set the platform for future growth, with a key focus on its traditional markets business. Since then it has introduced new listing rules and an updated fee structure to encourage more trading through the formal market.
Last month it announced Capital Markets 2029, an joint initiative with the FMA to look at ways of strengthening the capital markets.
Daniel and other shareholders said a review of the company's current business given the widely accepted view of limited growth would be more appropriate.
"Shareholders invest for earnings and the only way to increase earnings in the face of revenue stagnation is to reduce costs with renewed vigour."
An NZX spokeswoman confirmed Miller had received a letter from Mike Daniel.
"We take shareholder concerns seriously, and our chair is in touch with Mike Daniel to discuss these concerns. We continue to be open to discuss any matter with all shareholders."
