The fund had a net asset value of $6 million at the end of March.
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Its investments include Boardingware, an app used by boarding school students and their parents, gym management app InfluxHQ and Weirdly, a recruitment app.
Fund director Wiggs said the crowdfunding campaign had made a solid start.
"One thing we learned from our failed public offering back in 2013 is not to get too confident about these things," he said.
Wiggs said he would like have another go at conducting an IPO and sharemarket listing of the fund within the next three to five years.
Punakaiki is managed by Lance Wiggs Capital Management, owned by Wiggs and Chris Humphreys.
The fund is also running a private offer for eligible (high net-worth) investors.
"In theory we can go beyond $2 million," Wiggs said.
He said there was no shortage of investment opportunities for the fund.
"Deal flow has never been our problem," he said. "The main issue with Punakaiki Fund and for myself before has been access to funds."
A 25.7 per cent stake in the fund will be sold if $2 million is raised through the Snowball Effect offer.
The minimum investment is $1450.