Two brokers say the Fonterra Shareholders' Fund is overpriced and are recommending investors cut their holdings.
The units have surged by up to $2 or 33% since they listed last November at an issue price of $5.50.
They are now in the NZX 50 index of top shares and are trading at $7.25, down from a high of $7.53.
But Morningstar values the units at $5.50 a share, and Forsyth Barr has set a 12-month price target of $6.50 despite forecasting Fonterra's 2013 profits to be 7% higher than the prospectus.
Morningstar senior equities analyst Nachi Moghe says Fonterra's fortunes are linked to growth in dairy consumption in Asia and Latin America.
He says the company lacks competitive advantages or what Morningstar calls an "economic moat".
Mr Moghe says Fonterra faces challenges becoming a higher value-added dairy player in the global market because it will have to compete with established multinations such as Nestle and Danone.
Forsyth Barr says the volatile milk price may drag down earnings, and Fonterra faces challenges becoming a higher value-added dairy player with global expansion plans.
The shareholders' fund gives outsiders the chance to access Fonterra for the first time, but some fund managers complained that the allocation for New Zealand investors was unfair as the majority went offshore.