Shares in one of New Zealand's biggest private health insurers, NIB Holdings, rose from $A3.10 last month to $A3.19 this month.
That resulted in analysts Morningstar re-rating the stock from accumulate to hold, saying the ASX-listed shares had moved through the trigger level.
Morningstar said the business had attractive long-term industry dynamics because it was supported by a growing population.
In New Zealand, NIB bought the Tower's healthcare business and has made a substantial investment here, with huge promotional and rebranding campaigns.
Morningstar said the business had strong growth potential.
"NIB is an active and fast growing private health insurer in Australia and New Zealand. Policyholders and insurance premiums are growing strongly, complemented by attractive returns on equity," Morningstar's David Ellis said.
About half Australia's 23 million people were covered by private health insurance and
Morningstar said people bought it to give them shorter waiting times for treatment, a choice of doctor and hospital, tax benefits and for cover for ancillary health services.
NIB reported premium revenue of A$1.5 billion in the 2014 year and is Australia's fourth-largest health fund, Morningstar said.
Information released in New Zealand last year showed the insurer had about 160,000 kiwi customers with about 80,000 policies but about 1.1m customers when combined with Australia.