Despite the recent exit of National Australia Bank Ltd. (ASX: NAB) from the significant shareholders list, The share price of health insurer Medibank Private Ltd (ASX: MPL) has continued to rise, passing through $3 to hit a high of $3.06 just yesterday.

Investors in the Initial Public Offering (IPO) who held on through the bumpy ride – hopefully all of them – have been well rewarded for their patience, and I believe they should continue to hold. However, is there value to be had in buying Medibank shares today?

I don’t believe so for a number of reasons laid out below.

For every benefit to shareholders, such as legislated revenue increases and a defensive business model, there’s a drawback. These are issues of premium costs, which is reportedly encouraging many Australians to downgrade or cancel their health cover. There’s intense competition, which has seen competitors like Bupa and NIB Holdings Limited (ASX: NHF) take market share from Medibank. And Medibank’s own cheap brand ahm even appears to be cannibalising the premium Medibank brand.

There’s a reasonable chance several of these negatives could come out in favour of Medibank. For instance, reduced private health insurance will push more Australians into the already strained public health system, which is not ideal. Thus, further steps could be taken by the federal government to encourage residents to lift their private health cover, which could grow the overall size of the health insurance market.

Additionally, Medibank is large enough to achieve more favourable terms from suppliers and thus achieve better cost outcomes for policyholders. However, with the cost of insurance rising around 5.5% per year for the past 5 years and no signs of it slowing, more drastic steps must be taken to reduce the price burden.

Factor in the uncertainty of a new CEO and an ongoing government investigation into the healthcare system, and I feel there is too much uncertainty to justify a new investment at today’s prices. That’s not to say Medibank is a bad business because it’s not. It’s just that the likelihood of market-beating returns decreases as the company’s price rises, which is why I would call the company a ‘Hold’ today.

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Motley Fool contributor Sean O'Neill has no position in any stocks mentioned. The Motley Fool Australia has no position in any of the stocks mentioned. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy. This article contains general investment advice only (under AFSL 400691). Authorised by Bruce Jackson.