[s28l]

The risk profile is different. Yes, both have a payout that depends on your own mortality, but there are other risk factors to consider.

An annuity is also a credit risk: if the counter-party goes under, then your payments will stop. Since most of the time the counter-party is a well-capitalized insurance company (potentially with an implicit government backstop), this risk is pretty small.

On the other hand, a tontine has a risk profile that depends on the mortality of the other nominees who participate: your payout in a given year depends on the number of nominees still alive. Also, depending on how it's structured, there might be some market risk as well.

From another perspective, for there to be an arbitrage opportunity, you'd need a way to create a synthetic annuity using a tontine (or vice-versa). But the risk profile of the tontine, which depends on the mortality of the other nominees, is hard to come by unless you are an insurance company. You can view a participant in a tontine as owning a certain life annuity as well as having sold the other participants a smaller life annuity. So each time one of them dies, you no longer have to pay that life annuity and can keep more of the income from the annuity you own.