Air New Zealand Air Points - Oversold PE on NZ39 - what would be our rights in the event of involuntary downgrade?

I have been unable to request seats for either sector on NZ39 next month for my wife & I (we are stopping over in HKG). I called NZ reservations today and they told me that the flight is oversold in PE. Having been in this situation before with BA (and, I admit, rather paranoid as a result), I have been trying to find out what our rights would be if we were involuntarily downgraded at either AKL or HKG. We will be flying around Easter time, so there is a good chance of all cabins being full and IMO "no shows" are unlikely.

Within the EU we have Regulation 261/04, which sets out passenger rights in the event of being denied boarding or involuntarily downgraded. However, can anyone please point me to any policy (either Air NZ policy or a regulatory policy) which would be applicable in similar circumstances either within New Zealand or at HKG?

Many thanks in advance.

I wouldn't worry about it at this stage. Weeks to go until your flight and I bet there will be some cancellations, no shows and pax changing to other flights. NZ seems to be pretty good at managing loads - almost certainly if PE is oversold on the day and all check in there will be space in business class for some op-ups.