[greiskul]

Not anymore then proof of work has I think. Want to join bitcoin mining? You need to invest in mining hardware, and have access to cheap electricity.

[masmullin]

Do you have to mine for proof of stake, or is simply owning the underlying asset enough to "generate interest on the investment?"

[lt]

For block rewards you'd have to mine. In particular you'd have to have a server running a node joined in the network ready to generate a block whenever your number is called.

Not everyone would want to do that, so there's usually a mechanism to indicate you want to be eligible to do so, depositing your coins or similar.

That's for block rewards - nothing prevents a blockchain currency to be designed to generate inflation and add interest on everyone's investment - some do exactly that.