Legally...
Strikes me as something that should be included in Merkley and Hawley's bill that proposes to ban congressional insider trading. Different branch of government, and it's not stock trading, but the core principle is the same.
Not that their bill will ever pass, but unless someone can convince me otherwise, neither Congress nor the President should be in a position to manipulate the value of something they own.
I don't know what you do in the instance where someone owns something prior to holding office. It also seems wrong to force them to divest what they obtained legally because they go into public service.