A venture capitalist has to be willing to take risks when ___ invests ___ money.

__ they /their
__ he / his
__ she /her
__ he or she /his or her

Answer he or she / his or her Correct?

Yes. It's awkward but it's correct.

I know you can't change the question -- but a better wording would be:

Venture capitalists have to be willing to take risks when they invest their money.