YC is much closer to an index fund than typical VC (or even other accelerators - due to YC's much larger scale), but there's a big difference as index funds don't use any "gut instincts" - the criteria for a stock to be included in an index are fixed rules.

A better (though less succinct) analogy for YC in the public markets would be an "actively managed mutual fund investing in a broad range of early stage companies with a long-term time horizon."