I actually have essentially such a thing.. I started it last class, I completely randomly select 10 YC companies and invest $50K in each at their current demo day terms. All accepted the investment last time so it should actually be a valid random sampling. If you’re an accredited investor and possibly interested in joining this “lucky fund” for W19 (I’m doing it again), PM me!
I run one of the YC Demo Day funds on Angel List (not sure if it's an SEC violation to link to it) and therefore spend weeks assessing founders and startups in each batch to make about 15 investments. It'd be very very interesting to compare our returns and outcomes to see if your approach destroys mine or not. Will send you a note!
While a pure YC ETF doesn't exist, there are several YC demo day funds that approximate it. Both FundersClub and AngelList run funds you can invest in every batch that invest in many of the YC companies.