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SCI would have to think, with the expenses involved, that a fund investing would only be interested in individual items of $1000+ (and that's a pretty low level), probably certified, and probably key cards that are widely traded (i.e. no condition scarcities, or set scarcities).
You would probably only want to focus on the very top players (Ruth, Cobb, Wagner, Gehrig, DiMaggio, Williams, Mantle - how many other iconic players are there??), and perhaps key/rookie cards of some of the top players from the 50s (Aaron, Koufax, Mays, etc.) How much can you spend on those items? Even less if you kept to the standard & most recognized issues of T206, Goudey, Bowman, Topps?
On a smaller level, I've always felt there was money to be made by making a market in one or two issues. What if someone just decided to buy every Aaron rookie that makes it to the market? I count about 20 Aarons in closed auctions on ebay, another dozen or so live. If you only look at PSA, it's a fraction of that. Doesn't seem it would take much $$ to move the market.