If I have $200,000 in an index fund that mirrors the S&P 500, then I own the equivalent of 4+ thousand dollars in multiple high capitalization stocks. If I think that one of those stocks I already (kind of) own in the index is overvalued, I'd like to buy a short roughly equal to that stock's value in my fund. Let's say I think Facebook isn't worth its valuation, if I short $3,000 in Facebook shares (equal to my holding of Facebook in the index) and buy more of the index, it's like I own an index without Facebook. If Facebook goes up, my index goes up, but I lose all that gain when I close out the short. If Facebook goes down, I lose money in the index, but gain it all back in the short. The only way I lose money on the short is through the stock loan fee. But, from the perspective of the person loaning me the Facebook shares, this is the perfect loan; I'm never going to go bankrupt and leave them in the lurch.
Is there a financial instrument (maybe an index-backed short) that lets people short shares they already own as part of indexes for very low stock loan fees, since these loans are extremely low risk? If not, why is this a dumb or extremely niche idea?