When you buy and sell shares in the "real" market, you do so in whole numbers. If you're going to construct an index fund just for you, the smallest amount of any stock you can buy is 1, so you'd need an enormous capital investment: if you want e.g. 1% of your fund to be Google (currently trading at $934), and assuming all the share prices work out just right -- in practice, they won't -- your smallest unit of investment would be $93,400.
In practice, the closest approximation of what you describe is just having a passive portfolio: pick a bunch of stocks, buy them, and then don't look at them again.
Basically, you determine the dollar amount you want to spend on each stock, and the plan purchases that amount, including fractional shares.
I don't think they do the same for selling.
http://www.sectorspdr.com/sectorspdr/
So, you can either:
1) Buy all the sector ETFs (XLY, XLP, XLF, XLV, XLI, XLB, XLRE, XLK, XLU) except for the energy sector (XLE)
2) Buy the SPY, short sell XLE.
Different tickers apply for iShares, or other indicies / sectors, but you get the idea - it's easy enough to focus on specific sectors using a mixture of ETFs.
Have fun,
Edit: I see a $110M Series C in April '17 reported for Robinhood.
Not great for research, but functional to buy/sell.
As in: you select the stocks and their proportion and supply the money/demand money out, and stocks are then bought/sold automatically?
Say I want to follow index X, but I don't want stocks in oil or coal companies because I believe they're going to die before I need the money out. There doesn't seem to me to be an easy way to build that customized index.
I guess you need a low-fee stock broker and an algorithm that's aware of the fees for this to not end up drowning in fees.