Index Futures at Sell-side desk

Hi WSO,
 

I’m at the periphery of an equity index futures trading role at an investment bank. I trade single names on my PA and I’ve been in FX most of my career. Index futures will be new to me. While index futures may be similar to FX spot in that they’re in the macro linear products group, I’ll be glad if I can get some info from the pros here.
 

1. Given that equities and index futures, say S&P500 on CME, are exchange traded, can a bank quote bid offers for ES to their clients? Maybe a lower offer for a larger ES size if the trader knows he can better manage the risk?
    
2. If a bank can’t price ES like it does for OTC FX, does its edge come from inventory management when the trader places his own bid offers on the exchange. Seems like prop with very tight risk limits; not saying it’s wrong.
    
3. For an Index Arb ES and SPX trade, does a buy SPX, sell ES actually entails buying the 500 single name stocks in the index? Also, is the Fed Fund Rate used for SPX carry cost?
    
4. Are there volume targets for index futures, i.e. Bank A consistently buying and selling ES on CME? And are these targets used to draw customers to the bank’s platform?

Much appreciated. Nijikon