In order to protect some gains in some small cap mutual funds I was thinking of hedging these with the Russell 2000 or IJT and IJS options. How can I make sure this cross hedge is as close to dollar for dollar as possible?
No way to make it 100% sure, but you can calculate correlation and/or beta between the fund and the index/etf you're going to use to hedge. Then use that correlation to adjust the position size on the options.
Suppose, you estimate the beta of the index with respect to the mutual fund to be 1.1. Also suppose you have $100K in mutual fund position so your adjusted position is 1.1*100K=110K. So now you can use that number to estimate the required position size. Say you use IWM (Russell 2000 ETF), which is @ 71.24. So 110K/71.24=1544 shares or roughly 15 option contracts. So if you want to be hedge at expiry then you just buy 15 puts and that's it. If you want Delta hedge then your position is 1544 long deltas so you need roughly 31 ATM puts to hedge the deltas. Delta hedging is not a static hedge though you need to rebalance it. You can also use the following formula to estimate the hedge ratio: Hedge ratio= (standard deviation of asset)/(standard deviation of hedge)*correlation