Smoothing / hedging indexes; book5, pg 17 between, actually, index, part, comparing

tikfed

While comparing performance returns, there are comparisons between - NAREIT index ‘vs’ NAREIT index hedged;  NCREIF index ‘vs’ NCREIF index unsmoothed.
As part of smoothing/unsmoothing, what does they actually do? Similarly as part of hedging, what do they do, that gave new values of return, std. dev. and so?
TY.