▁ β . ▁ ▁Note ▁ 1 : ▁the ▁expected ▁market ▁rate ▁of ▁return ▁is ▁usually ▁estimated ▁by ▁meas uring ▁the ▁arithmetic ▁average ▁of ▁the ▁historical ▁returns ▁on ▁a ▁market ▁port folio ▁( e . g . ▁S & P ▁ 5 0 0 ). ▁ ▁Note ▁ 2 : ▁the ▁risk ▁free ▁rate ▁of ▁return ▁used ▁for ▁determ ining ▁the ▁risk ▁prem ium ▁is ▁usually ▁the ▁arithmetic ▁average ▁of ▁historical ▁risk ▁free ▁rates ▁of ▁return ▁and ▁not ▁the ▁current ▁risk ▁free ▁rate ▁of ▁return . ▁ ▁For ▁the ▁full ▁deriv ation ▁see ▁Modern ▁port folio ▁theory . ▁ ▁Mod ified ▁Bet as ▁There ▁has ▁also ▁been ▁research ▁into ▁a ▁mean - re ver ting ▁beta ▁often ▁referred ▁to ▁as ▁the ▁adjust ed ▁beta , ▁as ▁well ▁as ▁the ▁consumption ▁beta . ▁However , ▁in ▁empir ical ▁tests ▁the ▁traditional ▁C AP M ▁has ▁been ▁found ▁to ▁do ▁as ▁well ▁as ▁or ▁out perform ▁the ▁modified ▁beta ▁models . ▁ ▁Security ▁market ▁line ▁The ▁S ML ▁essentially ▁graphs ▁the ▁results ▁from ▁the ▁capital ▁asset ▁pr icing ▁model ▁( C AP M ) ▁formula . ▁The ▁x - axis ▁represents ▁the ▁risk ▁( beta ), ▁and ▁the ▁y - axis ▁represents ▁the ▁expected ▁return . ▁The ▁market ▁risk ▁prem ium ▁is ▁determined ▁from ▁the ▁slope ▁of ▁the ▁S ML . ▁ ▁The ▁relationship ▁between ▁ β ▁and ▁required ▁return ▁is ▁pl otted ▁on ▁the ▁se cur ities ▁market ▁line ▁( S ML ), ▁which ▁shows ▁expected ▁return ▁as ▁a ▁function ▁of ▁ β .