▁their ▁assets ▁and ▁optimize ▁one ▁port folio . ▁This ▁is ▁in ▁sharp ▁contradiction ▁with ▁port fol ios ▁that ▁are ▁held ▁by ▁individual ▁share hold ers : ▁humans ▁tend ▁to ▁have ▁fragment ed ▁port fol ios ▁or , ▁rather , ▁multiple ▁port fol ios : ▁for ▁each ▁goal ▁one ▁port folio ▁— ▁see ▁behavior al ▁port folio ▁theory ▁and ▁Mas low ian ▁port folio ▁theory . ▁ ▁Emp ir ical ▁tests ▁show ▁market ▁anom al ies ▁like ▁the ▁size ▁and ▁value ▁effect ▁that ▁cannot ▁be ▁explained ▁by ▁the ▁C AP M . ▁For ▁details ▁see ▁the ▁F ama – F rench ▁three - factor ▁model . ▁ ▁Roger ▁Day ala ▁ ▁goes ▁a ▁step ▁further ▁and ▁claims ▁the ▁C AP M ▁is ▁fund ament ally ▁fla wed ▁even ▁within ▁its ▁own ▁narrow ▁assumption ▁set , ▁illustr ating ▁the ▁C AP M ▁is ▁either ▁circular ▁or ▁ir r ational . ▁The ▁circular ity ▁refers ▁to ▁the ▁price ▁of ▁total ▁risk ▁being ▁a ▁function ▁of ▁the ▁price ▁of ▁cov ar iance ▁risk ▁only ▁( and ▁vice ▁vers a ). ▁The ▁ir r ational ity ▁refers ▁to ▁the ▁C AP M ▁proc laimed ▁‘ re vision ▁of ▁prices ’ ▁resulting ▁in ▁identical ▁disc ount ▁rates ▁for ▁the ▁( lower ) ▁amount ▁of ▁cov ar iance ▁risk ▁only ▁as ▁for ▁the ▁( high er ) ▁amount ▁of ▁Total ▁risk ▁( i . e . ▁identical ▁disc ount ▁rates ▁for ▁different ▁amounts ▁of ▁risk . ▁Roger ’ s ▁find ings ▁have ▁later ▁been ▁supported ▁by ▁La i ▁& ▁Sto