Samplequestion:Youhavethefollowingratesofreturnforariskyportfolioforseveralrecentyears:1
Ifyouinvested$1,000atthebeginningof2005yourinvestmentattheendof2008wouldbeworth___________
$2,176
$1,785
$1,645
$1,247
87Ifyouinvest1,000,attheendofyearone,youwillhave1000*(1+35
23%),Attheendofyear2,youwillhave1000*(1+35
23%)*(1+18
67%),dothesameworkforyear3and4,then$1000(1+35
23%)(1+18
67%)(1-9
87%)(1+23
45%)=$1785
TheannualizedaveragereturnonthisinvestmentisA
60%Becausegeometricaveragerateofreturnismoreaccurate,wewillusegeometricaveragerateofreturnhere
Geometricaveragerateofreturn=((1+r_1)(1+r_2)*…(1+r_n))^(1/n)-1,thenwehaveHint:wehavealreadycalculated1000(1+35
23%)(1+18
67%)(1-9
87%)(1+23
45%)=$1785
56,thus(1+35
23%)(1+18
67%)(1-9
87%)(1+23
45%)=1