Solutions Chapter 06 - RISK Aversion AND Capital Allocation TO Risky Assets PDF

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All the solutions to this chapter., All the solutions to this chapter....

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Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets

CHAPTER6 :RI SK AVERSI ONAND CAPI TALALLOCATI ONTORI SKYASSETS PROBLEM SETS 1. ( e ) 2. ( b)Ahi gh e rbo r r o wi n gi sac on s e q ue nc eoft her i s koft hebor r o we r s ’de f a ul t .I npe r f e c t ma r k e t swi t hnoa ddi t i ona lc os tofde f a ul t ,t hi si nc r e me ntwou l de qu a lt hev a l ueoft he bo r r o we r ’ sopt i ont ode f a ul t ,a ndt heSh a r peme a s ur e ,wi t ha ppr op r i a t et r e a t me ntoft he d e f a ul top t i o n,woul dbet hes a me .Ho we v e r ,i nr e a l i t yt he r ea r ec os t st ode f a ul ts ot ha t t hi spa r toft hei nc r e me ntl o we r st heSha r per a t i o .Al s o ,no t i c et ha ta ns we r( c )i snot c or r e c tbe c a us edoub l i n gt h ee xpe c t e dr e t ur nwi t hafix e dr i s k f r e er a t ewi l lmor et ha n do ubl et her i s kp r e mi um a ndt heSh a r per a t i o . 3. As s umi n gnoc h a ng ei nr i s kt o l e r a nc e ,t ha ti s , a nunc h a ng e dr i s ka v e r s i onc oe ffic i e nt( A) , t he nhi gh e rpe r c e i v e dv ol a t i l i t yi nc r e a s e st hede nomi na t oroft hee qu a t i o nf o rt heop t i ma l i n v e s t me nti nt her i s kypor t f ol i o( Equ a t i on6. 12) .Thep r opor t i oni n v e s t e di nt h er i s ky po r t f o l i owi l lt he r e f or ede c r e a s e . 4. a . Th ee x pe c t e dc a s hflo wi s :( 0. 5 $ 70, 0 00)+( 0. 5 200, 000)=$1 35, 000 Wi t har i s kpr e mi um of8% o v e rt her i s k f r e er a t eof6%, t her e q ui r e dr a t eof r e t u r ni s14%. The r e f o r e ,t hepr e s e ntv a l ueoft hepor t f o l i oi s : $1 35, 000/ 1. 14=$118 , 421 b . I ft h epo r t f o l i oi sp ur c ha s e df or$118 , 421,a ndpr o v i de sa ne xp e c t e dc a s hi nflo wof $1 35, 000,t he nt hee x pe c t e dr a t eofr e t ur n[ E( r ) ]i sde r i v e da sf o l l o ws : $1 18, 421 [ 1+E( r ) ]=$1 35, 000 Th e r e f o r e ,E( r )=14%. Thepor t f o l i opr i c ei ss e tt oe q ua t et hee xp e c t e dr a t eor r e t u r nwi t ht h er e q ui r e dr a t eofr e t ur n. c . I ft h er i s kpr e mi um o v e rTbi l l si sn o w12%, t he nt her e qu i r e dr e t u r ni s : 6% +12 % =18 % Th ep r e s e ntv a l ueoft hepor t f o l i oi sn o w: $1 35, 000/ 1. 18=$114 , 407

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Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets

d. Fo ragi v e ne xp e c t e dc a s hflo w, por t f o l i ost ha tc omma ndgr e a t e rr i s kpr e mi a mus ts e l la tl o we rpr i c e s .Thee xt r adi s c ountf r o me xp e c t e dv a l uei sape na l t y f orr i s k. 5. Whe nwes pe c i f yut i l i t yb yU=E( r )–0. 5 A,t heut i l i t yl e v e lf o rTbi l l si s :0. 07 2 Theut i l i t yl e v e lf o rt h er i s kypor t f o l i oi s :U=0. 12–0. 5A( 0. 18)=0. 12–0. 0162 A I nor d e rf ort her i s kypor t f o l i ot obepr e f e r r e dt obi l l s ,t hef ol l o wi n gi ne q ua l i t ymus t ho l d: 0. 12–0. 016 2A>0. 07 A...