本文格式為Word版，下載可任意編輯——新風(fēng)險(xiǎn)管理復(fù)習(xí)資料PV2

Hence:Choosethenewapartment

3.ConsiderthetwoprojectswhosecashflowsareshowninthefollowingTable.FindtheIRRsofthetwoprojectsandtheNPVsat5%.

year012

Project1-503030

Project2-754242

Solution:

3.(1)Given:

Cashflowstream1：(x0,x1,x2)

Cashflowstream1：(y0,y1,y2),r=5%x0=-50，x1=30，x2=30y0=-75，y1=42，y2=42Hence:NPV1=X0+

x230x130+=－50++=$5.78

1?0.05(1?0.05)21?r(1?r)2NPV2=y0+

y242y142+=-75++=$3.10221?0.05(1?0.05)1?r(1?r)NPV1>NPV2

Hence:Recommendproject1(2)Given:

Cashflowstream1：(x0,x1,x2)Cashflowstream1：(y0,y1,y2)

x0=-50，x1=30，x2=30,y0=-75，y1=42，y2=420=X0+X1C+X2C2

0=-50+30C1+30C12C1=0.880=-75+42C2+42C22C2=0.93IRR1=

11-1=0.136IRR2=-1=0.075C1C2IRR1>IRR2

Hence:Recommendproject1

4.(Bondselection)ConsiderthefourbondshavingannualpaymentsasshowninthefollowingTable.Theyaretradedtoproducea15%yield.EndofyearpaymentsBondABondBBondCBondDYear1Year2Year3100100100+1000505050+1000000+10000+100000(a)Determinethepriceofeachbond.(b)Determinethedurationofeachbond(notthemodifiedduration).(c)Witchbondismostsensitivetoachangeinyield?

Solution:

（a）BondA:

Given:couponrate=10%yieldtomaturity=15%，m=1，n=3Hence:

pA?CkCkF?Ck1001001100?????=$885.8423231?r?1?r??1?r?1?0.15(1?0.15)(1?0.15)BondB:

Given:couponrate=5%yieldtomaturity=15%，m=1，n=3Hence:

pB?CkCkF?Ck5050????=$771.681?r?1?r?2?1?r?31?0.15(1?0.15)2BondC:

Given:couponrate=0%yieldtomaturity=15%，n=3

3?k?1Hence:DB?k1*502*503*50?????23?1??1?0.151?0.151?0.15?????2???$657.52

pB771.677kCk2BondD:

Given:couponrate=0%yieldtomaturity=15%，n=1Hence:pC?(b)

3F1000=$869.57?1?r1?0.15kCk2?k?1BondA:DAk1*1002*1003*100?????23?1???2??1?0.15?1?0.15??1?0.15??2.718pA885.84?k?13BondB:DB?k1*502*503*50?????23?1??1?0.151?0.151?0.15????2????2.838

pB771.677kCk2given:forBondC,BondD,thecouponrate=0hence:DC=3,DD=1

(c)So：DC>DB>DA>DD,Hence：BondCisthemostsensitive.

5.Considertwo5-yearbonds:onehasa9%couponandsellsfor101.00;theotherhasa7%couponandsellsfor93.20.Findthepriceofa5-yearzero-couponbond.

Solution:

Giventhefirstbondλ

1=9%,p2=101;thesecondbondλ

2=7%,p2=93.2.This

portfoliowillhaveafacevalueof0.9*100-0.7*100=20andapriceofp=0.9*93.2-0.7*101=13.18.Thecouponpaymentscancel,sothisisazero-couponportfolio.The10-yearspotrates5mustsatisfy(1+s5)p=20.This(1+s5)=20/13.18=1.517.Sothepriceofa5-yearszero-couponbondpv=d0,5F=F/(1+s5)5=100/1.517=65.92.

556.Ifthespotratesfor1and2yearsares1=6.3%ands2=6.9%,whatistheforwardratef1,2?

Solution:

Given,s1=6.3%ands2=6.9%,forthespotrates,theforwardratessatisfy:

(1+s2)2=(1+s1)(1+ｆ1,2)

hence,ｆ1,2=[(1+s2)2/(1+s1)]-1=[(1+0.069)2/(1+0.063)]-1=0.075

7.Thecorrelation?betweenassetsAandBis0.1,andotherdataaregiveninthefollowingtable.r?AssetA10.0%15%B18.0%30%

(a)Findtheproportions?ofAand(1-?)ofBthatdefineaportfolioofAandBhavingminimumstandarddeviation.

(b)Whatisthevalueofthisminimumstandarddeviation?(c)Whatistheexpectedreturnofthisportfolio?

solution:a)givenE(r?10%1)?r1E(r)2?r?218%?1?15%?2?30%?1?20.1?12??12??0.1?1?2??12?0.1*0.15*0.3?0.0045??21since?2?i,j?1?ww?ij2ijinwhichw1??,w2?1??sowecanget?2??2?11??(1??)?12??(1??)?21?(1??)2?22??2?11?2?(1??)?12?(1??)2?22inordertofindaminimumstandarddeviation,weletd?2d?d?2d??0;?2?11??2(1?2?)?12?2(1??)?22?0.207??0.171?0???0.8261???0.174so,wecanfindaportfolio,0.826ofAand0.174ofB,thatwillhaveaminimumstandarddeviation.b).theminimumstandarddviation2?????2?i,j?1?ww?ijij0.152?2?2?(1