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Unformatted text preview: 35. I z: Cateuiate the duration refs common sleek that pays dividends at the end at" each year into penuetuity. Assume that the dividend is mnslant, and that the effective rate at" interest is “1%. {A} 7'
{B} s
(e) 11
{D} 19 {E} 2? F's
L' “meme P 3?. Calculate the duraticn of a ccmrncn stcht that pays dividends at the end cf each year
inlc perpetuity. Assume thatihe dividend increases by 2% each year and that the effective rate at interest is 5%. is) 2?
is} as
{C} 44
{D152 (E) SE r 1 1IDBJ'D4 C “.1. I Calculate the lll‘lazzaula},r duration of an eightyear lﬂﬂ par value hand wilh “3% annual w I I 'Iaaupans and an aﬁacliva rala afintaraal equal to 3%.
.i
'{AJ 4
(E) 5
.' {C} 15
{u} a
'{E} 3 (ix November 29(35 3 Ca uraa FM c 3. A band will pay a CDUpDn el‘ I [ll] aL lhe end areaeh a!" [he nem three years and will pay the face value of l Hill) at the end of the threeyear period. The bundle dunalien . [Macaulay duration] when valued using an annual effective inlereal rate of 213% iaX. Calculate X.
(A) 2.6]
{a} 2.10
{C} 2.1?
(D) 1.39
{E} 3110 C Course FM a. John purehased three bonds to form a portfolio as Foiiows: Bond A has semiannual coupons at 4%, a duration onI .415 years,
and was purchased for 9%. Bond E is a 15year bond with a duration of 2.35 years and
was purehased for “315. Bond (3 has a duration of 16.6? years and was purehased for 11300. Caieulate the duration ol’ the portfolio at the time ol'purehasa. {A} 1.5.62 years
{B} “5.6? years
{C} 145.?1 years
(D) 16.?! years [E]: 145.32 years  r
May zero g Course FM C? ﬂx‘.
Ev :35. The current price at an annual ccupcn bond is ml]. The derivative cf the price crthe bcnd 1with respect to the yield to maturity is JED. The yield to maturity is an annual eﬁective rate of 5%. Calculate the duration at the bend. (A) We
{a} 149
{c} v.55 [:x~ {p} rec {E} EDD c ﬁrearm ' a 1]. “Which of the following stolements about immunization strategies are true“? ' " 1. To achieve immunization, Ihc eonyE‘Jtiry of the assets must
equal Ihe convexity of the liabilities. ll. The full immunization Ieehnique is designed to work for any
change in the interest rate. .11]. The theory of immunization was developed to proleet against
adverse efi‘ eels ereeled by ehanges in interest rates. [A] None (B) l and ll only
it) I and Ill only
[I'll] ll and Ill only ‘, I (E) The correct answer is not given by {A}. (B), (C), and (D). m 8' a November 2ﬂﬂ5 Course FM’ i ll]. I A company musi pay liabilities of IDDD and EDDIE} at the end ofyearsi and 2, ' "reapeclively. The onlyr inveslmenla available lo the company are ihe following ' '1r  3' than zerocoupon bonds: ears annual ield Far
man Determine lhe coal to the companyr iocla}.r 1o maich its liabililiea exactly. Ls.) 2am  (a) 2259 ‘1' ' I (o) 2533
{o} 21'56 . {E} 30m November 2151135 _ . Course FM 9? r 15. An insurance company accepts an obligation to pa},r 10,000 at the end of each year for
2 years. The insurance company purchases a combination of the Following two bonds at a tolal cost ofJL’ in order to exactly.r match its obligation: [i]: 1—year 4% annual coupon bond with a yield rate ol'5% {ii} 2year 6% annual coupon bond wilh a yield raic of5%. Calculate X.
(A) 13,564
{a} I can
I“. ((3) 10,5 04
{o} I 3,594
[E] 10,604 r. Course FM P so. As of12i31iﬂa_an insurance company has a known obligation to pay $11tititi,tititi on
12i31i2uDT. To fund this liability. the company immediately purchases 4year 5%
annual coupon bonds totaling $322,?D3 of par value. The company anticipates
reinvestment interest rates to remain constant at 5% through 12l31!ﬂ?. The matun‘tyr value of the bond equals the par velue. Under the following reinvestment interest rete movement scenarios effe ctive 'll'li'2tiﬁ4,
what best describes the insurance company’s proﬁt or {loss} as oi 12l31i2i2iﬂ? after the liability is paid? {B} {1435?} +14.4ts
{Ci {18.9111 +1s,1ss {Di p.313) Interest Rates Interest
Increase by 125% Rates Drop by mass r 1 1IDBID4 The following information applies to questions 51 thru 53. Joe must pay: liabilities of 1000 due 0 months from now and another 1000 due one year from now_ There are two available investments: a 0month bond with face amount of 1.000, a 0% nominal annual coupon rate convertible semiannuallyn and a 0% nominal annual vield rate convertible semiannuallv; and a oneyear bond with face amount of 1,000, a 5% nominal annual coupon rale convertible semiannuallv, and a T% nominal annual vielo rate convertible semiannuallv 5‘1. How much of each bond should Joe purchase in order to exactly: {absolutele rnalch the liabilities? Band 
{F0 _ '1
{a} some
{C} £0501
to} .saaos
{E} 00345
lliDBiﬂd Bond I .QTSEH 34293 .9?551 .E?5Ei1 r The following information applies to questions 51 tth 53. .Joe must pay liabilities of1.EllJlJ clue E months from now and another LUBE} due one year from now. There are two available investments: a 8—month bond with face emount of LUCIE, e 8% nominal ennuel coupon rate convertible semiannuallv. and a 5% nominal annual vield rate oonverlible semiannuellv; and a onervear bond with face amount of LUBE}. e 5% nominal annual coupon rate oonverlibie semiannuallvi and a ﬁt: nominal annual vieid rate convertible semiannuailv 52. What is Joe‘s total oost of ourohesing the bonds required to exactly [absolutele metoh r the Iiabililjes? {A} 1 sea
{a} 1 em
(a; 1914
{o} 1924 {E} 1934 r 1 1l'ClElﬂJIll r The following information applies to questions 51 thru 53. Joe must pay liabilities of LUCIE! due 8 months from now and another 1.DDD due one year from now. There are two available investments: a 5month bond with face amount of 1.13130, a 8% nominal annual coupon rate convertible semiannually, end a 5% nominal annual yield rate convertible semiannually; and a oneyear bond with face amount of ‘lﬂﬂﬂ, a 5% nominal annual coupon rate convertible semiannually. and e We nominal annual yield rate convertible semiannuelly 53. What is the annual effective yield rate for investment in the bonds required to exactly r {absolutely} match the liabililias'FI is} see
re) 5.5%
to) are
to) sea
{E} save r 1 ‘lfﬂBID‘i ...
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This note was uploaded on 03/02/2012 for the course MATH 172 taught by Professor Kong during the Winter '09 term at UCLA.
 Winter '09
 kong

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