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Unformatted text preview: p ' u I 11
EMAL .' Calculata 1h: duraiiunnf E: common stock l‘hat pays dividends at the end ofeach y'éar into pcfpeluity. assume than Ilhe dividend is constarﬂ, and'iha: The effeétiv; Tataoi'intlefest is 10%: ' ' . . "m 1w"
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“Cateutate the deratidn at a common stock that pays diyidends at the endsf each year inle perpetuity. Assume that the' d'Iyidend increases by 2% each year and that the eﬁectiye rele Df interest is 5%. ﬂ.
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NmIEmbar 2m: 1_ Calculaia 1hr: Macaulay duration or an eightyear lUIJ par value hand with 10% annual Course FM A bond win pat},r a coupon of Hill] a! the end of each ed" the next three years and will pay the faee'tralue (if lﬂﬂﬂ at IhE'Eﬁﬁ‘ﬁf the lh‘reeﬁﬂ‘r period. The band’s dinalien , {Macaulay duration} when valued using an annuai effective inlerem rale eflﬂﬁ‘ﬁ is X. Calculaie X. 1.
{A} Mi NELLDM/k '5 {B} 2.1:: M U {C} m ' 2, H, 1 a A 7
_— I i I_ L (D) 2.39 "' 7 E‘i [E] 3 .ﬂﬂ Course FM I :5 May ﬂit‘05 ﬂ. John purchased three bonds to form a portfolio as foliows: Bond A has semiannual coupons a1 4%, a duration 0111.415 years,
and was purchased For 980. Bond B is a 15year bond wilh a duralion of $1.35 years and
was purchased for 1015. ' Bond C has a duration ol‘ 1 6.6? years and was purchased for Iﬂﬂﬂ. ML: Calculate Lire duration of the portfolio at the limo onurehaso. (a) [sea years
(a) 16.5? years
' (C) 1531 years
(D) 163? years (E) [6.82 years a“; xZILLU ilKS‘uiolr 4 1mm grasp Managua: ' h—ﬂ' Oi‘ioeioirr km r I i677 F6 May 2005 9 Course F M C?
p 35. The current price of en ennual‘ccupcn bond is 10D. The cieriyeliye cf the price at the trend with respect to the yield to maturity is JED. The yield to maturity is an annual effective rate of 5%. Caiculete the dureticn cf the bend. {Anne 041A ._ PC )
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1131334334 .39" p 21. “Which of the following statements about immunization strategies are true? ' '11: . ' ii. To achieve immunization, the conve'xity oi" the assets must
1 69,951 the convexity of the liabilities.
H... ll. The full immunization technique is designed Io work for any
i _'. _ change in the interesl rate. flll. The theory of immunization was developed toprotect against
. r adverse effects created by changes in interest rates. {A} Hone
(B) l and ll only (C) l and lll only II and in only (E) The conch answer is not given by {A}, {E}, (C), and (D). p CM November 295'5 2# Course FM ’ 1D. A cumpany must pay Iiabiﬁlies nfmﬂﬂ and 20m] at the end ufyears l and 2, ' ' "Ircspeclively. The only investmenlsavailablc In the company are1h: {allowing 'w
~ '1‘ ﬁvu zerocqnpnn bends: Demnnine the can In the cumpany iodny to match its liabilities exactly. . (A) 2am
 . I (B 2259 ___...——— + L
' ' n: } 2503 {J ‘ l' l?“
(D) 27515 1.: Z I {#0 3
~ {E} 3ﬂﬂ] ' 6‘10 November 200.5 1.1 Came F M Course PM An inaurance company accepts an obligation [a pay lﬂ,ﬂl}ﬂ a1 Lhe end of each year for 2 ycars. The insurance company pmchasas a ccrnbinaliun cFlhc Fullcwing {wet hands at Calculate X. (A) 13,564
(a) 111,574
_{C} 111,534
{D} 13,594
{E} 13,604 {ll
(ii) lycaJ' 4% annual ccupun hand wiih a yicld rate cf5%  a total cual ui‘X in crdar to exactly match its uhligalicn: lwycar 6% annual ccupuu band with a yield rate ofﬁ'l'r‘é. 13 May 2005 30. As of matroe, an insurance company has a known obligation to pay $1,ﬂﬂﬂ,ﬂﬂﬂ on
‘lZlﬂ‘lﬂﬂﬂ'i'. To fund this liability1 the company immediately purchases 4year 5%
annual coupon bonds totaling $822,?DS of par value. 'The company anticipates reinvestment interest rates to remain constant at 5% through 12f31i’ﬂ7. The maturity value of the bond equals the par value] I at}
= 931.170}. at =93
1m castM» I .
: Lt LIE! Under the following reinvestment interest rate movement scenarios effective 1i'1i'2ﬂﬂ4.
what best describes the insurance company's prof it or (loss) as of tzfa‘ltZﬂDT after the liability is paid? Interest Interest Rates Rates Drop
by 141%
t +6. cos +11.14?
{a} {1435?} +14,4ia
“ {teem +1Q,'1i35
«a... (1,313) +i,323 Breakeven Breakaven Increase by Wit. nun Twas —i9‘W.m ‘: rtlﬁgtcg7 P The following iniormation applies to questions 51 thru 53. Joe mustpav'liabilities of LUCIE clue E months from now and another Loon due one year from now. There are Mo available investments: a 6month bond with face amount of “LUCIE, a 3% nominal annual coupon rate convertible semiannuallv1 anda 6% nominal annual vieicl rate convertible semiannuallv: and a oneyear bond with face amount of 1 rIL‘IlZiti, a 5% nominal annual coupon rate convertible semiannuellv, and a "its nominal annual 11.irieli:l rate convertible semiannuailiir 1 WM i~—~———t—~——l
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How much of eaéﬁb‘bﬁd should Joe purchaseiiit orde? R: exactly (absolutely) match the liabilities? k 6M3 C 1 W )
Elond l Bond H (Al 1 .El'i'ﬁEH (at. .ssaos 1 to) .9?551 .94293 to}~ same .3153 {E} scams .QTEE‘l Iﬁgl i iiosioi of“ p The following information applies to questions 51 thru 53. Joe must pay liabilities of LUCIE] due 5 months from now and another 1.ooo due one . year from now. There are two available investments: a 5month bond with face amount of LUCIE,a 8% nominal annual coupon rate convertible semiannuaily, and a 6% nominal annual yield rate convertible semiannually;  and a one—year bond with face amount of LOUD, a 5% nominal annual coupon rate convertible semiannually. and a ﬁt: nominal annual yield rate convertible semiannUally 52. What is'Joe‘ls total cost of purchasing the bonds required to exactly (absolutely) match ’ the liabilities? {A} 1594
(a) ' tend
to} ' 1914
{Di 1924
{E} ' 1saxlr p 1‘iIDBltﬂd Z z L \IL n The [allowing information applies to questions 51 thru 53 .Joen'iust*pavIiabi1ities of 11ooovdue 5 months from now and another mono due one year from now. There are two available investments: a 5month bond with face amount of 1,0ﬂﬂ, a 6% nominal annual coupon rate convertible semiannuallv1 and a 5% nominal annual yield rate convertible semiannuallv; and a oneyear bond with face amount of 1,033, e 5% nominal annual coupon rate convertible semiannuallv1 and a 7'“le nominal annual yield rate convertible semiannually 53. What is the annual effective vielo rate for investment in the bonds required to exactlyr b {absolutely} match the liabilities?I (A) 6.5% {B} 5.5% ﬂ
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