Page 1 FRM PART I BOOK 4: VALUATION AND RISK MoDELs VALUATION AND RISK MoDELs ...

260 Pages·2012·2.27 MB·English

FRM Parr I Book 4:
VALUATION AND Risk MopELs

‘Vauariow avo Risk Mooms
36: Bond Feces, Diseoune Bao, ara Arbitrage
37: Bod Prices, Spot Rags, anal Forward Rae
18s Yield co Manag
39 OneFaxus Menures of Price Sensi,
“4: Binomial Troe
Als 'The Blush Scholes Meron Model
42the

43: Meaeane of Feel Rie

ek Lew

4: Purring Yak on Wark
45: Cpereional Risk
‘4 areuing che Va Approach 19 Opsracional Risk

4: Sots Tesing
4; Principles (or Sound Sense Testing Pratiees and Superson
149: The Rating Agencies

5 sternal aad Ener Racings

Si: Unexpected Los
Concuanc Paoneace

CrraLuuncae Pramas Anwar

GARP FRM Pagcrice Exam Questions
GARP FRM Pracsior Exane Anewens
Fonworas

Avpexonx

Iwprx

Pye
Page 2

FRR PART DDK 4: VACONGION ANE: RSE MODES
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Bonn Prices, Discount Facrors, AND
ARBITRAGE

rope

Exam Focus

his opie pss aa overview of furan oMTwed valuation. "The vias ofa boc
in Seng the preset wai oi cask Rows sammie ache appropriate pelic requ
rerun, ize Faron tensed fo cig coupon bone and for detornitig whether
Tuan aad ohn ai. > eipringees aman sein ele abit
prof es be mace Som the violation ofthe lw of ne pre,

ATM 36.1; Dexaibe and course individval
value of wowey.

od manor axes

Peas ote To bolp annoer ATM 36.1, seal fe eines value af roomy
(priniplerprsentd im Bua$ 2, A dale tday will be woreh nore tn the fatare
‘ven a pattie raze af rvarm Sisley a llr paid im tbe furnve wil be
‘wor fis prevent vais srs

Derennunune Boxp Cast: Flows

Before computing the value of« bond ist detemine the appropriate cach tlons. Th cash
nr ef coupon bend her cn coniporents periodic coupons and pa value x mucin
(Coupons are aften sated in annua crms and must be adjuste for perodicey, Orr the
cas Hows are dstcimined,ehe reson value (PV) of ce exo flows can be computed

Beata How ea let

Suppote we bave 431,000 par vals, 1-yete Buta hac pays 210% coupon setwanially,
Destine he cash Rowe of es td

Answer
joao.

Wher ne20 mina payments of $50 [27,000 Amp sam payen of

5,000 eccus atch end of the 20e pind fe 10 yea

an Raghacoe, Page>
iets

‘Grow Helecence GARD Avsgnad Rening, Tackman, Chapter 1

age

Funpatetazs oF Bonp VALUATION

‘The vale (or price! of any financial aeee—auch ae a bond can ne dstermined by
summing the ater discoumed cask Hows. There are chee sep inthe bond valuaciow
proces:

1. Baise the oa fs. For 2sond, hove es em types of esk lows: (1) che ane ot
Sesame sinpom payavents aml (2 the rary Hf pti aarti, a» whe,

the bond ie erred,

2, _Detvnuine the apprepriredlivotne nate The approximate dicouae cate iether the
‘ond’ yield co inatutigy (PTM) oa ses of spar as

3. Candee eh PV of ee enim ch fs, The BV i terminal by dacs Be
bone cash How srream by the appropiate dicount atl.

‘As prosumsly aoced, bond investors are entitled to wo tise lyper of csh Rows: 1) che
periods. -resine af sompam inci cner the fie ofc bora ae (2 the renavety af prsial
(or par ale the lof the bones fie, Tho, valng a bond eels wich ams
super paymenes pls age ing cashflow, a epreentel by the recovery of prinsal

sr matarigg or when the bond ie retized, Thee cath floms, slong with the rie ate of
"e1um un thine lane, ae them use ina presen valus-baved bool valuation mad 19
<aleulate che dollar price of ie boa

tn eis rapi, ch eancanrtrion oral tha pay pen seminal in
month inne fom stele

Privs Quorarions

Sone an quont an png: hase late met ve (ID) Ral picid ar porate
qua 1005 hosed accu are priced tes ha 100; fo ol
[MESIUM sie gtr a 10, US esry neta and es “Se?
anes, Alege 9 97-4 o> 9706 0 97.4 asp x6 976495 of pa
sale the yr soi li, te pi the bene 297.1875 fe pa
Svs, 0 $977,85 00, Compra tad muripal bond ae quote cighihs

fog. 102), inde the ae ofthe bo 102125% of par, ether ce sen

‘rice quotation inc a ollie price ssuphy by adding the decimal equals of te rtm.
tw dhe base aumber of the quote and using thac asa percentage of che par amount to
amputee yove,

A"? ia the ques nia hs ck or ceanple, Fhe pce te qored 210-124, shen
selon would el at 10: 112349
Vipic 36
oss Relecce to GARP Asigned Reading ~ Tashan, Chapter

Disevuny Eacrons

AIM 36.2: Define diswount fator aul wae a discotit Funerioa te compute preset
fand fiture values.

icone cso deine the preset. The dicount faction expe
asd), whese #enoces cine in yas
anuple:Calealaging bood value wing disapane factors
Suppose Hat eh sce face for the fst 18-day coupon patie i at Follows
0.5) = 092432
Caleate the price a «bond that pers $108 six months Soa oy,

Ane

Since $1 robe receive in six months is worth $0.92432 tly, SECS recive in six
trond is words 0.9262 x $108 » $99.83 toby,

D> hors se tea f 8s sine 1

Bonds are securities cht pomize x frre sires of enh ows, ws «wie of Tresor fund
(Phun prices can be ore 0 generate the dixourt Gace,

‘Example: Calculating dicoum facts given bond prices
gue 1 shoves selected Thond prices for semiannual coupon $100 fice value bonds

Figuee I: Select Tretnny Ror Prices

Tare Ren SYN is Cacao

Fond Maury Biss
T 425% —~STSI06——«IOLIG
2 Tas% MSM? 5
3 20% Sie?
4 ow 50a 20-30
3 S75 WASH te

(Gencrate dhe dicount fcc fr the dane ndicared.

‘OUI apa Pays
vii 36

toss Refeeuce 19 GAR Aesiged Rea ~ Tacha, Chapter |

Pa 6

Aner:
Bond fp <= a a
‘Wher this bond matures on LW/ESIO6, imakesits les ineret payment of

‘sous

2125 - 20U5,.s1¢] pate psn pment of 10 Three fhe

102128 ena ee pee of 101-16, 10.50,

price) = CHN3) 05)

10.5 - 102.125 a0}
Salving fn che dacousn fusion yields
(0.5) 0.9939

Maring fsther our on the crs he function benomcs slightly ayrecomples ae cach
pint af the russe sus Benched, For example, to solve for Bond 2, wet include
A03).8 wel

Pan 2
‘he coupon payment 3¢ tae 0.5 is 3625 = 7.25 52, The final eth ew a ine

4 108,625 ~ 100 + 3.625, Those ro cash fo discounted back to 5/14/05 sing the
soot Tunesion should egal te pice of ce bord

10531 = 105.9844 ~ 3.625 d10.5) - 103.625 dL)

Since it sleady owe thar (0.5) ~ 0.9939, eubsttate thar value rap the equation el
sole fo aD

10S 9844 ~ (9.635 » 0.9939) + 103.625 €U1)1

a} = 09s

Begin he
Fepie so

(Cros Refaeace to GARD Asvgned Resiog ~ Taclonan, Chapter f

Using the same methodology for Bonds 3. 4, sa 5

Fond:

101.2188 = T.0410.5) + 1.0 a(t) + 101.4015)

Pi
aKT.5) 0.9825
Bord $ and Bond 5

<2m-05731
42.5) =0.9633

Figars 2: Disoount Factors

Toneim Matar Dlcoent Frome

03 0.9599
10 980
1s ngs
20 097s
a5 09638

TDiererwmning Vauoe Ustns Discount FoNctions
AIM 26.5: Define the “law of onc pricey” suppatt it using an arbitrage argument,
and describe hawit ean he aplied ta bam pa

AIM 36.6: Wenrify
cash lls,

hitrage oppertunities far fied income sceuitics with certain

‘The discounefuncsions previouly mensianed can be wed wo estimate che vale of a bond,
Since ineesor de nor care about the agin of cas How all else equal, a cash fw fom
fone bond i ose as god as» cath How ftom another bond. Thi phenentenoa i concmenly
feta ica che law oF one pics. Iocaare ae able wo explic a mpricing because of Ue
Tae of ome pig, ii eri ena a abige oppoveaniy

opus
ees

‘Cron Reiners to GARP Asin Reading ~ Tachnan, Chapter 1

age

Baample: denying abieage oppormaniica

Suppor you observe the anoual coup

cd aw a Re

Fignre 3: Obsetsed Pn Yiellsand Pricer,

Masry Enna Sess he (fd)
Te cy Ears
or) oe wS734
Dyers a a 00.000

‘The 2-year spat ate ie 8.167%, Is thre ap atbicage opporcarin? Hs, deerbe the
rads noessny ta exploit che aieags appomaniy

Anse

The anes ij ao atbieage profs ay bovealized becauss che YIM on the 2-year ze
coupon i 100 Tv (8% versus 8.16758), which means the bud ie wading 1b (te bord
pric it no high). Ta expla ths vila ion ofthe lave of one piss buy the 2-year, 8
‘uapor bond, stipe enupons, and shar: wll them separa he disco fctors are
‘Sexived om the piensa rhe serorcoupor: bonds

Fignee 4 Disa Frets

Tine Mwy Dit ator
10 039614
an ast

Yo demonsite rhe proass af epltng the asbitage opprnnity bes, eansdss the
allowing 3 sp proces de dllar guns gon sears)

Step f+ Bay $1 milion of the 2-yeee, 89% coupon borate besa chey ae rain singe
Step 2: Shore sell $80,000 ofthe 1-year, zero-coupon bones ar 96.154
‘Segp 3 Shore sell $1.08 min of the 2-year, 210-cougon bord a 85.74

igure 5: Cash Flow Diagram

Tine - 0 Ler Zin

T oral Pye,
cexgoa bands

sso.a00 | emt | 1080000 | ‘courene

=H909.00000 intent nua

lower 3 1 gona | sacri
ii hend tooo | enaciri a

me _ tet aa 1,680,600 | ‘rami

[Taxa Ne 7 no

79x20"

723.20 - 096156 « 8,000,
195,927.20 = 0.85734 «1,080,060

Boo Ryn he,
Tees

(GroxTefrance to GALL signed Hending~ Tackman, Chapter

‘The reul is receiving pore Hncome rey in retur Sor no fare ebigtion, aici 20
arbitrage eppomunny. The ein ofthe 2-vear STRIPS woul force the prive coven to
85.469 (che price ar-hich the YTM~ 8.167%, at whith poine the arbimage oppurmimicy
would disapaeae

‘Treaseny Couron Bonos anp Tasasuy STRIPS

[AIM 36.4: Discuss the components of a U.S. Treasury coupon bond, and compare
and contrast the structure ro Treasury STRIPS, inuluding the diference berween
P-STRIPS and C-STRIPS.

Yenw-oupon ‘nds ied by he Treasury are calla SHIPS (epaateuaing of wylstered
inter an prvi ecu). STRIPS wre eatod by reyust when a enupan bow is
nesnid to the Tresny. The bol i Seipped ini cy eoiuputiin:prwipal and
‘pupal (PASTRIPS and C-STRIPS. vepestivey.

"oe Tees a al retine 4 SUTIP by galing ta one upto momaitae, ot rena,
the eoupon honed, C-STRIPS eae he pur with ay bond taser, but STRIPS.

deatiged with specific bonds the rig bose that i as spp Foe, What this
means is chat ee eae of D-STRIP comes fom the utwersing bund, ebe uncetying
swat cheap, she C-STRIP wil be cheap. ifthe underlying was ich, the PATRIP will ao be
eh,

[STRIPS are of intsrest 9 ivesone boca

‘+ Zesoscoupon bonds can be ew used to ceeae any type nf ov How seam and char
mutch are cash tows with abt eah Howe (eg m provide fr cxlege expense.
Jhowst-purchase down payment, or other lability auding). Ths miigtes elavestment
risk (The concept of elavesrmerc rik wil be elscussed a later topics)

+ Zerocoupon bonds ate more tensive eo interest ete changes than are coupon bonds.
‘Tass could be an issue for asset lablicy oanagemenc or hedging purposes.

STRIPS do hove some dsedvaneage, which include the following:

“They canbe iliquid,
emmy STRIPS sna ena ich,

catty OSTRIPS cond cade hcp.

PASTRIDS pally ade at Bi valu

“Lange institu exe pont profi Tram STRIP nvepicngssltive ta the

underlying bowel, Ty cant ds Us yetber buying Trcnutes and auipping them

or revontioting STRIPS, Because of tae invoked wilh sipping tenstnating,

Svestorspenecally pay a preaina for aero-conpom bates

Bana phe

Per
“Tayi
Crows Reference 19 CARP Sesigoed Reading ~ Taso, Chapusr 1

Consraverme 4 Revtieatine PortPouo

fordcr to match the cash Flows oF x single given xed iwcome security.

Suppose 2-year fal income scarily exits with $100 face value ved a 10% esnyon se,
Thy emapons a pa 8 semiannaal bak, and the secaci’s YTM iv aswamed i be 459%.
"The presen value this bond, Bond, and its exh Hows ate caeulte as Fallows

ss

Py ee.
Toes Tea

No2K2- GLY 4502 225% FY LOO EMT 102 HCPL PY S1I04T

chs bond is determined robe rading “cheap” then a uader can conduct a. arbitrage
trae by purchasing he madesvaued bond and shorting 2 replicating peril hat enimies
the howl cath lows, Ts demorstra the creation of «rearing porfolis, sorume

the follwing four fined income secnees exer. addition ro the bond wea ying

‘een
a er
2 7 sion 5105 Frronths 05 ye
5 ime sions sto U2 ead ys
‘ Sw stone 1 mtr tL ya
5 ow enss avo erway

‘Te cree repicatng portilio sing spl urd-incare scutes, we amuse deeraine
she fre amounts ofeach bond to poschae, which match ond 1 cashflows in each
semisannal period,

™

PN gi a

Boo REx

“When doing chis calelation by itand, ce eases eo sear fan che end—wich the bond that
suatches Bond 1 rime Yorizan, In eh cae, dar secures ond 5. Since the other bord
donot make payments in 24 months. bey ate war cossiderd in this Bcscstep Ley hel

Solsing his oy ian fr ld the fag amouoe petunia we nea purchase of Bond
54K, ~ 101.9). Sau thsGoupon rate os Bod 53 wr tha shat of Bond 1, mee
‘onsechat well nce to parca more oF Boral 5 [101 409} chan the £1.00 face sale 0”
Bond 1. Wie em now ite the valle of Fy to sive for Fy

Poe lt oni oamcd