Questions #4-9 of 172
We canthenreadofftheright-handsideoftheequationto createasynthetic positioninthe call. Wewouldneedto buy the Europeanput, buy thestock,andshortorissuearisklesspure-discount bondequal invaluetothepresentvalueofthe exerciseprice.
Steve Millerisaseniorfixedincometraderfora large hedgefund basedin New York. Miller hasrecently hiredC.D. Johnson toassist Millerinimplementingsomederivative-basedtrades. Millerwould liketoensurethat Johnsonunderstandsthe basics ofinterestratederivatives beforeallowing himto beinvolvedintosomemore complicatedtradingstrategies. Miller createsa hypothetical bondscenariofor Johnsontoanalyzeinorderfor himtoevaluate Johnson'sexpertiseinthearea. Millerinstructs Johnsonto considerthe London Interbank OfferedRate (LIBOR)interestrateenvironmentinTable1.
Table
1
90-Day
LIBOR
F
orward
Rates
and
Implied
Spot
Rates
Period
(in
months) LIBOR
F
orward
Rates Implied
Spot
Rates
0 ×
3
5
.
500%
5
.
5000%
3
× 6
5
.7
50%
5
.
6
2
50%
6 × 9
6
.
000%
5
.7
499%
9 ×
1
2
6
.2
50%
5
.
8
7
49%
1
2
×
1
5
7.
000%
6
.
099
7
%
1
5 ×
1
8
7.
000%
6
.2
496%
48 × 5
1
8
.
1
00%
7.
1
22
8%
5
1
× 54
8
.2
00%
7.
1
8
2
6%
54 × 5
7
8
.3
00%
7.2
4
1
3
%
5
7
× 60
8
.
400%
7.2
99
2
%
60 × 6
3
8
.
500%
7.3
56
3
%
6
3
× 66
8
.
600%
7.
4
1
27
%
66 × 69
8
.7
00%
7.
4686%
69 ×
72
8
.
800%
7.
5
2
40%
72
×
7
5
8
.
900%
7.
5
7
89%
7
5 ×
7
8
9
.
000%
7.
6
33
5%
7
8 × 8
1
9
.
1
00%
7.
68
77
%
8
1
× 84
9
.2
00%
7.7
4
1
6%
84 × 8
7
9
.3
00%
7.7
95
3
%
Question #6 of 172
Question ID: 464268ᅞ A) ᅚ B) ᅞ C)
Question #7 of 172
Question ID: 464269ᅞ A) ᅞ B) ᅚ C)
Question #8 of 172
Question ID: 464270Incorrectanswerexplanations:
Sellinganinterestrate capisnota hedgeagainstrisinginterestrates.
Buyinganinterestratefloor hedgestherisk ofdecreasinginterestrates.
(Study Session17, LOS 55.a)
Millernowasks Johnsonto computethepayoffofthe capandfloorinTable2assumingthat LIBOR hasrisento7% at expiration.Specifically, Millerwants Johnsontodeterminethenetpayoffofthe correspondingshort collar (buyingthefloorand
sellingthe cap)forthetotal outstandingamountofthefloatingrate bond. Which ofthefollowingistheclosestto Johnson's answer?
$300,000. -$300,000. −$450,000.
Explanation
Thefloorexpiresworthlesswhilethe capisexercisedandtheseller hastopay thedifference betweenthe capstrikerateand LIBORwhich is1% inthis case. Hencethe calculationisasfollows:
Net Payoff = (6.00% − (7.00%)) × $30,000,000 = −$300,000
Theanswer −$450,000 isincorrect becausethepayoffisdetermined by the LIBORrate,not by thespreadover LIBORforthe
floatingrate bond. (Study Session17, LOS 55.b)
Next, Millerasks Johnsontodeterminethenetpayoffofthe corresponding long collar (buyingthe capandsellingthefloor)for thetotal outstandingamountofthefloatingrate bond.Assumethat LIBOR hasrisento 8% atexpiration. Which ofthefollowing istheclosestto Johnson'sanswer?
−$600,000. $900,000. $600,000.
Explanation
Thefloorexpiresworthlesswhilethe capisexercisedandtheseller hastopay thedifference betweenthe capstrikerateand LIBORwhich is2% inthis case. Hencethe calculationisasfollows:
Net Payoff = (8.00% − (6.00%)) × $30,000,000 = $600,000
(Study Session17, LOS 55.b)
Question #11 of 172
Question ID: 464208ᅞ A) ᅚ B) ᅞ C)
Question #12 of 172
Question ID: 464119ᅚ A) ᅞ B) ᅞ C)
Question #13 of 172
Question ID: 464227ᅞ A) ᅞ B) ᅚ C)
Thefloating-ratepayerinasimpleinterest-rateswap hasapositionthatisequivalentto: a series of long forward rate agreements (FRAs).
aseriesofshortFRAs.
issuingafloating-rate bondandaseriesof longFRAs.
Explanation
Thefloating-ratepayer hasa liability/gainwhenratesincrease/decreaseabovethefixed contractrate;theshortpositioninan
FRA hasa liability/gainwhenratesincrease/decreaseabovethe contractrate.
Fora changeinwhich ofthefollowinginputsintotheBlack-Scholes-Mertonoptionpricingmodel will thedirectionofthe changeinaput'svalueandthedirectionofthe changeina call'svalue bethesame?
Volatility. Exerciseprice.
Risk-freerate.
Explanation
Adecrease/increaseinthevolatility ofthepriceoftheunderlyingassetwill decrease/increase both putvaluesand call values. A changeinthevaluesoftheotherinputswill haveoppositeeffectsonthevaluesofputsand calls.
Considerafixed-ratesemiannual-pay equity swapwheretheequity paymentsarethetotal returnona $1millionportfolioand
thefollowinginformation: 180-day LIBORis 4.2% 360-day LIBORis 4.5%
Div. yieldontheportfolio = 1.2% Whatisthefixedrateontheswap?
4.5143%. 4.3232%. 4.4477%.
Question #14 of 172
Question ID: 464235ᅞ A) ᅚ B) ᅞ C)
Question #15 of 172
Question ID: 464168ᅞ A) ᅞ B) ᅚ C)
Question #16 of 172
Question ID: 464212ᅞ A) ᅚ B) ᅞ C)
= 0.022239 × 2 = 4.4477%
Aninvestorwhoanticipatestheneedtoexitapay-fixedinterestrateswappriortoexpirationmight:
buy a payer swaption. buy areceiverswaption.
sell apayerswaption.
Explanation
Areceiverswaptionwill,ifexercised,provideafixedpaymenttooffsettheinvestor'sfixedobligation,andallow himtopay floatingratesifthey decrease.
Comparedtothevalueofa call optiononastock with nodividends,a call optiononanidentical stock expectedtopay a
dividendduringthetermoftheoptionwill havea:
higher value only if it is an American style option. lowervalueonly ifitisanAmericanstyleoption. lowervalueinall cases.
Explanation
Anexpecteddividendduringthetermofanoptionwill decreasethevalueofa call option.
Writingaseriesofinterest-rateputsand buyingaseriesofinterest-rate calls,all atthesameexerciserate,isequivalentto: a short position in a series of forward rate agreements.
beingthefixed-ratepayerinaninterestrateswap. beingthefloating-ratepayerinaninterestrateswap.
Explanation
Ashortpositionininterestrateputswill haveanegativepayoffwhenratesare belowtheexerciserate;the callswill have
Question #34 of 172
Question ID: 464162ᅞ A) ᅚ B) ᅞ C)
Question #35 of 172
Question ID: 464225ᅚ A) ᅞ B) ᅞ C)
Arisklessportfolioisdeltaneutral;thedeltais zero.
Which ofthefollowingisthebestapproximationofthegammaofanoptionifitsdeltaisequal to 0.6 whenthepriceoftheunderlying
security is100 and 0.7whenthepriceoftheunderlyingsecurity is110?
1.00.
0.01.
0.10.
Explanation
Thegammaofanoptionis computedasfollows:
Gamma = changeindelta/changeinthepriceoftheunderlying = (0.7 - 0.6)/(110 - 100) = 0.01
90 daysagotheexchangeratefortheCanadiandollar (C$)was $0.83andthetermstructurewas:
180
d
a
y
s
3
60
d
a
y
s
LI
BOR
5
.
6%
6%
C
DN
4
.
8%
5
.
4%
.
Aswapwasinitiatedwith paymentsof 5.3% fixedinC$ andfloatingratepaymentsin USD onanotional principal of USD 1
millionwith semiannual payments.
90 days havepassed,theexchangerateforC$ is $0.84 andthe yield curveis:
90
d
a
y
s 2
70 days
LIBOR
5.2%
5.6%
CDN
4.8%
5.4%
Whatisthevalueoftheswaptothefloating-ratepayer?
$10,126. $3,472. −$2,708.
Explanation
Question #3
6
of 172
Question ID: 464165ᅞ A) ᅞ B) ᅚ C)
Question #37 of 172
Question ID: 464118ᅚ A) ᅞ B) ᅞ C)
Question #3
8
of 172
Question ID: 464294(1.028 / 1.013) = 1.014808
1.014808 × 1,000,000 = $1,014,808
ThepresentvalueofthefixedC$ paymentsper1CDN is:
(0.0265 / 1.012) + (1.0265 / 1.0405) = 1.012731andforthewholeswapamount,in USD is1.012731 × 0.84 × (1,000,000 / 0.83) = $1,024,932
−1,014,808 + 1,024,932 = $10,126
Gammaisthegreatestwhenanoption: is deep out of the money. isdeepinthemoney. isatthemoney.
Explanation
Gamma,the curvatureoftheoption-price/asset-pricefunction,isgreatestwhentheassetisatthemoney.
Which ofthefollowingoptionsensitivitiesmeasuresthe changeinthepriceoftheoptionwith respecttoadecreaseinthetimeto
expiration?
Theta.
Delta.
Gamma.
Explanation
Thetadescribesthe changeinoptionpriceinresponsetothepassageoftime.Sinceoption holderswouldpreferthatvaluenotdecay too
quickly,anoptionwith a lowthetavalueisdesirable.
ᅞ A) ᅞ B) ᅚ C)
Question #3
9
of 172
Question ID: 464139ᅚ A)
ᅞ B) ᅞ C)
Question #
4
0 of 172
Question ID: 464238ᅚ A) ᅞ B) ᅞ C)
Questions #
4
1
-46
of 172
couponrateof 5%.ThedurationoftheCDS = 4.
Theupfrontpaymentmade/received by theprotection buyerona $4 millionnotional CDSisclosestto:
$400,000 received by the protection buyer. $300,000 paid by theprotection buyer. $320,000 received by theprotection buyer.
Explanation
Upfrontpayment= (CDSspread − CDS coupon) × duration × notional principal
= (0.03 − 0.05) × 4 × 4,000,000 = −$320,000
Theprotection buyerwill receiveanupfrontpremiumof $320,000.
Thedeltaofanoptionisequal tothe:
dollar change in the option price divided by the dollar change in the stock price.
dollar changeinthestock pricedivided by thedollar changeintheoptionprice. percentage changeinoptionpricedivided by thepercentage changeintheasset price.
Explanation
Thedeltaofanoptionisthedollar changeinoptionpriceper $1 changeinthepriceoftheunderlyingasset.
Which ofthefollowingisleastlikelyto beauseofaswaption?
Hedging the risk of a current fixed-rate commitment. Exitinganoffsettingswapattheexercisedate.
Hedgingtherisk ofananticipatedfloating-rateobligation.
Explanation
Swaptionswill not beagood hedgefora currentobligationsincetheswaptionisforaswapinthefuture.
Frank Potter,CFA,afinancial adviserforStarFinancial, LLC has been hired by John Williamson,arecently retiredexecutivefromReston
Industries.Overthe years Williamson hasaccumulated $10 millionworth ofRestonstock andanother $2millionina cash savings
account. Potter hasanumberofunconventional investmentstrategiesfor Williamson'sportfolio;many ofthestrategiesincludetheuseof
ᅞ C)
Question #
4
7 of 172
Question ID: 464249ᅞ A) ᅚ B)
ᅞ C)
Question #
48
of 172
Question ID: 464292ᅞ A) ᅞ B) ᅚ C)
Buy a collar.
Explanation
Buyingafloor combinedwith afloatingrateassets limitstheexposuretointerestratedecreases (i.e.noexposuretointerest
ratedecreases belowstrikerate)whilethefloatingrate holderisstill ableto benefitfrominterestrateincreases. Ideally, Potter should considermatchingthe bank'sassetpositionagainstthe bank's liability position.
(LOS 55.a)
Aswapspreadisthedifference between: LIBOR and the fixed rate on the swap.
thefixedrateonaninterestrateswapandtherateonaTreasury bondofmaturity
equal tothatoftheswap.
thefixed-rateandfloating-ratepaymentratesattheinceptionoftheswap.
Explanation
Aswapspreadisthedifference betweenthefixedrateonaninterestrateswapandaTreasury bondofmaturity equal tothat oftheswap.
Gill WestmoreisthefixedincomeportfoliomanagerforAllied Insurance. Westmore has boughtprotectionusinga2-yearCDS onCDX-IG (125 constituent)index.Thenotional is $200 million.Company X,anindex constituentdefaultsandtradesat25% ofpar.
ThepayoffontheCDSonaccountofdefaultof X andthenotional principal oftheCDSafterdefaultareclosestto: Payoff Notional
$1.5 million $198 million $1.6 million $200 million $1.2million $198.4 million
Explanation
Notional principal attributableto bondsof company X = $200 million/125 = $1.6 million.
PayoffontheCDS = $1.6 million − (0.25)($1.6 million) = $1.2million.
Question #
49
of 172
Question ID: 464290ᅚ A)
ᅞ B)
ᅞ C)
Question #
5
0
of 172
Question ID: 464194ᅞ A)
ᅚ B)
ᅞ C)
Question #
5
1 of 172
Question ID: 464215ᅞ A)
ᅚ B)
ᅞ C)
Assume that a three-yearsemi-annually settled cap with astrikerateof 8% andanotional amount of $100 million is being analyzed. The
referencerate issix-month LIBOR. LIBOR for thenext foursemi-annual periods isas follows:
Period LIBOR
1 7.5%
2 8.2%
3 8.1%
4 8.7%
What is thepayoff for the cap forperiod 4?
$350,000.
$700,000.
$0.
Explanation
Thepayoff foreach semi-annual period is computedas follows:
Payoff = notional amount × (six-month LIBOR - caprate)/2 so forperiod 4:
= $100 million × (8.7% - 8.0%)/2 = $350,000.
At the inceptionof a market-rateplain vanillaswap, the valueof theswap to the fixed-ratepayer is:
positive.
zero.
eitherpositiveornegative.
Explanation
A market-rateswap ispricedso that the value toeitherside is zeroat the inceptionof theswap.
If theone yearspot rate is 5%, the two-yearspot rate is 5.5%, and the three yearspot rate is 6%, the fixedrateona 3-yearannual pay
swap isclosest to:
1.99%.
5.65%.
4.50%.
Question #
5
2 of 172
Question ID: 464163ᅚ A)
ᅞ B)
ᅞ C)
Question #
5
3 of 172
Question ID: 464282ᅞ A)
ᅞ B)
ᅚ C)
Question #
5
4
of 172
Question ID: 464101The fixedrateon theswap is:
= 0.1525 / 2.7008 = 0.0565
Two call options have thesamedelta but option A hasa higher gamma thanoption B. When thepriceof theunderlying asset increases,
thenumberof option A callsnecessary to hedge thepricerisk in 100 sharesof stock, compared to thenumberof option B calls, isa:
smaller (negative) number.
largerpositivenumber.
larger (negative) number.
Explanation
For call options larger gamma means that as theasset price increases, thedeltaof option A increases more than thedeltaof option B.
Since thenumberof calls to hedge is (- 1/delta)x(numberof shares), thenumberof callsnecessary for the hedge isasmaller (negative)
number foroption A than foroption B.
An issuer who wishes to issuea floating ratenote with a collar would beequivalently issuing thenoteand:
buying a cap and a floor.
selling a capand buying a floor.
buying a capandselling a floor.
Explanation
Issuing a floating ratenote with a collar (a capanda floor) isequivalent to issuing thenote, buying a cap toput anupper limit on the
interest cost, andselling a floor which wouldput a minimum on interest expenseandoffset the cost of the cap tosomeextent.
A two-period interest rate tree has the following expectedone-periodrates:
t
= 0
t = 1 t = 27
.
12
%
6.83%
ᅞ A)
ᅚ B)
ᅞ C)
Question #
55
of 172
Question ID: 464273ᅞ A)
ᅚ B)
ᅞ C)
Questions #
5
6-6
1 of 172
6.17%
6
.
22
%
Thepriceof a two-period European interest-rate call optionon theone-periodrate with astrikerateof 6.25% andaprincipal amount of
$100,000 isclosest to:
$449.33.
$423.89.
$725.86.
Explanation
1. Calculate thepayoffson the call inpercent for I++ and I+− (= I−+):
I++ value = (0.0712 − 0.0625) / 1.0712 = 0.00812173.
I+− value = (0.0684 − 0.0625) / 1.0684 = 0.00552228.
Remember that thepayoff on the call value is thepresent valueof the interest ratedifference basedon theraterealizedat t = 2
because thepayment isreceivedat t = 3.
2. Calculate the t = 1 values (theprobabilities inan interest rate treeare 50%):
At t = 1 the valuesare I+ = [0.5(0.00812173) + 0.5 (0.00552228)] / 1.0683 = 0.00638585.
At t = 1 the valuesare I− = [0.5(0) + 0.5 (0.00552228)] / 1.0617 = 0.00260068.
3. Calculate the t = 0 value:
At t = 0 theoption value is [0.5(0.00638585) + 0.5(0.00260068)] / 1.06 = 0.00423893 0.00423893 × 100,000 = $423.89.
A capona floating ratenote, from the bondholder'sperspective, isequivalent to:
writing a series of interest rate puts.
writing aseriesof putson fixed incomesecurities.
owning aseriesof callson fixed incomesecurities.
Explanation
Fora bondholder, a cap, which putsa maximum on floating rate interest payments, isequivalent to writing aseriesof putson fixed
incomesecurities. These wouldrequire the buyer topay whenratesriseand bondprices fall, negating interest rate increasesabove the
caprate. Writing aseriesof interest rate calls, not puts, would beanequivalent strategy.Callson fixed incomesecurities wouldpay when
ratesdecrease, not when they increase.
Gina Davalos, CFA isaportfolio manager for the Herron Investments. She is interested in hedging theequity risk of oneof her clients,
Lou Gier. Gier has 200,000 sharesof astock with thesymbol QJX that he believes could takeadive in thenext 9 months. Davalos
Question #
5
8
of 172
Question ID: 464144increases, some option contracts would need to be sold in order to retain the delta
ᅞ B)
ᅚ C)
Question #
6
2 of 172
Question ID: 464193ᅞ A)
ᅚ B)
ᅞ C)
Question #
6
3 of 172
Question ID: 464231ᅞ A)
ᅞ B)
ᅚ C)
Questions #
64-69
of 172
Buying the futuresand buying thestock QJX.
Buying thestock QJX, andselling the futures.
Explanation
The calculated fair valueof the futures contract is $100 × (1+0.05) = $103.73. Theasset isrelatively underpricedand the futures
contract isoverpriced. By buying thestock andselling the futures we can lock inaprofit greater than therisk-freerate with norisk. (LOS
51.b)
Regarding deep in-the-money optionson futures, it is:
sometimes worthwhile to exercise calls early but not puts.
sometimes worthwhile toexercise both callsandputsearly.
never worthwhile toexerciseputsor callsearly.
Explanation
If putsor callson futuresaresignificantly in-the-money it may be worthwhile toexercise them early to generate the cash from the
immediate mark to market of the futures contract when theoption isexercised.
Which of the following statementsregarding swaptions is leastaccurate? A swaption isoftenused to:
provide the right to terminate a swap.
hedge therateonananticipatedswap transaction.
createasynthetic bondposition.
Explanation
A swaption is likeanoptionona bond with paymentsequal to the fixedpaymentson theswap. Theothersare commonusesof swaps.
Jacob Bower isa bondstrategist who would like to beginusing fixed-incomederivatives in hisstrategies. Bower hasa firm understanding
of theproperties fixed-incomesecurities. However, hisunderstanding of interest ratederivatives isnot nearly asstrong. Hedecides to
train himself on the valuationandsensitivity of interest ratederivativesusing various interest ratescenarios. He considers the forward
London Interbank Offered Rate (LIBOR) interest rateenvironment shown in Table 1. Using aroundeddaycount (i.e., 0.25 years foreach
quarter) he hasalso computed the corresponding impliedspot ratesresulting from these LIBOR forwardrates. Theseare included in Table
1.
T
a
b
le
1
90-
Day
LI
B
OR
F
or
w
ard
R
a
t
es
and
I
mpl
i
ed
S
po
t
R
a
t
es
Question #
64
of 172
Question ID: 464276ᅞ A)
ᅞ B)
ᅚ C)
Per
i
od
(i
n
mon
th
s
) LI
B
OR
F
or
w
ard
R
a
t
es
I
mpl
i
ed
S
po
t
R
a
t
es
0 ×
3
5
.
500%
5
.
5000%
3
× 6
5
.
7
50%
5
.
6
2
50%
6 × 9
6
.
000%
5
.
7
499%
9 ×
12
6
.
2
50%
5
.
8
7
49%
12
×
1
5
7
.
000%
6
.
099
7
%
1
5 ×
1
8
7
.
000%
6
.
2
496%
Bower hasalsoestimated the LIBOR forwardrate volatilities to be 20%. Theparticular fixed instruments that Bower would like toexamine
areshown in Table 2. Healso wants toanalyze thestrategy shown in Table 3.
T
a
b
le
2
I
n
t
eres
t
R
a
t
e
I
ns
t
rumen
t
s
Doll
a
r
Am
oun
t
o
f
F
lo
ati
n
g
Rat
e
B
on
d
$4
2,
000
,
000
F
lo
ati
n
g
Rat
e
B
on
d
p
a
y
i
n
g
LI
BOR
+
0
.
2
5%
Tim
e
t
o M
at
u
r
it
y (y
e
a
rs
)
8
C
a
p
St
r
i
k
e
Rat
e
7
.
00%
F
loo
r
St
r
i
k
e
Rat
e
6
.
00%
In
t
eres
t
P
a
y
m
e
n
t
s
qu
a
r
t
er
ly
T
a
b
le
3
I
n
iti
al
Pos
iti
on
i
n
90-
day
LI
B
OR
Eurodollar
Con
t
ra
ct
s
Con
t
ra
ct
Mon
th
(
f
rom
no
w
) St
ra
t
e
g
y
A
(c
on
t
ra
ct
s
) St
ra
t
e
g
y
B
(c
on
t
ra
ct
s
)
3
m
on
t
h
s
3
00
1
00
6
m
on
t
h
s
0
1
00
9
m
on
t
h
s
0
1
00
Bower isa bit puzzledabout how touse capsand floors. He wonders how he could benefit both from increasing anddecreasing interest
rates. Which of the following trades wouldmost likely profit from this interest ratescenario?
Sell at the money cap and at the money floor.
Buy at the money capandsell at the money floor.
Buy at the money capandat the money floor.
Explanation
This isastraddleon interest rates. The capprovidesapositivepayoff when interest ratesriseand the floorprovidesapositivepayoff
ᅚ C)
Question #7
0
of 172
Question ID: 464226ᅞ A)
ᅞ B)
ᅚ C)
Question #71 of 172
Question ID: 464228pay fixed interest rateswap.
Explanation
Since the interest ratesareexpected torise forall maturities, one can benefit from thisrise by receiving a floating rate (LIBOR) and
borrowing at a fixedrate (i.e.apay fixedswap). (Study Session 16, LOS 54.c)
Considera fixed-for-fixed 1-year $100,000 semiannual currency swap with ratesof 5.2% in USD and 4.8% inCHF, originated when the
exchangerate is $0.34. 90 days later, theexchangerate is $0.35 and the term structure is:
90 days
2
7
0
days
LI
BOR
5
.
2
%
5
.
6%
Swi
ss
4
.
8%
5
.
4%
What is the valueof theswap to the USD payer?
-$2,719.
$2,814.
$2,719.
Explanation
Thepresent valueof the fixedpaymentsononeCHF is
0.02372 + 0.98414 = 1.00786.
At the current exchangerate the value is 1.00786 × 0.35 = USD 0.35275.
Thenotional amount is 100,000/0.34 = 294,118 CHF so thedollar valueof theCHF payments is 0.35275 × 294,118 = $103,750.
Thepresent valueof the USD payments is
0.02567 + 0.98464 = 1.01031
1.01031 × 100,000 = $101,031.
The valueof theswap to thedollarpayer is 103,750 - 101,031 = $2,719.
Considera fixed-ratesemiannual-pay equity swap where theequity paymentsare the total returnona $1 millionportfolioand the following
ᅞ A)
ᅞ B)
ᅚ C)
Question #72 of 172
Question ID: 464179ᅚ A)
ᅞ B)
ᅞ C)
Question #73 of 172
Question ID: 464114ᅚ A)
ᅞ B)
ᅞ C)
Question #7
4
of 172
Question ID: 464274180-day LIBOR is 5.2%
360-day LIBOR is 5.5%
Dividend yieldon theportfolio = 1.2%
What is the fixedrateon theswap?
5.4197%.
5.1387%.
5.4234%.
Explanation
Which of the following statements concerning vega ismostaccurate? Vega is greatest whenanoption is:
at the money.
farout of the money.
far in the money.
Explanation
When theoption isat the money, changes in volatility will have the greatest affect on theoption value.
Which of the following is NOT oneof theassumptionsof the Black-Scholes-Merton (BSM) option-pricing model?
Any dividends are paid at a continuously compounded rate.
Thereareno taxes.
Options valuedare Europeanstyle.
Explanation
The BSM model assumes thereareno cash flowson theunderlying asset.
Which of the following bestdescribesan interest rate cap? An interest rate cap isapackageorportfolioof interest rateoptions that
ᅞ A)
ᅞ B)
ᅚ C)
Question #7
5
of 172
Question ID: 464240ᅞ A)
ᅚ B)
ᅞ C)
Question #7
6
of 172
Question ID: 464247ᅞ A)
ᅚ B)
ᅞ C)
Question #77 of 172
Question ID: 464291ᅚ A)
ᅞ B)
ᅞ C)
T-Bond futures exceeds the strike price.
referencerate is below thestrikerate.
referencerateexceeds thestrikerate.
Explanation
An interest rate cap isapackageof European-type call options (called caplets) onareference interest rate.
Thepayoff onareceiverswaption is most like that of a:
put option on a discount bond.
call optionona coupon bond.
put optionona coupon bond.
Explanation
Thepayoff onareceiverswaption is like that of a call optionona bond issuedat theexercisedateof theswaption, with a couponequal
to the fixedrateof theswap, anda term equal to that of theswap.
Compared toanequity swap, a currency swap has credit risk that is:
approximately the same during the life of the swap.
greater, later in theswap.
greater, earlier in theswap.
Explanation
A currency swap hasa final exchangeof principal, moving the maximum credit risk later in the lifeof theswap.
Which of the following bestrepresentsan interest floor?
A portfolio of put options on an interest rate.
A put optiononan interest rate.
A portfolioof call optionsonan interest rate.
Explanation
Question #7
8
of 172
Question ID: 464186the underlying asset, long a put at X, and short in a pure-discount risk-free bond that
Question #
8
7 of 172
Question ID: 464189A strip of three forward rate agreements, which obligates the party to pay a fixed rate of
6% and receive six-month LIBOR on a notional principal of $100,000,000.
increase as the volatility of the underlying asset increases because call options have
Question #
90
of 172
Question ID: 464169ᅚ A)
ᅞ B)
ᅞ C)
Question #
9
1 of 172
Question ID: 464183ᅞ A)
ᅞ B)
ᅚ C)
Question #
9
2 of 172
Question ID: 464116ᅞ A)
ᅚ B)
ᅞ C)
Question #
9
3 of 172
Question ID: 464140ᅞ A)
ᅞ B)
Dividendsonastock can be incorporated into the valuation model of anoptionon thestock by:
subtracting the present value of the dividend from the current stock price.
subtracting the future valueof thedividend from the current stock price.
adding thepresent valueof thedividend to the current stock price.
Explanation
Theoptionpricing formulas can beadjusted fordividends by subtracting thepresent valueof theexpecteddividend(s) from the current
asset price.
If weuse fourof the inputs into the Black-Scholes-Mertonoption-pricing model andsolve for theasset price volatility that will make the
model priceequal to the market priceof theoption, we have found the:
historical volatility.
option volatility.
implied volatility.
Explanation
The questiondescribes theprocess for finding theexpected volatility implied by the market priceof theoption.
The valueof aput option ispositively related toall of the following EXCEPT:
time to maturity.
risk-freerate.
exerciseprice.
Explanation
The valueof aput option isnegatively related to increases in therisk-freerate.
Thepriceof a June call option with anexercisepriceof $50 falls by $0.50 when theunderlying stock price falls by $2.00. Thedeltaof a
Juneput option with anexercisepriceof $50 isclosest to:
-0.25.
ᅚ C)
Question #
94
of 172
Question ID: 464177ᅞ A)
ᅞ B)
ᅚ C)
Question #
9
5
of 172
Question ID: 464224ᅞ A)
ᅚ B)
ᅞ C)
Question #
96
of 172
Question ID: 464222-0.75.
Explanation
The call optiondelta is:
Theput optiondelta is 0.25 - 1 = -0.75.
Which of the following is least likely a common form of external credit enhancement?
A corporate guarantee.
Bond insurance.
Portfolio insurance.
Explanation
External credit enhancementsare financial guarantees from thirdparties that generally support theperformanceof the bond. Portfolio
insurance isnot a thirdparty guarantee.
A U.S. firm (U.S.) anda foreign firm (F) engage ina fixed for floating currency swap. The fixedrateat initiationandat theendof theswap
was 5%. The variablerateat theendof year 1 was 4%, at theendof year 2 was 6%, andat theendof year 3 was 7%. At the beginning
of theswap, $2 million wasexchangedat anexchangerateof 2 foreignunitsper $1. At theendof theswapperiod theexchangerate was
1.75 foreignunitsper $1.
At the terminationof theswap, onaccount of exchangeof principal, firm F gives firm U.S.:
$1,750,000.
$2 million.
4 million foreignunits.
Explanation
At termination, thenotional principal will beexchanged. Firm F gives back what it borrowed, $2 million, and the terminal exchangerate is
not used.
Consideraone-year currency swap with semiannual payments. Thepaymentsare in U.S.dollarsandeuros. The current exchangerateof
theeuro is $1.30 and interest ratesare
ᅚ A)
ᅞ B)
ᅞ C)
Question #
9
7 of 172
Question ID: 464204ᅞ A)
ᅞ B)
ᅚ C)
Question #
98
of 172
Question ID: 464243ᅚ A)
ᅞ B)
ᅞ C)
days
days
U
S
D
LI
BOR
5
.
6%
6
.
0%
Eu
r
i
bo
r
4
.
8%
5
.
4%
What is the fixedrate ineuros?
5.318%.
2.659%.
5.245%.
Explanation
Thepresent valuesof 1 euroreceived in 180 daysand 1 euroreceived in 360 daysare:
1/(1 + 0.048 × (180/360)) = 0.9766 and 1/1.054 = 0.9488
The fixedrate ineuros is (1 - 0.9488) / (0.9766 + 0.9488) = 0.026592 × (360/180) = 5.318%. Thenotional principal is 100,000/1.30 =
76,923 euros.
The fixed-ratereceiver inaplain vanilla interest rateswap hasapositionequivalent toaseriesof:
long interest-rate puts.
short interest-putsand long interest-rate calls.
long interest-rateputsandshort interest-rate calls.
Explanation
The fixed-ratereceiver hasprofits whenshort rates fall and losses whenshort ratesrise, equivalent to buying putsand writing calls.
Cal Smart wrotea 90-day receiverswaptionona 1-year LIBOR-basedsemiannual-pay $10 millionswap with anexerciserateof 3.8%. At
expiration, the market rateand LIBOR yield curveare:
Fi
x
ed
r
at
e
3
.
7
6
3
%
1
80-
d
a
y
s
3
.
6%
3
60-
d
a
y
s
3
.
8%
Thepayoff to the writerof thereceiverswaptionat expiration isclosest to:
-$3,600.
$0.
Question #
99
of 172
Question ID: 464296ᅚ A)
ᅞ B)
ᅞ C)
Question #1
00
of 172
Question ID: 464246ᅞ A)
ᅞ B)
ᅚ C)
Explanation
At expiration, the fixedrate is 3.763% which is below theexerciserateof 3.8%. Thepurchaserof thereceiverswaption will exercise the
option which allows them toreceivea fixedrateof 3.8% from the writerof theoptionandpay the current rateof 3.763%.
Theequivalent of twopaymentsof (0.038 - 0.03763) × (180/360) × (10,000,000) will be made to thereceiverswaption. Onepayment
would have beenreceived in 6 monthsand will bediscounted back to thepresent at the 6-month rate. Onepayment would have been
received in 12 monthsand will bediscounted back to thepresent at the 12-month rate
The first payment, discounted to thepresent is (0.038 - 0.03763) × (180/360) × (10,000,000) × ( 1/1.018) = $1,817.28.
Thesecondpayment, discounted to thepresent is (0.038 - 0.03763) × (180/360) × (10,000,000) × ( 1/1.038) = $1,782.27
The total payoff for the writer is -$3,599.55.
Inanticipationof anannouncement of leveraged buyout of apublicly traded company, which of the following actions would bemost
appropriate?
Buy the stock of the company and buy CDS protection on company's debt.
Buy both thestock and the bondsof the company.
Sell protectionof the company's bondand buy put optionson the company'sstock.
Explanation
In the caseof a leveraged buyout (LBO), the firm will issuea great amount of debt inorder torepurchaseall of the company'spublicly
tradedequity. Thisadditional debt will increase theCDS spread becausedefault isnow more likely. An investor whoanticipatesan LBO
might purchase both thestock andCDS protection, both of which will increase in value when the LBO happens.
Which of the following statementsrelated to credit risk during the lifeof aswap ismost accurate:
Credit risk is greatest at the end of the swap term because creditworthiness of the
counterparty is likely to have deteriorated since swap initiation.
Credit risk is greatest at the beginning of theswap term because therearesignificant
payments yet to be madeover theremaining term of theswap.
Credit risk is greatest in the middleof theswap term when both the creditworthinessof the
counterparty may havedeterioratedsinceswap initiationand therearesignificant payments
yet to be madeover theremaining term of theswap.
Explanation
Credit risk is greatest in the middleof theswap term when both the creditworthinessof the counterparty may havedeterioratedsince
Question #1
0
3 of 172
Question ID: 464123ᅞ A)
ᅚ B)
Table 2: Option Characteristics
Reston S&P 500
Stock price $50.00 $1,400.00
Strikeprice $50.00 $1,400.00
Interest rate 6.00% 6.00%
Dividend yield 0.00% 0.00%
Time toexpiration (years) 0.5 0.5
Volatility 40.00% 17.00%
BetaCoefficient 1.23 1
Correlation 0.4
Potterpresents Fairfax with thepricesof variousoptionsasshown in Table 3. Table 3 detailsstandard European callsandput options.
Potterpresents theoptionsensitivities in Tables 4 and 5.
Table 3: Regular and Options (Option Values)
Reston S&P 500
European call $6.31 $6.31
Europeanput $4.83 $4.83
American call $6.28 $6.28
Americanput $4.96 $4.96
Table 4: Reston Stock Option Sensitivities
Delta
European call 0.5977
Europeanput −0.4023
American call 0.5973
Americanput −0.4258
Table 5: S&P 500Option Sensitivities
Delta
European call 0.622
Europeanput −0.378
American call 0.621
Americanput −0.441
Given the informationregarding the various Restonstock options, which option will increase themostrelative toan increase in the
underlying Restonstock price?
American call.
Question #11
0
of 172
Question ID: 464104earn an arbitrage profit of $0.03 per share by selling the call and borrowing the
Question #11
6
of 172
Question ID: 464295ᅞ A)
ᅞ B)
ᅚ C)
Question #117 of 172
Question ID: 464232ᅞ A)
ᅞ B)
ᅚ C)
Question #11
8
of 172
Question ID: 464248ᅚ A)
ᅞ B)
ᅞ C)
Question #11
9
of 172
Question ID: 464130ᅞ A)
being equal, the lowerpricereduces the valueof call optionsand increases the valueof put options.
Which of the following strategies would bemost appropriate useof CDS givenanexpectationof credit curvesteepening?
A curve flattening trade.
Engage inanakedCDS.
A curvesteepening trade.
Explanation
A credit curvesteepening expectation wouldentail the credit spread for longer maturities increasing relative to the change in credit spread
forshorter maturities. Insuch ascenario, one would buy protection for longer maturitiesandsell protection forshorter maturity (i.e., a
curvesteepening trade).
The writerof areceiverswaption has:
the right to enter a swap in the future as the floating-rate payer.
anobligation toenteraswap in the futureas the floating-ratepayer.
anobligation toenteraswap in the futureas the fixed-ratepayer.
Explanation
A receiverswaption gives itsowner theright toreceive fixed, the writer hasanobligation topay fixed.
The credit risk of an interest-rateswap is greatest:
at the middle of the term.
just before the final payment must be made.
late in the term.
Explanation
The credit risk inan interest-rateswap is greatest at the middleof theswap.
Inorder to form adynamic hedgeusing stock and calls with adeltaof 0.2, an investor could buy 10,000 sharesof stock and:
