interest rates solution.docx

8/19/2019 Interest Rates Solution.docx

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Risk and return Answer: d Diff: E

. Yield curve Answer: a Diff: E

If the expectations theory holds, the Treasury yield curve must be

downward sloping. Since everyone is expecting inflation to be declining,

then the average inflation rate for the next 5 years will be less thanthe average inflation rate for this year. Therefore, the IP will decline

as maturity increases, and statement a is true.

We cannot say for sure that the yield curve for corporate securities must

be downward sloping if the expectations theory holds because both the !P

and "!P increase with time. If the fall in inflation is small, but the

increase in !P and "!P through time is large, the yield curve for

corporate securities may be upward sloping. Therefore, statement b is

false.

Statement c depends on the relative magnitudes of the two premiums that

affect Treasuries, !P and IP. If the decline in IP is greater than the

increase in !P, then the yield curve will still be downward sloping.Therefore, statement c is false.

. Yield curve Answer: a Diff: E

. Yield curve Answer: c Diff: E

The shape of the yield curve depends primarily on two factors#

$%& expectations about future inflation and $'& the relative ris(iness of

securities with different maturities.

. Yield curve Answer: e Diff: E

The re)uired return on treasuries is# ( * (+ IP !P. Since !P * -,

( * (+ IP. onger/term treasuries will have lower yields than shorter/

term treasuries as the IP $inflation premium& is declining over time.

So, statement a is correct. 0 corporate bond of e)ual maturity to a

treasury bond will always have a higher yield because of the default ris(

on the corporate bond. So statement b is correct. 1rom statements a and

b, statement c is correct also.

. Yield curve Answer: c Diff: E

The maturity ris( premium $!P& and the expectations of future interest

rates determine the shape of the yield curve. Therefore, statements a

and b are false since they ignore interest rate expectations. Statement

d is false2 it is entirely possible to have a downward/sloping yield

curve under the expectations theory.



. Yield curve Answer: e Diff: E

The re)uired return on Treasuries is ( * (+ IP !P. Inflation

increases, so the IP on a %-/year Treasury is higher than the IP on a

'/year Treasury. 0lso, !P * -.%3$t / %&. !P on the '/year Treasury *-.%3$' / %& * -.%3. !P on the %-/year Treasury * -.%3$%- / %& * -.43.

Therefore, both the !P and the IP on the %-/year Treasury exceed the !P

and the IP on the '/year Treasury, so the overall yield on the

%-/year Treasury must be higher than the yield on the '/year Treasury.

Therefore, statement a is true.

($Treasury& * (+ IP !P. ($orporate& * (+ IP "!P P !P.

Since the corporate bond has the extra ris( premia, it will have a higher

yield for two bonds of the same maturity, but in statement b the bonds

have different maturities, so we cannot say for sure that this is true or

false. Therefore, statement b is false.



6ield

Treasury

%-7aturity

orporate

Since we (now that the corporate bond has to have a higher yield than the

Treasury bond for all bonds of the same maturity, we (now the yield curve

for the corporate bond must be higher than the yield curve for the

Treasury bond. We also (now that the yield curve is upward sloping

because inflation steadily increases over time. If you loo( at the

graph, it8s obvious that statement c must be true. Since statements a

and c are both true, then statement e is the correct choice.

. Interest rates Answer: c Diff: E

. Interest rates Answer: b Diff: E

The correct answer is statement b. If savings increase, money available

to lend increases $in other words, supply increases&. This would cause

interest rates to decrease. 9r, you can view this as the demand for

money decreases, which also causes interest rates to decrease. So,

statement a in incorrect. 0n increase in borrowing has the exact

opposite effect. The demand increases, so interest rates increase.

Thus, statement be is correct. Since ( * (+ IP "!P P !P, if IP

decreases, ( decreases. So statement c is incorrect.

. Interest rates Answer: d Diff: E N

The correct answer is statement d. 0n increase in household savings

increases money available, shifting the supply curve to the right,

causing interest rates to fall. So, statement a is incorrect. :oth

statements b and c are correct. 0n increase in demand will increase

interest rates, and an increase in expected inflation will increase

interest rates. So, statement d is the correct choice.

. Interest rates Answer: b Diff: E N

The correct answer is statement b. :oth statements a and c are incorrect

because expected inflation can be positive, ;ero, or negative. Without

further information on the expected future inflation rate, statements a

and c cannot be evaluated. 1or statement b, both bonds have the same

expected inflation. 0 corporate bond always has some default ris(

premium, while the Treasury bond does not, so the yield on the '/year

corporate bond must exceed the yield on the '/year Treasury bond.



. Cost of money Answer: c Diff: E N

The correct answer is statement c. If companies8 production opportunities

decline leading to a decline in the demand for funds, companies will be

borrowing less. If companies borrow less, the ban(s will need to lower

rates in order to entice them to (eep borrowing more. Whenever demandfalls, prices $that is, the cost of funds& will fall too. Therefore, this

will lead to a decrease in the cost of funds, not an increase, and

statement a is incorrect. If households save a larger portion of their

income, deposits at ban(s will increase. That is, the supply of funds

increases. If deposits go up, ban(s will reduce their interest rates

until they can entice companies to borrow more of these new funds.

Therefore, this will cause a decrease in the cost of funds, not an

increase, so statement b is incorrect. If households increase the money

they borrow from ban(s, ban(s will have decreased deposits. That is, the

supply of funds decreases. If the supply decreases, the price $that is,

the cost of funds& will increase. Therefore, statement c is correct.

. Exectations t!eory Answer: c Diff: E

This is assumed by the expectations theory.

. Exectations t!eory Answer: a Diff: E

The return on the Treasury would be (+ IP * <3 '3 * 53. If inflation

is expected to be ' percent forever, then the yield curve will be flat.

Statement a is true. If inflation will be constant forever, the yield

curve will not slope up or down//it will be flat forever. Therefore,

statement b is false. 6es, corporate bonds will yield more than 5 percent

because of default ris(. =owever, the yield curve will not be flat for

corporate bonds because default ris( increases with time to maturity. 0

company may have a low probability of default today, but can you say the

same with certainty for '- or <- years from today> Therefore, statement c

is false.

. Exectations t!eory Answer: d Diff: E

Statement d is correct2 the other statements are incorrect. Statement a

is incorrect2 the yield curve is upward sloping. Statement b is

incorrect2 the '/year rate is $?3 @3&A' * ?.53. Statement c is

incorrect2 see b above. Statement d is correct2 the </year rate is $?3

@3 73&A< * @3. Statement e is incorrect2 see d above.

. Exectations t!eory Answer: e Diff: E

Statement a is false2 the %-/year Treasury bond should have a higheryield than the 5/year Treasury bond because the yield curve is upward

sloping. Statement b is false2 the %-/year corporate bond should have a

higher yield than the 5/year corporate bond because the yield curve is

upward sloping. Statement c is false2 it ignores the default ris( of

corporate bonds. Statement d is false2 again, it ignores the default

ris( and li)uidity premia on the corporate bond. Statement e is correct2

both bonds have the same ris(, so the shape of the yield curve means that

the longer/maturity bond must have the higher yield.



. "inancial transactions Answer: d Diff: #

. "inancial transactions Answer: d Diff: #

Statements a, b, and c are incorrect. Spot and futures mar(ets are

distinguished by whether assets are sold for Bon/the/spotC delivery or

future delivery. ong/term debt issues are capital mar(et transactions.

Dew stoc( offerings are primary mar(et transactions regardless of whether

or not the company has issued stoc( in the past.

. Interest rates Answer: b Diff: #

. Interest rates Answer: b Diff: #

Statement b is correct2 the others are false. If the yield curve were

downward sloping, then the yield on a </year Treasury would be greater

than the yield on a %-/year Treasury. ost evidence suggests that there

is a positive maturity ris( premium.

. Interest rates Answer: a Diff: #

The corporate bond also has a default ris( premium, giving it a higher

yield.

. $erm structure t!eories Answer: b Diff: #

. Exectations t!eory Answer: e Diff: #

Statement e is correct2 the other statements are false. The expectations

theory would say that an upward sloping yield curve implies that future

interest rates are expected to be higher than current rates. Eiven the

information in statement b, the expectations theory would predict that

%/year interest rates one year from now would be 43. Then the '/year rate

would be -.5$@3& -.5$43& * 73. 1ive/year corporate bond yields might be

lower than </year treasury bills if the yield curve were downward sloping.

. Exectations t!eory Answer: a Diff: #

Statement a is correct2 the other statements are false. Fnowing '/year

rates and </year rates permits no inference regarding 5/year rates.

=owever, (nowing '/year rates and </year rates beginning in two years

would permit applying the expectations theory to infer 5/year rates.

Eiven the data concerning one/ and '/year rates in statement c, the

mar(et expects %/year rates in one year to be 73.

. Exectations t!eory Answer: c Diff: #

. Exectations t!eory Answer: e Diff: #



Statement a is incorrect. The yield curves could be such that the yield

on a '/year corporate bond exceeds the yield on a 5/year Treasury bond,

e.g., when the yield curve for corporate bonds is very steeply upward

sloping and the yield curve for Treasury bonds is relatively gradually

upward sloping.

. Exectations t!eory Answer: c Diff: #

?3 * $53 @3&A'.

. Exectations t!eory Answer: d Diff: #

. Yield curve Answer: e Diff: #


. Yield curve Answer: a Diff: #


Statement e is correct2 the others are false. Statement a is false2 Gust

because !P * -, it doesn8t mean the yield curve must be flat. The yield

curve could be upward or downward sloping. Statement b is false2 the

yield curve could be downward sloping, in which case the 5/year

T/bond would have a higher yield than the %-/year corporate bond.

Statement c is false2 the yield curve could be downward sloping.

Statement d is false2 the "!P could be upward sloping.

. Yield curve Answer: c Diff: #

The easiest way to see this is to draw a picture. The yield curve is

downward sloping, and a corporate bond always has a higher yield than a

Treasury because the corporate yield includes default ris( and li)uidity

premiums. 1or this )uestion, however, the li)uidity premium is ;ero.

T

Interest !ate

$3&

6ears to aturity%-5

Statement a is false. 6ou really can8t tell what the relationship

between the %-/year corporate and a 5/year Treasury would be. In this

diagram, the rate on the %-/year corporate loo(s li(e it has a higher

yield, but if "!P were slightly smaller, the lines would be closer



together, and the %-/year corporate could have a lower yield than the

5/year Treasury. Statement b is false. The %-/year Treasury will always

have a lower yield than a %-/year corporate because the corporate yield

includes the default ris( premium. Statement c is correct. :ecause the

yield curve is downward sloping, and because the Treasury curve is lower

than the corporate curve, the 5/year corporate will have a higher yield

than any %-/year bond of similar or less ris( $that is, a Treasury&.

. Yield curve Answer: d Diff: # N

The correct answer is statement d. 1rom the information given in the

)uestion, we (now that the yield curve is upward sloping. Statement a is

correct. Statement b is also correct2 the corporate bond has a longer

maturity and it carries additional ris( premiums $default ris( and

li)uidity premiums& over the government bond. Statement c is incorrect2

a @/year government bond could have a greater yield than the 5/year

corporate bond, but not necessarily. This depends upon the magnitude of

the default ris( and li)uidity premiums associated with the corporate

bond. Therefore, statement d is the correct choice.

. Yield curve Answer: d Diff: # N

The correct answer is statement d. !ecall that ( * (+ IP !P P

"!P, but "!P * P * -. Statement a is correct since IP%- !P%- H IP@

!P@. Statement b is correct2 "!P and P H - for corporate bonds, but

e)ual to ;ero for Treasuries. Statement c may or may not be correct2 it

depends on how fast the IP is rising.

. Cororate yield curve Answer: d Diff: #

:ecause the yield curve is upward sloping, all else e)ual, hurchill8s

bonds will have a lower yield than Eeorge8s bonds. 0s hurchill8s bonds

are also less ris(y, this will hold. Dote that statement b is false

because it doesn8t consider ris(. If hurchill8s bonds are ris(ier than

Eeorge8s, hurchill8s bonds will have a higher yield than Eeorge8s.

. Exected interest rates Answer: d Diff: E N

0verage inflation *

<

?3533

* 53.

(!1 * (+ IP * <3 53 * 73.

. Exected interest rates Answer: a Diff: E

If the %/year rate in one year is J2 $?3 J&A' * 5.532 J * 53.

. Exected interest rates Answer: a Diff: E



(' * $(% in 6ear % (% in 6ear '&A'

%-.53 * $%'3 (% in 6ear '&A'

(% in 6ear ' * 43.

. Exected interest rates Answer: b Diff: E

%/year T/bill * ?3.

'/year T/note * ?.@3.

?.@3 *'

J,?3

J * ?.@3$'& / ?3

* @.3.

. Exected interest rates Answer: b Diff: E

Ksing the expectations theory, the rate on '/year securities is the

arithmetic average of %/year securities now and %/year securities in one

year. -.-?@ * $-.-?< J&A'. J * -.-@% * @.%3.

. Exected interest rates Answer: c Diff: E

If '(% is the yield on a %/year treasury in two years, we can say#

< L ?3 * $' L 5.53 '(%&

%73 * %%3 '(%

'(% * @3.

. Exected interest rates Answer: c Diff: E N

IP is going to be the average inflation rate over the %-/year period.

There will be < years of ' percent inflation, then @ years of 5 percent

inflation.

( * (+ IP !P * 3 $'3 × < 53 × @&A%- -.%$%- / %&3

* 3 $?3 <53&A%- -.%$43&

* 3 .%3 -.43

* 4.-3.

. Exected interest rates Answer: d Diff: E N

The pure expectations hypothesis allows us to say that a long/term

security yield is comprised of a weighted average of securities with

shorter maturities.

?.53 * $5.53 J&A5

<'.53 * 5.53 J

'@.-3 * J

?.@53 * J.

. Inflation rate Answer: c Diff: E

(Dom * (+ IP "!P P !P

7.53 * <3 IP - - -

IP * 5.53.

. Inflation rate Answer: d Diff: E



IP5 * $53 ?3 43 %<3 %'3&A5 * 43.

. Default risk remium Answer: b Diff: E N

(@ * (+ IP@ !P@ "!P@ P@

@.?3 * <.-3 $'3 × < <.53 × &A@ -.-3 "!P@ -.3

@.?3 * <.-3 '.75@%3 -.-3 "!P@ -.3

@.?3 * ?.'5@%3 "!P@

"!P@ * %.<'43.

. Exected interest rates Answer: c Diff: #

Dominal ris(/free rate#

(!1 * (+ IP * 3 @3 * %%3.

T/bond rate#

(!1 * (+ IP "!P P !P * 3 @3 -3 '3 %3 * %3.

Dote that there is no default ris( premium on a Treasury security.

. Exected interest rates Answer: b Diff: #

The !P for the /year bond is -.%3$ / %& * -.<3. 1ind the /year IP as @.3

* '.@3 -.<3 -.43 IP, or IP * <.53. alculate the @/year IP as M<.53$&

53$<&NA@ * .%3. The !P for the @/year bond is -.%3$@ / %& * -.?3.

1inally, the yield on the @/year bond is '.@3 -.?3 -.43 .%3 * 7.<3.


The return on the 5/year corporate bond is calculated as follows#

(5 * (+ IP !P "!P P

7.3 * <3 M$'3 × <& $3 × '&NA5 -.3 "!P P

"!P P * '.'3.

Dow, calculate the @/year corporate bond yield#

(@ * <3 M$'3 × <& $3 × &NA@ -.?3 '.'3

* <3 <.%'43 -.?3 '.'3

* 7.4'43 ≈ 7.43.


Step %# alculate P "!P for the 5/year bond# 73 * <3 IP5 -.3 P "!P

73 * <3 $<3 L < 53 3&A5 -.3 P "!P

73 * <3 <.?3 -.3 P "!P

P "!P * %3.

Step '# Dow, calculate the return for the %-/year bond#

(%- * <3 IP%- -.43 %3

(%- * <3 $<3 L 7 53 3&A%- -.43 %3



(%- * 7.'3.

. Exected interest rates Answer: d Diff: #

Step %# Ksing the %-/yr bond yield, determine the default ris( and

li)uidity premiums#

(%- * (!1 IP%- !P%- "!P P @.73 * '3 M$'3 × 5& $<3 × 5&NA%- $-.-53&$%- O %& "!P P

@.73 * '3 '.53 -.53 "!P P

'.753 * "!P P.

Step '# Solve for the %'/yr bond yield substituting "!P P * '.753, as

solved in Step %#

(%' * '3 M$'3 × 5& $<3 × @&NA%' $-.-53&$%' O %& "!P P

(%' * '3 '.57<<3 -.553 '.753

(%' * @.47<<3 ≈ @.473.


(+ * '32 !P * -.%3$t / %&2 "!P * -.-53$t / %&2 P * %3 corporate only.

I% * <32 I' * 32 I< * 532 I and after * ?3. %- / T%- * >

IP%- *

%-

?3$@&,53,3,<3

*

%-

5I3

* 5.3.

( * (+ IP P "!P !P.

%- * '3 5.3 %3 -.-53$4& -.%3$4& * 4.@53.

T%- * '3 5.3 -3 -3 -.43 * 7.<-3.

%- / T%- * 4.@53 / 7.<-3 * %.53.

. Exected interest rates Answer: a Diff: #

Say the %/year rate in three years is J.

1rom expectations theory# ?.53 * $?3$<& J$%&&A

?.53$& * ?3$<& J

'?3 * %73 J

J * 73.


(% * ?.432 (' * @.'3.

@.'3 * $?.43 J&A'

%.3 * ?.43 J

J * @.53.


1irst, find the total yield for %5 years#



@.'3 × %5 yrs. * %-73.

alculate the total yield for the first six years#

?.53 × ? yrs. * <43.

Dow, we can find the total yield that must be earned for the next nine

years#%-73 / <43 * ?43.

1inally, find the yield per year#

?43A4 yrs. * @.?@3.


6ou want to buy a security one year from today, and you want to hold it

for < years. 6ou will hold this investment to the end of the fourth

year. If an investor wants to invest for years, he has two choices#

$%& :uy a /year bond that yields ?.43 per year2 or $'& buy a %/year bond

that yields ?.'3, then buy a </year bond in % year. The )uestion is

as(ing for the yield on this bond. The expectations theory ma(es it

impossible for the investor to BprofitC by choosing $%& over $'&, or vice

versa. Since the expectations about future inflation are already in all

the interest rates, an investor will expect to get the same overall

return with either strategy. If the investor pic(s choice %, he will

get a /year return of ?.43 per year. If he pic(s choice ', he will get

a %/year return of ?.'3 and < years of an un(nown yield, %(<. Since the

investor shouldn8t do better with one strategy over the other, the two

strategies must e)ual each other.

× ?.43 * $% × ?.'3& $< × %(<&

'%.3 * < × %(<

@.%<3 * %(<.

Therefore, the yield on a </year Treasury one year from now will be @.%<3.


The return on the 5/year bond is 5.' percent, so an investor who buys

this bond gets a return of 5.' percent each year he holds the bond. The

return on the /year bond is .7 percent, so an investor who buys this

bond gets a return of .7 percent each year he holds the bond. 0fter he

holds the bond for four years, he can buy a bond for one year. =e must

get the same average return by holding this combination of a /year bond

and a %/year bond as he would have received by holding a 5/year bond.

9therwise, he would choose the combination of bonds that gives him the



highest return. The expected yield years from now on a %/year bond

is (%.

.73 × (% * 5.'3 × 5

%4.'3 (% * '?3

(% * ?.73.


If you wanted to invest your money in Treasuries for %- years, you have

several choices. 6ou can buy a %-/year Treasury, or you can buy a

@/year Treasury today, followed by a </year Treasury, or you can buy a </

year Treasury today, followed by a @/year Treasury. The expectations

theory concludes that you should receive the same total return for the %-

years, no matter which alternative you choose.

This )uestion gives us information about the %-/year security yield, and

some information about buying a @/year security followed by a </year

security. The return on a </year Treasury seven years from today is

written as @(<.

Since the returns must be e)ual, we can write the following e)uation#

%- × ?.'3 * $@ × 5.73& $< × @(<&

?'3 * -.?3 $< × @(<&

'%.3 * < × @(<

@.%<3 * @(<.


!emember, if you purchase a </year Treasury today, and then a 5/year

Treasury after that $for a total investment of 7 years&, you will have to

earn the same total yield as you would on an 7/year Treasury purchased

today. So, let <(5 be the interest rate on the 5/year Treasury three

years from now#

7 × @3 * $< × 53& $5 × <(5&

5?3 * %53 $5 × <(5&

%3 * $5 × <(5&

7.'3 * <(5.

Therefore, the yield on a 5/year Treasury three years from today, <(5,

is 7.'3.




6ou have a choice of purchasing one 7/year Treasury, or one 5/year

Treasury followed by one </year Treasury. We have the data for the 5/

year and 7/year securities, so we can solve for the yield on the </year

security five years from now. The return on the </year security five

years from today is 5(<.

7 × 5.@3 * $5 × 5.43& $< × 5(<&

5.?-3 * '4.5-3 $< × 5(<&

%?.%-3 * $< × 5(<&

5.<@3* 5(<.

. Exected interest rates Answer: e Diff: #

The return on the @/year bond is ?.? percent, so an investor who buys

this bond receives a return of ?.? percent each year he holds the bond.

The return on the 5/year bond is ?.' percent, so an investor who buys

this bond receives a return of ?.' percent each year he holds the bond.

0fter he holds the bond for 5 years, he can buy a '/year bond2 however,

according to the expectations theory, he must receive the same average

return by holding this combination of a 5/year bond and a '/year bond as

he would have received by holding a @/year bond. 9therwise, he would

choose the combination of bonds that gives him the highest return. The

return on the '/year bond five years from now is written as 5('.

@

3&?.?$@ ×

*

@

('3'.?5 '5×+×

@

3'.I?

*@

&('$3<% '5×+

%5.'3 * $' × 5('&

@.?3 * 5('.


The expected yield is <('. 0ccording to the expectations theory,

$< × 5.?3& $' × <('& * $5 × ?.-3&

%?.73 '$<('& * <-3

<(' * ?.?3.


1irst, find the amount of default and li)uidity premia built into the

5/year bond#

i)uidity default premia * (5 / (+ / IP5 / !P5.

IP5 * $<3 3 53 53 53&A5 * .3.

!P * -.%3$5 / %& * -.3.

i)uidity default premia * 7.53 / '.53 / .3 / -.3 * %.'3.



Dow, find the inflation premium and !P for a /year bond one year into

the future#

Inflation Premium * $3 53 53 53&A * .@53.

!P * -.%3$ / %& * -.<3.

1inally, calculate the yield on the /year bond one year from now#

%( * (+ IP

!P

$"efault i)uidity premia&

%( * '.53 .@53 -.<3 %.'3 * 7.@53.


( * (+ IP !P2 "!P * P * -.

IP * M$<3&5 $53&@NA%' * .%??@3.

!P * -.%3$%' O %& * %.%3.

(%' * <3 .%@3 %.%3

* 7.'@3.


( * (+ IP !P "!P P

1or the %-/year corporate bond#

7.?3 * '3 M$<3&$5& $53&$5&NA%- $-.%3&$%- / %& "!P P

"!P P * %.@3.

1or the 7/year corporate bond#

( * '3 M$<3&$5& $53&$<&NA7 -.%3$7 / %& %.@3 * 7.%53.


Ksing the expectations theory#

?3 * M$%- × ?.53& $5 × %-(5&NA%5. Solving for %-(5, the rate on a 5/year

bond in %- years, we get# %-(5 * 53.


( * (+ IP !P "!P P

onsider the %-/year corporate bond#

(%- * <3

%-

yrs&5$<3yrs&53'$ ×+×

-.%3$%- O %& "!P P

@.73 * <3

%-

3%53%- +

-.43 "!P P

%.3 * "!P P.

Dow consider the %5/year corporate bond#

(%5 * <3

%5

yrs&%-$<3yrs&53'$ ×+×

-.%3$%5 O %& %.3

(%5 * <3

%5

3<-3%- +

%.3 %.3



(%5 * <3 '.???@3 %.3 %.3

(%5 * 7.?@3 ≈ 7.@3.


(%, (', (<,

Security aturity urrent !ate 6ear % 6ear ' 6ear <

% year 73

73

' year %-3

73 %'3

< year %'3

73 %'3 >

alculate (', the %/year rate in 6ear '#

%-3 * $73 ('&A'

(' * %'3.

alculate (<, the %/year rate in 6ear <#

%'3 * $73 %'3 (<&A<

<?3 * '-3 (<

(< * %?3.



yield $call it J&. Since he shouldn8t do better with one choice over the

other, the two strategies must e)ual each other#

× 5.?3 * ?3 <J

''.3 * ?3 <J

%?.3 * <J

5.@3 * J.

. Exected interest rates Answer: a Diff: # N

- %

% 6r.# Q Q

- % '

' 6rs.# Q Q Q

- % ' <

< 6rs.# Q Q Q Q

- % ' <

6rs.# Q Q Q Q Q

- % ' < 55 6rs.# Q Q Q Q Q Q

< 5

Q Q Q

5.73

?.'3 ?.'3

?.53

?.'3

?.-3

?.53 ?.53

?.'3 ?.'3 ?.'3

?.-3 ?.-3 ?.-3 ?.-3

J3 J3

If you wanted to have Treasuries for a total of five years, you would

have two choices. 6ou could buy a five/year Treasury, or you could buy a

three/year Treasury, and at its maturity, buy a two/year Treasury. 6our

overall expected return must be the same with both strategies. The

)uestion is as(ing for the yield on this '/year Treasury, three years

from now.

5$?.-3& * <$?.53& 'J

<-3 * %4.53 'J

%-.53 * 'J

5.'53 * J.

. Exected interest rates Answer: b Diff: # N

(% * 5.'32 ( * ?.<3.



%(< denotes the three/year rate, one year from now.

× ( * $% × (%& $< × %(<&

× ?.<3 * 5.'3 $< × %(<&

'-3 * < × %(<

?.?@3 * %(<.

. Exected interest rates Answer: c Diff: # N

We are given the yield on a @/year corporate bond, and we must find the

yield for a %-/year corporate bond. The fact that they have the same

default ris( and li)uidity premium is the (ey to solving this problem.

(@ * (+ IP@ !P@ $"!P P&

4.73 * <3 @

&<3$<&I3$I +

-.%3$@ / %& $"!P P&

4.73 * <3 <.5@3 -.?3 $"!P P&

'.?<3 * "!P P.

Dow that we have solved for the default ris( and li)uidity premiums, we

can carry the value forward and solve for the yield on a %-/year

corporate bond.

(%- * (+ IP%- !P%- $"!P P&

(%- * <3 %-

&?3$<&I3$I +

-.%3$%- / %& '.?<3

(%- * <3 <.3 -.43 '.?<3

(%- * 4.4<3.

. Real risk%free rate of interest Answer: d Diff: #

T/bill rate * (+ IP

73 * (+ 53

(+ * <3.

. Inflation rate Answer: c Diff: #

(T%- * (+ IP !P

@3 * <.%3 M'.53$5& 5JNA%- -.%3$%- / %&

@3 * <.%3 $%'.53 5J&A%- -.43

<3 * $%'.53 5J&A%-

<-3 * %'.53 5J

%@.53 * 5J

J * <.53.

. Inflation rate Answer: b Diff: #



. Inflation rate Answer: a Diff: #

Step %# ( * (+ IP "!P P !P.

Ksing (5, find "!P P#

-.-7 * -.-< -.-< "!P P -.--

"!P P * -.-%?.

Step '# Dow you can find J#

-.-4 * -.-< M5$-.-<& 5$J&NA%- -.-%? -.--4

J * -.- * 3.

. Inflation rate Answer: e Diff: #

Step %# alculate the default ris( and li)uidity premiums using

information for the 5/year bond#

( * (+ IP "!P P !P.

1or the 5/year corporate bond#

@.53 * '3 $'3 × 5&A5 "!P P -.%3$5 / %&

@.53 * '3 '3 "!P P -.3

<.%3 * "!P P.

Step '# alculate the average inflation rate for '--7 through '-%< by

substituting the information found in Step % using data for the

%-/year corporate bond#

7.'3 * '3 $'3 × 5 5J&A%- <.%3 -.%3$%- / %&

7.'3 * '3 $%-3 5J&A%- <.%3 -.43

7.'3 * ?3 $%-3 5J&A%-

'.'3 * $%-3 5J&A%-

''3 * %-3 5J

%' * 5J

'.3 * J.

. Default risk remium Answer: a Diff: #

We8re given all the components to determine the yield on Eator orp.

bonds except the default ris( premium $"!P& and !P. alculate the !P

as -.%3$%- / %& * -.43. Dow, we can solve for the "!P as follows# 73 *

<3 '.53 -.43 -.53 "!P, or "!P * %.%3.

. #aturity risk remium Answer: d Diff: #

(%- * (5 %3.

(%- * '3 M<3$<& $3&$@&NA%- !P%-

* '3 <.@3 !P%-

* 5.@3 !P%-.

(5 * '3 M<3$<& $3&$'&NA5 !P5

* '3 <.3 !P5

* 5.3 !P5.

!emember, (%- * (5 %3.

5.@3 !P%- * 5.3 !P5 %3

!P%- / !P5 * 5.3 %3 / 5.@3



Step %# Solve for the real ris(/free rate#

(T%- * (+ '.53

?3 * (+ '.53

<.53 * (+.

Step '# Solve for average inflation over next 5 years#

(T5

* (+ IP5

53 * <.53 IP5IP5 * %.53.

. Exected interest rates Answer: c Diff: # N

Kse (+ * <.53 and IP5 * %.53 from previous problem.

Step %# Solve for the sum of the default and li)uidity ris( premiums.

(%- * (+ IP%- !P "!P P

73 * <.53 '.53 - "!P P

'3 * "!P P.

Step '# Solve for the yield on the 5/year corporate bond.

(5 * (+ IP5 !P "!P P * <.53 %.53 - "!P P

* <.53 %.53 - '3

* @3.

. Exected interest rates Answer: c Diff: E N

IP< * $<3 3 53&A< * 3. So (< * (+ IP< * <3 3 * @3.

. Exected inflation Answer: e Diff: E N

(T * 73. IP * 73 / <3 * 53, which is the average inflation premium over

the /year period. So, 53 * $<3 3 53 J&A. So, J * 73, or I * 73.

. Exected interest rates Answer: a Diff: # N

%5 × @.'3 * %- × @.53 5 × J

%-73 * @53 5J

<<3 * 5J

?.?3 * J.

. Exected interest rates Answer: d Diff: # N

' × ?.53 % × ?.73 * % × ?3 ' × J

%4.73 * ?3 'J

%<.73 * 'J

?.43 * J.

interest rates solution.docx

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