Managementul Riscului de Rata de Dobanda

8/13/2019 Managementul Riscului de Rata de Dobanda

1/8

Calculate the repricing gap and the impact on net interest income of a 1 percent increase ininterest rates for each of the following positions:

Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million.

Repricing gap = R! - R" = $200 - $100 million = #$100 million.%% = &$100 million'&.01' = #$1.0 million( or $1(000(000.

Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $1)0 million.

Repricing gap = R! - R" = $100 - $1)0 million = -$)0 million.

%% = &-$)0 million'&.01' = -$0.) million( or -$)00(000.

Rate-sensitive assets = $1)0 million. Rate-sensitive liabilities = $1*0 million.

Repricing gap = R! - R" = $1)0 - $1*0 million = #$10 million.

%% = &$10 million'&.01' = #$0.1 million( or $100(000.

a. Calculate the impact on net interest income on each of the above situations assuming a1 percent decrease in interest rates.

%% = &$100 million'&-.01' = -$1.0 million( or -$1(000(000.

%% = &-$)0 million'&-.01' = #$0.) million( or $)00(000.

%% = &$10 million'&-.01' = -$0.1 million( or -$100(000.

b. +hat conclusion can ,ou draw about the repricing model from these results

he /%s in parts &1' and &' are eposed to interest rate declines &positive repricing gap'while the /% in part &2' is eposed to interest rate increases. he /% in part &' has thelowest interest rate ris eposure since the absolute value of the repricing gap is the lowest(while the opposite is true for part &1'.

Consider the following balance sheet for +atchover3 avings( %nc. &in millions':

!ssets "iabilities and 45uit,

/loating-rate mortgages 6emand deposits&currentl, 107 annuall,' $)0 &currentl, 87 annuall,' $900-,ear fied-rate loans ime deposits

&currentl, 97 annuall,' $)0 &currentl, 87 annuall,( 1 ,ear' $2045uit, $10

otal !ssets $100 otal "iabilities ; 45uit, $100

a. +hat is +atchover3


2/8

Current epected interest income: $)m # $.)m = $.)m.4pected interest epense: $*.2m # $1.2m = $).*m.4pected net interest income: $.)m - $).*m = $.1m.

b. +hat will be the net interest income at ,ear-end if interest rates rise b, 2 percent

!fter the 200 basis point interest rate increase( net interest income declines to:)0&0.12' # )0&0.09' - 90&0.0' - 20&.08' = $>.)m - $8.m = $2.9m( a decline of $0.*m.

c. 3sing the cumulative repricing gap model( what is the epected net interest income fora 2 percent increase in interest rates

+achovia


3/8

)otal Assets #01% )otal Liabilities and !uity #01%

7hat is the maturity gap for 6ebentures = $.*EIK%/!n=20(i=7 # $120EIK%/n=20(i=7= $10.22B"= D0E100 # )E201.> # 20E10.22FG&100 # 201.> # 10.22' = 9.9* ,ears

he maturit, gap = BH!I = 2.80 J 9.9* = 1).8 ,ears. he maturit, gap increasedbecause the average maturit, of the liabilities decreased more than the average maturit, ofthe assets. his result occurred primaril, because of the differences in the cash flowstreams for the mortgages and the debentures.


4/8

c. +hat will happen to the maret value of the e5uit,

he maret value of the assets has decreased from $*0 to $**2.091( or $9.>2>. hemaret value of the liabilities has decreased from $*0 to $*0>.81( or $20.8>. hereforethe maret value of the e5uit, will decrease b, $9.>2> - $20.8> = $19.2>( or *.*

percent.

d. %f interest rates increased b, 2 percent( would the ban be solvent

he value of the assets would decrease to $*0>.0*( and the value of the liabilities woulddecrease to $>1.2. herefore the value of the e5uit, would be $19.92. !lthough theban remains solvent( nearl, 8) percent of the e5uit, has eroded because of the increase ininterest rates.

he following is a simplified /% balance sheet:

Assets Liabilities and !uity"oans $1(000 6eposits $)0 0 45uit, $1)0

otal !ssets $1(000 otal "iabilities ; 45uit, $1(000

he average maturit, of loans is four ,ears( and the average maturit, of deposits is two,ears. !ssume loan and deposit balances are reported as boo value( ero-coupon items.

a. !ssume that interest rates on both loans and deposits are > percent. +hat is the maretvalue of e5uit,

he value of loans = $1(000G&1.0>'*

= $90.*( and the value of deposits = $)0G&1.0>'2

=$91).*. he net worth = $90.* - $91).* = -$9.002. &hat is( net worth is negative.'

b. +hat must be the interest rate on deposits to force the maret value of e5uit, to beero +hat economic maret conditions must eist to mae this situation possible

%n this case the deposit value should e5ual the loan value. hus( $)0G&1 # x'2= $90.*.olving for ( we get >.)9*7. hat is( deposit rates will have to increase more becausethe, have a shorter maturit,. ote: for those using calculators( ,ou need to compute%GL4!R after entering )0 = /K( -90.* = IK( 0 = IB( 2 = .

c. !ssume that interest rates on both loans and deposits are > percent. +hat must be theaverage maturit, of deposits for the maret value of e5uit, to be ero

%n this case( we need to solve the e5uation in part &b' for . he result is 2.11*1 ,ears. %finterest rates remain at > percent( then the average maturit, of deposits has to be higher inorder to match the value of a *-,ear loan.

*


5/8

Irobleme cu duration

1>. /inancial %nstitution ML has assets of $1 million invested in a 0-,ear( 10 percent

semiannual coupon reasur, bond selling at par. he duration of this bond has beenestimated at >.>* ,ears. he assets are financed with e5uit, and a $>00(000( 2-,ear( 9.2)percent semiannual coupon capital note selling at par.

a.+hat is the leverage-adNusted duration gap of /inancial %nstitution ML

he duration of the capital note is 1.>9) ,ears.

wo-,ear Capital ote

Iar value = $>00 Coupon = 0.092) emiannual pa,ments

H)M : %.%(1 Baturit, = 2

ime Cash /low IK%/ IK of C/ IKEC/E0.) $2.8 0.>8)01 $1.* $1).9* IK%/ = 1G&1#LBG2'O&imeE2'

1 $2.8 0.>1280 $0. $0.

1.) $2.8 0.>8 $2>.2 $*.>

2 $>2.8 0.892*) $0.1 $1(819.8

Irice = $>00.00

umerator = $1(909.9 6uration = 1.>9) = umeratorGIrice

he leverage-adNusted duration gap can be found as follows:

[ ] yearskDDgapdurationadjustedLeverage LA 2.=000(000(1$000(>00$

=>9).1>*.> ===

b. +hat is the impact on e5uit, value if the relative change in all maret interest

rates is a decrease of 20 basis points ote( the relative change in interest rates is RG

&1#RG2' = -0.0020.

he change in net worth using leverage adNusted duration gap is given b,:

[ ] [ ] *8*(18$'000(000(1'&002.&10

>'=>9).1&>*.>

21

EE ==

+

=

R

RAkDDE

LA

c. 3sing the information that ,ou calculated in parts &a' and &b'( infer a general statementabout the desired duration gap for a financial institution if interest rates are epected toincrease or decrease.

%f the /% wishes to be immune from the effects of interest rate ris( that is( either positiveor negative changes in interest rates( a desirable leverage-adNusted duration gap &"!6H'

)


6/8

is ero. %f the /% is confident that interest rates will fall( a positive "!6H will providethe greatest benefit. %f the /% is confident that rates will increase( then negative "!6Hwould be beneficial.

d. Kerif, ,our inference b, calculating the change in maret value of e5uit,

assuming that the relative change in all maret interest rates is an increase of 0 basispoints.

[ ] [ ] 8>9(2*$'00'&.000(000(1&222).=

21

EE ==

+

=

R

RAkDDE

LA

e. +hat would the duration of the assets need to be to immunie the e5uit, fromchanges in maret interest rates

%mmuniing the e5uit, from changes in interest rates re5uires that the "!6H be 0. hus(

&6!-6"' = 0 6!= 6"( or 6!= 0.>E1.>9) = 1.9099) ,ears.

20. he balance sheet for Hotbucs @an( %nc. &H@%' is presented below &$ millions':

!ssets "iabilities and 45uit,Cash $0 Core deposits $20/ederal funds 20 /ederal funds )0

"oans &floating' 10) 4uro C6s 10"oans &fied' 8) 45uit, 20otal assets $220 otal liabilities ; e5uit, $220

P4 P Q4 @!"!C4 Q44: he /ed funds rate is .) percent( the floating loan rate is"%@PR # * percent( and currentl, "%@PR is 11 percent. /ied rate loans have five-,earmaturities( are priced at par( and pa, 12 percent annual interest. Core deposits are fied-rate for

2 ,ears at percent paid annuall,. 4uros currentl, ,ield > percent.

a. +hat is the duration of the fied-rate loan portfolio of Hotbucs @an

/ive-,ear "oan

Iar value = $1(000 Coupon = 0.1200 !nnual pa,ments

LB = 0.12 Baturit, = )

ime Cash /low IK%/ IK of C/ IKEC/E

1 $120.00 0.>2)9 $109.1* $109.1* IK%/ = 1G&1#LB'O&ime'

2 $120.00 0.9>91>* $>).88 $1>1.

$120.00 0.91190 $).*1 $2)8.2** $120.00 0.8))1 $98.28 $0).0)

) $1(120.00 0.)89*29 $8).)2 $(199.)>

Irice = $1(000.00

umerator = $*(09.) 6uration = *.09 = umeratorGIrice

he duration is *.09 ,ears.

8


7/8

b. %f the duration of the floating-rate loans and fed funds is 0.8 ,ears( what is the durationof H@% ,ears

f. +hat is the impact on the maret value of e5uit, if the relative change in all maretinterest rates is an increase of 1 percent &100 basis points' ote( the relative change in

interest rates is &RG&1#R'' = 0.01.

ince H@% E &0.01' E $220 = -$1(>88(80 &new net worth will be $1(0(8*0'.

g. +hat is the impact on the maret value of e5uit, if the relative change in all maretinterest rates is a decrease of 0.) percent &-)0 basis points'

ince H@% E &-0.00)' E $220 = $>(10 &new net worth will be $20(>(10'.

9


8/8

f. +hat variables are available to H@% to immunie the ban Qow much would eachvariable need to change to get 6H!I e5ual to 0

%mmuniation re5uires the ban to have a leverage-adNusted duration gap of 0.0.herefore( H@% could reduce the duration of its assets to 0.))) ,ears b, using more fed

funds and floating rate loans. Pr H@% could use a combination of reducing asset durationand increasing liabilit, duration in such a manner that "!6H is 0.0.

Managementul Riscului de Rata de Dobanda

Documents

Transcript of Managementul Riscului de Rata de Dobanda