INVESTMENT ANALYSIST

(CONVEXITYREILLY & BROWN

CHAPTER 19P. 764-----

DETERMINASI PRICE VOLATILITY OF BONDS

MENGAPA BOND’S YIELD BERUBAH INTERST RATE OF BONDS SENSITIVE ? CAUSE OF VASTLY DIFFERENT % TAGE

PRICE CHANGE FOR ALTERNARTIVE BONDS?

BAGAIMANA MEMAKSIMUMKAN ROR DARI PENURUNAN EXPECTED RATE ?

Perubahan harga Bond dapat diukur dengan % tage

Rumusnya : EPB/BPB – 1

EPB = The ending price of the bondsBPB = the beginning price of the bond

4 FAKTOR YANG MEMPENGARUHI BONDS VOLATILITY

1. Par Value.2. Bond’s coupond3. Tenor (jangka waktu) bonds4. Prevailing Tingkat Bunga Pasar.

Macaulay Duration (D)

n

tt

t

n

tt

t

kCktC

D

1

1

)1(

)1()(

P

t = periode waktu untuk.Ct = Kupon pada tahun ke tI = tingkat diskonto

P

Kasus : Bond A Bond B- Face value $ 1000 $ 1000- Maturity 10 tahun 10 tahun- Coupon 4% 8%- Discount factor 8% 8%- Hitung Macaulay Duration

Jawab (daftar terlampir, tabel 18-15) - D “A” = 8,12 years- D ”B” = 7,25 years

MODIFIED DURATION AND BOND PRICE VOLATILITY

A Bond with a macaulay duration 10 years , a yield to maturity (i) 8 % (semi annual payment, m = 2 x setahun)

)1(mod

.62,9)

208,01(

10mod

MYTMDD

yrsD

Estimate of the % tage change in bond price equals the change in yield times modified duration

ixDx

PP

mod100

Delta P = perubahan in price for bondP = nilai awal bond- Dmod = The modified duration of bondDelta I = the yield change in basis point interest

rate dari 8 % ------ 8,5%Delta i = 50/100 = 0,50 (membacanya 50 BP)

Dari % tage perubahan harga Bila bond dengan macaulay D = 8 yrsI (interest) = 0,10 expect bond YTM decline 75

basis point (dari 10%… menjadi … 9,25 %Berapa Bond odified dauration ?(bila m = 2 x )D mod = .62,7

)210,01(

8 yrs

Delta P =

%72,5

)10075)(62,7(.

100mod

ixD

Nampak Bond price menunjukkan peningkatan : 5,72% dampak respon 75 basis point decline YTM. Bila bond price sebelum decline $ 900,- after decline menjadi $ 900 x 1,0572 = $. 951,48

( YTM = 0,75 turun ;;; Bond Price = 5,72% naik )

CONVEXITYDSOMPUTATION

CONVEXITY Chapter 18 page. 729

(exhibit 18.22) orPage 733………….R & B See computation of convexity exibit 19.22

CONVEXITYDETERMINANTS CONVEXITYADALAH UKURAN DARI THE CARVATURE OF

PRICE YIELD RELATIONSHIP . BECAUSE MODIFIED DURATION IS THE SLOPE OF THE CURVE AT A GIVEN YIELD. CONVEXITY INDICATES CHANGE IN DURATION

Page 733………….R & B See computation of convexity exibit 19.22

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t

t tti

CFiid

pd

turninpidPd

CONVEXITY

1

222

2

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2

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1

Computation of Convexity(E.18.22)Example : 3 year Bond, 12% Coupon , 9% YTM dengan

par value $.1.000,-

1 2 3 4 5 6YEAR CFt PV9% PV9%xCF T2 + t (4 x 5 )

1 120 0,9174 $.110.09 12 + 1 =2 $. 220,182 120 0,8417 101 22+2 = 6 $. 6063 120 0,7722 92,66 32+3 =12 1111,923 1000 0,7722 772,20 12 9266,40

Price $.1.075,95 $.11.204,50

84,0)09,1(

1)1(

122

i

$.11.204,50 x 0,84 = $. 9.411,78Convexity = 9411,78 / 1.075,95 = 8,75

50,204.11)]()1(

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2

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t

t tti

CF

EXHIBIT 18.23ANALYSIS OF BOND PRICE

CHANGE DENGAN MEMPERTIMBANGKAN

DURATIONDAN

CONVEXITY(Chapter 18 p.731 R & B)

Kasus : Analyisis Bond Price Chamge dengan mempertimbangkan Durasi dan Convexity

Diketahui :18 year Bond ; coupon 12%/tahun, YTM 9% per tahun Modified Duration = 8,38 (D*)Convexity = 107,70

Estimate of the Price Change Using Duration :Percent Delta Price = D* (Delta in Yield/100)Estimate of Price Change from Convexity :Price Change = 0,5 x P x Convexity x (Delta in Yield)2

Diminta :Combine Effect (Duration dan Convexity change) bila a. Change in yield = - 100 Bpb. Change in yield = - 300 BP

DENGAN 300 BP CHANGE, maka Modified Duration Effect adalah dari

126,50 menuju ke 158,30 (berarti peningkatan 25,14%)

Dimana pada kenyatannya Actual price adalah 164,41 (kenaikan 30%)

(Perhitungan : lihat halama berikutnya)

PERSAMAAN THE PRICE CHANGE ATTRIBUTABLE TO

THE CONVEXITY EFFECT

THE PRICE CHANGE DUE TO CONVEXITY =

½ X Price x Convexity x (Delta in Yield)2

PContoh Analysis of Bond price Change Considering and

Convexity 18 year Bond, 12 % Coupon , 9 % YTM Price $. 126,50Modified Dutration ; 8,38 (D*)Convexity : 107,70Estimate of price Change using DurationPercent delta Price = D* (delta in yield/100)Estimate of Price Change from ConvexityPrice Change = ½ x Price x Convexity x (delta in yield)2

A. Change in yield = - 100 BP Duration = -8,38 x (-100/100) = + 8,38 %

= 8,38% x 126,5 = + 10,60Convexity Change = ½ x (126,50) x 107,70 x (0,01)2

= 63,25 x 107,7 x 0,0001 = 6,812,03 x 0,0001 = 0,68Combine effecyt 126, 50

+ 10,60 (duration 137,10 +0,68 (Convexity) 137,78

B. Change in yield = - 300 BPDuration Change = -8,38 x (-300/100) = + 25,14

25,14% X 126,5 = 31,80Convexity effect = ½ x (126,5) x 107,7 x (0,03)2 =

6,812.03 x 0,0009 = 6,11Combined Effect = 126,50

+ 31,80 (Duration) 158,30 + 6,11 ( Convexity) 164,41

.

B. Change in yield = + 300 BPDuration Change = -8,38 x (-300/100) =

-25,14-25,14% X 126,5 = - 31,80

Convexity effect = ½ x (126,5) x 107,7 x (0,03)2 =

6,812.03 x 0,0009 = 6,11

Combined Effect = 126,50 - 31,80 (Duration) 94,70 + 6,11 ( Convexity) 100,81

.B. Change in yield = + 100 BPDuration Change = -8,38 x ( +100/100) =

- 8,38- 8,38% X 126,5 = - 10,6

Convexity effect = ½ x (126,5) x 107,7 x (0,01)2 = 0,68

Combined Effect = 126,50 - 10,6 (Duration) 115,90 + 0,68

( Convexity) 116,58

.

.