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Unformatted text preview: Fall 2008
Engineering 120 Industrial Engineering & Operations Research September 8, 2008
Page 1 of 1 Mortgage Emample I‘Quick Nav w 3%: fentedéu 95th a' i'ender rate tabﬁe based on yéﬁr mbut ‘that dispéys torrent rakes relekant ts yam? man criterion“ You may modify the {emits a? the teams: by using the "modify your search“ section bemw. WW4MM «a r, :...4 ~
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say; He gem mtg Fall 2008 September 15, 2008
Engineering 120 Industrial Engineering & Operations Research Page 1 of 1 Price Yield Curves f’tice 480
300
200
398
M View m
g r ‘ _ i k maturity
0 5 ’56 E 5 r 20 Priceyield times and maturity. We price—yield curve is shown for three maturities.
AH have a 30% coupon. , f'ﬁces of 9% Coupon Bands
Yeah?
“ﬁrm to maimi’ty 5% 8% 9% 1 0% 1 i yea: 193.85 100.94 199.98 99.97 94.5}
5 yeazs 51750 134.36 1963.90 96.34 79.41
1‘13 years 231.38 3845,80 1136,00 93.7? 69.42 N A Zﬁ‘yea’rs 150.3 33999 106.85 9132 62.22 m
30 years; 161.82 311.31 390.8% 9954 6052 ~ , The Wise; (ﬂan: sensitive it: ﬂew changes Wine “W Yield to
'  ' maturity
{I S 3 0 3 5 2C? Priscayield and rowan me. All bonds Shawn have a maturity'of 36 years and
the taupe!) rams indicated an the respective curves. Prices as expressed as a percentage 1)? par. Fall 2008 September 15, 2008
Engineering 120 Industrial Engineering & Operations Research Page 1 of 2 Interest Rate Risk and Duration Interest rate risk refers to the possibility of a reduction in the value (price) of a bond resulting
from a rise in the interest rate (YTM). Note that if you are planning to hold the bond until its
maturity, the interest rate risk is irrelevant, since you are not concerned with the price of the bond. Everything else being identical,1 o Bonds with long maturities have more interest rate risk than bonds with short maturities.
For instance, — A zero~coupon 30~year bond is riskier than a zerocoupon 2—year bond.
— A 5% 30—year bond is riskier than a 5% 2—year bond. This means that if YTM changes from its current value, the price of the 30year bond will
change relatively more compared to the change in the price of the 2—year bond. 0 Bonds with low coupon rates have more interest rate risk than bonds with high coupon rates.
For instance, ~ A zerdcoupon 30—year bond is riskier than a 5% 30—year bond.
— A 5% 30year bond is riskier than a 10% 30year bond. Maturity T 2; Interest Rate Risk T
Coupon Rate T => Interest Rate Risk 1 Although these rules are helpful, they don’t give a complete measure of the interest rate risk. For
example, we cannot compare the two bonds below using these rules of thumb (Why?): 0 A 10% 10—year bond, 0 A zero coupon 5year bond. However, another measure of time length called duration gives a direct measure of the interest
rate risk: Duration T => Interest Rate Risk T Deﬁnition Duration of a cash ﬂow is a weighted average of the times that payments are made
where the weights depend on the present values of the corresponding payment: PV(tO)to + PV(t1)t1 +    + PV(tn)tn D ' z
uratlon Total Present Value
PV(t0) Pi/(tl) PV(t,,)
.— . . . th
TotalPVtO + TotalPth + + TotalPV 1Please see the handout about PriceYield Curves. This is Handout 5 on the website. Fall 2008 Sept€m§§1‘_1§733008
Engineering 120 Industrial Engineering 84'. Operations Research page 2 of 2 where lawn.) is the present value of the 1:)ayinent received at time 7;... All present values must be
mlculated using the YTM. Example Consider a 7% bond with 3 years to maturity that makes semiannual coupon payments.
Fame value is $100. Assume that the bond is selling at 8% yield. We can find the duration and the
prim of the bond using a spreadsheet layout as shown below: A B C D E
Year Payment PV of the Payment Weight PV times Weight
0.15 3.5 3.365 ‘ 0.035 0.017
1 3.5 3.235 0.033 0.033
1.5 3.5 3.111 0.032 0.048
2 3.5 2.992 0.031 0.061
2.5 3.5 2.877 0.030 0.074
3 103.5 81.798 0.840 2.520
Sum 97.379 1000‘] 2.753
Price Duration Or equivalently, 3.5 3.5 3.5 103.5
—————0.5+ .1+ 1.5+~+ 3
. _ 1.04 1.0412 1.043 1.046 ._.
Duration .— 35 3'5 3.5 103.5 — 2.753 I074" + 1.042 + 1.043 + ' ' ' + 1.046 ...
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This note was uploaded on 09/21/2008 for the course E 120 taught by Professor Alder during the Spring '08 term at University of California, Berkeley.
 Spring '08
 ALDER

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