Handout1_fall2008 - Fall 2008 Engineering 120 Industrial...

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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 ~ Rate seareh Results i “a. “a. «2 mm: Lander abate ' am A?!“ , } M‘orsthivis) W 92/04/38 6.375 5.5913 $1,409 kg}? 39 $2,602 E . AimLoan.cgm 1334/ @3 02/04/08 5875 was $1,995 6mg 33 $2,463? mgr/figs! WEEK—5% 02/04/08 5.000 6.374 35?,888 25%;? 39 $2,500 SEE * Downey , “LA 01/30/08 7.500 7.730 $890 2'08”; 36 $2,916 (3.300 E Modify Luca! fiearch sax/ma 393W ,, .. Edit Loan Amount: $413031 :9 $2,099 Edit Product Type: 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 Price-yield 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? Prisca-yield 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 zero-coupon 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 30-year 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% 30-year bond is riskier than a 10% 30-year 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 5-year 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.

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Handout1_fall2008 - Fall 2008 Engineering 120 Industrial...

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