Visualization of Macaulay duration as a point of total immunization

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• A Numerical Example

In this section we consider a basic numerical immunization example. Suppose you are trying to immunize a year-10 obligation whose present value is $1,000; that is, at the current interest rate of 6 percent, its future value is: $1,000[pic][pic]= $1,790.85 You intend to immunize the obligation by purchasing $1,000 worth of a bond or a combination of bonds. You consider three bonds:

i. Bond 1 has 10 years until maturity, a coupon rate of 6.7 percent, and a face value of $1,000. ii. Bond 2 has 15 years until maturity, a coupon rate of 6.988 percent, and a face value of $1,000. iii. Bond 3 has 30 years until maturity, a coupon rate of 5.9 percent and a face value of $1,000.

[pic]
If the yield to maturity doesn’t change, then you will be able to reinvest each coupon at 6 percent. [pic]

The upshot of this table is that purchasing $1,000 of any of the three bonds will provide—10 years from now—funding for your future obligation of $1,790.85, provided the market interest rate of 6 percent doesn’t change.

Now suppose that, immediately after you purchase the bonds, the yield to maturity changes to some new value and stays there. This change will obviously affect the calculation we just did. For example, if the yield falls to 5 percent, the table will now look as follows:

[pic]

Thus, if the yield falls, bond 1 will no longer fund our obligation, whereas bond 3 will overfund it. Bond 2’s ability to fund the obligation—not surprisingly, in view of the fact that its duration is exactly 10 years—hardly changes.

...The Harvard Management Company and Inflation-Protected Bonds
1(a) Regular Treasury bonds are purchased at face value in the beginning or an adjusted price prior maturity. And in every period, normally annul or semiannual, investor will receive a coupon as an interest and at the maturity a principal plus coupon.
(b) Coupon and principal of the Regular Treasury bonds are fixed, therefore if the inflation rate increases in the forecasting future,...

...NAME: MASSAWE BARAKA, REG. NO: 2010-04-03894.
12
FINANCE 202 INDIVIDUAL ASSIGNMENT
UDBS
Consider a 10 year bond that has a face value shs 1000, a coupon rate of 6% and pays interest once a year.
(a)Suppose person A bought this bond at par when it was initially issued and sold it 1 year later to person B for shs 1024.What is B’s total return?
Soln
Total return =[ Interest paid +(selling price – buying price)]/buying price
Given; Annual interest paid =...

...perpetual bond is currently selling for RS. 95/-. The coupon rate of interest is 13.5%. The approximate discount rate is 15%. The value of the bond and the YTM is:
(a) Rs. 90/- and 14.2% Value is (13.5*15%=90) and YTM is ((13.5/95)*100=14.21%)
(b) Rs. 100/- and 13.5%
(c) Rs. 90 and 15%
(d) Rs. 90/- and 13.5%
902. In 2001, Meridian Ltd. has issued bonds of Rs. 10,000/-each due in 2011 with a 14% per annum coupon rate payable at the end of...

...BOND PROBLEM SOLUTIONS
1. Six years ago, The Corzine Company sold a 20-year bond issue with a 14 percent annual coupon rate and a 9 percent call premium. Today, Corzine called the bonds. The bonds originally were sold at their face value of $1,000. Compute the realized rate of return for investors who purchased the bonds when they were issued and who surrender them today in exchange for the call price.
PV =...

...BONDSBonds pay fixed coupon (interest) payments at fixed intervals (usually every six months) and pay the par value at maturity.
Par value = $1,000
Coupon = 6.5% or par value per year,
or $65 per year ($32.50 every six months).
Maturity = 28 years (matures in 2032).
Issued by AT&T.
Types of Bonds
Debentures - unsecured bonds.
Subordinated debentures - unsecured “junior” debt.
Mortgage bonds - secured bonds....

...assets composed solely of a 10-year, 12 percent, $1 million loan. The loan is financed with a 10-year, 10 percent, $1 million CD. Bank B has assets composed solely of a 7-year, 12 percent zero-coupon bond with a current (market) value of $894,006.20 and a maturity (principal) value of $1,976,362.88. The bond is financed with a 10-year, 8.275 percent coupon, $1,000,000 face value CD with a yield to maturity of 10 percent. The loan and the CDs pay interest annually,...

...Tutorial 2
Q1. Why do most international bonds have high Moody’s or Standard & Poor’s credit ratings?
Credit Rating is a social intermediary service to provide credit information and reference for the community. Credit rating is aim to show the size of a credit default risk the rating object, rating agencies focus on financial conditions and historical data to give the overall valuation of object. Currently, credit rating on the issue of international bonds is...

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