# Government Bonds

Development Team Montego Data Limited
September 2003

#### Requires

• Brief Money Market Knowledge

Introduction
Yield Example
Coupon and Yield
STRIPS
Conclusion

## Introduction

• Governments borrow money, mostly by selling fixed-coupon bonds
• ( Price Up == Yield Down ) ; ( Price Down == Yield Up )
• For any given Change in Yield, Longer Bonds change in price by more than Shorter Bonds
• Dealers borrow bonds ising repo
• Dealers buying a bond may well borrow the money to do so, cheapening that borrowing using repo
• Some Government Bonds are STRIPpable; they can be exchanged for the same bundle of cashflows in sperately traded form
• Entities other than Government also issue bonds. The additional Yield over the Debt of the Government is dependant upon Credit Rating

## Yield Example

Entity Nominal Notional FaceCouponTerms Maturity
German Government100 6.5% Annual31 Dec 2033

Prices of bonds with a 6% nominal coupon

MaturityYield(4%)Yield(5%)Yield(6%)Yield(7%)Yield(8%)
1 101.92 100.95100.00 99.07 98.15
2 103.77 101.86100.00 98.19 96.43
5 108.90 104.33 100.00 95.00 92.01
10 116.22 107.72 100.00 92.98 86.58
30 134.58 115.37 100.00 87.59 77.48
At what price would a one-year 6% bond yield 5% ?
If the yield is 5% then 100 currency units today are worth the same as 105 units in 1 year.
100 today = 105 in 1 year ; 1 today = 1.05 in 1 year ; 1 / 1.05 today = 1 in 1 year ; 106 / 1.05 today = 106 in 1 year.
Thus, at a 5% yield, 106 in 1 year is worth 106 / 1.05 is approx 100.95 today.
In the case of a Two-Year Bond annual coupon 6% and yield 5%
6 / 1.05 today = 6 in 1 year ; 1 today = 1.05 in 1 year ; 1 in 1 year = 1.05 in 2 years ; 1 today = 1.05 * 1.05 in 2 years ( 1.1025 )
( 6 / 1.05 ) + (106 / 1.052) approx 101.86

## Coupon and Yield

• The coupon of a bond defines the payments made. The coupon is known when the bond is first issued, and remains constant until maturity. The bond's coupon is not altered by a change in the bond's price
• The yield is the effective interest rate, calculated from the price of the bond. The market determines the price, and hence the yield. As time passes, or as the price changes, the yield also changes.
• ## STRIPS

A US Government Bond pays coupons every half-year until maturity, when the principal of \$ 100.00 is also paid.
But what if, for some particular need, an investor wishes to acquire a different shape of cashflows ?
For example, what if an investor wishes to put money away until 2021 and not receive any coupons before then ?
Or what if that investor wishes to receive coupons, and only coupons, from 2016 until 2021 ?
Since there is sometimes a demand for such customised collections of cashflows, the US Government allows bonds to be stripped.
This is an exchange facility; a dealer hands in a US Treasury Bond and receives in return the same cashflows but in separately tradable form.
These cashflows are called Separately Traded Registered Interest and Principal Securities.

## Conclusion

There is always another subtle issue to consider.