Transcript Chapter 6 Bonds, Bond Prices and the Determination of Interest Rates

Bond Prices
Zero-coupon bonds: promise a single future
payment, e.g., a U.S. Treasury Bill.
Fixed payment loans, e.g., conventional
mortgages.
Coupon Bonds: make periodic interest payments
and repay the principal at maturity, e.g., U.S.
Treasury Bonds and most corporate bonds.
Consols: make periodic interest payments
forever, never repaying the principal that was
borrowed, e.g., British consols.
Bond Prices
Zero-Coupon Bonds or Discount Bonds
Price of a $100 face value zero-coupon bond
$100

n
(1  i)
Where i = interest rate
n = time until the payment is made
Bond Prices
Zero-Coupon Bonds or Discount Bonds
Examples. Assume i=4%
Price of a One-Year Treasury Bill.
Price of a Six-Month Treasury Bill
100


$
98
.
06
1/ 2
(1  0.04)
Bond Prices
Fixed Payment Loans
Value of a Fixed Payment Loan =
FixedPayment FixedPayment
FixedPayment


2
n
(1  i )
(1  i)
(1  i )
Bond Prices
Coupon Bond
 CouponPayment CouponPayment
CouponPayment  FaceValue
PCB  


......


1
2
n
(1  i)
(1  i)
(1  i)
(1  i) n


Bond Prices
Consols
Yearly Coupon Payment
PConsol 
i
Bond Yields
Yield to Maturity
Price of One-Year 5 percent Coupon Bond =
$5
$100

(1  i ) (1  i )
The value of i that solves this equation is the
yield to maturity
Bond Yields
Yield To Maturity
• If the price of the bond is $100, then the
yield to maturity equals the coupon rate.
• Since the price rises as the yield falls,
when the price is above $100, the yield to
maturity must be below the coupon rate.
– If you pay more than the face value for a
bond, you are earning less than the
coupon rate.
Bond Yields
Yearly Coupon Payment
Current Yield 
Price Paid
Bond Yields
Relationship Between a Bond’s Price and
Its Coupon Rate, Current Yield and Yield to Maturity
Bond Price < Face Value
 Coupon Rate < Current Yield < Yield to Maturity
Bond Price = Face Value
 Coupon Rate = Current Yield = Yield to Maturity
Bond Price > Face Value
 Coupon Rate > Current Yield > Yield to Maturity
Bond Yields
Holding Period Return:
the return to holding a bond and selling
it before maturity.
The holding period return can differ
from the yield to maturity when you do
not hold the bond to maturity.
Bond Yields
Example:
10 year bond (Face value=$100) and a
6% coupon rate. Sold one year later.
• If the interest rate in one year is 5%,
one year holding period return =
$6 $107.11  $100 $13.11


 .1311
$100
$100
$100
Bond Yields
If the interest rate in one year is 7%
One year holding Period return =
$6 $93.48  $100  $.52


 .0052
$100
$100
$100
or -.52%
Bond Market and Interest Rates
One Year Zero-coupon (discount) Bond.
$100
P
1 i
or
$100  P
i
P
Bond Market and Interest Rates
Bond Market and Interest Rates
Factors that shift Bond Supply
• An increase in the government’s borrowing
increases the quantity of bonds
outstanding, shifting the bond supply curve
to the right.
• As business conditions improve, the bond
supply curve shifts to the right.
• An increase in expected inflation shifts the
bond supply curve to the right.
Bond Market and Interest Rates
Factors that Shift Bond Demand to Right
• An increases in wealth.
• A fall in expected inflation.
• If the return on bonds rises relative to the
return on alternative investments, the
demand for bonds increases.
• If a bond becomes less risky relative to
alternative investments, the demand for the
bond increases.
• When a bond becomes more liquid relative
to alternatives, the demand for the bond
increases.
Bond Market and Interest Rates
Bonds and Risk
Sources of Bond Risk
• Default Risk
• Inflation Risk
• Interest-Rate Risk