Chapter 6: Example
Example: A bond with a 6.5% annual coupon has three years to maturity. If
investors require a 5.1% return, what is the price of the bond? Assume the bond is
issued at par.
Coupon = 6.5% * 1000 = 65
Discount rate = 5.1%
Price of bond = PV of coupons + PV of principle

Chapter 6: Premiums vs. Discounts
Par: Coupon rate
= Discount rate
Discount: Coupon rate < Discount rate
Premium: Coupon rate > Discount rate
All else held equal,
the price of a premium bond falls over time
the price of par bond stays constant over time
the price of a discount bond rises over time

Chapter 6: Bond Yield
3 methods of measuring return an investor would receive on bond investment:
Current yield
Yield to Maturity (YTM or yield)
Rate of Return
Current yield = annual coupon payment / bond price
Yield To Maturity: discount rate for which the present value of the bond’s
payments equal the price.

Chapter 6: Example
Suppose you buy the bond and sell it after one year, and interest rates have not
changed. The price of the bond will be
P
= 100/(1+r) + 100/(1+r)^2 + 1,000/(1+r)^2 =1,092.97
Your
return is = 100 +1,092.97 −1,136.36 = 5% =
ytm
1,136.16
what if interest rates rise or fall
?
Instead if you hold it till maturity, reinvesting coupons, and interest rates do not
change, your return is
=[100 (1.05)^2 +100(1.05)+1100 - 1,136.36]/1136.16 =15.7625%
or, on an annualized basis, your return is =(1.157625)^(1/3)
−1=5%=
ytm
If interest rates rise (i.e., future bond prices fall), then your return is higher than the
YTM implied by current prices
,
for a holding period till maturity
.
Vice versa if
interest rates fall.
Exception: zero-coupon bonds, for which YTM = return till maturity regardless of
interest rate movements.

Chapter 6: Interest Rate Risk & Yield Curve
All else equal, a longer maturity bond has higher interest rate risk.
All else equal, a lower coupon bond has higher interest rate risk.
The principal measure of interest risk of a bond is called its
duration
The yield curve, at any point in time, plots the yield to maturity of otherwise
identical bonds that differ only in their time to maturity.
Since longer maturity bonds have higher interest rate risk, all else equal, investors
would require a higher rate of return on longer maturity bonds, or else they would
not be willing to hold these bonds.

Chapter 6: Managing Risk
A bond issuer faces the risk that interest rates may fall, but he is locked into paying
a fixed coupon.
One option is to make the bond callable, the issuer reserves the right to retire the
bond before maturity at a pre- specified call price.
all else equal, a callable bond should trade at a lower price than an otherwise identical non-callable
bond.
Similarly, to protect investors, bonds may be puttable
the buyer/holder reserves the right to demand repayment before maturity
all else equal, a puttable bond should trade at a higher price than an otherwise identical non-puttable
bond.