Bond Yields
Fixed Income Securities
Outline
Sources of Return for a Bond Investor
Measures of Return/Yield
Nominal Yield
Current Yield
Yield to Maturity
Impact of Reinvestment Assumption
Yield to Maturity for a Zero Coupon Bond
Yield to Call and the Yield to Worse
Yield Measures of a Portfolio of Bonds
Yield Measure for a Floating Rate Security
Total Return
Sources of Bond Return
Three sources of return:
Periodic coupon interest payments
Any capital gain (or capital loss)) when the
bond matures or is called back or is sold
Income from reinvestment of the periodic
coupon interest
Any measure of bond yield should be
based on the above three potential
sources of return
Nominal Yield
Nominal yield of a bond is the coupon
rate on the bond
A bond with 8 percent coupon has a 8%
nominal yield
Does not consider capital gain or capital
loss
Does not consider reinvestment income
Current Yield
Current yield relates the annual coupon
interest to the current market price of
the bond
Considers only coupon interest income
Does not consider capital gain or loss
Does not consider reinvestment income
Yield to Maturity
Also called the internal rate of return of a
bond
The interest rate that will make the present
value of the cash flows equal to the price (or
initial investment)
Rate of return promised to an investor if you
purchased the bond at the current market
price given coupon and maturity of the bond
Yield to maturity will equal the actual
rate of return to a bond investor if and
only if
The investor holds the bond to its maturity
and
All interim cash flows in the form of coupon
payments are reinvested at the computed
yield to maturity
YTM Contd…
The YTM takes into account
Coupon interest income
Capital gain or capital loss
Interest on interest income
How much YTM tells us about a bond’s
actual return?
Depends on reinvestment risk and
Interest rate risk
Reinvestment Risk and YTM
Higher the reinvestment risk, less we will
know from the YTM about the actual yield of
a bond
When will reinvestment risk be high?
For a given YTM and coupon, higher maturity
bonds have a high reinvestment risk
For a given YTM and maturity, high coupon bonds
have a high reinvestment risk
Which type of bonds will face higher
reinvestment risk?
Premium Bonds
Discount Bonds
Zero Coupon Bonds
Interest Rate Risk and YTM
Inverse relationship between bond prices and
bond yields
For an investor who plans to hold the bond to
maturity will not face interest rate risk and
YTM may be a good measure of actual yield
of bond assuming other things are held
constant
If you plan to trade bond before maturity, you
will face price risk and YTM may not be closer
to the actual yield of a bond
Impact of price will differ from bond to bond
YTM for a Zero Coupon Bond
A zero-coupon bond has only one cash
inflow
The rate at which maturity value of a
zero-coupon bond equals the current
market price of the bond
Yield to Call
Usually, bond market participants compute
both the yield to maturity and the yield to call
for a callable bond and use the lower of the
two to price bonds
When bonds are trading at or above a
specified crossover point, which is
approximates the bond’s par value plus one
year’s interest, the YTC will normally provide
the lowest yield measure
When is the bond issuer most likely to
call back callable bonds?
When the bond price rises to the price
above par and the computed YTM becomes
low enough that it would be profitable for
the issuer to call the bond and finance the
call by selling new bonds in the market.
Total Return of a Bond
An investor can make explicit
assumption about the reinvestment rate
instead of assuming that the coupon
interest will be reinvested at the YTM
Total return is a measure of yield that
makes explicit assumptions about the
reinvestment rate
Total Return
Why Total Return?
Suppose an investor who has a 5-year investment
horizon is considering the following 4-bonds:
Coupon
Maturity
YTM
Bond A
5% 3 years
9.0%
Bond B
6% 20 years
8.6%
Bond C
11% 15 years
9.2%
Bond D
8% 5 years
8.0%
Assuming that all the four bonds are of equal
credit quality, which is the most attractive to
this investor?
How do we find out the best bonds?
It depends on investor’s expectations.
Depends on the interest rate at which coupon income can be
reinvested until the investor’s planned investment horizon.
Also, for bonds with maturity higher than investment
horizon, it depends on the required yield in the market at
the end of the planned investment horizon.
Consequently, any of the bonds can be the best
alternative, depending upon some reinvestment rate
and some future required yield a
How to Compute Total Return?
Compute the total future dollars that will result from
investing in a bond assuming a particular
reinvestment rate
The total return is the interest rate that will make the
initial investment in the bond grow to the computed
total future dollars
Total return requires an investor to specify:
An investment horizon
A reinvestment rate, and
A selling price for the bond at the end of the investment
horizon (which depends on the assumed yield to maturity for
the bond at the end of the investment horizon)