CHAPTER 10.1 BOND CHARACTERISTICS AND TYPES
Bonds as IOU’s with coupon and principal payments.
Treasuries ($ 5T), Municipals ($2T), Agency ($2T), Corporates ($4T),
Mortgages ($4T), Asset Backed ($1.5T).
Larger than the equity market, muni market alone has over 50,000
issuers, securitization has made structures extremely complicated
particularly in the mortgage and credit markets. Issuers (esp. municipals
may purchase insurance). Munis have Federal tax-exempt status if the
issue is to benefit society at large. Some munis such as for sports facilities
may be taxable.
Good sites are www.investinginbonds.com and www.bondsonline.com.
ACCRUED INTEREST
Some bond prices are in 32nds. A price of 142-30 implies 142 30/32 =
142.9375 per $100 face value.
Bond prices are quoted with a mark-up, including commissions which
vary by company. Done this way because of low liquidity. Bond prices
are quoted net of accrued interest (flat prices)?
When bonds are purchased in between coupon payments, the buyer has to
pay the bond seller her part of the coupon which the buyer will receive
after purchase. Accrued interest is this interest payable on the bond from
the date of the prior coupon. T-bonds pay coupons semi-annually. The
Treasury provides a half-year calendar. For Feb/Aug cycles, the half-year
is 181 days (regular) and 182 days for a leap year. For March/September
cycles, half-year is 184 days.16+30+31+30+31+31+15). So, if you have a
March cycle bond paying an 8.875% coupon which is purchased 109 days
after the last payment, the accrued interest per $100 bond is:
= (109/184) * (0.50) * (0.08875) * 100 = 2.63
Bonds-1, 2010, Page 1
OPTION FEATURES AND BONDS
CALLABLE: Issuer can call & reissue if coupon > market yield (like a
refi). These bonds may be priced based upon call date not maturity date if
the chance of issuer exercise is high.
AND PUTTABLE (option with bondholder. If coupon < market yield,
put the bond, get the principal and reinvest at prevailing market yields (i.e
shorten bond’s life).
CONVERTIBLE (say $1000 bond converts to 40 shares of stock).
Conversion ratio is 1:40, If stock at $30, there is value to conversion,
price is $1,200, Conversion premium is $200.
FLOATING RATE BONDS
Here the coupon increases with interest rates. The floating rate may be
indexed to the Fed funds rate/T-bill rate/prime rate/LIBOR or other. At
times the rate is capped at some maximum. Frequency of reset could be
daily/weekly/monthly/semi-annual/annual. At any payment date, the price
of a floating rate bond is its par value.
Auction-rate securities are often muni bonds which are long-term
securities but the interest rate is set via a dutch auction, typically 7, 28 or
35 days. Many failed recently as there were few buyers and the banks
refused to take up the excess supply! Port Authority ended up with a 20%
effective rate !!
INVERSE FLOATERS: A plain vanilla bond may be repackaged as a
floater and an inverse floater. A 4% coupon bond is broken into a floater
at LIBOR + 1% and an inverse floater at (3% – LIBOR). So, if rates rise,
prices fall and coupon income falls too! Such bonds are hyper-sensitive to
rate changes.
Bonds-1, 2010, Page 2
Indexed Bonds: TIPS
Issued with 3, 5 and 10 year maturities. Suppose a 10-year TIP pays 6%
coupon and inflation is 2% for the past year. Then the face value is
adjusted by 2% to 1020 and a 6% coupon is paid on it.
Can think of the interest rate on these bonds as a risk-free real rate.
When do you buy them ? When inflation expectations are low.
P-I-K (Payment in Kind) Bonds
Can pay interest in cash or in other bonds. In some versions, interest is
added on to the principal for later payment.
MORTGAGES (not much in your book, but we’ve talked enough).
STRIPS
Coupon bearing Treasury bonds are stripped into a series of “stripped”
bonds of various maturities.
I-O and P-O STRIPS
Here a mortgage bond is separated into an interest component and a
principal component. The interest component is high in the early years
and the principal component is high in the later years.
Structured finance and securitizations refer to more complicated redistributions of the payoffs rather than just principal and interest. These
are leveraged and largely responsible for the credit crunch we are STILL
in!
Bonds-1, 2010, Page 3
10.2 AND 10.3 BOND BASICS (ALSO RECAP FROM FIN 323?)
1
2
100
100
3 ……..
100……..
20
100
1000
PRICE = ?
YIELD = ?
 COUPONS Usually semi-annual. We assume annual.
 FACE VALUE - we’ll assume $1000
 PRICE = PV OF ALL CASH FLOWS DISCOUNTED AT YIELD
 CURRENT YIELD = Coupon/Price (approx) vs. Yield to Mat.
SUPPOSE ABOVE BOND HAS A MARKET PRICE OF $1091.285.
Q: WHAT IS ITS YIELD TO MATURITY (YTM) ?
YTM = The rate at which the PV of cash flows equals bond price.
Treat as PV/FV Problem: FV = 1000, PMT = 100, PV = 1091.285, N =
20 YRS, SOLVE FOR INTEREST RATE AS 9%.
 IDENTICAL TO THE IRR ON A 20 YEAR PROJECT WITH:
INITIAL OUTLAY = $1091.285
ANNUAL CF = 100 for YRS 1-20
TERMINAL VALUE = $1000
 AS with IRR, this yield YTM is earned only if intermediate coupons
are reinvested. The YTM is calculated under the assumption that
coupon reinvestment occurs at the YTM (or that coupons are “put
back” into the bond).
Bonds-1, 2010, Page 4
REVERSE EXAMPLE: TO PRICE A BOND, GIVEN ITS YIELD
1
2
3
PRICE=?
80
80
80
1000
GIVEN YTM = YIELD = 12%
PRICE = 80 * PVIFA (3, 12%) + 1000 * PVIF (3, 12%)
=
192.15
+ 711.78
=
903.93 (DISCOUNT BOND)
SO,
YIELD > COUPON
PRICE < PAR (discount bond)
YIELD < COUPON
PRICE > PAR (premium bond)
YIELD = COUPON
PRICE = PAR (par bond)
IF, COUPONS ARE SEMI-ANNUAL, THEN DOUBLE THE
MATURITY HALVE THE YTM AND COUPON RATES
Price
premium
Mat.
(par) 1000
time
discount
With time, prices of all bonds move towards par. Path may be jagged because
as interest rates change.
Bonds-1, 2010, Page 5
FOR “PLAIN VANILLA” BONDS, maturity and coupon are fixed.
At the time of issue, bonds are priced at par with coupons near the
prevailing yield on similar bonds. The one exception is OID (original
issue discount) bonds.
After the issue, as rates change, yields on individual bonds change (not
exactly) and the bond becomes a discount or a premium bond.
Rate changes don’t really matter if your objective is to buy the bond and
hold till maturity, but there is still concern about default risk.
REALIZED COMPOUND YIELDS
Recall that YTM implies coupons re-invested in the bond at its yield.
Reality is that coupons may be re-invested (if at all) at a different rate
than the YTM. So, the rate of return REALIZED is different and is called
REALIZED COMPOUND YIELD (RCY).
Calculate it for the 3-year bond assuming a 5% reinvestment rate.
YTM = 12%
1
2
PRICE=903.93
80
80
3
80
1000
80 * FVIF (2,5%)= 88.2
80 (1.05) = 84.0
903.93
* FVIF (3, X%)
X = 11.47% IS RCY
= 1252.2
Bonds-1, 2010, Page 6
TAXES AND OID BONDS.
Suppose a 30 year zero is issued when rates were 10% per year. The price
of the bond is 1000/(1.1)30 = $57.31 and it is issued at a $942.69
discount from par. After 1 year, the IRS imputes an interest rate of 10%
and correspondingly imputes the price of the bond as 1000/(1.1)29 =
63.04. The difference 63.04 – 57.31 or 5.73 is taxed as ordinary income.
However, over the year as rates change, the actual market price of the
bond may be different from 63.04. IF the bond is sold, the difference
between the market price and the IRS imputed bond price is treated as a
capital gain or loss.
10.4 BOND PRICING: BOND PRICE CHANGES WITH TIME-1
REVISIT THE 3-YEAR 12% DISCOUNT BOND ABOVE. FIRST
ASSUME THAT TIME PASSES AND RATES STAY THE SAME.
YTM STAYS AT 12%
1
2
3
PRICE=903.93
PRICE
80
80
80
1000
P=? = 80 PVIFA(2,12%)+1000 PVIF(2,12%)
= 932.39
EVEN THOUGH YTM STAYS THE SAME.
Q:
RATE OF RETURN IF YOU BUY BOND AT
903.93 AND SELL AFTER ONE YEAR AT 932.90 ?
(932.90 + 80 – 903.93)/903.93 = 12% (IS THE YIELD)
Q:
IS ABOVE TRUE FOR A PREMIUM BOND TOO?
(I.E DOES ITS PRICE INCREASE ?
NO
IS ITS RETURN STILL 12% ?
YES
Bonds-1, 2010, Page 7
WHAT HAPPENS TO BOND’S PRICE AS RATES CHANGE ?
SAY, YTM FALLS TO 8% IN 1 YEAR)
YTM DROPS TO 8%
1
2
3
PRICE=903.93
80
80
80
1000
12%
8%
P=? = 80 PVIFA(2,8%)+1000 PVIF(2,8%)
= 1000.
BOND BECOMES A PAR BOND, AFTER ONE YEAR.
Q:
RATE OF RETURN IF SELL AT THIS TIME?
(1000 + 80 – 903.93)/903.93 = 19.48%
OLD BUYER EARNED 19.48%, NEW BUYERS GET 8%
AVERAGE OVER 3 YEARS IS 12% (GEOMETRIC)
Q:
WHAT ABOUT AFTER ONE MORE YEAR?
a)
b)
Say yields stay the same ? price is the same too.
say yields increase ?
price declines.
Bonds-1, 2010, Page 8
10.5 CORPORATES AND DEFAULT RISK
Bond indenture is a contract between issuer and holder, essentially a set
of restrictions on the issuer, such as:
 Sinking funds—since eventual principal payments can create cash
crisis, bonds may be repurchased periodically instead.
 Subordination clauses—to restrict additional borrowing
Covenants on dividend—cannot payoff to stockholders
 Collateral—mortgages, securities, equipment, none.
Default risk: Primary source is bond ratings agencies (Moodys. S&P or
Fitch). Ratings are typically derived from examination of financial
ratios: interest coverage, leverage, liquidity, profitability. Typically,
lowest investment grade bonds are those deemed to have adequate
capacity to pay interest and repay principal.
Are ratings changes anticipated by the bond market? Generally, prices
tend to move in advance of agency action.
Bond Credit Quality Ratings
Rating agencies
Moody’s* Standard & Poor’s** Fitch Ratings**
Credit Risk
Investment grade
Highest quality
High quality (very strong)
Upper medium grade (strong)
Medium grade
Not investment grade
Lower medium grade (somewhat
speculative)
Low grade (speculative)
Poor quality (may default)
Most speculative
No interest being paid or bankruptcy
petition filed
In default
Aaa
Aa
A
Baa
AAA
AA
A
BBB
AAA
AA
A
BBB
Ba
BB
BB
B
Caa
Ca
B
CCC
CC
B
CCC
CC
C
D
C
C
D
D
* The ratings from Aa to Ca by Moody’s may be modified by the addition of a 1, 2 or 3 to show
relative standing within the category.
Bonds-1, 2010, Page 9
** The ratings from AA to CC by Standard & Poor’s and Fitch Ratings may be modified by the
addition of a plus or minus sign to show relative standing within the category.
HIGH YIELD BONDS
Origin with Drexel and Milken. About 25% are fallen angels, another
25% were issued below investment grade, about 50% from LBO
restructuring.
Credit quality appears higher these days. But a lot of the credit issues
have moved to the credit derivatives market (CDO’s).
BOND SPREADS
Fixed income market participants often make comparisons using spreads.
The treasury yield spread (compares short vs long maturities)
the NOB spread compares the spread between T-notes and bonds
the TED spread compares T-bills with Eurodollars.
The High-yield spread compares junk bond yields with AAA corporates
OPTION ADJUSTED SPREADS (OAS). Because of the various option
features embedded in bonds, it has become common to think in terms of
an option adjusted spread. For instance suppose a callable corporate bond
trades at a spread of 100 basis points over Treasuries. If 60 of those are
Bonds-1, 2010, Page 10
attributable to the risk differences of the bond over the Treasury and the
40 is attributable to the option feature. The OAS is 60 basis points.
CHAPTER 10.6 YIELD CURVES (bondtalk.com)
(Play with the dynamic YC in stockcharts.com/charts/)
a) Yield curves represent the interest rates available for investments of
Bonds-1, 2010, Page 11
different maturities, but with similar risks. Strictly speaking, the term
structure of rates refers to the relationship between default-free zero
coupon securities and their maturities. But can draw yield curves for
other risk classes as well.
b) Yield curves are rarely flat for all maturities as the YTM implies.
c) Yields are not known but are inferred from prices.
d) Sometimes prices are known only for bonds of some maturities and
have to be inferred.
IN THE REAL WORLD start with a set of zero-coupon Treasuries, for
which the following prices are quoted
Time to Mat
1-year
2-year
3-year
Price
909.09
811.62
711.78
Inferred Spot Rate
10%
11%
12%
Discount factor
0.90909
0.81162
0.71178
Discount factors are just the PV of a $1 face value bond. In reality, the
spot rates above are “inferred” by traders from the prices for pure
discount bonds of various maturities that they observe. So, the following
are equivalent statements:
a) 1-year zeros yield 10%
b) The 1-year spot rate is 10%
c) To discount cash flows in 1 year, use 10%
d) The price of a 1-year zero = 1000/(1.10)1 = 909.09
What happens when the Fed adjusts short-term rates? Do the rates on all
maturity adjust equally (parallel shift)?. During the last few rate hikes, the
long maturity yield did not move as much.
Bonds-1, 2010, Page 12
SLOPE OF THE YIELD CURVE
A steep yield curve often precedes an economic upturn.
A flat YC curve often precedes an economic slowdown (transitory)
An inverted yield curve often precedes a recession
Bonds-1, 2010, Page 13
THEORIES ABOUT THE SHAPE OF THE YC ARE:
a) THE PURE EXPECTATIONS HYPOTHESIS
Forward rates = Expected Future Spot Rates
b) Most investors are short-term, see risk in lending long-term. And
require a premium for giving up liquidity
Forward rates HIGHER than expected future short rates
Upsloped yield curve (always)
THIS IS THE LIQUIDITY PREFERENCE HYPOTHESIS
c) Financial institutions have a preference for different maturities because
of the nature of their business (Life insurers want long maturities,
property insurers want shorter..) THIS IS MARKET SEGMENTATION
STRATEGIES AROUND THE YIELD CURVE ARE:
a) bullet: concentrate on one maturity
b) barbell: concentrate on 2 extremes (very short + very long)
c) ladder: equal money across all maturities
d) Riding the yield curve (very short-term)
Bonds-1, 2010, Page 14
When YC’s are upward sloping, as a bond approaches maturity, it is
valued at lower yields and higher prices, so hold and sell before maturity
to pick up some return.
E.G CURRENT Yield curve is 1-yr bonds earn 6%, 2-year bonds earn
7% per year. EXPECT YIELD CURVE TO STAY THE SAME
WITH TIME, MAT
YIELDS
INTUITION
a) BUY 1-YR BOND => GET 6%
b) BUY 2-YR BOND AND SELL AFTER ONE YEAR
(YIELD CURVE SAME)
7%
873.44
7%
1000
6%
943.40
RETURN =
1000
(943.40 – 873.44)/873.44 = 8%
NOTE THAT “expecting the YC to stay the same” is one kind of
forecast of future interest rates.
YC same
Next year’s spot rate will be 6% (like this year). (1-yr
6%, 2-yr 7%). Expected spot rate will drop. This expectation is different
from what is implied in the forward rate. (forward rate is 8%).
e) Can forecast expected yields on bonds of different maturities (see
below).
Bonds-1, 2010, Page 15
HORIZON ANALYSIS (page 355)
Consider 3 bonds
A: 5-year maturity, 6% coupon,
B; 10-year maturity, 8% coupon,
C; 15-year maturity, 4% coupon,
YTM = 9%
YTM = 9%
YTM = 9%
You have a 5 year investment horizon, and if you buy longer bonds, they
will be sold at the prevailing market price. All coupons will be reinvested.
Forecasts of rates are 7% for years 1-5 AND 8% for yrs 6-15.
WHICH BOND TO CHOOSE?
A
B
C
YTM Price
FV
Bonds price Terminal HPR
(coupons) (in 5 yrs) value
9% 883.31
9% 935.82
9% 596.97
345.04 a
460.06 b
230.03
1000.00 1345.04
1000.00 c 1460.06
731.60 d 961.63
8.77%
9.30%
10.00%
PICK BOND C
a
For A, FV (coupons) are 60 * FVIFA (5, 7%) = 345.04
For B, FV (coupons) are 80 * FVIFA (5, 7%) = 460.06
c
For B, Price = par as prevailing yield is 8% = coupon
d
For C, Price = 40*PVIFA (10, 8%) + 1000*PVIF (10, 8%)=$ 731.60
b
Bonds-1, 2010, Page 16
CHAPTER 11. 1 BOND PRICE DYNAMICS
Prices at
BOND
% chg
YTM=12 YTM=10 YTM=8
% chg
___________________________________________________________
(1)
(2)
(3)
(4)
(5)
(6)
10-yr, 12%
-11.18%
1000.00
1125.85
1268.41
12.66%
15-yr, 12%
-13.20%
1000.00
1152.13
1342.34
16.51%
20-yr, 12%
-14.55%
1000.00
1170.23
1392.67
19.01%
20-yr, 4%
-17.72%
402.48
489.14
607.22
24.14%
20-yr, 0% -30.22%
103.70
148.60
214.50
44.35%
___________________________________________________________
FROM COL(2) FOR THE SAME COUPON, LONGER MATURITY
BONDS HAVE GREATER PRICE SENSITIVITY TO YIELD
CHANGES (1st 3 BONDS)
DOWN COL(2), FOR THE SAME MATURITY, LOW COUPON
BONDS GREATER PRICE SENSITIVITY TO YIELD CHANGES
(LAST 3).
SAME FOR COLUMN (6)
Bonds-1, 2010, Page 17