2. Straight Bond
• Obligates the issuer of the bond to pay the holder of the bond:
• A fixed sum of money (principal, par value, or face value) at
the bond’s maturity
• Constant, periodic interest payments (coupons) during the
life of the bond (Sometimes)
• Special features may be attached
• Convertible bonds
• Callable bonds
• Putable bonds
3. Straight Bond Basics
• $1,000 face value
• Semiannual coupon payments
Price
Bond
Coupon
Annual
Yield
Current
(10.2)
Value
Par
Coupon
Annual
Rate
Coupon
(10.1)
4. Straight Bonds
• Suppose a straight bond pays a semiannual coupon of $45 and is
currently priced at $960.
• What is the coupon rate?
• What is the current yield?
%
.
%
.
375
9
$960
2
$45
Yield
Current
(10.2)
00
9
$1,000
2
$45
Rate
Coupon
(10.1)
5. Straight Bond Prices & Yield to Maturity
•Bond Price:
•Present value of the bond’s coupon payments
+ Present value of the bond’s face value
•Yield to maturity (YTM):
•The discount rate that equates today’s bond price
with the present value of the future cash flows of
the bond
6.
7. Bond Pricing Formula
M
M
YTM
FV
YTM
YTM
C
2
2
2
1
2
1
1
1
Price
Bond
(10.3)
Where:
C = Annual coupon payment
FV = Face value
M = Maturity in years
YTM = Yield to maturity
PV of coupons PV of FV
8. Straight Bond Prices
41
457
2
08
1
1
1
08
60
Coupons
of
PV 24
.
$
.
.
M
M
YTM
FV
YTM
YTM
C
2
2
2
1
2
1
1
1
Price
Bond
(10.3)
PV of coupons PV of FV
12
390
2
08
1
1000
FV
of
PV 24
.
$
.
For a straight bond with 12 years to maturity, a coupon
rate of 6% and a YTM of 8%, what is the current price?
Price = $457.41 + $390.12 = $847.53
9. Par, Premium and Discount Bonds
Par bonds: Price = par value
YTM = coupon rate
Premium bonds: Price > par value
YTM < coupon rate
The longer the term to maturity, the greater the premium
over par
Discount bonds: Price < par value
YTM > coupon rate
The longer the term to maturity, the greater the
discount from par
10. Premium and Discount Bonds
• In general, when the coupon rate and YTM are held constant:
For premium bonds: the longer the term to maturity, the
greater the premium over par value.
For discount bonds: the longer the term to maturity, the greater
the discount from par value.
11. Relationships among Yield Measures
For premium bonds:
coupon rate > current yield > YTM
For discount bonds:
coupon rate < current yield < YTM
For par value bonds:
coupon rate = current yield = YTM
12. Bond Quotations
•If you buy a bond between coupon dates:
•You will receive the next coupon payment
•You might have to pay taxes on it
•You must compensate the seller for any accrued
interest.
13. Bond Quotations
• Clean Price = Flat Price
• Bond quoting convention ignores accrued interest.
• Clean price = a quoted price net of accrued interest
• Dirty Price = Full Price = Invoice Price
• The price the buyer actually pays
• Includes accrued interest added to the clean price.
14. Clean vs. Dirty Prices
• Today is April 1. Suppose you want to buy a bond with a 8%
annual coupon payable on January 1 and July 1.
• The bond is currently quoted at $1,020
• The Clean price = the quoted price = $1,020
• The Dirty or Invoice price = $1,020 plus (3mo/6mo)*$40 =
$1,040
15. Callable Bonds
• Gives the issuer the option to:
•Buy back the bond
•At a specified call price
•Anytime after an initial call protection period.
• IF bonds are callable Yield-to-call may be more relevant
16. Yield to Call
T
T
YTC
CP
YTC
YTC
C
2
2
2
1
2
1
1
1
Price
Bond
Callable
Where:
C = constant annual coupon
CP = Call price of bond
T = Time in years to earliest call date
YTC = Yield to call
17. Interest Rate Risk
• Interest Rate Risk = possibility that changes in interest
rates will result in losses in the bond’s value
•Realized Yield = yield actually earned or
“realized” on a bond
•Realized yield is almost never exactly equal
to the yield to maturity, or promised yield
21. Passive Portfolio Strategies
•Buy and hold
• Buy a portfolio of bonds and hold them to maturity
• Can be modified by trading in positions
•Indexing
• Match performance of a selected bond index
• Monitor tracking error.
22.
23. Portfolio Strategies
• Passive
- Pure Bond Indexing
-Enhanced Indexing- Matching Primary Risk Factors
- Enhanced Indexing- Minor Risk Factors Mismatches
Active
-Larger Risk Factors Mismatches
- Full blown Active
26. Active Management Strategies
•Interest-rate anticipation
• Risky strategy relying on uncertain forecasts of future
interest rates, adjusting portfolio duration
• Ladder strategy staggers maturities
• Barbell strategy splits funds between short duration and
long duration securities
27. Active Management Strategies
•Valuation analysis
• A form of fundamental analysis, this strategy selects bonds
that are thought to be priced below their estimated
intrinsic value
28. Active Management Strategies
•Credit analysis
• Determines expected changes in default risk
• Try to predict rating changes and trade accordingly
• Buy bonds with expected upgrades
• Sell bonds with expected downgrades
• High yield bonds may warrant special attention.
30. Active Management Strategies
•Bond swaps
• Selling one bond (S) and buying another (P)
simultaneously
• Swaps to increase current yield or YTM, take advantage of
shifts in interest rates or realignment of yield spreads,
improve quality of portfolio, or for tax purposes
31. Active Management Strategies
Bond Swaps
• Pure yield pickup swap
• Swapping low-coupon bonds into higher coupon bonds.
• Substitution swap
• Swapping a seemingly identical bond for one that is currently
thought to be undervalued.
• Tax swap
• Swap in order to manage tax liability (taxable & municipal).
• Swap Strategies and Market-Efficiency
• Bond swaps by their nature suggest market inefficiency
32. Duration
• Since price volatility of a bond varies inversely with its
coupon and directly with its term to maturity, it is necessary
to determine the best combination of these two variables to
achieve your objective
• A composite measure considering both coupon and maturity
would be beneficial
33. Duration
• a weighted average of individual maturities of all the bond’s
separate cash flows, where the weights are proportionate to
the present values of each cash flow.
34.
35. Macaulay Duration
% Bond Price ≈ -Duration x
2
YTM
1
ΔYTM
A bond has a Macaulay Duration = 10 years, its yield increases from 7%
to 7.5%.
How much will its price change?
Duration = 10
Change in YTM = .075-.070 = .005
YTM/2= .035
%Price ≈ -10 x (.005/1.035) = -4.83%
43. Duration and Portfolios
The duration for a bond
portfolio is just equal to the
weighted average of each
individual bond’s duration.
Mkt Value
Duration Weight
Weighted
Duration
Bond A $1 Million 10.5 years 0.125 1.3125
Bond B $3 Million 8 years 0.375 3.0000
Bond C $4 Million 5 years 0.500 2.5000
$8 Million 1.000 6.8125 years
44. Duration principles to remember:
• Changes in the Price of a bond are inversely related to
changes in the rate of return (YTM).
• Long-term bonds have greater interest rate risk than short-
term bonds.
• As the bond coupon increases, its duration decreases and the
bond becomes less sensitive to interest rate changes.
• As interest rates increase, duration decreases and the bond
becomes less sensitive to future rate changes.
48. Price Risk vs. Reinvestment Rate Risk
For a Dedicated Portfolio
• Interest rate increases have two effects:
in interest rates decrease bond prices, but
in interest rates increase the future value of reinvested
coupons
• Interest rate decreases have two effects:
in interest rates increase bond prices, but
Decreases in interest rates decrease the future value of
reinvested coupons
49. Immunization
• Immunization = constructing a dedicated portfolio that
minimizes uncertainty surrounding the target date value
•Engineer a portfolio so that price risk and
reinvestment rate risk offset each other (just
about entirely).
•Duration matching = matching the duration of
the portfolio to its target date
50. Duration and Immunization
In addition to helping us estimate how
sensitive a bond is to interest rates,
duration can tell us an approximate holding
period where price risk and reinvestment
rate risk offset.
Holding a bond to duration “immunizes” us
from interest rate changes.
52. Dynamic Immunization
•Periodic rebalancing of a dedicated bond
portfolio for the purpose of maintaining a
duration that matches the target maturity date
•Advantage = reinvestment risk greatly
reduced
•Drawback = each rebalancing incurs
management and transaction costs
53. Duration and Price Volatility
• Longest duration security gives maximum price variation
• Active manager wants to adjust portfolio duration to take
advantage of anticipated yield changes
• Expect rate declines (parallel shift in YC), increase
average modified duration to experience maximum price
volatility
• Expect rate increases (parallel shift in YC), decrease
average modified duration to minimize price decline
54. Convexity
• Modified duration approximates price change for
small changes in yield
• Accuracy of approximation gets worse as size of
yield change increases.
• Modified duration assumes price-yield
relationship of bond is linear when in actuality it is
convex.
• Result – MD overestimates price declines and
underestimates price increases
• So convexity adjustment should be made to
estimate of % price change using MD
55.
56.
57. Convexity
All else equal, the higher the duration
(longer time to maturity or lower coupon
payment), the more error (convexity) there
will be
All else equal, the bigger the change in
interest rates, the more error there will be
58. High-Yield Bonds
• Spread in yield between safe and junk changes over time
Ave. Cumul. Default Rates Corp Bonds
Years Since Issue
Ratings 5 10
AAA 0.08% 0.08%
AA 1.20% 1.30%
A 0.53% 0.98%
BBB 2.39% 3.66%
BB 10.79% 15.21%
B 23.71% 35.91%
CCC 45.63% 57.39%
60. Core-Plus Bond Management
• A combination approach of passive and active bond
management styles
• A large, significant part of the portfolio is passively managed
• The rest of the portfolio is actively managed
• Often focused on high yield bonds, foreign bonds,
emerging market debt
• Diversification effects help to manage risks
61. Matched-Funding Techniques
• Dedicated portfolio
• Exact cash match
• Optimal match with reinvestment
• Horizon matching
• Combination of immunization strategy and dedicated
portfolio
62. Matched-Funding Techniques
•Immunization Strategies
•Difficulties in Maintaining Immunization Strategy
•Periodic Rebalancing required as duration
declines more slowly than term to maturity
•Modified duration changes with a change in
market interest rates
•Yield curves shift
63. Global Fixed-Income Investment
Strategy
•Factors to consider
1. The local economy in each country including the effects
of domestic and international demand
2. The impact of total demand and domestic monetary
policy on inflation and interest rates
3. The effect of the economy, inflation, and interest rates on
the exchange rates among countries