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1. BOND
PORTFOLIO MANAGEMENT

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

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

18. Interest Rate Risk and Maturity

19. Bond Portfolio Strategies
1. Passive Portfolio Strategies
2. Active Management Strategies
3. Matched Funding Techniques

20. Benchmark
• Liability based Benchmark
• Index as a Benchmark

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.

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

24. Active Management Strategies
• Attempts to beat the Market
• Forecasting of Future Interest Rates.

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.

29. Active Management Strategies
•Yield-Spread Analysis
• Monitor spread within and across sectors, bond ratings, or
industries
• Trade in anticipation of changing spreads

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.

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%

36. Modified Duration
 
2
YTM
1
Duration
Macaulay
Duration
Modified


%Bond Price ≈ -Modified Duration x YTM
A bond has a Macaulay duration of 9.2
years and a YTM of 7%. What is it’s
modified duration?
Modified duration = 9.2/1.035 = 8.89 years

38. n = Years to Maturity
C = Coupon Payment
k = Market Rate of Interest
M = Maturity (Par) Value
B0 = Bond Price

39. Duration
•Find the duration of a 10-yearBond having 5%
coupon, payable annually, when the market rate
of interest is 7%.

41. Year Cash Flow PV of CF PV/B0 Year*(PV/B0)
1 $50 $46.73 0.0544 0.054
2 $50 $43.67 0.0508 0.102
3 $50 $40.81 0.0475 0.142
4 $50 $38.14 0.0444 0.177
5 $50 $35.65 0.0415 0.207
6 $50 $33.32 0.0388 0.233
7 $50 $31.14 0.0362 0.254
8 $50 $29.10 0.0339 0.271
9 $50 $27.20 0.0316 0.285
10 $50 $25.42 0.0296 0.296
10 $1000 $508.35 0.5914 5.914
$859.53 7.935

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.

45. Properties of Duration

46. US Treasury- 30 year Yield Curve

47. Dedicated Portfolios
•Bond portfolio created to prepare for a future
cash payment, e.g. pension funds
•Target Date = date the payment is due

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.

51. Immunization by Duration Matching

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

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%

59. Sample Yield Matrix
6-Dec-16 15-Dec-2016 31-Dec-2016 15-Jan-2017 31-Jan-2017 15-Feb-2017
Gilt 5.80% 5.80% 5.95% 5.95% 5.95%
AAA 0.93% 0.92% 0.73% 0.67% 0.68%
AA+ 1.05% 1.00% 0.80% 0.72% 0.72%
AA 1.20% 1.15% 0.98% 0.92% 0.93%
AA- 1.33% 1.28% 1.15% 1.05% 1.03%
A+ 1.63% 1.58% 1.52% 1.34% 1.56%
A 1.93% 1.88% 1.90% 1.62% 2.00%
A- 2.07% 2.02% 2.07% 1.76% 2.21%
BBB+ 2.58% 2.53% 2.71% 2.51% 2.88%

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