Fixed Income Instruments 2
Zvi Wiener
02-588-3049
mswiener@mscc.huji.ac.il
Fall-01
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
FIBI
Plan FI-2
• Example of Duration and Convexity
• Treasuries
• Agencies
• Corporate
• Municipals
The Treasury Securities Markets: Overview and Recent
Developments, by D. Dupont and B. Sack, Federal Reserve
Bulletin, Dec-99.
Zvi Wiener
FIFIBI - 2
slide 2
Example
Portfolio consists of $1M of a bond with
duration of 1 year and $1M worth of a bond
with duration of 20 years.
What is the duration of the portfolio?
Zvi Wiener
FIFIBI - 2
slide 3
Rough calculation
Duration of the first bond is 1 year, of the
second bond is 20 years.
This means that when IR go 1% up we will lose
1% of the first bond and 20% of the second.
All together we will lose 10.5% of the portfolio.
The duration is (roughly) 10.5 years.
Zvi Wiener
FIFIBI - 2
slide 4
Value
1.05
1.07 20
1.05
1.07 20



2
20
20
1  r1 1  r20 
1  0.05 1  0.07 
2.8
value
2.6
2.4
2.2
Parallel shift
-0.03
-0.02
-0.01
0.01
0.02
0.03
1.8
1.6
Zvi Wiener
FIFIBI - 2
slide 5
Duration
1 1
20 


  9.8212
2  1.05 1.07 
1 dA
DA  
A dr
D A B
ADA
BD B


A B A B

1 d  1.05
1.07 20




20 

2 dx  1  r1  x 1  r20  x  
Zvi Wiener
FIFIBI - 2
 9.8212
x 0
slide 6
Convexity
2
d A
CA  2
dr
20


d
1.05
1.07




368
20
2 
dx  1  r1  x 1  r20  x  
x 0
2
For a simple bond portfolio it does not
help much!
It is much more important to consider
2 risk factors!
Zvi Wiener
FIFIBI - 2
slide 7
Portfolio 2
Time
0
1
Money
+1
Term Structure 5%
value
5
20
-2
6%
+2
7%
1
2
2


 0.025
5
20
1.05 1.06 1.07
Assets duration = 7.19
Liabilities duration = 4.7169
Zvi Wiener
FIFIBI - 2
slide 8
8% Coupon Bond
Yield to Maturity
8%
9%
Price Change
T=1 yr. T=10 yr. T=20 yr.
1,000.00 1,000.00 1,000.00
990.64 934.96
907.99
0.94% 6.50%
9.20%
Zero Coupon Bond
Yield to Maturity
8%
9%
Price Change
Zvi Wiener
T=1 yr. T=10 yr. T=20 yr.
924.56 456.39
208.29
915.73 414.64
171.93
0.96% 9.15% 17.46%
FIFIBI - 2
slide 9
Macaulay Duration
(1)
(2)
(3)
(4)
(5)
Time until
Payment
column (1)
payment Payment Discounted Weight multiplied
(in Years)
at 5%
by (4)
Bond A
8%
0.5
1.0
1.5
2.0
$40
$40
$40
$1,040
$38.095
$36.281
$34.553
$855.611
$964.540
0.0395
0.0376
0.0358
0.8871
1.000
0.0198
0.0376
0.0537
1.7742
1.8853
0.5-1.5
2.0
0
$1,000
$0
$822.70
$822.70
0
1
1
0
2
2
Sum:
Bond B
zero
Sum
Zvi Wiener
FIFIBI - 2
slide 10
Understanding of Duration/Convexity
What happens with duration when a coupon is
paid?
How does convexity of a callable bond
depend on interest rate?
How does convexity of a puttable bond
depend on interest rate?
Zvi Wiener
FIFIBI - 2
slide 11
Callable bond
The buyer of a callable bond has written an
option to the issuer to call the bond back.
Rationally this should be done when …
Interest rate fall and the debt issuer can
refinance at a lower rate.
Zvi Wiener
FIFIBI - 2
slide 12
Puttable bond
The buyer of a such a bond can request the
loan to be returned.
The rational strategy is to exercise this option
when interest rates are high enough to provide
an interesting alternative.
Zvi Wiener
FIFIBI - 2
slide 13
Embedded Call Option
regular bond
strike
callable bond
r
Zvi Wiener
FIFIBI - 2
slide 14
Embedded Put Option
putable bond
regular bond
r
Zvi Wiener
FIFIBI - 2
slide 15
Convertible Bond
Payoff Convertible Bond
Stock
Straight Bond
Stock
Zvi Wiener
FIFIBI - 2
slide 16
Timing of exercise
• European
• American
• Bermudian
• Lock up time
Zvi Wiener
FIFIBI - 2
slide 17
Passive Bond Management
Passive management takes bond prices as
fairly set and seeks to control only the risk of
the fixed-income portfolio.
• Indexing strategy
– attempts to replicate a bond index
• Immunization
– used to tailor the risk to specific needs
(insurance companies, pension funds)
Zvi Wiener
FIFIBI - 2
slide 18
Bond-Index Funds
Similar to stock indexing.
Major indices: Lehman Brothers, Merill
Lynch, Salomon Brothers.
Include: government, corporate, mortgagebacked, Yankee bonds (dollar denominated,
SEC registered bonds of foreign issuers, sold
in the US).
Zvi Wiener
FIFIBI - 2
slide 19
Bond-Index Funds
Properties:
many issues
not all are liquid
replacement of maturing issues
Tracking error is a good measurement of
performance. According to Salomon Bros.
With $100M one can track the index within
4bp. tracking error per month.
Zvi Wiener
FIFIBI - 2
slide 20
Cellular approach
ttm\Sector Treasury Agency MBS
< 1yr
12.1%
1-3 yrs
5.4%
4.1% 3.2%
3-5 yrs
9.2% 6.1%
Zvi Wiener
FIFIBI - 2
slide 21
Immunization
Immunization techniques refer to strategies
used by investors to shield their overall
financial status from exposure to interest rate
fluctuations.
Zvi Wiener
FIFIBI - 2
slide 22
Net Worth Immunization
Banks and thrifts have a natural mismatch
between assets and liabilities. Liabilities are
primarily short-term deposits (low duration),
assets are typically loans or mortgages
(higher duration).
When will banks lose money, when IR
increase or decline?
Zvi Wiener
FIFIBI - 2
slide 23
Gap Management
ARM are used to reduce duration of bank
portfolios.
Other derivative securities can be used.
Capital requirement on duration (exposure).
Basic idea:
to match duration of assets and liabilities.
Zvi Wiener
FIFIBI - 2
slide 24
Target Date Immunization
Important for pension funds and insurances.
Price risk and reinvestment risk.
What is the correlation between them?
Zvi Wiener
FIFIBI - 2
slide 25
Target Date Immunization
Accumulated
value
Original plan
0
Zvi Wiener
t*
t
FIFIBI - 2
slide 26
Target Date Immunization
Accumulated
value
IR increased at t*
0
Zvi Wiener
t*
t
FIFIBI - 2
slide 27
Target Date Immunization
Accumulated
value
0
Zvi Wiener
t*
D
FIFIBI - 2
t
slide 28
Target Date Immunization
Accumulated
value
0
Zvi Wiener
Continuous rebalancing
can keep the terminal value
unchanged
t*
D
FIFIBI - 2
t
slide 29
Good Versus Bad Immunization
value
$10,000
Single payment obligation
0
Zvi Wiener
8%
FIFIBI - 2
r
slide 30
Good Versus Bad Immunization
value
Good immunizing strategy
$10,000
Single payment obligation
0
Zvi Wiener
8%
FIFIBI - 2
r
slide 31
Good Versus Bad Immunization
value
Good immunizing strategy
$10,000
Single payment obligation
0
Zvi Wiener
8%
FIFIBI - 2
r
slide 32
Good Versus Bad Immunization
value
Bad immunizing strategy
Good immunizing strategy
$10,000
Single payment obligation
0
Zvi Wiener
8%
FIFIBI - 2
r
slide 33
Standard Immunization
Is very useful but is based on the assumption of
the flat term structure. Often a higher order
immunization is used (convexity, etc.).
Another reason for goal oriented mutual funds
(retirement, education, housing, medical
expenses).
Zvi Wiener
FIFIBI - 2
slide 34
Cash Flow Matching and
Dedication
Is a very reasonable strategy, but not always
realizable.
Uncertainty of payments.
Lack of perfect match
Saving on transaction fees.
Zvi Wiener
FIFIBI - 2
slide 35
Active Bond Management
Mainly speculative approach based on ability
to predict IR or credit enhancement or market
imperfections (identifying mispriced loans).
Zvi Wiener
FIFIBI - 2
slide 36
Substitution Swap
Exchange of one bond for a very similar
bond.
Motivation: belief that one of them is
mispriced.
Example: 20-yr, 9% coupon Ford Motor bond
callable after 5 years at $1,050 versus a 9%
coupon Chrysler bond with 20 yr to maturity.
Zvi Wiener
FIFIBI - 2
slide 37
Contingent Immunization
value
$12,000
$10,000
0
Zvi Wiener
5 yr t
FIFIBI - 2
slide 38
Contingent Immunization
value
$12,000
$10,000
Stop boundary
0
Zvi Wiener
5 yr t
FIFIBI - 2
slide 39
Contingent Immunization
value
$12,000
$10,000
Stop boundary
0
Zvi Wiener
5 yr t
FIFIBI - 2
slide 40
Contingent Immunization
value
$12,000
$10,000
Stop boundary
0
Zvi Wiener
5 yr t
FIFIBI - 2
slide 41
Interest Rate Swap
One of the major fixed-income tools.
Example: 6m LIBOR versus 7% fixed.
Exchange of net cash flows.
Risk involved: IR risk, default risk (small).
Why the default risk on IR swaps is small?
Zvi Wiener
FIFIBI - 2
slide 42
Interest Rate Swap
7.05%
6.95%
Company B
Swap dealer
Company A
LIBOR
LIBOR
No need in an actual loan.
Can be used as a speculative tool or for hedging.
Zvi Wiener
FIFIBI - 2
slide 43
Currency Swap
A similar exchange of two loans in different
currencies.
Subject to a higher default risk, because of the
principal.
Is useful for international companies to hedge
currency risk.
Zvi Wiener
FIFIBI - 2
slide 44
The Treasuries Securities Market
US Treasury debt $3.6Trillion
daily transactions: $190B
yields are viewed as benchmarks
1776, first US issue (Revolutionary War)
Increase during the Civil war, WW1,
tripled during the great depression
exploded during WW2.
Zvi Wiener
FIFIBI - 2
slide 45
Types of Treasuries securities
• $3.2T - marketable
– Bills - up to one year
– Notes 1-10 years when issued
– Bonds longer then 10 years
• 57% are notes, 20% bills and 20% bonds.
• Some are callable (by the Treasury)
• 97% are nominal
Zvi Wiener
FIFIBI - 2
slide 46
Nonmarketable securities
• Government account series (83%)
• State and Local Government Series (7%)
• saving bonds (7%)
held by off-budget government programs, like
social security, local governments, etc.
yield is at least 5bp below marketable
Treasuries.
Zvi Wiener
FIFIBI - 2
slide 47
Issuance of Treasuries
• regularly scheduled auctions = primary
market.
• 2,000 brokers and dealers are registered
• Prime dealers are selected by NY Fed counterparites for open market operations.
Zvi Wiener
FIFIBI - 2
slide 48
Auctions
• The process begins several days before.
• “when issued market” after the
announcement but before it takes place.
• On the day of the auctions bids may be
submitted to FED.
• Competitive bids - quantity and yield
• Noncompetitive bids - small orders
Zvi Wiener
FIFIBI - 2
slide 49
Auctions
• Uniform price method for 2, 5 year notes, TIPS
• Other issues have multiple price auction
• Bidders get securities at their bid price.
• Non-competitive get at the average price of
competitive bids.
Zvi Wiener
FIFIBI - 2
slide 50
Auctions
• $6.5B of 13-week bills and $7.5B of 26
week bills - weekly
• $10B of 52 week bills - every four weeks
• $15B of 2-year notes, every 4 weeks
• $12B of ten -year notes and $10B of 30
years bonds - semiannually.
• Sometimes an old issue may be reopen.
Zvi Wiener
FIFIBI - 2
slide 51
Cancellations
1986
20 year bond
1990
4 year note
1993
7 year note
1998
3 year note
Zvi Wiener
FIFIBI - 2
slide 52
Market
Primarily OTC (over the counter) market.
Officially registered at NYSE, but volume is
negligible.
Market makers in Treasuries - bid-offer spread.
Six primary dealers - 50% of trades (22 hr/day).
94% - NY, 4% - London, 2% Tokyo.
Zvi Wiener
FIFIBI - 2
slide 53
Quoting conventions
Coupon securities are quoted in terms of price
expressed in dollars.
Clean price excludes accrued interest.
Accrued interest =
next coupon*fraction of time that passed.
Bills are quoted in terms of discount rate as %
of face value. Assuming 360 days in a year, i.e.
multiplied by 360 and divided by the actual
number of days remaining to maturity.
Zvi Wiener
FIFIBI - 2
slide 54
Price quotes for T-Bills
Bank discount basis
D 360
Yd 
F t
Yd - annualized yield on a bank discount basis
D - dollar discount = face - price
F - face value
t - number of actual days to maturity
Zvi Wiener
FIFIBI - 2
slide 55
Price quotes for T-Bills
Yd Ft
D
360
 Yd t 
price  F  D  F 1 

 360 
Zvi Wiener
FIFIBI - 2
slide 56
Price quotes for T-Bills
100 days to maturity
price = $97,569 will be quoted at 8.75%
100  97.569 360
Yd 
 8.75%
100
100
 0.0875 100 
$97,569  $100,0001 

360


Zvi Wiener
FIFIBI - 2
slide 57
Price quotes for T-Bills
The quoted yield is based on the face value
and not on the actual amount invested.
The yield is annualized on 360 days basis.
Bond equivalent yield = CD equivalent yield
360Yd
CD equiv. yiel 
360  t  Yd
360  8.75%
CD equiv. yiel 
 8.97%
360  100  8.75%
Zvi Wiener
FIFIBI - 2
slide 58
Price quotes for Notes and Bonds
Annual coupon Days in AI period
AI 
2
Days in coupon period
Actual/actual day count convention.
Example: 50 days have passed, 183 days in the
period and yearly coupon per $100 is $8, then
AI = $8/2 *50/183 = $1.0929
Zvi Wiener
FIFIBI - 2
slide 59
Recordkeeping
National Book-Entry System (NBES) maintains
records for depository institutions.
Most trades are delivery versus payment.
Federal Reserve grants finality and provides an
intraday credit to financially healthy depository
institutions.
Zvi Wiener
FIFIBI - 2
slide 60
Ownership
FED
12%
Depository institutions
7%
Institutional investors
27%
State and local governm.
7%
Foreign and international
33%
Others
14%
Zvi Wiener
FIFIBI - 2
slide 61
STRIPS
Separate Trading of Registered Interest and
Principal of Securities.
Stripping and reconstitution.
About 33% of all outstanding T-bonds are
stripped.
Creates zero-coupon securities.
US company must pay tax on accrued interest is
taxed every year, so strips create a negative CF.
Zvi Wiener
FIFIBI - 2
slide 62
Determinants of the Yield Curve
Federal Reserve sets a target level for the fed
funds rate - the rate at which depository
institutions make uncollaterized overnight
loans to one another.
Long-term rates reflect expectations of future
rates and can be influenced by the outlook for
monetary policy.
Zvi Wiener
FIFIBI - 2
slide 63
Liquidity
• Bid-offer spread 1-2 cents per $100 face
• Corporate bonds for example 13 cents
• High yield bonds 19 cents
• on-the-run - recently issued in a particular
maturity class. With time became off-the-run.
• Flight to Quality (fall 98) bid-ask 16-25
cents.
Zvi Wiener
FIFIBI - 2
slide 64
Repurchase Agreements
Borrowing and lending using Treasuries and
other debt as collateral.
Repo (loan). You sell a security to
counterparty and agree to repurchase the same
security at a specified price at a later date
(often next day).
Reverse Repo - you agree to purchase a
security and sell it back at a specified price
later.
Zvi Wiener
FIFIBI - 2
slide 65
Repurchase Agreements
Most repos are general-collateral repo rate.
Some securities are special (for example onthe-run).
Specialness peaks around next auction, then
declines sharply.
NY FED operates a securities lending for
primary dealers using FED’s portfolio while
posting other Treasury security as collateral.
Zvi Wiener
FIFIBI - 2
slide 66
Treasury Based Derivatives
Futures and options for 2, 5, 10 year notes and
bonds are listed by CBOT and CFFE. CNE
offers futures and options on bills and other
short term interest rate products.
End of October 99 open interest for CBOT
long-bond futures was 635,000 (each one
based on $100,000 face value).
Daily volume 300,000 contracts.
Zvi Wiener
FIFIBI - 2
slide 67
Treasury Based Derivatives
CBOT also offers options on Treasury futures
- contract that allows the holder to buy/sell a
future contract at a specified price.
Cheapest-to-deliver option and conversion
factor (compare to commodities).
Zvi Wiener
FIFIBI - 2
slide 68
TIIS = TIPS
Treasury Inflation Indexed (Protected) Securities.
Since 97, $92B were issued, based on the nonseasonally adjusted CPI lagged 2.5 months.
The quoted price do not reflect the accumulated
inflation compensation.
Real price = quoted*index ratio + accrued interest
I-bonds saving bonds that are also CPI indexed.
Zvi Wiener
FIFIBI - 2
slide 69
TIIS = TIPS
5, 10, 30 years notes and bonds.
Less liquid: 2-6 cents per $100 face.
CBOT offers options and futures on TIPS
Canada, France, England, Israel have similar
types of debt.
Zvi Wiener
FIFIBI - 2
slide 70
T-bills markets
Issuance of T-bills was cut sharply.
Between Dec-96 and Sep-99 the total
outstanding amount of coupon securities
declined 7% while bills declined 16%.
Treasury Debt buybacks. Reverse auctions
trying to remove small issues.
Zvi Wiener
FIFIBI - 2
slide 71