Transcript No Slide Title

Term Structure of Interest Rates
BKM Ch 15
Zvi Wiener
tel: 02-588-3049
Fall-02
[email protected]
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
Investments
Yield Curves
Yields
Upward
Sloping
Flat
Downward
Sloping
Maturity
Zvi Wiener
BKM Ch 15
slide 2
Expected Interest Rates
in Coming Years (Table 15.1)
Expected One-Year Rates in Coming Years
Year
Zvi Wiener
Interest Rate
0 (today)
8%
1
10%
2
11%
3
11%
BKM Ch 15
slide 3
Pricing of Bonds
using forward Rates
1
PVn 
(1  r1 )(1  r2 )...(1  rn )
PVn = Present Value of $1 in n periods
r1 = One-year rate for period 1
r2 = One-year rate for period 2
rn = One-year rate for period n
Zvi Wiener
BKM Ch 15
slide 4
Forward Rates
y1=8%
r1=8%
y2=8.995%
r2=10%
y3=9.660%
r3=11%
y4=9.993%
r4=11%
1
1

2
1.08995
1.08 1.1
Zvi Wiener
1
1

3
1.0966
1.08 1.11.11
BKM Ch 15
slide 5
Forward Rates from
Observed Long-Term Rates
(1  yn )
(1  f n ) 
(1  yn 1 ) n 1
n
fn = one-year forward rate for period n
yn = yield for a security with a maturity of n
n 1
(1  yn )  (1  yn1 ) (1  f n )
n
Zvi Wiener
BKM Ch 15
slide 6
Forward rates
r (T )T  r ( S ) S
y(S , T ) 
T S
Take a forward loan at S of 1 and repay it at T
0  1 e
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r ( S ) S
 xe
 r (T )T
BKM Ch 15
xe
r (T )T  r ( S ) S
slide 7
Instantaneous forward rates
r (T )T  r ( S ) S
y(S , T ) 
T S
r ( S )
f (S )  r (S )  S 
S


B(T )  exp   f ( s )ds
 0

T
Zvi Wiener
BKM Ch 15
slide 8
Zvi Wiener
BKM Ch 15
slide 9
Zvi Wiener
BKM Ch 15
slide 10
Example of Forward Rates
using Table 15.2 Numbers
4 yr = 9.993
3yr = 9.660
fn = ?
(1.0993)4 = (1.0966)3 (1+fn)
(1.46373) / (1.31870) = (1+fn)
fn = .10998 or 11%
Note: this is expected rate that was used
in the prior example.
Zvi Wiener
BKM Ch 15
slide 11
Downward Sloping
Spot Yield Curve
Zero-Coupon Rates Bond Maturity
12%
1
11.75%
2
11.25%
3
10.00%
4
9.25%
5
Zvi Wiener
BKM Ch 15
slide 12
Forward Rates for
Downward Sloping Yield Curve
1yr Forward Rates
1yr
[(1.1175)2 / 1.12] - 1
=
0.115006
2yrs [(1.1125)3 / (1.1175)2] - 1 =
0.102567
3yrs [(1.1)4 / (1.1125)3] - 1
=
0.063336
4yrs [(1.0925)5 / (1.1)4] - 1
=
0.063008
Zvi Wiener
BKM Ch 15
slide 13
Theories of Term Structure
Expectations
Liquidity Preference
Upward bias over expectations
Market Segmentation
Preferred Habitat
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BKM Ch 15
slide 14
Expectations Theory
Observed long-term rate is a function of
today’s short-term rate and expected future
short-term rates.
Long-term and short-term securities are
perfect substitutes.
Forward rates that are calculated from the
yield on long-term securities are market
consensus expected future short-term rates.
Zvi Wiener
BKM Ch 15
slide 15
Liquidity Premium Theory
Long-term bonds are more risky.
Investors will demand a premium for the risk
associated with long-term bonds.
The yield curve has an upward bias built into the
long-term rates because of the risk premium.
Forward rates contain a liquidity premium and are
not equal to expected future short-term rates.
Zvi Wiener
BKM Ch 15
slide 16
Liquidity Premiums
and Yield Curves
Yields
Observed Yield
Curve
Forward Rates
Liquidity
Premium
Maturity
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BKM Ch 15
slide 17
Liquidity Premiums
and Yield Curves
Yields
Observed Yield
Curve
Forward Rates
Liquidity
Premium
Maturity
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BKM Ch 15
slide 18
Market Segmentation
and Preferred Habitat
Short- and long-term bonds are traded in distinct markets.
Trading in the distinct segments determines the various
rates.
Observed rates are not directly influenced by expectations.
Preferred Habitat:
Modification of market segmentation
Investors will switch out of preferred maturity segments
if premiums are adequate.
Zvi Wiener
BKM Ch 15
slide 19
Using Spot Rates to Price
Coupon Bonds
A coupon bond can be viewed as a series of zero
coupon bonds.
To find the value each payment is discount at the
zero coupon rate.
Once the bond value is found, one can solve for the
yield.
It’s the reason that similar maturity and default risk
bonds sell at different yields to maturity.
Zvi Wiener
BKM Ch 15
slide 20
Chapter 15 Weblinks
http://www.smartmoney.com/bonds/
This site contains a good source for current rates, the current and past yield curves, and
explanations of how the shape of the yield curve can affect economic performance. It also has
a summary of current economic factors that are influencing rates.
http://www.bondresources.com/
The site listed above has price and yield curve information and the ability to chart Treasury
securities over time.
http://www.bloomberg.com/markets
The site listed above has price and yield curve information and the ability to chart Treasury
securities over time.
http://www.investinginbonds.com
The site listed above has price and yield curve information and the ability to chart Treasury
securities over time.
http://www.stls.frb.org/
Historical information on interest rates and other economic factors are available in the Federal
Reserve Economic Data Base (FRED) at the address shown above. Data in FRED can be
downloaded in a spreadsheet format.
Zvi Wiener
BKM Ch 15
slide 21
Summary
Term structure of interest rates
Zero-coupon
Government or LIBOR-Swap
Spread for risky bonds
OAS for bonds with embedded options
Forward rates
Expectation, Liquidity, Segmentation
Impact of taxation
Zvi Wiener
BKM Ch 15
slide 22
Home
At www.mhhe.com/bkm you can download
SPOTYA.XLS file that demonstrates the
bootstrapping technique used for derivation of
zero coupon curve from coupon bonds.
Zvi Wiener
BKM Ch 15
slide 23
Home Assignment
Required:
• problems 3, 5, 9, 13, 17 (3rd ed).
• problems 4, 6, 12, 17, 22 (5th ed).
• closely follow financial news!
Recommended:
• read ML publication on world bond markets
• visit recommended web links
Zvi Wiener
BKM Ch 15
slide 24
Treasuries
Investment grade
Swap
Par
Speculative grade
144A
Strips, zeros
Yield
Volatility
Callable
LIBOR
Puttable
Spread
CP, CD
TIPS
Floater
Securitization
GNMA, MBA
Convertible
Default risk
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BKM Ch 15
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End
Zvi Wiener
BKM Ch 15
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Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Default Risk and Ratings
Rating companies
Moody’s Investor Service
Standard & Poor’s
Duff and Phelps
Fitch
Rating Categories
Investment grade
Speculative grade
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BKM Ch 15
slide 27
Straight bond
Floater
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BKM Ch 15
slide 28
How to treat Floaters
Floater is similar to a constantly renewed loan
with fixed spread (!).
Thus the yield of a floater is equal to the yield
on the basis plus the spread.
Note that some of the Israeli government bonds
have funny linkage to other bonds.
Zvi Wiener
BKM Ch 15
slide 29
Reverse (Inverse) Floater
USD 5 year interest rates are 5%, however short
term interest rates are Libor =2%.
Libor = London Interbank offered rate
on Bloomberg see FWCV + currency
One can construct so-called reverse floater:
Zvi Wiener
BKM Ch 15
slide 30
Reverse Floater
Years
bond
loan
bond
Reverse Fl.
0
-100
+100
-100
-100
1
5
-L0
5
8
2
5
-L1
5
10-L1
3
5
-L2
5
10-L2
4
5
-L3
5
10-L3
5
105
-100- L4
105
110- L4
Zvi Wiener
BKM Ch 15
slide 31
Features of Corporate Bonds
(indentures)
Corporate trustee – represents bondholders
Term bonds – maturity
Under 10 years – notes
Some bonds have specific collateral
Others are debentures
Guaranteed bonds (third party’s guarantees)
Zvi Wiener
BKM Ch 15
slide 32
SEC rule 144A
Allows to trade private placements among
qualified institutions.
Zvi Wiener
BKM Ch 15
slide 33
Medium Term Notes (MTN)
Notes are registered with the SEC under Rule
415 (the shelf registration) and are offered
continuously to investors by an agent of the
issuer.
Maturities vary from 9 months to 30 years.
Can be either fixed or floating.
Very flexible way to raise debt!
Zvi Wiener
BKM Ch 15
slide 34
Primary Market (MTN)
Issuer posts spreads over Treasuries for a
variety of maturities.
Then an agent tries to find an investor.
Minimal size is between $1M and $25M.
The schedule can be changed at any time!
Often structured MTNs are used (caps, floors,
etc.) = structured notes.
Zvi Wiener
BKM Ch 15
slide 35
Structured Notes
Many institutional investors can use swaps
and structured notes to participate in markets
that were prohibited.
Another use of structured notes is in risk
management.
Financial Engineering is used to create
securities satisfying the needs of investors.
Zvi Wiener
BKM Ch 15
slide 36
Commercial Papers
Short term debt issued with less
documentation typically by large and stable
corporations for up to 270 days.
Much cheaper borrowing than banks.
Bridge financing.
Rollover Risk
An alternative to CD.
Zvi Wiener
BKM Ch 15
slide 37
Commercial Papers
Short term unsecured promissory note
An alternative to short term bank borrowing
A typical round-lot transaction is $100,000
In the USA maturity is up to 270 days
Requires less paperwork
Those with maturity up to 90 days can be
used as collateral for FED discount window.
Zvi Wiener
BKM Ch 15
slide 38
Commercial Papers
Typically rolled over
Rollover risk is backed by an unused bank credit
line
In order to issue CP one need either a high rating
or good collateral
Sometimes credit enhancement is used (LOC)
CP issued in the USA by foreigners are called
Yankee CP
Zvi Wiener
BKM Ch 15
slide 39
Commercial Papers
Between 71 an 89 there was one default on CP.
3 defaults occurred in 89 and 4 in 90
Direct paper is sold without an agent
Secondary market is thin
There is a special rating for CP, P-1,3, A-1,3
discount instruments, used by money market
Zvi Wiener
BKM Ch 15
slide 40
Bankruptcy and Creditor Rights
liquidation (Chapter 7) - all assets will be
distributed
reorganization (Chapter 11) - a new corporate
entity will result
a company that files for protection becomes a
debtor in possession and continues to operate
under the supervision of the court
Zvi Wiener
BKM Ch 15
slide 41
Bankruptcy and Credit Rights
Absolute priority rule - senior creditors are
paid in full before junior creditors are paid
anything.
Works in liquidation but often does not work
in reorganization.
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BKM Ch 15
slide 42
Merton’s model
$
firm
equity
debt
D
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V
BKM Ch 15
slide 43
Government Sponsored Enterprises
Federal Home Loan Bank System
Federal National Mortgage Association
Federal Home Loan Mortgage Corporation
Federal Farm Credit Bank System
Zvi Wiener
BKM Ch 15
slide 44