Transcript No Slide Title

Bond Prices and Yields
BKM Ch 14
Zvi Wiener
tel: 02-588-3049
Spring-03
[email protected]
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
Investments
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Bond Characteristics
Face or par value
Coupon rate
Zero coupon bond
Compounding and payments
Accrued Interest
Indenture
Zvi Wiener
BKM Ch 14
slide 2
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Different Issuers of Bonds
U.S. Treasury
Bills, Notes and Bonds
Corporations
Municipalities
International Governments and Corporations
Innovative Bonds
Indexed Bonds
Floaters and Reverse Floaters
Zvi Wiener
BKM Ch 14
slide 3
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Provisions of Bonds
Secured or unsecured
Call provision
Convertible provision
Put provision (putable bonds)
Floating rate bonds
Sinking funds
Preferred Stock
Zvi Wiener
BKM Ch 14
slide 4
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Bond Pricing
ParValue
T
C
t
PB  

T
t
(1 r )
t 1 (1 r )
T
PB =
Ct =
T =
r =
Price of the bond
interest or coupon payments
number of periods to maturity
yield to maturity
Fixed coupon only!
Zvi Wiener
BKM Ch 14
slide 5
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Solving for Price: 10-yr, 8% Coupon
Bond, Face = $1,000
20
40
1000
P

t
20
(1.03)
t 1  1.03
P  $1,148.77
Ct
P
T
r
Zvi Wiener
= 40 (SA)
= 1000
= 20 periods
= 3% (SA)
BKM Ch 14
slide 6
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Bond Prices and Yields
Prices and Yields (required rates of return)
have an inverse relationship
When yields get very high the value of the
bond will be very low.
When yields approach zero, the value of the
bond approaches the sum of the cash flows.
Zvi Wiener
BKM Ch 14
slide 7
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Prices and Coupon Rates
Price
Yield
Zvi Wiener
BKM Ch 14
slide 8
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Yield to Maturity
Interest rate that makes the present value of
the bond’s payments equal to its price.
Solve the bond formula for r
ParValue
T
C
t
PB  

T
t
(1 r )
t 1 (1 r )
T
Zvi Wiener
BKM Ch 14
slide 9
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Yield to Maturity Example
35 1000
950  

T
t
(1 r )
t 1 (1 r )
20
10 yr Maturity
Coupon Rate = 7%
Price = $950
Solve for r = semiannual rate
Zvi Wiener
BKM Ch 14
r = 3.8635%
slide 10
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Yield Measures
Bond Equivalent Yield
7.72% = 3.86% x 2
Effective Annual Yield
(1.0386)2 - 1 = 7.88%
Current Yield
Annual Interest / Market Price
$70 / $950 = 7.37 %
Zvi Wiener
BKM Ch 14
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
BKM Ch 14
slide 12
Embedded Call Option
regular bond
strike
callable bond
r
Zvi Wiener
BKM Ch 14
slide 13
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
BKM Ch 14
slide 14
Embedded Put Option
puttable bond
regular bond
r
Zvi Wiener
BKM Ch 14
slide 15
Convertible Bond
Payoff Convertible Bond
Stock
Straight Bond
Stock
Zvi Wiener
BKM Ch 14
slide 16
Timing of exercise
European
American
Bermudian
Lock up time
Zvi Wiener
BKM Ch 14
slide 17
Example
Cost: 101
Promised cashflow:
After 1 year
6
After 2 years
7
After 3 years
8
After 4 years
9
After 5 years
110
Zvi Wiener
BKM Ch 14
slide 18
Yield calculation
6
7
8
9
110
101




2
3
4
1  y (1  y ) (1  y) (1  y) (1  y )5
y = 7.6%
Zvi Wiener
BKM Ch 14
slide 19
Example 2
Cost: 101
Promised cashflow:
After 1 year
6
After 2 years
After 3 years
After 4 years
After 5 years
Zvi Wiener
7, callable at 100
8
9
110
BKM Ch 14
slide 20
Yield to Call calculation
6
107
101

1  y (1  y ) 2
y = 5.94%
Zvi Wiener
BKM Ch 14
slide 21
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Realized Yield versus YTM
Reinvestment Assumptions
Holding Period Return
Changes in rates affects returns
Reinvestment of coupon payments
Change in price of the bond
Zvi Wiener
BKM Ch 14
slide 22
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Holding-Period Return: Single Period
HPR = [ I + ( P0 - P1 )]
/ P0
where
I = interest payment
P1 = price in one period
P0 = purchase price
Zvi Wiener
BKM Ch 14
slide 23
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Holding-Period Example
CR = 8%
YTM = 8%
N=10 years
Semiannual Compounding P0 = $1000
In six months the rate falls to 7%
P1 = $1068.55
HPR = [40 + ( 1068.55 - 1000)] / 1000
HPR = 10.85% (semiannual)
Zvi Wiener
BKM Ch 14
slide 24
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Holding-Period Return: Multiperiod
Requires actual calculation of reinvestment
income
Solve for the Internal Rate of Return using the
following:
Future Value: sales price + future value of
coupons
Investment: purchase price
Zvi Wiener
BKM Ch 14
slide 25
Yield to Call
Yield to Put
Yield to Worst
Spread for a floater
Total return for a bond
Zvi Wiener
BKM Ch 14
slide 26
IRR of a portfolio
Aggregation of all cashflows and using the
same formula.
Zvi Wiener
BKM Ch 14
slide 27
Problems with yield
Many equivalent ways to measure?
Assumes reinvestment.
Does not reflect risk.
What if investment is very leveraged?
Options, Forwards, Swaps
Zvi Wiener
BKM Ch 14
slide 28
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
Zvi Wiener
BKM Ch 14
slide 29
Investment Grade
Moody’s
Aaa
Aa1
Aa2
Aa3
A1
A2
A3
Baa1
Baa2
Baa3
Zvi Wiener
S&P=F=D&P
AAA
AA+
AA
AAA+
A
ABBB+
BBB
BBBBKM Ch 14
slide 30
Speculative Grade
Moody’s
Ba1
Ba2
Ba3
B1
B2
B3
Caa
Ca
C
Zvi Wiener
S&P=F=D&P
BB+
BB
BBB+
B
BCCC+
CCC
CCCCC
C
BKM Ch 14
slide 31
High Yield Bonds
LBO, downgrading, refinancing
fallen angels
deferred interest bonds
Step-up bonds pay initially low interest which
increases with time
Spreads as a measure of risk and premium.
Zvi Wiener
BKM Ch 14
slide 32
Transition Matrix
One year transition matrix (very old)
Start\end
Aaa Aa
Aaa
91.9 7.38 0.72 0.00 0.00 0.00 0.00
Aa
1.13 91.26 7.09 0.31 0.21 0.00 0.00
A
0.10 2.56 91.20 5.33 0.61 0.20 0.00
Baa
0.00 0.21 5.36 87.94 5.46 0.82 0.21
Zvi Wiener
A
Baa
BKM Ch 14
Ba
B
C&D
slide 33
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Factors Used by Rating
Companies
Coverage ratios
Leverage ratios
Liquidity ratios
Profitability ratios
Cash flow to debt
Zvi Wiener
BKM Ch 14
slide 34
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Protection Against Default
Sinking funds
Subordination of future debt
Dividend restrictions
Collateral
Zvi Wiener
BKM Ch 14
slide 35
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Default Risk and Yield
Risk structure of interest rates
Default premiums
Yields compared to ratings
Yield spreads over business cycles
Zvi Wiener
BKM Ch 14
slide 36
Important Rates
Treasuries
Libor
Swap
Spread
Euribor
Telbor
Zvi Wiener
BKM Ch 14
slide 37
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 14
slide 38
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 14
slide 39
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 14
slide 40
Chapter 14 Weblinks
http://www.bloomberg.com/markets General price information
http://cnnfn.cnn.com/markets/bondcenter/rates.html
General price information
http://www.bondresources.com Detailed information on bonds can
be found at this site. It is comprehensive and has many related links.
http://www.investinginbonds.com/ Detailed information on bonds
can be found at this site. It is comprehensive and has many related
links.
http://www.bondsonline.com/docs/bondprofessor-glossary.html
Detailed information on bonds can be found at this site. It is
comprehensive and has many related links.
Zvi Wiener
BKM Ch 14
slide 41
Chapter 14 Weblinks
http://www.standardandpoors.com/ratings/corporates/index.htm
Information on bond ratings can be found here.
http://www.moodys.com
Information on bond ratings can be found here.
http://www.fitchinv.com
Information on bond ratings can be found here.
http://www.publicdebt.treas.gov USA public debt.
http://www.maalot.co.il/ Raing of Israeli bonds.
http://www.bba.org.uk/ Libor rates worldwide.
Zvi Wiener
BKM Ch 14
slide 42
Home Assignment
Required:
• problems 1, 2, 5, 7, 16 (3rd ed).
• problems 1, 2, 5, 8, 21 (5th ed).
• visit the web site and know Israeli bonds
• closely follow financial news!
• know yields on major classes of bonds:
US government
NIS linked
Zvi Wiener
NIS unlinked
BKM Ch 14
slide 43
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 14
slide 44
SEC rule 144A
Allows to trade private placements among
qualified institutions.
Zvi Wiener
BKM Ch 14
slide 45
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 14
slide 46
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 14
slide 47
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 14
slide 48
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 14
slide 49
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 14
slide 50
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 14
slide 51
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 14
slide 52
Bankruptcy and Creditor rights
Liquidation (Chapter 7)
Reorganization (Chapter 11)
Zvi Wiener
BKM Ch 14
slide 53
Bankruptcy and Credit Rights
liquidation - all assets will be distributed
reorganization - 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 14
slide 54
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.
Zvi Wiener
BKM Ch 14
slide 55
Merton’s model
$
firm
equity
debt
D
Zvi Wiener
V
BKM Ch 14
slide 56
Price quotation of bonds
In units of 1/32, for example 92-14 means that
the price is
92+14/32% of par (plus accrued interest)
+ means 1/64
Zvi Wiener
BKM Ch 14
slide 57
Accrued Interest
Additional payment for part of the coupon
$
time
Annualcoupon
daysin AI period
AI 

2
Daysin couponperiod
Zvi Wiener
BKM Ch 14
slide 58
Price Quotes and Accrued Interest
Assume that the par value of a bond is $1,000.
Price quote is in % of par + accrued interest
the accrued interest must compensate the
seller for the next coupon.
Zvi Wiener
BKM Ch 14
slide 59
STRIPS
Separate Trading of Registered Interest and
Principal of Securities.
Reconstitution of a bond.
Zvi Wiener
BKM Ch 14
slide 60
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 14
slide 61
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
BKM Ch 14
slide 62
UST example
8.75 UST 11/08
Security was purchased 06-Jun-01 @ 110-31
Security was sold 06-Sep-01 @ 109-27+
Calculate the loss (10,000 units) …
Zvi Wiener
BKM Ch 14
slide 63