fixed income
DESCRIPTION
Fixed Income. Zvi Wiener. Plan. Pricing of Bonds Measuring yield Bond Price Volatility Factors Affecting Yields and the Term Structure of IR Treasury and Agency Securities Markets Corporate Debt Instruments Municipals. Plan. Non-US Bonds Mortgage Loans - PowerPoint PPT PresentationTRANSCRIPT
1
Http:\\www.tfii.org
Zvi Wiener
Fixed Income
2
Http:\\www.tfii.org
Plan
• Pricing of Bonds
• Measuring yield
• Bond Price Volatility
• Factors Affecting Yields and the Term Structure of IR
• Treasury and Agency Securities Markets
• Corporate Debt Instruments
• Municipals
3
Http:\\www.tfii.org
Plan
• Non-US Bonds
• Mortgage Loans
• Mortgage Pass-Through Securities
• CMO and Stripped MBS
• ABS
• Bonds with Embedded Options
• Analysis of MBS
• Analysis of Convertible Bonds
4
Http:\\www.tfii.org
Plan
• Active Bond Portfolio Management
• Indexing
• Liability Funding Strategies
• Bond Performance Measurement
• Interest Rate Futures
• Interest Rate Options
• Interest Rate Swaps, Caps, Floors
5
Http:\\www.tfii.org
Characteristics of a Bond• Issuer
• Time to maturity
• Coupon rate, type and frequency
• Linkage
• Embedded options
• Indentures
• Guarantees or collateral
6
Http:\\www.tfii.org
Sources
• Fabozzi, “Bond Markets, Analysis and
Strategies”, Prentice Hall.
• P. Wilmott, Derivatives, Wiley.
• Hull, White, Manuscript.
7
Http:\\www.tfii.org
Sectors• Treasury sector: bills, notes, bonds
• Agency sector: debentures (no collateral)
• Municipal sector: tax exempt
• Corporate sector: US and Yankee issues– bonds, notes, structured notes, CP– investment grade and noninvestment grade
• Asset-backed securities sector
• MBS sector
8
Http:\\www.tfii.org
Basic terms• Principal• Coupon, discount and premium bonds• Zero coupon bonds• Floating rate bonds• Inverse floaters• Deferred coupon bonds• Amortization schedule• Convertible bonds
9
Http:\\www.tfii.org
Basic Terms
• The Money Market Account
• LIBOR = London Interbank Offer Rate, see BBA Internet site
• FRA = Forward Rate Agreement
• Repos, reverse repos
• Strips = Separate Trading of Registeres Interest and Principal of Securities
10
Http:\\www.tfii.org
Basic Terms
• gilts (bonds issued by the UK government)
• JGB = Japanese Government Bonds
• Yen denominated issued by non-Japanese institutions are called Samurai bonds
11
Http:\\www.tfii.org
Major risks
• Interest rate risk
• Default risk
• Reinvestment risk
• Currency risk
• Liquidity risk
12
Http:\\www.tfii.org
Time Value of Money
• present value PV = CFt/(1+r)t
• Future value FV = CFt(1+r)t
• Net present value NPV = sum of all PV-PV 5 5 5 5 105
5
4
1 )1(
105
)1(
5
rrPV
tt
13
Http:\\www.tfii.org
TT
T
tt
t
r
C
r
CPV
)1()1(1
Term structure of interest rates
TT
TT
tt
t
t
r
C
r
CPV
)1()1(1
Yield = IRR
TT
T
tt
t
y
C
y
Cice
)1()1(Pr
1
How do we know that there is a solution?
14
Http:\\www.tfii.org
Price-Yield Relationship
• Price and yield (of a straight bond) move in opposite directions.
yield
price
15
Http:\\www.tfii.org
General pricing formula
11
1 )1()1()1()1(
nv
nn
ttv
t
rr
C
rr
CP
periodmonthssixindays
couponnextandsettlementbetweendaysv
16
Http:\\www.tfii.org
Accrued Interest
Accrued interest = interest due in full period*
(number of days since last coupon)/
(number of days in period between coupon payments)
17
Http:\\www.tfii.org
Day Count Convention
Actual/Actual - true number of days
30/360 - assume that there are 30 days in each month and 360 days in a year.
Actual/360
18
Http:\\www.tfii.org
Floater
The coupon rate of a floater is equal to a
reference rate plus a spread.
For example LIBOR + 50 bp.
Sometimes it has a cap or a floor.
19
Http:\\www.tfii.org
Inverse Floater
Is usually created from a fixed rate security.
Floater coupon = LIBOR + 1%
Inverse Floater coupon = 10% - LIBOR
Note that the sum is a fixed rate security.
If LIBOR>10% there is typically a floor.
20
Http:\\www.tfii.org
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.
21
Http:\\www.tfii.org
Annualizing Yield
Effective annual yield = (1+periodic rate)m-1 examples
Effective annual yield = 1.042-1=8.16%
Effective annual yield = 1.024-1=8.24%
price
ratecouponannualyieldcurrent
22
Http:\\www.tfii.org
Bond selling at Relationship
Par Coupon rate=current yield=YTM
Discount Coupon rate<current yield<YTM
Premium Coupon rate>current yield>YTM
Yield to call uses the first call as cashflow.
Yield of a portfolio is calculated with the total cashflow.
23
Http:\\www.tfii.org
YTM and Reinvestment Risk
• YTM assumes that all coupon (and
amortizing) payments will be invested at the
same yield.
24
Http:\\www.tfii.org
YTM and Reinvestment Risk• An investor has a 5 years horizon
Bond Coupon Maturity YTM
A 5% 3 9.0%
B 6% 20 8.6%
C 11% 15 9.2%
D 8% 5 8.0%
What is the best choice?
25
Http:\\www.tfii.org
Bond Price Volatility
Consider only IR as a risk factor
Longer TTM means higher volatility
Lower coupons means higher volatility
Floaters have a very low price volatility
Price is also affected by coupon payments
Price value of a Basis Point = price change resulting from a change of 0.01% in the yield.
26
Http:\\www.tfii.org
Duration and IR sensitivity
27
Http:\\www.tfii.org
Duration
nn y
M
y
C
y
C
y
CP
)1()1()1()1( 2
nn y
nM
y
nC
y
C
y
C
P
DurationMacaulay
)1()1()1(
2
)1(
112
28
Http:\\www.tfii.org
Duration
y
DurationMacaulayDurationModified
1
DurationModifiedPdy
dP 1
29
Http:\\www.tfii.org
DurationBond duration price impact of +1%
YTM
A 3 yr
B 1 yr
C 10 yr
D 20 yr
-3%-1%-10%-20%
30
Http:\\www.tfii.org
Measuring Price Change
errordydy
Pddy
dy
dPdP 2
2
2
)(2
1
P
errordy
ConvDdy
P
dP 2)(
2
31
Http:\\www.tfii.org
The Yield to Maturity
The yield to maturity of a fixed coupon bond y is given by
n
i
ytTi
iectp1
)()(
32
Http:\\www.tfii.org
Macaulay Duration
Definition of duration, assuming t=0.
p
ecTD
n
i
yTii
i
1
33
Http:\\www.tfii.org
Macaulay Duration
What is the duration of a zero coupon bond?
T
tt
tT
tt y
CFt
iceBondwtD
11 )1(Pr
1
A weighted sum of times to maturities of each coupon.
34
Http:\\www.tfii.org
Meaning of Duration
Dpecdy
d
dy
dp n
i
yTi
i
1
r
$
35
Http:\\www.tfii.org
Convexity
r
$
2
2
y
pC
36
Http:\\www.tfii.org
FRA Forward Rate AgreementA contract entered at t=0, where the parties (a lender
and a borrower) agree to let a certain interest rate R*, act on a prespecified principal, K, over some future time period [S,T].
Assuming continuous compounding we have
at time S: -K
at time T: KeR*(T-S)
Calculate the FRA rate R* which makes PV=0hint: it is equal to forward rate
37
Http:\\www.tfii.org
ALM Duration
• Does NOT work!• Wrong units of measurement• Division by a small number
r
A
ADA
1r
L
LDL
1
r
LA
LAD LA
)(1
38
Http:\\www.tfii.org
ALM Duration
A similar problem with measuring yield
r
P
VaR P 1
39
Http:\\www.tfii.org
Do not think of duration as a measure of time!
40
Http:\\www.tfii.org
• Key rate duration
• Principal component duration
• Partial duration
41
Http:\\www.tfii.org
Factors affecting Bond yields and TS
• Base interest rate - benchmark interest rate
• Risk Premium - spread
• Expected liquidity
• Market forces - Demand and supply
42
Http:\\www.tfii.org
Taxability of interest• qualified municipal bonds are exempts from
federal taxes.
After tax yield = pretax yield (1- marginal tax rate)
43
Http:\\www.tfii.org
Do not use yield curve to price bondsPeriod A B1-9 $6 $110 $106 $101They can not be priced by discounting
cashflow with the same yield because of different structure of CF.
Use spot rates (yield on zero-coupon Treasuries) instead!
44
Http:\\www.tfii.org
On-the-run Treasury issues
Off-the-run Treasury issues
Special securities
Lending
Repos and reverse repos
45
Http:\\www.tfii.org
Forward RatesBuy a two years bond
Buy a one year bond and then use the money to buy another bond (the price can be fixed today).
(1+r2)=(1+r1)(1+f12)
46
Http:\\www.tfii.org
Forward Rates
(1+r3)=(1+r1)(1+f13)= (1+r1)(1+f12)(1+f13)
Term structure of instantaneous forward rates.
47
Http:\\www.tfii.org
Determinants of the Term Structure
Expectation theory
Market segmentation theory
Liquidity theory
Mathematical models: Ho-Lee, Vasichek,
Hull-White, HJM, etc.
48
Http:\\www.tfii.org
• What is the duration of a floater?
• What is the duration of an inverse floater?
• How coupon payments affect duration?
• Why modified duration is better than
Macaulay duration?
• How duration can be used for hedging?
Home Assignment