bond market maths
Post on 07-Apr-2018
219 Views
Preview:
TRANSCRIPT
-
8/4/2019 Bond Market Maths
1/74
4/15/12
Group Members
Swarana Biyani ---- 01
Sanket Desai ------02
Rohan Jadhav -----08
Shama Lonare ---- 14
Bond Market Maths
11
-
8/4/2019 Bond Market Maths
2/74
4/15/12
No Topic Slide Number
1 Features Of Debt Securities. 3---8
2 Bond Sector and Instruments. 9 -- 23
3 Convexity and Duration. 24 -- 37
4 Yield Spread. 38 -- 65
5 Yield Measures. 65 -- 76
22
Index
-
8/4/2019 Bond Market Maths
3/74
4/15/12
Bond Indenture:- It is the contract which specifies allthe rights and obligation of Issuer and holder of the debt
security.
33
-
8/4/2019 Bond Market Maths
4/74
4/15/12
Straight (Option free bond):- Consider a treasury bond
with 6% coupon and matures in 5 years in amount of 1000 Rs.
It will make 4 payments if 60 Rs annually for 4 years and a
payment of 1060 at the end of 5th year.
Zero coupon Bond:- They do not pay periodic interest, insteadthey are issued at discount to par value and pay the par values at the
end of maturity.
Eg A treasury bond issued at 98.5$ with a par value of 100% willpay 100$ at the end of maturity with effective return of 2.5%.
44
-
8/4/2019 Bond Market Maths
5/74
4/15/12
Step Up Notes :- A bond that pays an initial coupon rate for the
first period, and then a higher coupon rate for the following periods.
For example a five-year bond may pay a 4% coupon for the first twoyears of its life and a 6% coupon for the final three years.
Deferred coupon bond:- The initial interest/coupon payments aredeferred for a period. The coupon payments accumulate at compound rate
till deferred period after which they are paid as lump sum. After deferredperiod the bond start paying regular coupon payments.
Eg A bond with face value of 100Rs and coupon rate of 5%, deferred
period of 5 years will pay 34.01Rs at the end of 5 years and will startmaking annual payments if 5Rs thereafter. 55
-
8/4/2019 Bond Market Maths
6/74
4/15/12
Caps and Floors.:- The upper limit which is a cap puts
maximum limit on the interest rate paid by the issuer. Floor is thelower limit which puts minimum on the interest rate received by theowner.
Prepayment option:- This option gives the issuer the right topre pay the principle and hence in effect constitutes a pre paymentrisk to the holder.
66
-
8/4/2019 Bond Market Maths
7/74
4/15/12
Put Option:- It gives the right to the bond holders to sell the
bond to the issuer at a specified price. If the bond price fallsbelow certain level the bond holder can force the issuer to buyback the bond at a specified price.
As the put option gives the holder an advantage the yields onsuch bonds are lower than straight bonds.
Eg 6.72%GS2012 bond issued in 2002 with the put optionexercisable after every 2.5 years.
77
-
8/4/2019 Bond Market Maths
8/74
4/15/12
Call option:- This option gives the right to the issuer to buy back
the bond at a specific price. If the bond prices rise above certain levelthe issuer can buy back the bonds at a specified price.
Since this option gives the issuer an advantage the yields on suchcallable bonds are greater than straight bonds.
The same 6.72%GS2012 bond had a call option whereby the Govtcould call in the bonds after every 2.5 years.
88
-
8/4/2019 Bond Market Maths
9/74
4/15/12
Click to edit Master subtitle style
BOND SECTOR
&INSTRUMENTS
99
-
8/4/2019 Bond Market Maths
10/74
4/15/12
Corporate Debt Securities
1010
-
8/4/2019 Bond Market Maths
11/74
4/15/12
1111
-
8/4/2019 Bond Market Maths
12/74
4/15/12
UNSECURED DEBT:
They are not backed by any collateral.
Referred as debentures
If pledged assets generate excess funds they areused for unsecured debt.
CREDIT ENHANCEMENT :
Guarantee given that the corporate debt will berepaid.
Third party
1212
-
8/4/2019 Bond Market Maths
13/74
4/15/12
Fixed rate bonds have a coupon that remainsconstant throughout the life of the bond.
Floating rate notes (FRNs)
Zero-coupon bonds
Inflation linked bonds
Asset-backed securities
Registered bond
Types Of Bonds
1313
-
8/4/2019 Bond Market Maths
14/74
4/15/12
Subordinate bonds
Perpetual bonds
Bearer bonds
Treasury bonds
Lottery bonds
Municipal bonds
1414
V l ti Of D bt
-
8/4/2019 Bond Market Maths
15/74
4/15/12
Basic steps
1) Estimate the cash flow
2) The interest rate
3) Present value) Difficulties involved:
1) Principal repayment in unknown2) Coupon payments
Valuation Of DebtSecurities
1515
-
8/4/2019 Bond Market Maths
16/74
4/15/12
Valuation of bond when1) single coupon rate
PV= FV/(1+r)n
E.g. cash inflow= Rs100
N= 10 years
Future value= Rs 1000
Discount rate= 8%
100/(1.08)+ 100/(1.08)2+ 100/(1.08)3.
+100/(1.08)10 =Rs(1134.20)
Computation
1616
-
8/4/2019 Bond Market Maths
17/74
4/15/12
2) Zero coupon bonds
Bond value= maturity value/(1+i)n*2
E.G. N=10 years (semi annual)
YTM =8%
Face value= Rs1000
Zero coupon Bond
1000/(1+.08/2)10*2=1000/(1.04)20=Rs456.39
1717
-
8/4/2019 Bond Market Maths
18/74
4/15/12
Securitization is the process ofconversion of existing assets or future
cash flows into marketable securities.
It deals with the conversion of assetswhich are not marketable into
marketable ones.
Securitization
1818
-
8/4/2019 Bond Market Maths
19/74
4/15/12
Click to edit Master subtitle style
1919
-
8/4/2019 Bond Market Maths
20/74
4/15/12
The SPV is a separate entity formed
exclusively for the facilitation of thesecuritization process and providing fundsto the originator.
The SPV will act as an intermediary whichdivides the assets of the originator intomarketable securities.
These securities issued by the SPV to theinvestors and are known as pass-through-certificates (PTCs)
Special Purpose Vehicle
2020
-
8/4/2019 Bond Market Maths
21/74
4/15/12
Assemble an entire portfolio of credit riskexposures, segment that exposure intotranches with unique risk/return/maturity
profiles, which are then transferred or soldto investors.
Securitization issues backed by debt
obligations are called CDO CDOs reference (underlying) portfolio can
be assembled with physical cash flowassets such as bonds, loans, MBS, ABS etc
o a era ze eObligation
2121
M t B k d
-
8/4/2019 Bond Market Maths
22/74
4/15/12
Securitization issues backed bymortgages are called MBS
Mortgage BackedSecurities (MBS)
2222
A t B k d S iti
-
8/4/2019 Bond Market Maths
23/74
4/15/12
Securitization issues backed byconsumer-backed products - car loans,
consumer loans and credit cards,among others are called ABS
Assets Backed Securities
2323
-
8/4/2019 Bond Market Maths
24/74
4/15/12
Interest Rate Risk
- Uncertainty about bond prices due to change
in market interest rates
Call Risk
-The risk that the bond will be called prior to
maturity under the terms of call provision and thefunds must be reinvested at the then current yield.
Prepayment Risk
-The uncertainty about the amount of bond
principal that will be repaid prior to maturity
Risk Associated
2424
-
8/4/2019 Bond Market Maths
25/74
4/15/12
Liquidity Risk
-The risk that an immediate sale will result in a pricebelow fair value
Exchange Rate Risk-The risk that the domestic currency value of bond
payments in a foreign currency will decrease
Event Risk
-The risk of decrease in a security value fromdisasters, corporate restructuring, or regulatory changesthat negatively affect the firm
Sovereign Risk
Risk Associated
2525
Bonds Price Relative To
-
8/4/2019 Bond Market Maths
26/74
4/15/12
Bonds Price Relative ToPar
2626
-
8/4/2019 Bond Market Maths
27/74
4/15/12
Characteristic Interest Rate Risk Duration
Maturity Up Interest Rate Risk Up Duration Up
Coupon Up Interest Rate RiskDown
Duration Down
Add a Call Interest Rate RiskDown
Duration Down
Add a Put Interest Rate RiskDown
Duration Down
Bond Characteristic & Interest RateRisk
2727
-
8/4/2019 Bond Market Maths
28/74
4/15/12
The term duration has a special meaning in the
context of bonds. It is a measurement of how long,in years, it takes for the price of a bond to berepaid by its internal cash flows.
For each of the two basic types of bonds theduration is the following:
1. Zero-Coupon Bond Duration is equal toits time to maturity.
2. Vanilla Bond - Duration will always be lessthan its time to maturity.
2828
Duration
Duration of a Zero
-
8/4/2019 Bond Market Maths
29/74
4/15/12
2929
Duration of a ZeroCoupon Bond
The entire cash flow of a zero-coupon bond occursat maturity, so the fulcrum is located directlybelow this one payment.
Duration of a Vanilla
-
8/4/2019 Bond Market Maths
30/74
4/15/12
Consider a vanilla bond that pays couponsannually and matures in five years.
The straight bond pays coupon payments
throughout its life and therefore repays the full3030
Duration of a Vanillaor Straight Bond
Factors Affecting
-
8/4/2019 Bond Market Maths
31/74
4/15/12
3131
Factors AffectingDuration
Duration is decreasing as time moves closer tomaturity
But duration also increases momentarily on the
Duration: Other
-
8/4/2019 Bond Market Maths
32/74
4/15/12
Other factors that affect abond's duration: the couponrate and its yield
Bonds with high couponrates and, in turn, highyields will tend to have
lower durations than bondsthat pay low coupon rates oroffer low yields.
3232
Duration: Otherfactors
-
8/4/2019 Bond Market Maths
33/74
4/15/12
Types of durations are :-
Macaulay duration
Modified duration
Effective duration
3333
Types of Duration
http://var/www/apps/conversion/current/tmp/scratch7307/slide46.xmlhttp://var/www/apps/conversion/current/tmp/scratch7307/slide47.xmlhttp://var/www/apps/conversion/current/tmp/scratch7307/slide47.xmlhttp://var/www/apps/conversion/current/tmp/scratch7307/slide46.xml -
8/4/2019 Bond Market Maths
34/74
4/15/12
The formula usually used to calculate a bond's
basic duration is the Macaulay duration, which wascreated by Frederick Macaulay in 1938
3434
Macaulay Duration
n = number of cash flows
t = time to maturityC = cash flowi = required yieldM = maturity (par) valueP = bond price
-
8/4/2019 Bond Market Maths
35/74
4/15/12
Example 1: Betty holds a five-year bond with
a par value of $1,000 and coupon rate of 5%.For simplicity, let's assume that the couponis paid annually and that interest rates are
5%. What is the Macaulay duration of thebond?
3535
Example
= 4.55 years
-
8/4/2019 Bond Market Maths
36/74
4/15/12
Modified duration is a modified version of the
Macaulay model that accounts for changinginterest rates.
Modified formula shows how much the duration
changes for each percentage change in yield
3636
Modified Duration
-
8/4/2019 Bond Market Maths
37/74
4/15/12
Betty's bond and run through the calculation of her
modified duration. Currently her bond is selling at$1,000 or par, which translates to a yield tomaturity of 5%.
We calculated a Macaulay duration of4.55 Years.
If the bond's yield changed from 5% to 6%, theduration of the bond
3737
Example
= 4.33years
-
8/4/2019 Bond Market Maths
38/74
4/15/12
Cash flows from securities with embeddedoptions or redemption features will changewhen interest rates change.
For calculating the duration of these types ofbonds, effective duration is the most
appropriate.
3838
Effective Duration
-
8/4/2019 Bond Market Maths
39/74
4/15/12
For any given bond, a graph of the
relationship between price and yield isconvex.
The degree to which the graph is curvedshows how much a bond's yield changes inresponse to a change in price.
Convexity
3939
-
8/4/2019 Bond Market Maths
40/74
4/15/12
Convexity and Duration
The exact point where thetwo lines touch representsMacaulay duration.
The yellow portions of thegraph show the ranges in
which using duration forestimating price would beinappropriate.
Convexity shows how much4040
-
8/4/2019 Bond Market Maths
41/74
4/15/12
A bond with greater convexity is less affected
by interest rates than a bond with lessconvexity.
Bonds with greater convexity will have ahigher price than bonds with a lowerconvexity, regardless of whether interestrates rise or fall.
Properties of Convexity
4141
-
8/4/2019 Bond Market Maths
42/74
4/15/12
Graphical Illustrations
If two bonds offer the same duration and yield butone exhibits greater convexity, changes ininterest rates will affect each bond differently4242
-
8/4/2019 Bond Market Maths
43/74
4/15/12
Kinds of Convexities Plain Vanilla bond
Positive convexity.
The price-yield curve
will increase as yielddecreases, and viceversa.
As market yields
decrease, the durationincreases .
Callable bond
Negative convexity atcertain price-yieldcombinations.
Negative convexitymeans that as marketyields decrease, durationdecreases as well.
4343
Convexity allows the
-
8/4/2019 Bond Market Maths
44/74
4/15/12
To better comprehend the way in whichduration is best measured
how changes in interest rates affect theprices of both plain vanilla and callablebonds.
Convexity allows theinvestor :
4444
-
8/4/2019 Bond Market Maths
45/74
4/15/12
Click to edit Master subtitle style
UnderstandingYield Spreads
4545
Yield Curve & Various
-
8/4/2019 Bond Market Maths
46/74
4/15/12
Yield Curve:
Yield curve gives the relationship between the
maturity and the yield of the bond.
Various shapes of Yield Curve
1. Normal or Upward Sloping
2. Inverted or Downward Sloping
3. Flat
4. Humped
Yield Curve & VariousShapes of Yield Curve
4646
Theories of term
-
8/4/2019 Bond Market Maths
47/74
4/15/12
Pure Expectation Theory
The yield for a particular maturity is an average
of the short-term rates that are expected in thefuture.
If short-term rates are expected to rise in future,interest rate yields on longer maturities will be
higher and the yield curve will be Upward sloping.
Theories of termstructure of interest rates
4747
Theories of term
-
8/4/2019 Bond Market Maths
48/74
4/15/12
Liquidity Preference Theory
Investors require a risk premium for holding long
term bonds. Interest rate risk is greater for longermaturity bonds.
The size of the liquidity premium depends on howmuch additional compensation investor requires
to take on a greater risk for long term bonds.
Theories of termstructure of interest rates
4848
Theories of term
-
8/4/2019 Bond Market Maths
49/74
4/15/12
Theories of termstructure of interest rates
4949
Theories of term
-
8/4/2019 Bond Market Maths
50/74
4/15/12
Market Segmentation Theory
Investors & borrowers have different pref. for
different maturity ranges.
The supply and demand determines equilibriumyields for various maturity ranges.
Eg: Life insurers & pension funds may prefer longmaturities due to their long term liablities.
Theories of termstructure of interest rates
5050
Theories of term
-
8/4/2019 Bond Market Maths
51/74
4/15/12
Preferred Habitat Theory
This is somewhat weaker version ofMarket
Yields depends on the supply and demand
for various maturityranges but investors can be induced to
move from theirpreferred maturity ranges when yields are
sufficiently higher in
Theories of termstructure of interest rates
5151
-
8/4/2019 Bond Market Maths
52/74
4/15/12
Q. An annual-pay bond of 1000 with 10%coupon rate and 3 years to maturity.
Suppose the spot rates are:1 year = 8%
2 year = 9%
3 year = 10%
Find the value of bond?
Spot Rate
5252
-
8/4/2019 Bond Market Maths
53/74
4/15/12
Solution:
Value of bond =
100/1.08 + 100/(1.09) + 1100/(1.10)
= 1003.21Spot rate is the discount rate for individual
future payments.
Spot Rate
5353
-
8/4/2019 Bond Market Maths
54/74
4/15/12
Yield spread is the difference between theyields on two bonds or two types of bonds.
Three different yield measures are:
1. Absolute Yield Spread
2. Relative Yield Spread
3. Yield Ratio
Yield Spread
5454
i ld d
-
8/4/2019 Bond Market Maths
55/74
4/15/12
Absolute Yield Spread
It is the difference between yields on two
bonds.
It is expressed in basis point (100th of 1%)
Absolute yield spread = yield on thehigher yield bond yield on the lower yieldbond
Yield Spread
5555
i ld S d
-
8/4/2019 Bond Market Maths
56/74
4/15/12
Relative yield spread
It is absolute yield spread expressed as a
percentage of the yield on the benchmark bond.
Relative yield spread = absolute yield
spread----------------------------------
benchmark bond yield
Yield Spread
5656
Yi ld S d
-
8/4/2019 Bond Market Maths
57/74
4/15/12
Yield ratio
It is the ratio of the yield on the subject bond to
the yield on the benchmark bond
Yield ratio = subject bond yield
-----------------------------------
benchmark bond yield
Yield Spread
5757
Yi ld S d
-
8/4/2019 Bond Market Maths
58/74
4/15/12
Q. Consider two bonds X & Y. Their resp. yields are6.50% & 6.75%.
Using bond X as the benchmark bond,
Compute the absolute yield spread, relative yieldspread & yield ratio.
Yield Spread
5858
Yi ld S d
-
8/4/2019 Bond Market Maths
59/74
4/15/12
Solution:
Absolute yield spread = 6.75% - 6.50% = 0.25%
or 25 basis
Relative yield spread = 0.25% / 6.50% = 3.8%
Yield ratio = 6.75% / 6.50% = 1.038
Yield Spread
5959
Aft t i ld
-
8/4/2019 Bond Market Maths
60/74
4/15/12
Computing after-tax yield on taxablesecurities
After-tax yield = taxable yield x (1- marginaltax rate)
Q. Calculate after-tax yield on a corporate bondwith yield of 10% for an investor with 40%marginal tax rate?
After-tax yield
6060
Aft t i ld
-
8/4/2019 Bond Market Maths
61/74
4/15/12
Solution:
After-tax yield = 10% (1-40%)
= 10% (1-0.4)
= 6% after tax
After-tax yield
6161
T i l t i ld
-
8/4/2019 Bond Market Maths
62/74
4/15/12
Taxable-equivalent yield:
It is a yield a particular investor must earn on a
taxable bond to have the same after-tax returnthe investor may receive from a tax-exempt bond.
Taxable-equi. yield = tax free yield--------------------------------
(1-marginal tax rate)
Tax-equivalent yield
6262
T i l t i ld
-
8/4/2019 Bond Market Maths
63/74
4/15/12
Q. Municipal bond offers yield of 4.5%. If an
investor consider buying taxable Treasury securityoffering 6.75% yield. Should the investor buy the
Treasury security or municipal bond, given themarginal tax rate is 35%.
Tax-equivalent yield
6363
T i l t i ld
-
8/4/2019 Bond Market Maths
64/74
4/15/12
Solution:
Taxable-equivalent yield = 4.5%
-------------------------
(1 - 0.35)
= 6.92%
Therefore, municipal bond is preferred overtreasury security as taxable-equivalent onmunicipal bond is higher than that of treasurysecurity.
Tax-equivalent yield
6464
Yi ld M
-
8/4/2019 Bond Market Maths
65/74
4/15/12
Current yield is the simplest measure of valuing a bond
Current yield = annual cash interest payment / Bond Price
Consider a 20 year bond with a face value of $ 1000 which
pays 6% annually, the bond is trading at $ 802.07.
The current yield is 6% * 1000 / 802.07 = 7.48%.
Yield Measures
6565
Yi ld M
-
8/4/2019 Bond Market Maths
66/74
4/15/12
Yield to Maturity : - It values the bond on the PV of thefuture payments.
Bond Price = ( CP (T) / ( 1 + YTM) ) + ( CP (2) / ( 1 + YTM )^2 ).
+( CP ( N ) + par / ( 1 + YTM )^ N).
YTM and price give the same information, given YTM wecan calculate price and given price we can calculate YTM.
Yield Measures.
6666
Yi ld M
-
8/4/2019 Bond Market Maths
67/74
4/15/12
Consider an annual pay 20 year $ 1000par value bond with a 6% coupon ratetrading at a price of $ 802.07 Calculate
the YTM.6767
Yield Measures.
Yi ld M
-
8/4/2019 Bond Market Maths
68/74
4/15/12
Yield to call : - It is used to measure yield on callablebonds which are trading at premium.
Typically callable bonds cant be called for a fixedperiod of time after issuance.
If within that period the bond price goes above thecall price yield to call is used.
Yield Measures.
6868
Yi ld M
-
8/4/2019 Bond Market Maths
69/74
4/15/12
Consider a 10% semiannual pay bond
with a current price of $112 that can becalled in 5 years at 102. Calculate the
YTM and YTC.6969
Yield Measures.
Yi ld M
-
8/4/2019 Bond Market Maths
70/74
4/15/12
Yield to put : - It measures the yield of bonds having putoption which are trading a discount.
Typically put option in a bond cant be invoked for a fixedperiod of time after issuance.
If within that period the bond price starts trading at
discount to the actual value of the bond then yield to put isused.
The yield to put is higher than YTM due to lower bondrice.
Yield Measures.
7070
Yield Meas res
-
8/4/2019 Bond Market Maths
71/74
4/15/12
Consider a 3 year, 6%, $ 1000 semiannualpay bond. The bond is selling for a price of925.40. The opportunity for put is at par in2 years. Calculate YTM and YTP. 7171
Yield Measures.
Reinvestment Income
-
8/4/2019 Bond Market Maths
72/74
4/15/12
If a bond holder holds a bond until maturity and
reinvests the interest payments then the totalamount generated by the bond over the life is
1. Bond Principle.
2. Interest payments.
3. Interest on reinvested Income.
. If the reinvestment income is less than YT, of thebond the total return generated will be less than
YTM.
Reinvestment Income.
7272
Reinvestment Income
-
8/4/2019 Bond Market Maths
73/74
4/15/12
If you purchase a 6% 10 year bond how much
reinvestment income must be generated over its lifeto provide the investor with a compound return of 6%on annual basis. The par value of bond is Rs 100.
If the investment yields 6% compounded annualreturn the total value will be 100 * ( 1.06 ) ^ 10 =179.084.
The bond will make 10 annual payments of Rs 6 andan end payment of Rs 100.
There fore it will make total payment of 160RS
The required reinvestment Income is 179.084 160 =
Reinvestment Income.
7373
The End
-
8/4/2019 Bond Market Maths
74/74
Thank You
The End
top related