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Characteristics of Bonds
Various types of Bonds.
Yield Curve
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Debt Security
A Debt Security is a claim on a specified
periodic stream of income. They are also called Fixed Income
Securities.
Payment cash flows are determined in
advance, so easy to value.
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Bonds and their Characteristics
A Bond is an instrument which obligates the issuer tomake specified payments to the bondholder.
Bonds can be described through the below 3 values Par Value This is also the Face Value of the Bond. It
represents the amount which the issuer promises to payat maturity.
Maturity Date - This is the date when the principleamount is payable to the Bond Holder.
Coupon Rate This is the interest rate payable to theBond Holder at regular intervals.
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Types of Bonds
Government Bonds Government of Indiaperiodically issues Bonds called G-Secs or Gilt EdgedSecurities. Interest paid semi annually. Mostly mediumto long term bonds.
Corporate Bonds These are bonds issued by
companies in order to borrow money. A securedcorporate debt is called Corporate Bondwhereas anunsecured corporate debt is known as CorporateDebentures.
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Another Differentiation of BondsType of Bond Charecteristics
Straight Bonds Plain Vanilla Bond. Pays a fixed couponover its life and returns the principle onmaturity.
Zero Coupon Bonds Does not carry any interest payment.Issued at a discount over its face value
and redeemed at Par on maturityFloating Rate Bonds Interest rate is linked to a benchmark
rate such as the Treasury Billinterestrate.
Bonds with Embedded Options These are bonds which give special
rights to the investors:-Convertible Bonds Bond Holder canconvert them into equity at maturity-Callable Bonds Issuer has the right toredeem the bond prematurely- Puttable Bonds Investor has the
right to sell them prematurely back tothe issuer
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Bond Pricing
P = Price of the Bond (Present Value)
C = Interest Amount or Coupon Payments (pmt)
T = Number of Periods (nper)
r = Discount Rate/ Yield to Maturity
)1()1(1 r
ParValue
r
CP TT
T
t
t
tB
* Yield to maturity is the prevailing interest rate for an instrument of
similar maturity.
B
t
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Relationship between Bond Price
and Yield What should be the price of a 10 year , 8% coupon Bond,
with a par value of 1000? Interest paid semi-annually.
What happens to the value of the Bond if the interest rategoes down to 7% per annum?
What happens to the value of the Bond if the interest rate
increases to 9%.
Can you explain the relationship between the Bond Pricingand the Yield (interest rate)?
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Bond Prices and Yield
Bond Prices and Yields (required rates of return) have
an inverse relationship.When yields get very high, the intrinsic value of the
bond would be very low, since the bond becomes lessattractive.
When yields approach Zero, the value of the bondapproaches the sum of the total cash flows.
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Yield Curve A relationship
between Price and YieldPrice
Yield
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Yield To Maturity
It is the rate at which the present value of the BondsPayments is equal to its price.
It is the total yield that an investor would get, giventhe discounted price (present value) of a bond andfuture cash inflows in a bond.
What should be the YTM of an 8% bond, issued for 30years, with a par value of 1000? The price quoted forthe bond is 1276.76.
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Yield to Maturity - Formula
Example Find the Yield to Maturity of a 10 yearbond, with a coupon rate of 7%. The price quoted is950 and the par value is 1000.
)1()1(1 r
ParValue
r
CPT
T
T
t
t
tB
)1(
1000
)1(
35950
20
1 rr
T
t
t
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Expected and Stated YTM
Stated Yield to Maturity The Yield to Maturityachieved at by discounting the stated information inthe bond.
Expected Yield to Maturity The Yield to Maturity(YTM) achieved at by considering the chances ofdefault in the stated information.
The stated YTM is the maximum possible YTM on abond, while the Expected YTMis a realistic YTM whichis usually lower than the Stated YTM.
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Expected and Stated YTMExample : Beta company issued a 12% coupon bond 10
years ago at par value of Rs 1000. The bond now has 5years left to maturity. However, Beta is facing somefinancial problems, due to which it assumes that it
would be able to pay only 80% of the par value atmaturity.
Inputs Expected YTM Stated YTM
Coupon Payments Rs 60 Rs 60
Number of Semiannual periods 10 10Final Payment 800 1000Price 850 850
YTM 7% 8%
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Are Bonds Risk
Free ??
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Main Risks Associated with
Bonds.. Interest Rate Risk Increase in interest rate make the
Bond less attractive and vice versa.
Default Risk/ Credit Risk The issuer of a bond mightdefault in the payment of the coupon amount or thefinal amount at maturity.
Inflation Risk Inflation rate also impacts bond pricesdirectly by increasing or decreasing the bond prices.
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Main Risks Associated with
Bonds.. Liquidity Risk A Bond might not be able to be
liquidated when the need arises.
Tax Attributes Tax implications, post the purchase ofthe bond, might make the same less attractive.
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SolveA Rs 100 par value bond bearing a coupon rate of 12%
will mature after five years. What is the value of thebond, if the discount rate is 15%?
The Market Price of a Rs 1000 par value bond carryinga coupon rate of 14% and maturing after 5 years is 1050.What is the yield to maturity of this bond?
A Rs 100 par value bond bears a coupon rate of 14%and matures after five years. Interest is payable semi-annually. Compute the value of the bond if therequired rate of return is 16%.
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Rating of Bonds
Debt Ratings Debt Ratings reflect the probability oftimely payments of interest and principle by a borrower.
Debt Ratings are not recommendations for purchase, but a
grading of debt instruments on the basis of theirinvestment quality.
Main Rating Agencies
International Moodys, Standard and Poors,Austrailian
Ratings etc. Indian Crisil, ICRA etc.
All Debt instruments need to be necessarily ratedaccordingly
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Functions of Debt RatingsDebt ratings rate Debt instruments only on the basis of theirCredit Risk.
Main functions of credit ratings: Provide superior information.
Low cost information.
Basis for proper Risk-Return trade off.
Healthy Discipline on Corporate Borrowwers. Greater credence to Financial and Other Representations
Formulation of Public Policy guidelines on InstitutionalInvestments.
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Crisil Debt Rating Symbols
Crisil The largest Credit Rating Agency in India.There are 3 kinds of rating symbols given by Crisil
1. High Investment Grades 1. AAA - represents a very highly rated investment, issued by
an institution which is fundamentally very strong.2. AA These investments are assumed to offer high safety of
timely payments of interest and principle.
2. Investment Grades1. A - Adequate safety of timely payments, but changes in
circumstances, might affect their ability to payback.2. BBB Sufficient Safety of timely payments, but any
changes, would weaken and reduce their ability to makepayments.
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Crisil Debt Rating Symbols
3. Speculative Grades1. BB Inadequate Safety of timely payments, however
less susceptible to default in the near future.
2. B Currently managing to make timely payments,however, any changes would lead to a lack of ability or
willingness to payback.
3. C Timely payments will continue only till the time,
the circumstances are favorable. Highly susceptible todefaults.
4. D There is a high expectation of default onmaturity. Probably other instruments issued by thesame organization are already in default or arrears.
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Yield Curve A relationship
between YTM and Maturity Shows the relationship between the Yield
to Maturity and Years to Maturity
Information on expected future short terminterest rates can be implied from the yield
curve
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Expected One Year Rates in comingyears
Expected One-Year Rates in Coming Years
Year Interest Rate
0 (today) 8%
1 10%
2 11%
3 11%
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Pricing of Bonds using Expected
Rates
A Zero Coupon Bond, paying Rs 1000 after 1 year wouldsell today at Rs 925.93.
A Zero Coupon Bond, paying Rs 1000 after 2 years
would sell today at Rs 841.75.
)1)...(1)(1( 21 nn
rrr
ParValuePV
r1 = One-year rate for period 1
r2 = One-year rate for period 2
rn = One-year rate for period n
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Bond Prices using Expected RatesTime to Maturity Price of Zero* Yield to Maturity
1 925.93 8.00%
2 841.75 8.995
3 758.33 9.660
4 683.18 9.993
* Rs 1,000 Par value zero coupon Bond
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Pricing of Bonds Using Spot Rates
A B
Maturity 4 years 4 years
Coupon Rate 6% 8%Par Value 1,000 1,000
Cash Flow in 1-3 60 80
Cash Flow in 4 1,060 1,080Assuming Annual compounding
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Price of Bonds using Spot Rates
Bond A
Period
Spot
Rate
Cash
Flow
PV of
Flow
1 .05 60 57.14
2 .0575 60 53.65
3 .063 60 49.95
4 .067 1,060 817.80
Total 978.54
* Since spot rates are different for each year, we would have to calculate the PV ofeach year separately
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Price of Bonds using Spot Rates
Bond B
Period
Spot
Rate
Cash
Flow
PV of
Flow
1 .05 80 76.19
2 .0575 80 71.54
3 .063 80 66.60
4 .067 1080 833.23
Total 1047.56
* Since spot rates are different for each year, we would have to calculate the PV ofeach year separately
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Solving for Yield To Maturity
Bond A
Bond Price 978.54YTM 6.63%
Bond B
Price 1,047.56
YTM 6.61%
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Bond Pricing Relationships
Inverse relationship between price and yield.
An increase in a bonds yield to maturity resultsin a smaller price decline than the gainassociated with a decrease in yield.
Long-term bonds tend to be more pricesensitive than short-term bonds.
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Bond Pricing Relationships
As maturity increases, price sensitivity increases at
a decreasing rate.
Price sensitivity is inversely related to a bondscoupon rate.
Price sensitivity is inversely related to the yield to
maturity at which the bond is selling.
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DurationA measure of the effective maturity of a bond.
The weighted average of the times until each
payment is received, with the weightsproportional to the present value of the payment.
Duration is shorter than maturity for all bonds
except zero coupon bonds. Duration is equal to maturity for zero coupon
bonds.
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Duration Calculationt t
tw CF y ice ( )1 Pr
twtDT
t
1
CF Cash Flow for period tt
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Duration Calculation - Spreadsheet
8%Bond
Timeyears
Payment PV of CF(10%)
Weight C1 XC4
.5 40 38.095 .0395 .0197
1 40 36.281 .0376 .0376
1.5
2.0
40
1040
sum
34.553
855.611
964.540
.0358
.8871
1.000
.0537
1.7742
1.8852
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Duration/Price Relationship
Price change is proportional to duration and not to
maturity.
P/P = -D x [(1+y) / (1+y)
D* = modified duration
D* = D / (1+y)
P/P = - D* x y
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Rules for Duration
Rule 1 The duration of a zero-coupon bond equals its timeto maturity.
Rule 2 Holding maturity constant, a bonds duration ishigher when the coupon rate is lower.
Rule 3 Holding the coupon rate constant, a bondsduration generally increases with its time to maturity.
Rule 4 Holding other factors constant, the duration of acoupon bond is higher when the bonds yield tomaturity is lower.
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Rules for Duration
Rules 5 The duration of a level perpetuity is equal to:
Rule 6 The duration of a level annuity is equal to:y
y)1(
1)1(
1
Ty
T
y
y