Bond Market Investments

7/30/2019 Bond Market Investments

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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

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Bond Market Investments