fixed income-i

Fixed Income Securities – I

www.edupristine.com

Fixed Income Securities – I

Mapping to Curriculum

• Reading 57: Introduction to the Valuation of Debt

Securities

• Reading 53: Features of Debt Securities

• Reading 54: Risks Associated with Investing in Bonds

• Reading 55: Overview of Bond Sectors and Instruments

Expect around 15 questions in the exam from today’s lecture

© Neev Knowledge Management – Pristine 2


• Reading 57: Introduction to the Valuation of Debt

Securities

• Reading 53: Features of Debt Securities

• Reading 54: Risks Associated with Investing in Bonds

• Reading 55: Overview of Bond Sectors and Instruments


www.edupristine.com2


Key Concepts

• Discount, Par, Premium• Bond Pricing• Yield-Price Relationship• Clean Price, Dirty Price• Embedded Options• Risks Associated With Investing In Bonds• Effect of Maturity and Coupon on Duration• Types of Government Bonds• ABS, MBS,CMO,CDO

© Neev Knowledge Management – Pristine


3


www.edupristine.com


3

Fixed Income (Introduction)

Fixed income refers to any type of investment that is not equity, which obligates the borrower/issuerto make payments on a fixed schedule, even if the number of the payments may be variableA bond is simply a promise to pay interest on borrowed money, there is some important terminologyused by the fixed-income industry:

• The issuer is the entity (company or govt.) who borrows an amount of money (issuing the bond) and paysthe interest.

• The principal of a bond – also known as maturity value, face value, par value – is the amount that theissuer borrows which must be repaid to the lender.

• The coupon (of a bond) is the interest that the issuer must pay.• The maturity is the end of the bond, the date that the issuer must return the principal.• The bond Indenture is the contract that states all of the terms of the bond. It contains the obligations,

rights, and any options available to the issuer or buyer of a bonds. A written agreement betweenthe issuer of a bond and his/her bondholders, usually specifying interest rate, maturity date, convertibility.







4






www.edupristine.com






4

Basic Structure Of A Plain Vanilla Bond

50

100

150


-150

-100

-50

0T0 T1 T2 T3 T4 T5

5

Basic Structure Of A Plain Vanilla Bond

www.edupristine.com

T5 T6 T7 T8 T9 T10

5

Key Issues In Introduction To The Valuation OfDebt Securities

• Bond Valuation Process

• Problems encountered in Valuation

• Computing the value of a bond

• Change in value with passage of time

• Value of a zero-coupon bond

• Arbitrage-free valuation approach


• Bond Valuation Process

• Problems encountered in Valuation

• Computing the value of a bond

• Change in value with passage of time

• Value of a zero-coupon bond

• Arbitrage-free valuation approach

6

Key Issues In Introduction To The Valuation OfDebt Securities


Important Points

• When interest rates rise, market prices of bonds fall (and vice versa)• The longer the time until maturity, the more sensitive the bond price is to changes in interest rates• In practice most bonds pay interest semi-annually, so we have to find the appropriate semi-annual

rate and adjust coupon payments• The yield to maturity (YTM)of a bond is the discount rate which equates the price of a bond with the

PV of its expected future cash flow• Bond valuation is the determination of the fair price of a bond. As with any security or capital

investment,• The theoretical fair value of a bond is the present value of the stream of cash flows it is expected to

generate.






generate.

7





generate.

www.edupristine.com





generate.

7

Bond Valuation

• The value of a bond is obtained by discounting the bond's expected cash flows to the present usingan appropriate discount rate.

• If the coupon rate of the security is equal to the market yield then the bond will sell at parCoupon Rate = Market Yield --- Price = Par Value

• If the coupon rate of the security is more than the market yield then the bond will sell at premiumCoupon Rate>Market Yield - Price> Par Value

• If the coupon rate of the security is less than the market yield then the bond will sell at discountCoupon Rate<Market Yield - Price<Par Value






8





www.edupristine.com





8

Bond Valuation Process

Example :

• Par BondBond value 1000, Interest Rate 10%, Coupon Rate : 10% Term 5 year.

Calculate the PV by discounting method…. (100)

• Premium BondBond value 1000, Interest Rate 9 %, Coupon Rate : 10% Term 5 year.

Present Value : 1038.89

• Discount BondBond value 1000, Interest Rate 11 %, Coupon Rate : 10% Term 5 year.Present Value : 963.04


Example :






9

Example :






www.edupristine.com

Example :






9

Bond Valuation Process

• It is a simple three step process:1. Estimate all the cash flows expected on a security2. Determine the appropriate discount rate3. Calculate the present value of the estimated cash flows

• Formula for finding value of a bond:

where CP (N) -> coupon payment for year N,YTM -> yield to maturity (interest rate)PAR -> Face Value of teh bond

N32 YTM)(1PARC......

YTM)(1C

YTM)(1C

YTM)(1CbondaofValue





10


YTM)(1C

YTM)(1C

YTM)(1CbondaofValue

trFVPV)1(





YTM)(1C

YTM)(1C

YTM)(1CbondaofValue

www.edupristine.com




10


YTM)(1C

YTM)(1C

YTM)(1CbondaofValue

trFVPV)1(

Example: Bond Prices

Consider a 5 year vanilla bond with a face value of $1000 and 10% annually paid coupon. Calculate itsprice if the interest rates are 9%, 10%, and 11%.

Time Cash flow PV @11% PV @ 10%T=1 100 90.09 90.91

T=2 100 81.16 82.64

T=3 100 73.12 75.13

T=4 100 65.87 68.30

652.80 683.01


T=5 1100 652.80 683.01

Total 963.04 1,000.00

Comment Bond tradingat a Discount

Bond tradingat Par

Consider a 5 year vanilla bond with a face value of $1000 and 10% annually paid coupon. Calculate itsprice if the interest rates are 9%, 10%, and 11%.

PV @ 10% PV @ 9%90.91 91.74

82.64 84.17

75.13 77.22

68.30 70.84

683.01 714.92


683.01 714.92

1,000.00 1,038.90

Bond tradingat Par

Bond tradingat a Premium

Future Value Of An Ordinary Annuity:

• Future value is the value of an asset or cash at a specified date in the future that is equivalent invalue to a specified sum today.

• Future value of an annuity (FVA) is the future value of a stream of payments (annuity), assumingthe payments are invested at a given rate of interest

• Future value is the value of an asset at a specific date. It measures the nominal future sum of moneythat a given sum of money is "worth" at a specified time in the future assuming a certain interest rate,or more generally, rate of return; it is the present value multiplied by the accumulation function.





12

nRatePVFV )1(*

Future Value Of An Ordinary Annuity:




www.edupristine.com




12

Bonds Where Estimating Cash Flow Is Difficult

Problems Encountered in Valuation:• Coupon payments are reset periodically based on some reference rate.

− Example: Floating Rate Bonds

• Issuer or Investor has the option to change the contractual due date for the payment of theprincipal.− Example: Callable or Putable Bonds

• The principal payments are not known with surety because of the risk of prepayment− Example: MBS‘s

• The investor has the choice to convert the bond into common sock.− Convertible Bonds







13

Bonds Where Estimating Cash Flow Is Difficult






www.edupristine.com






13

Computing The Value Of A Bond

• Value of a bond is the present value of its cash flows

• In the exam you will deal with the following parameters:

(Refer the Texas Instrument BA II Plus Professional calculator)

• N=?; PMT=?; FV=?; I/Y=?; and then Compute PV.

Usually four of the above five terms will be given and the fifth will have to be calculated

• Example 1: Calculate the value of a security which has coupon rate of 10%, maturing in 6 years at par

value($100). The discount rate is 9%.

Solution: N=6; PMT=10; FV=100; I/Y=9%;

Using the Texas Instrument BA II Plus Professional calculator: then PV=104.48.

• Example 2: A market value of a security is $ 98.50. Calculate the discount rate if the security has coupon

rate of 10%, maturing in 6 years at par value($100).

Solution: N=6; PMT=10; FV=100; PV=-98.50;

Using the Texas Instrument BA II Plus Professional calculator: then I/Y=10.34%.

• Note:Give attention to the sign of the cash flows
















14















www.edupristine.com















14

Computing The Value Of A Zero Coupon Bond

• Value of a Zero Coupon Bond• It is the present value of the face value of the bond.

Value = Maturity Value / (1+i)Number of years *2

• In the above formula we are using the semi-annual discount rate to value the bond. The annual ratecan also be used.





15

Computing The Value Of A Zero Coupon Bond




www.edupristine.com




15

How Discount Rates And Maturity Date Affect Price

• Interest rates and Bond Values are inversly related

• A decrease in the interest rate will result in an increase in the bond price as the bond is giving a

higher coupon rate compared to the reduced market interest rate

• As a result, the price yield curve is a downward sloping curve

• Changes in Value with Passage of Time:

• Whether the bond is trading at a premium or at a discount,

as a bond approaches maturity, its value converges to the par value.









16

How Discount Rates And Maturity Date Affect Price








www.edupristine.com








16

Bond Valuation

• Pull to Par is the effect in which the price of a bond converges to par value as time passes.At maturity the price of a debt instrument in good standing should equal its par or face value.

• Pull to Par is the phenomenon that as time passes, the price of a credit instrument in good standingmoves towards its par value. The nearer to maturity the greater the influence because the security willonly pay out the stated principal amount

• The calculation process of the bond amortization (Pull to Par ) is in the next slide..





17




www.edupristine.com




17

Bond Valuation: Pull To Par Concept

Price of $100 Face Value Bond Yielding 6%versus Years to Maturity At Various Coupons (4%

- 8%)$140$130

$120

$110

$100

$906.00%

7.00%

8.00%


Years to Maturity30 121416182022242628

$90

$80

$70

$60 4.00%

5.00%

6.00%

Price “pulled to par” as bond nears maturitymaturity

Bond Valuation: Pull To Par Concept

Price of $100 Face Value Bond Yielding 6%versus Years to Maturity At Various Coupons (4%

- 8%)


Years to Maturity2468101214 0

Price “pulled to par” as bond nears maturitymaturity

Pull To Par

• Consider two bonds. One trading at a discount and the other trading at a premium:

Bond-Discount

Coupon 5%

Tenure 10

YTM 10%

Face Value 100

FY 0 FY 1 FY 2 FY 3 FY 4Price Bond-Discount


Price Bond-Discount $69.28 $71.20 $73.33 $75.66 $78.22Price Bond-Premium $138.61 $135.54 $132.32 $128.93 $125.38

$0.00$20.00$40.00$60.00$80.00

$100.00$120.00$140.00$160.00

FY 0 FY 2 FY 4 FY 6

Pull to Par

Price Bond-Discount

• Consider two bonds. One trading at a discount and the other trading at a premium:

Bond-Premium

Coupon 10%

Tenure 10

YTM 5%

Face Value 100

FY 4 FY 5 FY 6 FY 7 FY 8 FY 9 FY 10


$78.22 $81.05 $84.15 $87.57 $91.32 $95.45 $100.00

$125.38 $121.65 $117.73 $113.62 $109.30 $104.76 $100.00

FY 6 FY 8 FY 10 FY 12

Pull to Par

Price Bond-Discount Price Bond-Premium

Arbitrage-free Valuation Approach

• Discounting all cash flows of a bond with the same discount rate is a flaw in the traditional approach.

• In the arbitrage free valuation approach, each cash flow is discounted by the discount rate that

pertains to the maturity of that cash flows. This discount rate is nothing but the Spot Rate

• We had studied earlier about STRIPS

• As per this approach, the value of the Treasury Bond as a whole should be equal to the value of its

individual parts

• Each part =

• If this is not the case, a person can achieve arbitrage-free profits by buying the whole and selling the

parts or vice-versa







individual parts

• Each part =


parts or vice-versa

20

periodsrate/2Spot1flowCash






individual parts

• Each part =


parts or vice-versa

www.edupristine.com






individual parts

• Each part =


parts or vice-versa

20

Questions

1. If the current yield is 8%, what is the value of a security carrying a annual coupon of 7%, maturing in 8years, redeemable at par value of $1,000?

A. $942.53B. $1,000C. $1,059.71

2. If the current value of a bond is $1,065, what is the YTM of the bond carrying a annual coupon of 7%,maturing in 6 years, redeemable at par value of $1,000?

A. 5.69%B. 7%C. 6.69%

3. The current price of a bond is $985. An increase in the yield by 50 basis points will most likely result in theprice becoming:

A. $1,000B. $1,015C. $970

4. The value of a $10,000 face value zero-coupon bond with 10 years to maturity and a semi-annual pay yieldof 8% is:

A. $2,145.48B. $4,563.95C. $4,635.67



A. $942.53B. $1,000C. $1,059.71


A. 5.69%B. 7%C. 6.69%


A. $1,000B. $1,015C. $970


A. $2,145.48B. $4,563.95C. $4,635.67

21


A. $942.53B. $1,000C. $1,059.71


A. 5.69%B. 7%C. 6.69%


A. $1,000B. $1,015C. $970


A. $2,145.48B. $4,563.95C. $4,635.67

www.edupristine.com


A. $942.53B. $1,000C. $1,059.71


A. 5.69%B. 7%C. 6.69%


A. $1,000B. $1,015C. $970


A. $2,145.48B. $4,563.95C. $4,635.67

21

Solutions

1. A. $942.53

2. A. 5.69%

3. C. $970. This is a trick question requiring no calculations as the value of a bond will decrease asyields increase.

4. B. $4,563.95 [ = 10000/(1 + 0.08/2)] ^ (10*2)


1. A. $942.53

2. A. 5.69%

3. C. $970. This is a trick question requiring no calculations as the value of a bond will decrease asyields increase.

4. B. $4,563.95 [ = 10000/(1 + 0.08/2)] ^ (10*2)


Key Issues In Features Of Debt Securities

• Bond‘s Indenture

• Basic features of a Bond

• Definitions

• Redemption and Retirement of Bonds

• Embedded Options

• Institutional Investors


Key Issues In Features Of Debt Securities


Bond‘s Indenture

A bond‘s Indenture is the document which specifies the rights and obligations of both the issuer and thebuyer of the bond.

– Contains Affirmative Covenents wich requires the borrower to affirm to certain actions.– Examples:

• Maintaining minimum financial ratios• Pay interest and principal on a timely basis

– Contains Negative Covenants which prevent the borrower from doing certain things.– Examples:

• raising additional amount of debt• pledging the same assets







24






www.edupristine.com






24

Example

• Company XYZ’s debt is trading in the market. A covenant in its bond indenture states that furtherborrowing above $100 million is restricted. This is:A. An Affirmative CovenantB. A Negative CovenantC. A Positive Covenant


• Company XYZ’s debt is trading in the market. A covenant in its bond indenture states that furtherborrowing above $100 million is restricted. This is:A. An Affirmative CovenantB. A Negative CovenantC. A Positive Covenant


Basic Features Of A Bond

Basic Features of a Bond:• Can be issued in the domestic or foreign currency• Make annual or semi-annual payment of interest• Bonds that do not pay interest during their tenure are called Zero-coupon bonds• Step-up notes are bonds for which the coupon rate increases one or more times during their tenure• Deferred-coupon bonds are bonds for which the initial coupon payments are deferred for a certain

period• Floating-rate securities bonds whose coupon is linked to some benchmark reference rate like the

LIBOR rate. (Varities: Inverse Floaters and Inflation-indexed bonds)





26




www.edupristine.com




26


• Optionality: A bond may contain an embedded option; that is, it grants option like features to thebuyer or issuer:

• Callable Bond—Some bonds give the issuer the right to repay the bond before the maturity date onthe call dates. With some bonds, the issuer has to pay a premium, the so called call premium. This ismainly the case for high-yield bonds.

• Putable Bond—Some bonds give the bond holder the right to force the issuer to repay the bondbefore the maturity date on the put dates





27




www.edupristine.com




27


Basic Features of a Bond:• Floating-rate securities bonds whose coupon is linked to some benchmark reference rate like the LIBOR

rate. (Varities: Inverse Floaters and Inflation-indexed bonds)• Cap is the maximum interest that will be paid by the borrower• Floor is the minimum interest that will be received by the lender• Combination of both is called a Collar


Basic Features of a Bond:• Floating-rate securities bonds whose coupon is linked to some benchmark reference rate like the LIBOR

rate. (Varities: Inverse Floaters and Inflation-indexed bonds)• Cap is the maximum interest that will be paid by the borrower• Floor is the minimum interest that will be received by the lender• Combination of both is called a Collar


Questions

1. The price per $1 of a par value bond is $1.2538 when the par value is $10,000. The quoted price andthe dollar price is closest to:

2. If the interest rate falls, the reinvestment income from a Zero-coupon bond will:A. IncreaseB. DecreaseC. Unaffected

Quoted Price Dollar Price

A 125 3/8 $12,538

B 122 1/8 $11,438

C 125 1/2 $14,620




29



www.edupristine.com



29

Answers

1. A. Dollar Price = 1.2538 * 10,000 = 12,538

Quoted Price = 12,538/1,000 = 125 3/8

2. C. Unaffected

© Neev Knowledge Management – Pristine 30 www.edupristine.com30

Definitions

• Accrued interest: Interest accrued on a bond from the last coupon date and the date of sale of thebond

• Full Price/Dirty Price: Total amount paid by the buyer to the seller for the bond• Clean price: Full price less the accrued interest

Dirty Price = Clean Price + Accrued Interest


• Accrued interest: Interest accrued on a bond from the last coupon date and the date of sale of thebond

• Full Price/Dirty Price: Total amount paid by the buyer to the seller for the bond• Clean price: Full price less the accrued interest

Dirty Price = Clean Price + Accrued Interest


Questions

1. A person pays $1,050 for a bond. The accrued interest till the date of purchase was $36. The cleanprice of the bond is:

A. $1,050B. $1,086C. $1,014


1. A person pays $1,050 for a bond. The accrued interest till the date of purchase was $36. The cleanprice of the bond is:

A. $1,050B. $1,086C. $1,014


Answers

1. C. $1,014

© Neev Knowledge Management – Pristine 33 www.edupristine.com33

Redemption And Retirement Of Bonds

• Non amortizing securities pay only interest during the tenure of the bond and the entire principal isrepaid on the maturity of the bond

• Amortizing securities repay both the the interest and the pricipal amount over the tenure of the bond



• Non amortizing securities pay only interest during the tenure of the bond and the entire principal isrepaid on the maturity of the bond

• Amortizing securities repay both the the interest and the pricipal amount over the tenure of the bond


Redemption and Retirement of Bonds

• Prepayment option allows the borrower to repay the principal before the due date• Call option on a bond is similar to a prepayment option and allows the borrower to “call“ repay

the entire or part of the bond outstanding• Nonrefundable bonds prohibit the issuer from redeeming a bond by issuing fresh bonds at a

lower coupon rate


Redemption and Retirement of Bonds

• Prepayment option allows the borrower to repay the principal before the due date• Call option on a bond is similar to a prepayment option and allows the borrower to “call“ repay

the entire or part of the bond outstanding• Nonrefundable bonds prohibit the issuer from redeeming a bond by issuing fresh bonds at a

lower coupon rate



• Sinking Fund Provision require the issuer to repay the principal amount over the life of the bondthrough regular payments.

• Accelerated Sinkind Fund Provision allows the Issuer to repay an amount more than that stipulated bythe Sinking Fund provisions



• Sinking Fund Provision require the issuer to repay the principal amount over the life of the bondthrough regular payments.

• Accelerated Sinkind Fund Provision allows the Issuer to repay an amount more than that stipulated bythe Sinking Fund provisions


Embedded Options

• Options favourable to the Issuer:

– Call Provisions: grant the Issuer the right to redeem the bond before the maturity date at a fixed price.

– Cap: sets the maximum amount of interest that will be paid to the bondholder for a floating rate bond.

– Prepayment option: allows the Issuer to prepay amount before maturity.

– Accelerated Sinkind Fund Provision: allows the Issuer to reapy an amount more than that stipulated bythe Sinking Fund provisions.







37






www.edupristine.com






37

Embedded Options

• Options favourable to the Bondholder:

– Put Provisions: grant the bondholder the right to demand repayment of the amount before the maturitydate at a fixed price.

– Floor: sets the minimum amount of interest that will be paid to the bondholder for a floating rate bond.

– Conversion Option: grants the bondholder to convert the bond into a fixed number of shares of theissuer.






38





www.edupristine.com





38

Questions

1. Assuming a common issuer and maturity, which of the following bonds will most likely have the lowestyield?

A. A plain vanilla bondB. A bond with an embedded call optionC. A bond with an embedded put option


1. Assuming a common issuer and maturity, which of the following bonds will most likely have the lowestyield?

A. A plain vanilla bondB. A bond with an embedded call optionC. A bond with an embedded put option


Solutions

1. B

– An embedded call option is favorable to the bond issuer. Further, its price cannot appreciate much in a falling

interest rate scenario since the bond since the issuer would chose to exercise its call option. Hence, to

compensate, it would trade at a higher yield than the other options.


1. B

– An embedded call option is favorable to the bond issuer. Further, its price cannot appreciate much in a falling

interest rate scenario since the bond since the issuer would chose to exercise its call option. Hence, to

compensate, it would trade at a higher yield than the other options.


Questions

1. Which of the following is true about a bond with a deferred call provision?:A. It could be called at any time after the deferment periodB. Principal repayment can be deferred until it reaches maturityC. It could not be called right after the date of issue

2. Which of the following is right:A. A put provision will benefit the buyer in times of rising interest ratesB. A put provision will benefit the buyer in times of falling interest ratesC. A put provision will benefit the seller in times of rising interest rates

3. An mortgage security:A. Repays only the principal amount during the tenure of the securityB. Repays the principal and the interest amount during the tenure of the securityC. Cannot be retired earlier than the period of the security





41




www.edupristine.com




41

Answers

1. A. A deferred call provision means the issue is initially (say, for the first 5 to 7 years) non-callable, after

which time it becomes freely callable. In other words, there is a deferment period during which time the bond

cannot be called, but after that, it becomes freely callable.

2. A. A put provision will benefit the buyer in times of rising interest rates.

3. B. Repays the principal and the interest amount during the tenure of the security


1. A. A deferred call provision means the issue is initially (say, for the first 5 to 7 years) non-callable, after

which time it becomes freely callable. In other words, there is a deferment period during which time the bond

cannot be called, but after that, it becomes freely callable.

2. A. A put provision will benefit the buyer in times of rising interest rates.

3. B. Repays the principal and the interest amount during the tenure of the security


Agenda

• Features of Debt Securities

• Risks Associated with Investing in Bonds

• Overview of Bond Sectors and Instruments

• Understanding Yield Spreads







• Interest Rate risk: refers to the effect of change in the market interest rates on the price of the bond.

The overall interest rates will change from the levels extant when the security is sold, causing an

opportunity cost

• Yield Curve risk: results from the change in the yield curve and its impact on the bond

• Call Risk: is the risk that the Issuer will exercise the call option on a callable bond if the interest rates

fall

• Prepayment risk: is the risk to prepayment of the principal amount before its due date

• Reinvestment risk: is the risk that the cash flows from the securities will be reinvested at a lower rate

• Credit risk: is the risk that the borrower will default on the installment payments

Risks Associated with Investing in Bonds




opportunity cost



fall




44



opportunity cost



fall





www.edupristine.com



opportunity cost



fall




44

• Currency risk – that exchange rates with other currencies will change during the security's term,causing loss of buying power in other countries

• Default risk – that the issuer will be unable to pay the scheduled interest payments due to financialhardship

• Repayment of principal risk – that the issuer will be unable to repay the principal due to financialhardship

• Soveriegn risk: refers to the risk arising out of change in government policies

• Volatility risk: refers to the change in value of securities which have embeded options as a result of

interest rate volitality









45








www.edupristine.com







45

• Inflation risk: It refers to the risk of errosion of the purchasing power of the returns from the securityas a a result of unexpected rise in inflation, – that the buying power of the principal will decline duringthe term of the security .

• Liquidity risk: The risk that the security will sell for a amount lower than its fair value due to lack ofliquidity. The buyer will require the principal funds for another purpose on short notice, prior to theexpiration of the security, and be unable to exchange the security for cash in the required time periodwithout loss of fair value

• Exchange rate risk: Is the uncertainity regarding movement in the exchange rates and theconsequent impact on the rerurns from the securities






46





www.edupristine.com




46

Discount, Premiuim, At Par

• If the coupon rate of the security is equal to the market yield then the bond will sell at par

Coupon Rate = Market Yield --- Price = Par Value

• If the coupon rate of the security is more than the market yield then the bond will sell at premium

Coupon Rate>Market Yield - Price> Par Value

• If the coupon rate of the security is less than the market yield then the bond will sell at discount

Coupon Rate<Market Yield - Price<Par Value

If Interest Rates Increase -- Price of a Bond Decreases

If Interest Rates Decrease -- Price of a Bond Increases










47









Imp

www.edupristine.com









47

Maturity, Coupon, Options, Yield Affect Interest RateRisk

VariableDuration or Interest

Rate RiskMaturity in Longer Higher

Coupon Rate is Higher LowerEmbedded Call Option LowerEmbedded Put Option Lower


Maturity, Coupon, Options, Yield Affect Interest RateRisk

Duration or Interest

Rate Risk

Imp


Present Value Of The Cash Flow

• Present value of an annuity An annuity is a series of equal payments or receipts that occur at evenlyspaced intervals

• The current worth of a future sum of money or stream of cash flows given a specified rate of return.Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower thepresent value of the future cash flows.

• In example Assume the Interest Rate is 5% so the Discounted cash flow is as follows:


• Present value of an annuity An annuity is a series of equal payments or receipts that occur at evenlyspaced intervals

• The current worth of a future sum of money or stream of cash flows given a specified rate of return.Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower thepresent value of the future cash flows.

• In example Assume the Interest Rate is 5% so the Discounted cash flow is as follows:

trFVPV)1(


trFVPV)1(

Callable Bonds

• Bonds which have an embedded call option give the Issuer the right to call the bond before its maturity

• Duration is a good measure when the changes in yield are small

• However if the yield changes are high then we use the measure of convexity

• Convexity is a measure of the curvature of the price/yield relationship

• Value of a callable bond = Value of a option-free bond – Value of embedded option

• As the yield falls, the price of the bond increases

• But this increase in the price of a bond is capped in the case of a callable bond at the call price









50








www.edupristine.com








50

Duration And Dollar Duration

Duration of a Bond:

• It is the sensitivity of the price of the bond in response to a change in the interest rates/yield

Duration = - (Percentage change in bond price/Percentage change in Yield)

negative sign is used because of the inverse relation between yield and bond prices

Thus, increase in the yield results in a fall in the bond price

Dollar Duration

• The approximate dollar price change for a 100bps change in yield.

• Given by:


Duration of a Bond:





Dollar Duration


• Given by:

51

decimal)inYieldin(ChangePrice)(Inintial2RiseYieldifPrice-DeclineYieldifPrice

Duration of a Bond:





Dollar Duration


• Given by:

www.edupristine.com

Duration of a Bond:





Dollar Duration


• Given by:

51

decimal)inYieldin(ChangePrice)(Inintial2RiseYieldifPrice-DeclineYieldifPrice

Interest Rate Risk Of A Floating Rate Security

• Floating rate security: It is one whose coupon rate is reset at each coupon date so that it matched the

current market yield. It is typically a reference rate(say, LIBOR) + additional margin

• This implies that a floating rate security will always sell at par

• However, it is possible for a floating rate security to quote below or above par if there is a change in

the market yield in between the reset dates

Example: If a floating rate security which pays interest every six months, is reset in the month of April

and the interest rates fall, it will trade at a premium till the next reset date in October









52

Interest Rate Risk Of A Floating Rate Security








www.edupristine.com








52

Yield Curve Risk

• Yield Curve: Shows the relationship between Yield and Maturity

• Yield curve risk refers to the change in the Yield curve

• The risk of experiencing an adverse shift in market interest rates associated with investing in a fixed

income instrument.

• The risk is associated with either a flattening or steepening of the yield curve, which is a result of

changing yields among comparable bonds with different maturities

With reference to a Portflolio of bonds: a non parallel shift in the yield curve will result in varying

impact on short maturity and long maturity bonds, makes duration a poor measure for Portfolio of

bonds





income instrument.





bonds

53




income instrument.





bonds

www.edupristine.com




income instrument.





bonds

53

Reinvestment Risk

Reinvestment Risk

• Reinvestment risk: Interest and Principal payments that are available to be reinvested will be done so at a

lower rate than the security that generated the proceeds.

• A security which is amortising, with higher coupon; a call feature; a prepayment option; will have a higher

reinvestment risk

• Prepayable securities have a higher reinvestment risk because a reduction in the interest rates results in an

increase in prepayments which will have to be reinvested at the lower rate

• Zero-Coupon bonds eliminate reinvestment risk.


Reinvestment Risk




reinvestment risk




54

Reinvestment Risk




reinvestment risk




www.edupristine.com

Reinvestment Risk




reinvestment risk




54

Credit Risk

• A security issued by the U.S. government is considered risk free as it has no credit risk

• Default risk premium:

– The spread over a risk free asset of similar maturity for bearing the credit risk of the security.

• Credit spread risk:

– The increase in this default risk premium

• Downgrade risk:

– The risk that a bond‘s rating maybe downgraded by the credit rating agency which results in an increase

the return demanded by the investors for bearing the increased credit risk







• Downgrade risk:



55






• Downgrade risk:



www.edupristine.com






• Downgrade risk:



55

Liquidity Risk

• Liquidity Risk: The risk that the investor will have to sell a bond below its indicated value.– Indicated value: last traded price

• The primary risk measure – The bid/ask spread

• The wider the bid-ask spread, the lower the liquidity, the greater the liquidity risk.

• Retail Investors– For investors who plan to hold the security until maturity, not need to mark to market and liquidity risk is

not a major concern.

• Institutional Investors– Need to mark to market, even if they plan to hold until maturity.– This is needed to calculate Net Asset Value (NAV)








56







www.edupristine.com







56

Exchange Rate Risk

• Exchange Rate Risk:– The risk of receiving less of the domestic currency when investing in a bond that makes payments in a

currency other that the manager’s domestic currency is called exchange rate risk or currency risk.

• When you invest in a bond whose payments are not in your domestic currency, the cash flows youreceive depend on the exchange rate at the time of the cash inflows.

• If the foreign currency depreciates relative to the domestic currency, you receive less units of thedomestic currency upon exchange.






57





www.edupristine.com





57

Inflation Risk

• Inflation risk: refers to the risk of errosion of the purchasing power of the returns from the security as a

result of unexpected rise in inflation

• Example: Last year, you purchased a 1 year zero coupon bond with a 8% interest rate and the inflation was

3%. That means your purchasing power only increased by (8%-3% = 5%)..

• Inflation protection bonds eliminate inflation risk.


• Inflation risk: refers to the risk of errosion of the purchasing power of the returns from the security as a

result of unexpected rise in inflation

• Example: Last year, you purchased a 1 year zero coupon bond with a 8% interest rate and the inflation was

3%. That means your purchasing power only increased by (8%-3% = 5%)..

• Inflation protection bonds eliminate inflation risk.


Yield Volatility

• Price of a Callable Bond = Price of Option Free Bond – Price of Embedded Option

• Price of a Putable Bond = Price of Option Free Bond + Price of Embedded Option

Type of Embedded Option Volatility Risk Due toCallable Bonds An increase in expected yield

volatilityPutable Bonds A decrease in expected yield volatility


• Price of a Callable Bond = Price of Option Free Bond – Price of Embedded Option

• Price of a Putable Bond = Price of Option Free Bond + Price of Embedded Option

Volatility Risk Due toAn increase in expected yieldvolatilityA decrease in expected yield volatility


Questions

1. Ted works for a fixed income fund; he wants to buy a bond for his portfolio. Which of the following bondswill have the least sensitivity to interest rate risks

A. A 10% coupon bond with a maturity of 15 yearsB. A zero-coupon bond with a maturity of 20 yearsC. A 8% coupon bond with a maturity of 15 years

2. A company has to make a balloon loan payment of $5,000,000 in 3 years. Which of the following options isbest for the company to make repayment and to minimize reinvestment risk. All bonds are non-callable andare otherwise similar except as noted with face values of $5,000,000. Market rates are at 5.0%.

A. 4-year, zero coupon bond priced to yield 5.5%B. 2-year, zero-coupon bond priced to yield 9.0%.C. 3-year, zero coupon bond priced to yield 5.0%.

3. Which of the following has the highest interest rate risk?:A. Zero coupon bondB. Floating rate bondC. Fixed coupon bond







60






www.edupristine.com






60

Questions (Cont...)

4. The value of a putable bond will be:A. Higher than the value of an option-free bond.B. Lower than the value of an option-free bond.C. More or less equal to the value of an option-free bond

5. On the reset date, the value of a floating rate security will be:A. Trading at a premium.B. Trading at a discount.C. Trading at par

6. Which of the following is least correct?:A. A Treasury security has no credit risk.B. A floating rate bond protects against inflation risk.C. A AAA bond has no credit risk.





61




www.edupristine.com




61

Solutions

1. A. The longer the maturity the higher the interest rate sensitivity. Lower coupon rates also increasethe sensitivity of bond prices to changes in interest rates. A ZCB has the highest sensitivity to interestrate changes

2. C. Since all the choices are non-callable, the treasurer will prefer a zero-coupon to a coupon bond.While a bond investor can eliminate price risk by holding a bond until maturity, he usually cannoteliminate reinvestment risk. One exception is zero-coupon bonds, since these bonds deliverpayments in one lump sum at maturity. Although the 3-year coupon bond fulfills the treasurer’srequirement concerning funds for repayment, it does not minimize reinvestment risk.Among the zero-coupon bonds, the one that best matches the loan’s maturity will minimizereinvestment risk. The treasurer will thus prefer the 3-year, zero-coupon bond. If he purchased the 4-year zero-coupon bond, he would have to sell the bond prior to maturity to payoff the loan and wouldface price risk. The 2-year zero-coupon bond is attractive because of the higher yield. However, thebond matures one year before the loan is due and would expose the firm to reinvestment risk.

3. A. Zero coupon bond4. A. Higher than the value of an option-free bond5. C. Trading at par6. C. A AAA bond has no credit risk





62




www.edupristine.com




62

Agenda











Key Issues In Overview Of Bond Sectors And Instruments

• Characteristics of Government Securities

• Types of Securities

• Stripped Treasury Securities

• Securities issued by US Federal Agencies

• Mortgage-backed securities

• Collateralized Mortgage Obligation

• Securities issued by Municipalities in US

• Securities issued by Corporations

• Asset-Backed Security

• Collateralized debt Obligation

• Issuing bonds in the Primary market


• Characteristics of Government Securities

• Types of Securities

• Stripped Treasury Securities

• Securities issued by US Federal Agencies

• Mortgage-backed securities

• Collateralized Mortgage Obligation

• Securities issued by Municipalities in US

• Securities issued by Corporations

• Asset-Backed Security

• Collateralized debt Obligation

• Issuing bonds in the Primary market

64

Key Issues In Overview Of Bond Sectors And Instruments


Characteristics Of Government Securities

Government securities are considered to be free of default risk. It is also known as sovereign debt.

Bonds issued by national governments in foreign currencies are normally referred to as sovereignbonds.

However for a person in the US, the sovereign debt of another company will have credit risk.





65

Characteristics Of Government Securities




www.edupristine.com




65

Types Of Government Securities

Types of Securities

• Treasury Securities:

– Treasury Bills: Maturity of less than one year and do not make interest payment. Issued at discount topar.

– Treasury Notes: Pay semiannual interest rates. Maturities of 2, 3, 5, 10 years.– Treasury Bonds: Pay semiannual interest rates. Maturities of 20, 30 years.– Treasurt Inflation Protected Securities(TIPS): Pay semiannual interest rates. Maturities of 5, 10, 20 years.

The par value is adjusted semi annually to account for the change in inflation.

• On-the-run Treasury Securities: Most recent auctioned securities.

• Off-the-run Treasury Securities: Older issued securities


Types of Securities







66

Types of Securities







www.edupristine.com

Types of Securities







66

Stripped Treasury Securities

• Separate Trading of Registered Interest and Principal Securities(STRIPS): Introduced by Treasury in

1985

• As the Treasury did not issue and zero-coupon bonds, bankers separated the coupons due on normal

securities and sold the coupons and the principal amount as zero-coupon bonds

– Coupon STRIPS: STRIPS created from coupon payments

• Coupon STRIPS: Acrrued Interest is Taxed every year even though interest is not paid until maturity.

• Thus, they have negative cash flows until maturity.

– Principal STRIPS: STRIPS created from the Principal

• For some foreign players, the interest gained on Principal STRIPS are taxed as capital gains tax.

• They are preferred by those foreign entities.



1985









67


1985









www.edupristine.com


1985









67

Types Of U.S. Federal Agencies Securities

Securities Issued by US Federal Agencies

Debt securities issued by various US Federal Agencies are called Agency Bonds. These can be:

– Federally related institutions

• Export-Import Bank of the United States

• Goverment National Mortgage Association (Ginnie Mae)

– Government sponsered enterprises(GSEs)

• Federal National Mortgage Association (Fannie Mae)

• Federal Home Loan Mortgage Corportion (Freddie Mac)

• These two institutions issued CMO‘s.

Debentures are unsecured securities. Generally issued by GSEs












68

Types Of U.S. Federal Agencies Securities











www.edupristine.com











68

Mortgage-backed Securities

• MBS is a security which is backed by a pool of loans. These pool of loans act as a collateral for these

securities and also provide the regular cash flows to service these securities.

• Cash Flows from a mortgage:

– Interest payment

– Scheduled principal repayment

– Excess Principal repayment

• As there is no restriction on the repayment of the principal amount, investors face a high Prepayment

risk.









risk.

69








risk.

www.edupristine.com








risk.

69


• Mortgage Loans

– It is a loan secured by the collateral of some specified real estate.

– Default -“Foreclosure“

– Each payment includes both interest and principal -> Ammortized

– Prepayment has no penalty and can be:

• For the entire principal outstanding

• Partial Amount – called Curtailment

• Mortgage Pass-through Security:

– Homeowners' payments pass from the original bank through a government agency (like Ginnie Mae, Fannie

Mac, Freddie Mac) or investment bank to investors of the securities in proportion of their holding. That is why the

name, Pass-through.

– Prepayments are more predictable based on historical prepayment experience.


• Mortgage Loans










name, Pass-through.


70

• Mortgage Loans










name, Pass-through.


www.edupristine.com

• Mortgage Loans










name, Pass-through.


70


• Stripped MBS:

– These STRIPS are either Interest-only(IO) of Principal-only(PO) STRIPS. The holder of a IO loses out on

interest as a result of prepayment of the principal. The PO gains as a result of prepayment.

• Collateralized Mortgage Obligations (CMO)

– Created to distribute prepayment risk among different classes of bonds.


• Stripped MBS:





71

• Stripped MBS:





www.edupristine.com

• Stripped MBS:





71

Collateralized Mortgage Obligation

• This is complex version of a Mortgage Passthrough security. The payments are not disbursed in the

proportion of the holding. Tranches are created out of the passthrough security. These Tranches

have varying properties. For ex: A CMO with Tranche I, II and III maybe structured such that Tranche

I is repaid first followed by Tranche II and Tranche II.

• The reason for creating a CMO is:

– To redistribute the prepayment risk. In the above example: Tranche III bears most of the credit risk and

Tranche I bears most of the prepayment risk.

– To create securities with varying maturities. Trance II will have the longest maturity in the above example.

• Investors invest in a particular Tranche as per their requirements depending on the risks they are

willing to take on of the risk they want to avoid.












72











www.edupristine.com











72

Securities Issued By Corporations

• Structured Notes: These are basically debt securities that also contains an embedded derivativecomponent. One example is Equity Linked Notes (ELNs) wherein the return on the debt instrument islinked to the return on the equity.

• Commercial Paper: is a short-term, unsecured debt instrument used by corporate to raise funds.Maturities range from 2 days to 270 days.– Directly-placed paper is sold directly to the investors (large investors).– Dealer-placed paper is sold to investors through a commercial-paper dealer.

• Certificate of Deposit: is issued by banks to raise money from the public. Negotiable CDs can bebought and sold in the secondary market.

• Bankers Acceptance: is a bank gaurantee that a loan will be repaid. This is used primarily tofacilitate foreign trade.






73





www.edupristine.com





73

Asset-Backed Security

• Asset-backed security: It is a security whose value and income payments are backed by a specified

pool of underlying assets. These can be auto loans, corporate receivables, etc.

• In order to enhance the rating of these securities, the financial assets are transferred to a Special

Purpose Vehicle(SPV). This ensures that the SPV becomes a bankruptcy remote entity and the

securities receive a higher rating resulting in lower borrowing costs

• Apart from the above, the SPV may go for some external credit enhancements to improve the ratings

it receives:

– Corporate Guarantee

– Letters of Credit

– Bond Insurance








it receives:



– Bond Insurance

74







it receives:



– Bond Insurance

www.edupristine.com







it receives:



– Bond Insurance

74

Collateralized Debt Obligations (CDO‘s)

• Collateralized Debt Obligation(CDO): It is a type of structured asset-backed security (ABS) whose

value and payments is derived from a underlying pool of debt securities.

• The pool can consist of one or more of the following:

– US Domestic Investment grade and high yield corporate bonds (CBO)

– US Domestic Bank Loans (CLO)

– Emerging market bonds (CBO)

– Special Situation loans and distressed debt

– Foreign bank loans (CLO)

– Asset backed securities

– Residential and commercial MBS’s

– other CDOs

• The CDO is structure into Tranches, each with its own rating.












– other CDOs


75

Collateralized Debt Obligations (CDO‘s)











– other CDOs


www.edupristine.com











– other CDOs


75

Primary And Secondary Bond Markets

Primary market

• The deal is underwritten by investment bankers. This can be by way of:

– Firm Commitment (or)

– Best Efforts basis

• In private placements, the issuer must furnish a private placement memorandum. This is similar to a

prospectus except it does not contains ‚“ non-material“ information and not subject to SEC review.

Secondary market

• Fair values are determined

• Liquidity

• Can be traded

– Over the Counter

– Over Exchanges


Primary market






Secondary market


• Liquidity

• Can be traded


– Over Exchanges

76

Primary And Secondary Bond Markets

Primary market






Secondary market


• Liquidity

• Can be traded


– Over Exchanges

www.edupristine.com

Primary market






Secondary market


• Liquidity

• Can be traded


– Over Exchanges

76

Questions

1. An investor wants to invest in a security with the least prepayment risk. From the following list ofsecurities he is least likely to invest inA. Mortgage loansB. Mortgage pass throughsC. CMOs

2. Transferring the assets to a Special Purpose Vehicle helps do all of the following except:A. Improve the credit ratings of the issue.B. Creates a bankruptcy remote entity.C. Reduce the risk associated with the securities.

3. A bond has more reinvestment risk when?A. It is bullet payment bondB. It has an embedded put optionC. It has higher coupon rate than currently available market interest rate

4. A Treasury Security with a 10 year maturity is called a:A. Treasury BillB. Treasury BondC. Treasury Note






77





www.edupristine.com





77

Questions(Cont...)

5. Which of the following bonds has the highest risk:A. Unlimited tax general obligation bondsB. Prefunded BondsC. Revenue Bonds

6. Which of the following is not an reason for creating a CMO:A. To reduce the total riskB. To redistribute the prepayment riskC. To create securities with varying maturities

7. Which of the following bonds is not an external credit enhancement for a SPV:A. Letters of CreditB. Over CollateralizationC. Bond Insurance





78




www.edupristine.com




78

Solutions

1. A. Mortgage pass throughs have lower prepayment risks as compared to individual mortgages as the

prepayment risk is spread over the entire portfolio of loans pooled in the pass through. CMOs or

Collateralized Mortgage Obligations are a type of mortgage pass throughs.

2. C. By converting the assets to liquid cash the originating agency can improve its liquidity ratios. The

liquid cash can then be reused in the business. By improving its capital adequacy ratio it can improve

its credit ratings. Also a SPE can be structured in such a manner that it is bankruptcy remote.

However the risk associated with the securities is not removed.

3. C. The correct answer is It has higher coupon rate than currently available market interest rate.

Higher the coupon rate, greater the reinvestment risk.

4. C. Treasury Note

5. C. Revenue Bonds

6. A. To reduce the total risk

7. B. Over Collateralization











4. C. Treasury Note

5. C. Revenue Bonds



79










4. C. Treasury Note

5. C. Revenue Bonds



www.edupristine.com










4. C. Treasury Note

5. C. Revenue Bonds



79

Extra-Quiz Questions

1. A floating rate issue has the following provision in which the coupon rate is calculated as 6-monthLIBOR – 80 basis points. The issue has a floor at 5.5%. If the 6-month LIBOR on the reset date is5.8%, the coupon rate is closest toA. 4.5%B. 5.5%C. 5.0%

2. A $100 par value bond has duration of 12.7 If the price rises to 104.57 when the yield declines by 50basis points, the price when the yield drops by 50 basis points is closest toA. 95.7B. 91.8C. 92.5

3. Carl and Karen are CFA Level I candidates. Carl says that a zero coupon bond has higher interestrate risk than a coupon bond of the same maturity. While Karen says that a callable bond has highervolatility risk than an option-free bond. Which of the two statements are most likely correct





80

Carl Karen

A No Yes

B Yes No

C Yes Yes




www.edupristine.com




80


4. For a 100 basis points downward shift in the yield curve which of the following bonds will have thelowest percentage price changeA. An option-free bondB. A callable bondC. A putable bond

5. A $ 10mn par value bond can be redeemed at the following pricesSuppose the investor decides to redeem the $10 mnbond on 31st December 2005.The price that the investor will get is closest toA. $10.4 mnB. $12mnC. $16mn

6. Value of a 15-year, 8.5% annual coupon bond callable in five years is at 94.4 (prices are statedas a percentage of par). A straight bond that is similar in all other aspects as the callable bond ispriced at 100.0. Which of the following is closest to the value of the call option?A. 2.8B. 4.4C. 5.6





81




2001- 2003 106%2003-2005 104%2005-2007 102%

2007 onwards 100%

www.edupristine.com




81

2007 onwards 100%


7. Carl an analyst with a fixed income hedge fund states that investments in high yield securities fromemerging economies carries a number of risk factors. Which of the following is least likely to be listedas a risk when investing in high yield securities from emerging marketsA. Sovereign riskB. Exchange rate riskC. Downgrade risk

8. What is least likely to be accurate regarding Interest rate risk?A. It is a risk of having to reinvest at rates that are lower than what an investor is currently receivingB. Interest rate risk is commonly measured by the bond's durationC. Can be reduced by buying bonds with longer duration




82



www.edupristine.com



82

Solutions

1. B.– Coupon rate = ref rate + quoted margin = 5.8% - 80 basis points = 5.0%. Since the floater has a floor at

5.5%. The coupon is set to 5.5% on the reset date.2. B.

Duration = Price if yield declines – price if yield rises2 * (initial price) * (change in yield in decimals)

Price if yield declines = 104.57 – 12.7*2*100*0.005 = 91.83. B.

– Callable options have lower volatility risk than option-free bond because of the embedded call option inthe bond. Zero-coupon bonds have a higher interest rate risk and their prices can change significantly ifthe yields change.

4. B.– The value of a callable bond does not rise as much as a comparable option-free bond. Price of a putable

bond = price of an option-free bond + price of the embedded put. So when the yield curve is shifteddownwards the price of a putable bond will change more than a comparable option-free bond.

5. A.– The redemption price is calculated as $10mn * 104% = %10.4 mn.










83









www.edupristine.com









83

Solutions

6. C.– The bond rated as B+ has low credit worth and hence is highly speculative. Since the objectives of the

fund allow them to invest in only investment grade securities. Sally cannot invest in the 16% 10-yearcoupon bond.

7. C.– A high yield bond has generally a low-credit and is of speculative nature. Investments in foreign currency

bonds carry exchange rate risks. The bonds also have sovereign risk due to the risk of actions of theforeign government in case of default.

8. B– Interest rate risk can be reduced by buying bonds with a longer duration.







84






www.edupristine.com






84

Five Minute RecapRisks associated withInvesting in Bonds:• Interest Rate risk• Yield Curve risk• Call Risk• Prepayment risk• Reinvestment risk• Credit risk• Currency risk• Default risk• Repayment of

principal risk• Soveriegn risk• Volatility risk• Inflation risk• Liquidity risk• Exchange rate risk

VariableDuration or Interest

Rate Risk

Maturity in Longer Higher

Coupon Rate is Higher Lower

Embedded Call Option Lower

Embedded Put Option Lower

The following features of a security issubject to higher Reinvestment Risk:• Amortising• Higher coupon• Call feature• Prepayment option


Risks associated withInvesting in Bonds:• Interest Rate risk• Yield Curve risk• Call Risk• Prepayment risk• Reinvestment risk• Credit risk• Currency risk• Default risk• Repayment of

principal risk• Soveriegn risk• Volatility risk• Inflation risk• Liquidity risk• Exchange rate risk


Price of a Callable Bond = Price of Option Free Bond – Price of Embedded OptionPrice of a Putable Bond = Price of Option Free Bond + Price of Embedded Option

Interest rate tools used toimplement the Fed‘s monetarypolicy:• Discount rate• Open Market Operations• Bank Reserve requirements• Pursuation

Agency Bonds are issued by various US Federal Agencies• Federally related institutions

• Export-Import Bank of the United States• Goverment National Mortgage Association (Ginnie Mae)

• Government sponsered enterprises(GSEs)• Federal National Mortgage Association (Fannie Mae)• Federal Home Loan Mortgage Corportion (Freddie Mac)

Dirty Price = Clean Price + Accrued InterestDuration or Interest

Rate Risk

Higher

Lower

Lower

Lower


Special Purpose Vehicle(SPV).• Used to enhance the rating of ABS• SPV becomes a bankruptcy remote entity

ratetaxMarginal1*YieldTaxableYieldTaxAfter



Price of a Callable Bond = Price of Option Free Bond – Price of Embedded OptionPrice of a Putable Bond = Price of Option Free Bond + Price of Embedded Option

Expandingeconomy, creditspreads becomenarrowContractingeconomy, creditspreads widen.

Agency Bonds are issued by various US Federal Agencies• Federally related institutions

• Export-Import Bank of the United States• Goverment National Mortgage Association (Ginnie Mae)

• Government sponsered enterprises(GSEs)• Federal National Mortgage Association (Fannie Mae)• Federal Home Loan Mortgage Corportion (Freddie Mac)

fixed income-i

Documents

variablea bond

bond indenture

bonds effect of maturity

overview of bond sectors

maturity value

fixedincome industry

maturity date

fixed income securities