Fixed Income-I

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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

This files has expired at 30-Jun-13 Expect around 15 questions in the exam from today’s lecture

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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 This files has expired at 30-Jun-13 ABS, MBS,CMO,CDO

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Fixed Income (Introduction) Fixed income refers to any type of investment that is not equity, which obligates the borrower/issuer to make payments on a fixed schedule, even if the number of the payments may be variable A bond is simply a promise to pay interest on borrowed money, there is some important terminology used by the fixed-income industry: • The issuer is the entity (company or govt.) who borrows an amount of money (issuing the bond) and pays the interest. • The principal of a bond – also known as maturity value, face value, par value – is the amount that the issuer borrows which must be repaid to the lender. This files has expired at 30-Jun-13 • 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 between the issuer of a bond and his/her bondholders, usually specifying interest rate, maturity date, convertibility.

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Basic Structure Of A Plain Vanilla Bond 150

100

50

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T0

T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

-50

-100

-150

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Key Issues In Introduction To The Valuation Of Debt 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 This files has expired at 30-Jun-13

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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 thehas present value of the of cash flows it is expected to This files expired atstream 30-Jun-13 generate.

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Bond Valuation

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

• 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

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• If the coupon rate of the security is less than the market yield then the bond will sell at discount Coupon Rate yield to maturity (interest rate) PAR -> Face Value of teh bond

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PV 

FV (1  r ) t

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Example: Bond Prices

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

Time

Cash flow

PV @11%

PV @ 10%

PV @ 9%

T=1

100

90.09

90.91

91.74

T=2

100

81.16

82.64

84.17

T=3

100

73.12

75.13

77.22

T=4

100

65.87

68.30

70.84

T=5

1100

This 652.80 files has 683.01 expired at714.92 30-Jun-13 963.04

Total Comment

Bond trading at a Discount

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1,000.00

1,038.90

Bond trading at Par

Bond trading at a Premium

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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 in value to a specified sum today.

• Future value of an annuity (FVA) is the future value of a stream of payments (annuity), assuming the 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 money that 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.

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FV  PV * (1  Rate ) n

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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 the principal. − Example: Callable or Putable Bonds

• The principal payments are files not knownhas with surety because the risk of prepayment This expired atof30-Jun-13 − Example: MBS‘s

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

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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

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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

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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 rate can also be used.

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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,

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

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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 standing moves towards its par value. The nearer to maturity the greater the influence because the security will only pay out the stated principal amount

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

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Bond Valuation: Pull To Par Concept

$140 $130

Price of $100 Face Value Bond Yielding 6% versus Years to Maturity At Various Coupons (4% - 8%) 8.00%

$120 $110 $100 $90 $80

7.00%

6.00%

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5.00%

$70 $60

4.00%

30 28 26 24 22 20 18 16 14 12 10 8 Years to Maturity

6

4

2

0

Price “pulled to par” as bond nears maturity maturity

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Pull To Par

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

ce Bondcount ce Bondemium

Bond-Premium

Bond-Discount Coupon

5%

Coupon

Tenure

10

Tenure

YTM

10%

Face Value

100

10% 10

YTM

5%

Face Value

100

FY 0

FY 1

FY 2

FY 3

FY 4

FY 5

FY 6

FY 7

FY 8

FY 9

FY

$69.28

$71.20

$73.33

$75.66

$78.22

$81.05

$84.15

$87.57

$91.32

$95.45

$100

$138.61

$135.54

$132.32

$128.93

$125.38

$121.65

$117.73

$113.62

$109.30

$104.76

$100

$160.00 $140.00 $120.00 $100.00 $80.00 $60.00 $40.00 $20.00 $0.00 FY 0

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Pull to Par

FY 2

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FY 4

FY 6

Price Bond-Discount

19

FY 8

FY 10

FY 12

Price Bond-Premium

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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 =

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Cash flow 1  Spot rate/2periods

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

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Questions

1. If the current yield is 8%, what is the value of a security carrying a annual coupon of 7%, maturing in 8 years, redeemable at par value of $1,000? A. $942.53 B. $1,000 C. $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% This files has expired at 30-Jun-13 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 the price becoming: A. $1,000 B. $1,015 C. $970 4. The value of a $10,000 face value zero-coupon bond with 10 years to maturity and a semi-annual pay yield of 8% is: A. $2,145.48 B. $4,563.95 C. $4,635.67

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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 as yields increase.

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

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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

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Bond‘s Indenture A bond‘s Indenture is the document which specifies the rights and obligations of both the issuer and the buyer 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. This files has expired at 30-Jun-13 – Examples: • raising additional amount of debt • pledging the same assets

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Example

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

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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 This files has at 30-Jun-13 LIBOR rate. (Varities: Inverse Floaters andexpired Inflation-indexed bonds)

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Basic Features Of A Bond

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

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

• Putable Bond—Some bonds give the bond holder the right to force the issuer to repay the bond before the maturity date on thefiles put dateshas expired at 30-Jun-13 This

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Basic Features Of A Bond

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

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Questions

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

Dollar Price

A

125 3/8

$12,538

B

122 1/8

$11,438

C

125 1/2

$14,620

files has expired at 30-Jun-13 2. If the interest rate falls,This the reinvestment income from a Zero-coupon bond will: A. Increase B. Decrease C. Unaffected

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Answers 1. A. Dollar Price = 1.2538 * 10,000 = 12,538 Quoted Price = 12,538/1,000 = 125 3/8 2. C. Unaffected

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Definitions

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

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Questions

1. A person pays $1,050 for a bond. The accrued interest till the date of purchase was $36. The clean price of the bond is: A. $1,050 B. $1,086 C. $1,014

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Answers

1.

C. $1,014

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Redemption And Retirement Of Bonds

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

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

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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

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Redemption And Retirement Of Bonds

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

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

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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 SinkindThis Fund Provision: allowsexpired the Issuer to at reapy30-Jun-13 an amount more than that stipulated by files has the Sinking Fund provisions.

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Embedded Options

• Options favourable to the Bondholder: – Put Provisions: grant the bondholder the right to demand repayment of the amount before the maturity date 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 the issuer. This files has expired at 30-Jun-13

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Questions

1. Assuming a common issuer and maturity, which of the following bonds will most likely have the lowest yield? A. A plain vanilla bond B. A bond with an embedded call option C. A bond with an embedded put option

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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.

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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 period B. Principal repayment can be deferred until it reaches maturity C. 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 rates B. A put provision will benefit the buyer in times of falling interest rates C. A put provision will benefit seller in times rising interest Thisthefiles has ofexpired atrates 30-Jun-13

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

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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

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Agenda • Features of Debt Securities • Risks Associated with Investing in Bonds • Overview of Bond Sectors and Instruments • Understanding Yield Spreads

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Risks Associated with Investing in Bonds

• 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

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• 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

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Risks Associated with Investing in Bonds

• 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 financial hardship

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

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• 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

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Risks Associated with Investing in Bonds

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

• Liquidity risk: The risk that the security will sell for a amount lower than its fair value due to lack of liquidity. The buyer will require the principal funds for another purpose on short notice, prior to the expiration of the security, and be unable to exchange the security for cash in the required time period without loss of fair value

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

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Discount, Premiuim, At Par

Imp

• 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

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