Fixed – income Securities

Long Term Debt: A Review

Corporate debt can be short-term (maturity less than one year) or long-term.

Different from common stock:– Creditor’s claim on corporation is specified– Promised cash flows– Most are callable

Over half of outstanding bonds are owned by life insurance companies & pension funds

Features of Fixed Income Securities Maturity :

- The length of time until the agreement expires.- Borrowers (Issuers) are committed to meet their obligations over this period

Coupon :- The rate which used for calculating the amount of interest to be paid.

Frequency :- Quarterly : coupon will be paid every 3 months.- Semi-annual : coupon will be paid every 6 months.- annually : coupon will be paid every 1 years.

Features of Fixed Income Securities

Par Value ( redemption or face value)- The amount that borrowers promises to pay

lenders at the maturity.

Remark : Bond’s price depends on movement in interest rates. If market interest rates move above (below) the coupon rate, then a bond will sell below/discount (above/premium) par value.

Bond price is the net present value of bond’s cash flow.

The indenture, a written agreement between the borrower and a trust company, usually lists– Amount of Issue, Date of Issue, Maturity– Denomination (Par value)– Annual Coupon, Dates of Coupon Payments– Security– Sinking Funds– Call Provisions– Covenants

Features that may change over time– Rating– Yield-to-Maturity– Market price

Features of Fixed Income Securities

Issue amount $20 million Bond issue total face value is $20 million Issue date 12/15/98 Bonds offered to the public in December 1998 Maturity date 12/31/18 Remaining principal is due December 31,

2018 Face value $1,000 Face value denomination is $1,000 per bond Coupon interest $100 per annum Annual coupons are $100 per bond Coupon dates 6/30, 12/31 Coupons are paid semiannually Offering price 100 Offer price is 100% of face value Yield to maturity 10% Based on stated offer price Call provision Callable after 12/31/03 Bonds are call protected for 5 years after

issuance Call price 110 before 12/31/08,

100 thereafter Callable at 110 percent of par value through 2008. Thereafter callable at par.

Trustee United Bank of Florida

Trustee is appointed to represent bondholders

Security None Bonds are unsecured debenture Rating Moody's A1, S&P A+ Bond credit quality rated upper medium

grade by Moody's and S&P's rating

Features of Fixed Income Securities

Protective Covenants Agreements to protect bondholders

Negative covenant: They should not:– pay dividends beyond specified amount– sell more senior debt & amount of new debt is

limited– refund existing bond issue with new bonds paying

lower interest rate– buy another company’s bonds

Positive covenant: They should:– use proceeds from sale of assets for other assets– allow redemption in event of merger or spin-off– maintain good condition of assets– provide audited financial information

Yield Curve

Thai Government Bond Yield Curve

1.5000%

2.5000%

3.5000%

4.5000%

5.5000%

6.5000%

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

years

%

16/9/2002

Bond Ratings What is rated:

– The likelihood that the firm will default.– The protection afforded by the loan contract in the

event of default.

Who pays for ratings:– Firms pay to have their bonds rated.– The ratings are constructed from the financial

statements supplied by the firm.

Ratings can change.

Raters can disagree.

Bond Rating and SymbolsS&P Moody's ExplanationAAA Aaa Prime grade, highest safetyAA+ Aa1AA Aa2AA- Aa3A+ A1A A2A- A3

BBB+ Baa1BBB Baa2BBB- Baa3

High credit quality

Upper-medium credit quality

Lower-medium credit quality

Investmen

t grade

Bond Rating and Symbols

Junk bonds Anything less than an S&P “BB” or a Moody’s

“Ba” is a junk bond.

A polite euphemism for junk is high-yield bond.

There are two types of junk bonds:– Original issue junk—possibly not rated– Fallen angels—rated

Current status of junk bond market– Private placement

Yield premiums versus default risk

Types of Bond Fixed rate : the coupon rate constantly fixed.

Floating rate : the coupon rate based on a reference rate (i.e. LIBOR)

Amortizing bond : some partial of principle were scheduled to pay out before the maturity.

Zero-coupon bond : pay no interest and are sold at a discount from their par value. The difference represents the interest costs to the borrower.

Types of Bond

Callable bond : issuer has right to redeem a bond before maturity at a formula price.

To compensate the call risk, investors usually need additional rate of return which may incur higher cost of borrowing to the issuer.

When market interest rate keeps lowing, issuer might execute call since he upsets with his high cost of borrowing

Types of Bond

Puttable bond : investors have right to redeem the bond before maturity at a formula price.

Put option is a sweetener which help issuer to lower his cost of borrowing.

When market interest keeps soaring, investors might execute put option since they can reinvestment at the higher rate of return.

Types of Bond Convertible bonds :

- Why are they issued? Cheap interest burden- Why are they purchased? Right for converting

- Conversion ratio:Number of shares of stock acquired by conversion

- Conversion price:Bond par value / Conversion ratio

- Conversion value:Price per share of stock x Conversion ratio

- In-the-money versus out-the-money

Reasons for Issuing Warrants and Convertibles Convertible debt carries a lower coupon rate than

does otherwise-identical straight debt.

Since convertible debt is originally issued with an out-of-the-money call option, one can argue that convertible debt allows the firm to sell equity at a higher price than is available at the time of issuance. However, the same argument can be used to say that it forces the firm to sell equity at a lower price than is available at the time of exercise.

Convertible bonds also allow young firms to delay expensive interest costs until they can afford them

Types of Bond Convertible bonds (continue) :

- Conversion ratio: 2 shares per 1 unit

- Conversion price: = (1,000 Baht / unit ) / (2 shares / unit)= 500 Baht / share

- Conversion value:= (40 Baht / share ) x ( 2 shares /

unit)= 80 Baht / unit

Types of Bond

Convertible bonds (continue) :

-The value of a convertible bond has three major components:

1. Straight bond value

2. Option value

3. Conversion value

Types of Bond Convertible bonds (continue) :

Example; Litespeed, Inc., just issued a zero coupon convertible bond due in 10 years.

- The appropriate interest rate is 10%.

- Each convertible is trading at $400 in the market.

– What is the straight bond value?– What is the option value of the bond?

Types of Bond

Convertible bonds (continue) :– What is the straight bond value?

– What is the option value of the bond?

$400 – 385.54 = $14.46

54.385$)10.1(

000,1$10

SBV

Convertible Bond Value

Stock Price

Straight bond value

Conversion Value

= conversion ratio

floor value

floor value

Convertible bond values

Option value

Types of Bond

Types of Bond

Other Convertible bonds (continue) :

Exchangeable bonds– Convertible into a set number of shares of a

third company’s common stock.

Bond Pricing Example : Thai government bond (LB04NA) par 1,000

Baht which will mature on Nov 30, 2002 pay coupon 3.50% semi-annually.

A) What is the amount of interest paid in each coupon date?

Coupon = 1,000 x (3.50%)/2 = 17.50 Baht

B) How many times that investor who bought this bond on Dec8,2002 and hold it until maturity receive the coupon?

The number of period = 4 periods

C) Suppose investor buy this bond on Nov 30,2002 (just after the coupon was paid). How much he need to pay, if the market interest rate for 2 year equals to 3.50%?

Price = PVIA(A=17.5,i = 1.75%,n=4) + PVIF(F=1000,i =1.75%,n=4) = 17.5 / ( 1.0175 )1 + 17.5 / ( 1.0175 )2 + 17.5 / ( 1.0175 )3 + 1,017.5 / ( 1.0175 )4 = (PMT = 17.5; FV = 1,000; n = 4; i = 1.75%; Find PV)= 1,000 It is a par bond.

11/02 05/03 11/03 05/04 11/04

17.5 17.5 17.51,017.5

P = ?

i = 1.75%

Nov-02 May-03 Nov-03 May-04 Nov-04

0 1 2 3 4

0 17.50 17.50 17.50 1,017.50

PV on Nov02 if mkt rate = 3.50%1,000.00 17.20 16.90 16.61 949.29

Date

Period

Coupon and Principle will receive

Bond Pricing

Price = PVIA(A=17.5,i = 2.00%,n=4) + PVIF(F=1000,i =2.00%,n=4) = 17.5 / ( 1.02 )1 + 17.5 / ( 1.02 )2 + 17.5 / ( 1.02 )3 + 1,017.5 / ( 1.02 )4 = (PMT = 17.5; FV = 1,000; n = 4; i = 2%; Find PV)= 990.48 It is a discount bond.

D) If everything held constant except the market interest rate for 2 year equals to 4.00%. Is this premium or discount bond? And what is the price?

Nov-02 May-03 Nov-03 May-04 Nov-04

0 1 2 3 4

0 17.50 17.50 17.50 1,017.50

PV on Nov02 if mkt rate = 4.00% 990.48 17.16 16.82 16.49 940.01

Date

Period

Coupon and Principle will receive

Bond Pricing

Price = PVIA(A=17.5,i = 1.50%,n=4) + PVIF(F=1000,i =1.50%,n=4) = 17.5 / ( 1.015 )1 + 17.5 / ( 1.015 )2 + 17.5 / ( 1.015 )3 + 1,017.5 / ( 1.015 )4 = (PMT = 17.5; FV = 1,000; n = 4; i = 1.50%; Find PV)= 1,009.64 It is a premium bond.

F) If everything held constant except the market interest rate for 2 year equals to 3.00%. Is this premium or discount bond? And what is the price?

Nov-02 May-03 Nov-03 May-04 Nov-04

0 1 2 3 4

0 17.50 17.50 17.50 1,017.50

PV on Nov02 if mkt rate = 3.00%1,009.64 17.24 16.99 16.74 958.67

Date

Period

Coupon and Principle will receive

Bond Pricing

Bond Pricing Concept checking;

Bond X and Y have the same features except

A) If X pay coupon higher than Y, how should investors value the bonds?

B) If the coupon was equally set and X has better credit rating than Y, how should investors value the bonds?

Bond X will be priced higher than Y.

Investors will require lower rate of return (represent the market rate) on X rather than Y. So, Bond X will be priced higher than Y.

Bond Pricing Example : Thai government bond (LB04NA) par

1,000 Baht which will mature on Nov 30, 2002 pay coupon 3.50% semi-annually. Suppose an investor buy this bond on Jan15,2003. How much he need to pay, if he satisfies with 2% yield? How much for accrued interest and clean price? (Use Actual/365 )

30/11/04

17.5 17.5 17.51,017.5

P = ?

i = 1.00%30/5/0430/11/0330/5/03

15/1/03

30/11/02

Bond Pricing Solution :

= 17.3706 + 17.1986 + 17.0283 + 980.2729

= 1,031.8704 buyer pay dirty price to seller.

7397.37397.27397.17397.0 )01.1(

5.017,1

)01.1(

5.17

)01.1(

5.17

)01.1(

5.17P

30/11/04

17.5 17.5 17.51,017.5

P = ?

i = 1.00%30/5/0430/11/0330/5/03

15/1/03

30/11/02

7397.05.182

135

Bond Pricing Solution :

Dirty Price = 1,031.87

A.I. = (46 / 182.5) x 17.5 = 4.41

Clean Price = Dirty Price – A.I. = 1,027.46

Coupon Rate, Current Yield, and YTM

Annual coupon

Coupon ratePar value

Bond’s coupon rate:

Bond’s current yield:

priceBond

couponAnnualyieldCurrent

The discount rate that equates a bond’s price with the present value of all future cash flows.

Yield to Maturity:

Example: Assume a bond has 12 years to maturity, a 8% coupon (paid semi-annually),and the price is $1039.11.

Coupon rate = $80/$1000= 8%Current yield = $80/$1039.11=7.7%

24 -1039.11 40 1000N I/YR PV PMT FV

3.75

INPUTS

OUTPUT

2(12) 80/2

YTM=3.75%x2=7.5%

Coupon Rate, Current Yield, and YTM

Now assume a bond has 25 years to maturity, a 9% coupon,and the YTM is 8%. What is the price? (remember all bonds pay semi-annual interest payment)

50 4 45 1000N I/YR PV PMT FV

-1107.41

INPUTS

OUTPUT

More on Bond Prices/Yields

2(25) 8/2 90/2

Now assume a bond has 25 years to maturity, a 9% coupon,and the YTM is 10%. What is the price? (remember all bonds pay semi-annual interest payment)

50 5 45 1000N I/YR PV PMT FV

-908.72

INPUTS

OUTPUT

2(25) 10/2 90/2

More on Bond Prices/Yields

Now assume the same bond has 5 years to maturity (9% coupon & YTM of 8%) What is the price? Is the bond selling at premium or discount?(remember all bonds pay semi-annual interest payment)

10 4 45 1000N I/YR PV PMT FV

-1040.55

INPUTS

OUTPUT

2(5) 8/2 90/2

More on Bond Prices/Yields

Now assume the same bond has a YTM of 10%. (9% coupon & 5 years to maturity) What is the price? Is the bond selling at premium or discount?(remember all bonds pay semi-annual interest payment)

10 5 45 1000N I/YR PV PMT FV

-961.39

INPUTS

OUTPUT

2(5) 10/2 90/2

More on Bond Prices/Yields

Where does this leave us? We found:Coupon Years YTM Price 9% 25 8% $1,107 9% 25 10% $ 908 9% 5 8% $1,040 9% 5 10% $ 961

$900

$950

$1,000

$1,050

$1,100

$1,150

8% 9% 10% 11%

25 years

5 years

More on Bond Prices/Yields

Figure 10.1: Premium, par, and discount bond prices over time (if yield does not change)

70

80

90

100

110

120

130

140

30 25 20 15 10 5 0

Time to maturity (years)

Bo

nd

pri

ces

(% o

f p

ar)

Interest Rate Risk and Maturity

Malkiel’s TheoremsSummarizes the relationship among bond prices, yields, coupons, and maturity:(all theorems hold assuming everything else constant):1) Bond prices move inversely with interest rates.2) The longer the maturity of a bond, the more sensitive is it’s price to a change in interest rates.3) The price sensitivity of any bond increases with it’s maturity, but the increase occurs at a decreasing rate.4) The lower the coupon rate on a bond, the more sensitive is it’s price to a change in interest rates.5) For a given bond, the volatility of a bond is not symmetrical, i.e. a decrease in interest rates raises bond prices more than a corresponding increase in interest rates lower prices.

Duration (Macaulay’s duration) : A widely used measure of a bond's sensitivity to a 1% (1% = 100 bps) changes in interest rate (yield).

The 1st derivative of the bond’s price function with respect to yield. It’s the slope of bond price curve.

The present value-weighted number of years to maturity

Duration

Although modified duration allows us to estimates of price change in a bond’s price for a small change in required yield, it does not provide good estimates of a large price change in required yield. This is because of the convexity in the price/yield relation ship.

Convexity: a measure of the degree of curvature or convexity in the price/yield relationship.

Duration

Duration formula

tPriceBond

CFPVDurationMacaulay

n

1t

t

DurationModified duration

YTM1

2

YTMinChangeDurationModifiedpricebondinΔ%

To compute the percentage change in a bond’s priceusing Modified Duration:

Figure 10.3: Calculating bond duration

Discount Present Years x Present valueYears Cash flow factor value / Bond price

0.5 40 0.96154 38.4615 0.01921 40 0.92456 36.9822 0.0370

1.5 40 0.88900 35.5599 0.05332 40 0.85480 34.1922 0.0684

2.5 40 0.82193 32.8771 0.08223 1040 0.79031 821.9271 2.4658

$1,000.00 2.7259Bond price Bond duration

Example: A 3-year bond with 8% annual coupon selling at par.

Modified duration = (2.7259) / (1.04) = 2.6211 years

Duration Calculation

5.24%2.6211pricebondin Δ%

5.24%

2.08

1

.10)(.082.7259pricebondinΔ%

)10.008.0(

From previous example, if YTM will go to 10%, calculate the percentage change in bond price and the new bond price.

Therefore; Approx. new price = $1,000 x (1 - 5.24%)= $947.60

Duration Calculation

Duration Calculation

Properties of Duration All else the same, the longer a bond’s

maturity, the longer is its duration.

All else the same, a bond’s duration increases at a decreasing rate as maturity lengthens.

All else the same, the higher a bond’s coupon, the shorter is its duration.

All else the same, a higher yield to maturity implies a shorter duration, and a lower yield to maturity implies a longer duration.

Figure 10.3: Bond duration and maturity

0

2

4

6

8

10

12

0 5 10 15 20 25 30

Bond maturity (years)

Bo

nd

du

rati

on

(ye

ars

) 0% Coupon

5% Coupon 10% Coupon

15% Coupon

FRN Pricing

Under the assumption of no default risk, the bond should always be 100% on reset dates.

Once the coupon is fixed on a reset date, the bond tends to behave like a ST fixed-coupon bond until the next reset date.

FRN prices are more volatile just after the reset date, because that is when they have the longest fixed-coupon maturity.

Dedicated Portfolios

Dedicated portfolioA bond portfolio created to prepare for a future cash outlay, e.g. pension funds.The date the payment is due is commonly called the portfolio’s target date.

Immunization Interest rate risk: The possibility that changes in

interest rates will result in losses in a bond's value.

Reinvestment rate risk: The uncertainty about target date portfolio value that results from the need to reinvest bond coupons at yields not known in advance.

Price risk: The risk that bond prices will decrease, which arises in dedicated portfolios when the target date value of a bond or bond portfolio is not known with certainty

Immunization: Constructing a portfolio to minimize the uncertainty surrounding its target date value.

Problem 1

CIR Inc. has 7% coupon bonds on the market that have 11 years left to maturity. If the YTM on these bonds is 8.5%, what is the current bond price?

Solution:

$894.16

2.0851

1000

2.0851

11

2) / (.085

35priceBond 2222

Problem 2

Trincor Company bonds have coupon rate of 10.25%, 14 years to maturity, and a current price of $1,225. What is the YTM? The current yield?

Solution:

2828

21

1000

21

11

)2/(

)2/50.102(225,1$

YTMYTMYTM

YTM = 3.805% x 2 = 7.61%

Current yield = $102.50 / $1,225 = 8.37%

Problem 3

XYZ Company has a 9% callable bond outstanding on the market with 12 years to maturity, call protection for the next 5 years, and a call premium of $100. What is the YTC for this bond if the current price is 120% of par value?

Solution:

1010

2YTC1

1100

2YTC1

11

YTC

90200,1$

YTC = 3.024% x 2 = 6.05%

[see next slide for additional information]

What is the YTM, with zero call premium?

Solution:

If interest rates stay at current levels, the bond issuer will likely call the bonds to refinance at the earliest possible time.

Problem 3 (cont’d)

2224

2YTM1

1000

2YTM1

11

YTM

90200,1$

YTM = 3.283% x 2 = 6.57%

[see next slide for additional information]

Problem 3 (cont’d)

What would be the break-even call premium? (If interest rates don’t change, at what level would the call premium have to be to not call the bonds?)

Solution:

1010

203283.1

X1000

203283.1

11

03283.

90200,1$

X = $134.91

The bond will not be called if the call premium is greater than $134.91.

Problem 4

YTM = 5.249 x 2 = 10.498%

66

2YTM1

1000

2YTM1

11

YTM

80937$

What is the Macaulay duration of an 8% coupon bond with 3 years to maturity and a current price of $937.10? What is the modified duration?

Solution:

First calculate the yield:

Calculating bond duration

Discount Present Years x Present valueYears Cash flow factor value / Bond price

0.5 40 0.95 38.00 0.0201 40 0.90 36.11 0.039

1.5 40 0.86 34.31 0.0552 40 0.81 32.60 0.070

2.5 40 0.77 30.97 0.0833 1040 0.74 765.07 2.449

937.06 2.715Bond price Bond duration

Problem 4 (cont’d)

Problem 4 (cont’d)

Mac. Duration = 2.715 years

Modified duration

= 2.715 / (1 + .10498/2) = 2.58 years