Topics What is a bond? Introduction to Fixed-Income Time Value of - - PowerPoint PPT Presentation

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Introduction to Fixed-Income Securities

Financial Risk Management Nattawut Jenwittayaroje, PhD, CFA NIDA Business School

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Topics

• What is a bond?
• Time Value of Money and Bond Pricing
• Yield Measurement
• Risks of Fixed-Income Securities
• Interest Rate Risk Measurement: Duration

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What is a bond?

• A bond is a form of loans or debt securities (i.e., fixed-

income securities), which is a claim on a specified periodic stream of income.

• A borrower issues (i.e., sells) a bond to a lender for some

amount of cash. The bond obligates the borrower (i.e., issuer) to make specified payments on specified dates.

• An investor who purchases a bond is lender or creditor
• A (typical) bond generally makes a regular interest payment,

called a coupon, at regular intervals, and a terminal payment, called the face value at the maturity date.

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What is a bond?

• In general, the bond must specify its



Issuer (the borrower)



Face value or par value (principal of the loan)

• Face value is the amount that is to be paid to an investor at the maturity

date of the security.



Maturity date and term-to-maturity

• The final coupon and the face value of a bond are repaid to the investor
• n its maturity date.



Coupon rate (per annum)

• used to calculate a coupon payment, or interest payment, paid at regular

intervals by the issuer to bondholders.



Frequency of coupon payments

• Usually are semi-annually, annually or quarterly.

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• Example 1: Illustrate a cash flow stream of a 3-year bond with

a $80 coupon (8% coupon rate), and a face value of $1,000. Coupons are paid annually. End of year Today year 1 year2 year 3 $80 $80 $80+1,000 Price = (-)$1,000

Investors buy the bond today, and is entitled to a payment of $80 per year for 3 years and par value of $1,000 at the end of year 3

Lending $1,000 for 3 years

Borrower issues the bond to a buyer for $1,000

Borrowing $1,000 for 3 years

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• Example 2: illustrate a zero-coupon bond that makes no coupon
• payments. Investors receive par value (e.g., $1,000) at the maturity

(e.g., 4 years) but receive no interest payments. The zero-coupon bond are issued at prices considerably below par value, e.g., $750.

End of year Today year 1 year2 year 3 year 4 $0 $0 $0 $1,000 Price = (-)$750

Investors buy the bond today, and is entitled to a par value of $1,000 at the end of year 4

Lending $1,000 for 4 years

Borrower issues the bond to a buyer for $750

Borrowing $1,000 for 4 years

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Time Value of Money and Bond Pricing

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มูลค่าอนาคต

เช่น ฝากเงินวันนี้ = 100 บาท ที่อัตราดอกเบี้ย (อัตราผลตอบแทน) 5% ต่อปี จํานวนหนึ่งและสองปี FV หรือ มูลค่าของเงิน 100 บาท ในหนึ่งและสองปีข้างหน้า

มูลค่าปัจจุบัน

i นั้นคือ อัตราดอกเบี้ยต่องวด หรือ อัตราคิดลด (discount rate). PV บางครั้งเรียกว่า มูลค่าคิดลด (discounted value) หรือ มูลค่าของเงินรวมในอนาคตที่คิดกลับมา ที่จุดเริ่มต้น หรือ มูลค่าปัจจุบัน PV (มูลค่าปัจจุบัน) ของเงิน 100 บาทในสองปีข้างหน้า ที่ discount rate ที่ 4%

มูลค่าอนาคต (Future Value) และ มูลค่าปัจจุบัน (Present Value)

หนึ่งปีข้างหน้า สองปีข้างหน้า

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มูลค่าปัจจุบัน (Present Value ) ของ Ordinary Annuity

• ผู้ลงทุนต้องการซื้อเครื่องมือทางการเงิน ที่จ่ายเงินสด $500 ต่อปีเป็น

เวลา 20 ปี โดยเริ่มจ่าย 1 ปี ต่อจากวันนี้

• ผู้ลงทุนต้องการอัตราดอกเบี้ย (ผลตอบแทน/อัตราคิดลด) ต่อปีที่ 5.5%

จากการลงทุนดังกล่าว

• ถ้าราคาเครื่องมือทางการเงินดังกล่าวซื้อขายกันที่ $5,300.
• ผู้ลงทุนควรจะซื้อเครื่องมือทางการเงินดังกล่าวหรือไม่

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ผลรวมทั้งหมดของค่า PV = $5,975.19

$500

ณ ปลายปี 0 1 2 3…..…10…….20

$500

$500

$500 $500

ตัวอย่าง: มูลค่าปัจจุบันของ Ordinary Annuity

ซื้อ

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มูลค่าปัจจุบัน (Present Value ) ของOrdinary Annuity

มูลค่าในปัจจุบันของเงินที่เกิดขึ้นทุกสิ้นงวด อธิบายเป็นสูตรได้ดังนี้ A =เงินงวดเป็นจํานวนเงินคงที่เท่ากันทุกงวด i = อัตราดอกเบี้ยทบต้น n = จํานวนงวดของกระแสเงินสด

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Bond Pricing

• The price paid for a bond today depends on the value of dollars to be received

in the future under the bond indenture.

• The fair price of a bond is the present value of future cash flows (coupons and

face value) that it makes.

[1]

where PB = price of bond C = coupon payment ($) = n = number of years to maturity i = discount rate (i.e., required yield = ผลตอบแทนที่ต้องการ) F = face value

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• As can be seen in [1], the price of a bond is comprised of



the PV of a series of the coupon payments



the PV of the face value.

• The coupon payments are equivalent to an ordinary annuity.
• If the coupon payments are made more than one time per year.



n = number of periods to maturity



i = periodic interest rate



C = Annuity Factor (i,n)

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Bond Pricing (Con’t)

• Example 3: Mills Company, a large defense contractor, on January

1, 2007, issued a 10% coupon interest rate, 10-year bond with a $1,000 par value that pays interest annually.

• Investors who buy this bond receive the contractual right to receive

two cash flows: (1) $100 annual interest (10% coupon interest rate  $1,000 par value) at the end of each year, and (2) the $1,000 par value at the end of the tenth year.

• Let’s assume the required yield is 10%.
• C = $100, i = 10%, F = $1,000, and n = 10 years.

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Bond Pricing (Con’t)

P

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• Calculate the price of a 10%

coupon bond with 10 years to maturity and a face value of $1,000. The coupon payments are made annually, and the required yield is 12% per annum.

• Calculate the price of the

bond in previous example, but with the required yield

• f 8% per annum.

Bond Pricing (Con’t)

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i P

Bond Values and Required Returns

• Negative relationship between price of a bond and its yield.

 As the required yield increases, the PV of the cash flows must decrease;

therefore, the price decreases.

 As the required yield decreases, the PV of the cash flows must increase;

therefore, the price increase.

196-19

Bond Values and Required Returns

i P

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• ราคาของตราสารหนี้แปรผกผันกับอัตราผลตอบแทนที่นักลงทุนต้องการ

(required yield; y) ในขณะที่ อัตราผลตอบแทนที่นักลงทุนต้องการแปรผันไป ตามอัตราดอกเบี้ยตลาด (interest rate; i)

• ดังนั้นราคาของตราสารหนี้แปรผกผันกับอัตราดอกเบี้ยตลาด (interest rate; i)

Price/yield relationship (ความสัมพันธ์ของราคากับอัตราดอกเบี้ย)

interest rates  Required yield  interest rates  Required yield 

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Par, premium and discount bonds

• 1. Par bonds (price = face value (i.e. par value))
• required yield = coupon rate
• When yields in the marketplace equal to the coupon rate at a given

time, the price of the bonds will be at the par value.

• 2. Discount bonds (price < face value)
• required yield > coupon rate
• When yields in the marketplace rise above the coupon rate at a given

time, the price of the bonds will decrease below the par value because

• f the higher discount rates.
• 3. Premium bonds (price > face value)
• required yield < coupon rate
• When yields in the marketplace drop below the coupon rate at a given

time, the price of the bonds will increase above the par value because

• f the lower discount rates.

When this condition occurs When this condition occurs When this condition occurs

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Bond Pricing: Bond Value Behavior

In practice, the value of a bond in the marketplace is rarely equal to its par value.

 Whenever the required return on a bond differs from the bond’s coupon

interest rate, the bond’s value will differ from its par value.

 The required return is likely to differ from the coupon interest rate

because either

• (1) economic conditions have changed, causing a change in the

(long-term) interest rates, or

• (2) the firm’s risk has changed.

 Increases in the (long-term) interest rates or in risk will raise the

required return; decreases in the (long-term) interest rates or in risk will lower the required return.

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• Example 4: Calculate the price of a 8% coupon bond with 20 years

to maturity and a face value of $1,000. The coupon payments are made semi-annually, and the required yield is 12% per annum.

Bond Pricing: Semiannual Interest payment

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Bond Pricing: zero coupon bonds

• No periodic coupon payments.
• Single payment of par value at maturity.
• The price of bond (PB) is simply the present value (PV) of the face value (F)

(i.e., the face value discounted at market rate).

where n = number of years to maturity and i = discount rate (i.e., required

yield)

• The zero bonds are therefore issued at prices considerably below par value,

and the return comes solely from the difference between issue price and the par value received at maturity.

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Bond Pricing: zero coupon bonds

• Example 5: Assume that the discount rate in the market is 8.6%

p.a., compute the price of a zero-coupon that matures in 10 years and has the face value of $1,000?

• Issued at discount from par.

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Yield Measurement (การคํานวณผลตอบแทนของตราสารหนี้)

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• Today, Bond A has the following feature;

 a government bond  a coupon rate of 5% per year (coupon paid annually),  6 year to maturity  1,000 face value.

• If today I buy Bond A at $940.5 and hold it until maturity, what

would be the rate of return of my bond investment?

Yield to Maturity (YTM)

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• The Yield to maturity (or Promised yield or Internal rate of return

(IRR)) can be computed from bond pricing formulas [1] when a bond’s price is known. (Solve for i)

• YTM will be realised when:

 bond is held to maturity.  Coupon payments are reinvested at the same rate as the YTM.

Yield to Maturity (YTM)

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• Example 6: Compute the YTM for a 6 year, 5% coupon (annual

payments) bond selling for $940.50.

=IRR(B5:B11)

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YTM for a zero-coupon bond

• From
• Rearrange the above equation, we get:
• Example 7: The YTM for a zero-coupon bond selling for $274.8

with a face value of $1,000, maturing in 15 years can be computed as:

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Risks of Fixed-Income Securities

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Risks of Fixed-Income Securities



ความเสี่ยงของตราสารหนี้มีหลายประเภทแต่ ความเสี่ยง 2 ประเภทหลัก คือ



ความเสี่ยงในการผิดนัดชําระดอกเบี้ยหรือเงินต ้ น (Credit / Default Risk)

 Credit Rating



ความเสี่ยงจากการเปลี่ยนแปลงของอัตราดอกเบี้ย (Interest Rate Risk)

 ความเสี่ยงด ้

านราคา (Market / Price Risk)  วัดได ้ โดย

• Price volatility
• Duration

 ความเสี่ยงในการลงทุนต่อ (Reinvestment Risk)

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Credit ratings ของตราสารหนี้ เป็นเครื่องมือที่ช่วยบ่งบอกถึงความเสี่ยงทางด้าน เครดิต (credit and defaults risk) ของตราสารหนี้ บริษัทจัดอันดับเครดิต Moody’s Investor Service (Moody’s), Standard & Poor’s (S&P), Fitch TRIS (Thai Rating and Information Service) ความน่าเชื่อถือสูงสุด, ความเสี่ยงตํ่าสุด (Investment grade bonds) Aaa ถึง Baa สําหรับ Moody’s AAA ถึง BBB สําหรับ S&P ความน่าเชื่อถือตํ่าสุด, ความเสี่ยงสูงสุด (Speculative-grade bonds or junk bonds) ตํ่ากว่า Baa สําหรับ Moody’s ตํ่ากว่า BBB สําหรับ S&P

การจัดอันดับเครดิตของตราสารหนี้ (Bonds’ Credit Rating)

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กลุ่ม Investment grade: อันดับความน่าเชื่อถือ : สูง - ปานกลาง กลุ่ม Speculative, Junk Bonds

อันดับความน่าเชื่อถือ : ตํ่า - มีโอกาสที่จะเกิดการผิดชําระคืนเงินต้นและดอกเบี้ยสูง

การจัดอันดับของตราสารหนี้

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Source: ThaiBMA

Credit Rating & Agency

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Credit Rating and Spread

spread

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Interest rate risk

• Risk related to changes in interest rates that cause a bond’s price

to change.

• Interest rate risk comprises:

 Price risk is the variability in bond prices caused by their

inverse relationship with interest rates.

 Reinvestment risk is caused by changing market rates at

which coupons can be reinvested.

• Only face the price risk if to sell the bond before maturity.
• Since the bond price can change due to the change in the

interest (yield) during the holding period.

• the reinvestment rate risk occurs even though a bond is held

until maturity.

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Bond price volatility

• Bond prices are inversely related to bond yields.
• Measure sensitivity of a change in a bond’s price to a change

in yield.

• Percentage change in price for given change in interest rates:

where %∆PB = percentage change in price Pt = new price in period t Pt – 1 = bond’s price one period earlier A measure of PRICE RISK

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Bond price volatility and maturity

Considering 1-year bond, when i rises from 5% to 6%

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Bond price volatility and coupon rate

100.56

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Bond price volatility, coupon rate, and maturity

• Consider three loan plans, each of which have different maturities in
• years. The loan amount is $1,000 and the current interest rate is 3%.

 Loan #1 (3 years), is a three-payment loan with three equal

payments of $353.53 each.

 Loan #2 (2 years) is structured as a 3% annual coupon bond.  Loan # 3 (1.5 years) is a discount loan, which has a single

payment of $1,045.33.

 Which loan(s) are more “risky”????

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Interest Rate Risk Measurement: Duration

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• The duration measures the approximate sensitivity of a

change in a bond’s price to a change in yield.

• We take the first derivative of the price of bond equation with

respect to the required yield to determine the approximate dollar price change for a change in yield,

Duration - a measure of interest rate risk (price risk)

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• The dPB/di is the dollar change of the price when the yield
• changes. The percentage change of the price can be computed

by dividing both side of the equation above by the price (PB).

• Macaulay duration (D) is :

Duration - a measure of interest rate risk (price risk)

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• Modify duration (MD) is :

Duration - a measure of interest rate risk (price risk)

percentage change in price

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• Example 9: Suppose we have a bond with a 3-year term to

maturity, an 8% coupon paid annually, and a market yield of 10%. Durations are: PB

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• From example 9, MD = 2.5249. If the yield rises by 100 basis

points (1.00%), the % price change can be estimated by:

Using duration to estimate % price change

% price change

• In other words, MD = 2.5249 means that

if the yield rises (drops) by 1.00%, the bond price will decrease (increase) 2.5249%

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Interpretation and Significance of Duration

• Duration is used to measure the price sensitivity of a fixed

income security due to a change in interest rates.

• The higher the duration number, the greater interest rate risk.
• Combines the effects of differences in coupon rates and

differences in maturity.

• Duration is the weighted average time to maturity of a bond.

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Properties of duration: Duration Versus Maturity

12% Coupon

1.00 1.89 2.70 3.42 4.07

Premium bond Discount bonds

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Properties of duration: Duration Versus Maturity

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Duration as Index of Interest Rate Risk

• Consider three loan plans, each of which have different maturities in
• years. The loan amount is $1,000 and the current interest rate is 3%.

 Loan #1 (3 years), is a three-payment loan with three equal

payments of $353.53 each.

 Loan #2 (2 years) is structured as a 3% annual coupon bond.  Loan # 3 (1.5 years) is a discount loan, which has a single

payment of $1,045.33.

 D1 = 1.920, D2 = 1.971, D3 = 1.5

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Rearrange from lowest to highest duration

a) 6-year maturity with 6% coupon paid semiannually. b) 6-year maturity with 6% coupon paid annually. c) 6-year maturity with zero coupon rate. d) 3-year maturity with 7% coupon paid semiannually. e) 4-year maturity with 6.5% coupon paid semiannually. f) 5-year maturity with 6.5% coupon paid semiannually

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