Chap014 Bond Prices and Yields(金融工程-南开大学,王小麓))

14-1

Chapter 14

Bond Prices and Yields

McGraw-Hill/Irwin

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

14-2

Bond Characteristics

Face or par value Coupon rate- Zero coupon bond

Compounding and payments- Accrued Interest

Indenture

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14-3

Different Issuers of Bonds

U.S. Treasury - Notes and Bonds Corporations Municipalities International Governments and Corporations Innovative Bonds - Indexed Bonds - Floaters and Reverse FloatersMcGraw-Hill/IrwinCopyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

14-4

Provisions of Bonds

Secured or unsecured Call provision Convertible provision Put provision (putable bonds) Floating rate bonds Sinking fundsMcGraw-Hill/IrwinCopyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

14-5

Bond Pricing

C t ParValueT PB T t (1 r ) t 1 ( r ) 1T

PB = Price of the bond Ct = interest or coupon payments T = number of periods to maturity y = semi-annual discount rate or the semi-annual yield to maturity

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14-6

Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000

P 40 t 1

20

1

1.03

t

1000 (1.03)20

P $1,148.77Ct P T rMcGraw-Hill/Irwin

= 40 (SA) = 1000 = 20 periods = 3% (SA)Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

14-7

Bond Prices and Yields

Prices and Yields (required rates of return) have an inverse relationship When yields get very high the value of the bond will be very low. When yields approach zero, the value of the bond approaches the sum of the cash flows.

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14-8

Prices and Coupon Rates

Price

YieldMcGraw-Hill/IrwinCopyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

14-9

Yield to Maturity

Interest rate that makes the present value of the bond’s payments equal to its price.

Solve the bond formula for r

C t ParValueT PB T t (1 r ) t 1 ( r ) 1TMcGraw-Hill/IrwinCopyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

14-10

Yield to Maturity Example

35 1000 950 T t (1 r ) t 1 ( r ) 120

10 yr Maturity Price = $950

Coupon Rate = 7%

Solve for r = semiannual rate

r = 3.8635%

McGraw-Hill/Irwin

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14-11

Yield Measures

Bond Equivalent Yield 7.72% = 3.86% x 2 Effective Annual Yield (1.0386)2 - 1 = 7.88% Current Yield Annual Interest / Market Price $70 / $950 = 7.37 %McGraw-Hill/IrwinCopyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

14-12

Realized Yield versus YTM

Reinvestment Assumptions Holdin

g Period Return- Changes in rates affects returns- Reinvestment of coupon payments - Change in price of the bond

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14-13

Holding-Period Return: Single Period

HPR = [ I + ( P0 - P1 )] where I = interest payment P1 = price in one period

/ P0

P0 = purchase price

McGraw-Hill/Irwin

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

14-14

Holding-Period Example

CR = 8%

YTM = 8%

N=10 years

Semiannual Compounding P0 = $1000

In six months the rate falls to 7%P1 = $1068.55

HPR = [40 + ( 1068.55 - 1000)] / 1000HPR = 10.85% (semiannual)McGraw-Hill/IrwinCopyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

14-15

Holding-Period Return: Multiperiod

Requires actual calculation of reinvestment income

Solve for the Internal Rate of Return using the following:- Future Value: sales price + future value of coupons - Investment: purchase price

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Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

14-16

Default Risk and Ratings

Rating companies- Moody’s Investor Service - Standard & Poor’s

- Duff and Phelps- Fitch

Rating Categories- Investment grade - Speculative grade

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14-17

Factors Used by Rating Companies

Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt

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14-18

Protection Against Default

Sinking funds Subordination of future debt Dividend restrictions Collateral

McGraw-Hill/Irwin

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14-19

Default Risk and Yield

Risk structure of interest rates Default premiums- Yields compared to ratings- Yield spreads over business cycles

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Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

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