Chap014 Bond Prices and Yields(金融工程-南开大学,王小麓))
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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
McGraw-Hill/Irwin
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
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
McGraw-Hill/Irwin
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
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.
McGraw-Hill/Irwin
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
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
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
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
McGraw-Hill/Irwin
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
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
McGraw-Hill/Irwin
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
McGraw-Hill/Irwin
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
14-17
Factors Used by Rating Companies
Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt
McGraw-Hill/Irwin
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
14-18
Protection Against Default
Sinking funds Subordination of future debt Dividend restrictions Collateral
McGraw-Hill/Irwin
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
14-19
Default Risk and Yield
Risk structure of interest rates Default premiums- Yields compared to ratings- Yield spreads over business cycles
McGraw-Hill/Irwin
Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
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Chap014 Bond Prices and Yields(金融工程-南开大学,王小麓))09-01
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