Post on 22-Dec-2015
CHAPTER 14
Bond Prices and Yields
• Face or par value• Coupon rate– Zero coupon bond
• Compounding and payments– Accrued Interest
• Indenture
Bond Characteristics
Different Issuers of Bonds
• U.S. Treasury– Notes and Bonds
• Corporations• Municipalities• International Governments and Corporations• Innovative Bonds– Floaters and Inverse Floaters– Asset-Backed– Catastrophe
1 (1 )(1 )
T
TB tt
ParValueCPrr
PB = Price of the bond
C = interest or coupon paymentsT = number of periods to maturityr = semi-annual discount rate or the semi-annual yield to maturity
Bond Pricing
C = 40 (SA)P = 1000T = 20 periodsr = 3% (SA)
Price: 10-yr, 8% Coupon, Face = $1,000
77.148,1$
)03.1(
1000
03.1
140
20
20
1
P
Pt
t
• 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
Bond Prices and Yields
Figure 14.3 The Inverse Relationship Between Bond Prices and Yields
Table 14.2 Bond Prices at Different Interest Rates (8% Coupon Bond, Coupons Paid Semiannually)
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
1 (1 )(1 )
T
Ttt
BParValueCP
rr
Yield to Maturity Example
)1(1000
)1(35950
20
1 rrT
tt
10 yr Maturity Coupon Rate = 7%
Price = $950
Solve for r = semiannual rate r = 3.8635%
Yield Measures
Bond Equivalent Yield7.72% = 3.86% x 2
Effective Annual Yield(1.0386)2 - 1 = 7.88%
Current YieldAnnual Interest / Market Price$70 / $950 = 7.37 %
Yield to Call
Figure 14.4 Bond Prices: Callable and Straight Debt
Realized Yield versus YTM
• Reinvestment Assumptions• Holding Period Return– Changes in rates affect returns– Reinvestment of coupon payments– Change in price of the bond
Figure 14.5 Growth of Invested Funds
Figure 14.6 Prices over Time of 30-Year Maturity, 6.5% Coupon Bonds
Holding-Period Return: Single Period
HPR = [ I + ( P0 - P1 )] / P0
whereI = interest paymentP1 = price in one period
P0 = purchase price
Holding-Period Return Example
CR = 8% YTM = 8% N=10 yearsSemiannual Compounding P0 = $1000
In six months the rate falls to 7%P1 = $1068.55
HPR = [40 + ( 1068.55 - 1000)] / 1000 HPR = 10.85% (semiannual)
Figure 14.7 The Price of a 30-Year Zero-Coupon Bond over Time at a Yield to
Maturity of 10%
• Rating companies– Moody’s Investor Service– Standard & Poor’s– Fitch
• Rating Categories– Investment grade– Speculative grade/Junk Bonds
Default Risk and Ratings
Figure 14.8 Definitions of Each Bond Rating Class
• Coverage ratios• Leverage ratios• Liquidity ratios• Profitability ratios• Cash flow to debt
Factors Used by Rating Companies
Default Risk and Yield
• Risk structure of interest rates• Default premiums– Yields compared to ratings– Yield spreads over business cycles
Figure 14.11 Yields on Long-Term Bonds, 1954 – 2006