Bond Prices and Yields

CHAPTER 10 10.1 BOND CHARACTERISTICS Bond Prices and Yields Bond Characteristics Face or par value Coupon rate Treasury Notes and Bonds Compounding and payments T Note maturities range up to 10 years T bond maturities range from 10 – 30 years Bid and ask price Indenture Accrued interest – Zero coupon bond – Accrued Interest Figure 10.1 Listing of Treasury Issues – Quoted in points and as a percent of par – Quoted price does not include interest accrued Corporate Bonds Most bonds are traded over the counter Registered Bearer bonds Call provisions Convertible provision Put provision (putable bonds) Floating rate bonds Preferred Stock Figure 10.2 Investment Grade Bonds Other Domestic Issuers Federal Home Loan Bank Board Farm Credit Agencies Ginnie Mae Fannie Mae Freddie Mac Innovations in the Bond Market Reverse floaters AssetAsset-backed bonds PayPay-inin-kind bonds Catastrophe bonds Indexed bonds 10.2 BOND PRICING – TIPS (Treasury Inflation Protected Securities) Bond Pricing PB ∑ T = t =1 Ct T (1 + r ) + Par Value T T + (1 r ) PB = Price of the bond Ct = interest or coupon payments T = number of periods to maturity r = semisemi-annual discount rate or the semisemi-annual yield to maturity Price of 8%, 10-yr. with yield at 6% P P B = 40 × ∑ B = 1,148 .77 20 t =1 1 1 + 1000 × t 20 (1.03) (1 .03) Coupon = 4%*1,000 = 40 (Semiannual) Discount Rate = 3% (Semiannual) Maturity = 10 years or 20 periods Par Value = 1,000 Bond Prices and Yields 10.3 BOND YIELDS Yield to Maturity 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 Figure 10.3 The Inverse Relationship Between Bond Prices and Yields YTM is the discount rate that makes the present value of a bond’ bond’s payments equal to its price 8% coupon, 3030-year bond selling at $1,276.76: $1, 276.76 = ∑ 60 t =1 $40 $1, 000 + t (1 + r ) (1 + r )60 Alternative Measures of Yield Current Yield Yield to Call – Call price replaces par – Call date replaces maturity Holding Period Yield – Considers actual reinvestment of coupons – Considers any change in price if the bond is held less than its maturity Figure 10.4 Bond Prices: Callable and Straight Debt Figure 10.5 Growth of Invested Funds 10.4 BOND PRICES OVER TIME Premium and Discount Bonds Premium Bond Figure 10.6 Premium and Discount Bonds over Time – Coupon rate exceeds yield to maturity – Bond price will decline to par over its maturity Discount Bond – Yield to maturity exceeds coupon rate – Bond price will increase to par over its maturity Figure 10.7 The Price of a ZeroCoupon Bond over Time 10.5 DEFAULT RISK AND BOND PRICING Default Risk and Ratings Rating companies Figure 10.8 Definitions of Each Bond Rating Class – Moody’ Moody’s Investor Service – Standard & Poor’ Poor’s – Fitch Rating Categories – Investment grade – Speculative grade Factors Used by Rating Companies Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt Protection Against Default Sinking funds Subordination of future debt Dividend restrictions Collateral Figure 10.9 Callable Bond Issued by Mobil 10.6 THE YIELD CURVE Term Structure of Interest Rates Relationship between yields to maturity and maturity Yield curve - a graph of the yields on bonds relative to the number of years to maturity Figure 10.10 Yields on Long-Term Bonds – Usually Treasury Bonds – Have to be similar risk or other factors would be influencing yields Figure 10.11 Treasury Yield Curves Theories of Term Structure Expectations – Long term rates are a function of expected future short term rates – Upward slope means that the market is expecting higher future short term rates – Downward slope means that the market is expecting lower future short term rates Liquidity Preference – Upward bias over expectations – The observed longlong-term rate includes a risk premium Figure 10.12 Returns to Two 2-year Investment Strategies Forward Rates Implied in the Yield Curve (1+ y n ) (1 .12 ) 2 n = (1+ y n −1) (1+ f n ) n −1 = (1 . 11) 1 (1 .1301 ) For example, using a 1-yr and 2-yr rates Longer term rate, y(n) = 12% Shorter term rate, y(n-1) = 11% Forward rate, a one-year rate in one year = 13.01% Figure 10.13 Illustrative Yield Curves Figure 10.14 Term Spread