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Bond Prices and Yields

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Bond Prices and Yields. CHAPTER 14. Bond Characteristics. Face or par value Coupon rate Zero coupon bond Compounding and payments Accrued Interest Indenture. Different Issuers of Bonds. U.S. Treasury Notes and Bonds Corporations Municipalities

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  1. Bond Prices and Yields CHAPTER 14

  2. Bond Characteristics • Face or par value • Coupon rate • Zero coupon bond • Compounding and payments • Accrued Interest • Indenture Bahattin Buyuksahin, Derivatives Pricing

  3. 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 Bahattin Buyuksahin, Derivatives Pricing

  4. Figure 14.1 Listing of Treasury Issues Bahattin Buyuksahin, Derivatives Pricing

  5. Figure 14.2 Listing of Corporate Bonds Bahattin Buyuksahin, Derivatives Pricing

  6. Provisions of Bonds • Secured or unsecured • Call provision • Convertible provision • Put provision (putable bonds) • Floating rate bonds • Preferred Stock Bahattin Buyuksahin, Derivatives Pricing

  7. Convertible Bonds • Give bondholders an option to exchange each bond for a specified nb of shares of common stock • Conversion ratio • = number of shares per convertible bond • Market conversion value • = conversion ratio * current market value per share • Conversion premium • = bond value - conversion value • intuitively: extra amount to pay so as to become a shareholder Bahattin Buyuksahin, Derivatives Pricing

  8. Conversion Example Bahattin Buyuksahin, Derivatives Pricing

  9. Conversion Example Bahattin Buyuksahin, Derivatives Pricing

  10. Innovation in the Bond Market • Inverse Floaters • Asset-Backed Bonds • Catastrophe Bonds • Indexed Bonds Bahattin Buyuksahin, Derivatives Pricing

  11. Table 14.1 Principal and Interest Payments for a Treasury Inflation Protected Security Bahattin Buyuksahin, Derivatives Pricing

  12. Bond Prices and Yields • Time value of money and bond pricing • Time to maturity and risk • Yield to maturity • vs. yield to call • vs. realized compound yield • Determinants of YTM • risk, maturity, holding period, etc. Bahattin Buyuksahin, Derivatives Pricing

  13. 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 Bond Pricing Bahattin Buyuksahin, Derivatives Pricing

  14. Price: 10-yr, 8% Coupon, Face = $1,000 Ct = 40 (SA) P = 1000 T = 20 periods r = 3% (SA) Bahattin Buyuksahin, Derivatives Pricing

  15. Bond Pricing • Equation: • P = PV(annuity) + PV(final payment) • = • Example: Ct = $40; Par = $1,000; disc. rate = 4%; T=60 Bahattin Buyuksahin, Derivatives Pricing

  16. 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 Bahattin Buyuksahin, Derivatives Pricing

  17. Prices vs. Yields • P   yield  • intuition • convexity • Fig 14.3 • intuition: yield   P   price impact  Bahattin Buyuksahin, Derivatives Pricing

  18. Figure 14.3 The Inverse Relationship Between Bond Prices and Yields Bahattin Buyuksahin, Derivatives Pricing

  19. Table 14.2 Bond Prices at Different Interest Rates (8% Coupon Bond, Coupons Paid Semiannually) Bahattin Buyuksahin, Derivatives Pricing

  20. 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 Bahattin Buyuksahin, Derivatives Pricing

  21. Yield to Maturity Example 10 yr Maturity Coupon Rate = 7% Price = $950 Solve for r = semiannual rate r = 3.8635% Bahattin Buyuksahin, Derivatives Pricing

  22. 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 % Yield to Call Bahattin Buyuksahin, Derivatives Pricing

  23. Pure Discount Bonds (Zero-Coupon Bonds) A zero rate (or spot rate), for maturity T is the rate of interest earned on an investment that provides a payoff only at time T • Discount bonds, also called zero-coupon bonds, are securities which “make a single payment at a date in the future known as maturity date. The size of this payment is the face value of the bond. The length of time to the maturity date is the maturity of the bond” (Campbell, Lo, MacKinley (1996)). Bahattin Buyuksahin, Derivatives Pricing

  24. Pure Discount Bond • The promised cash payment on a pure discount bond is called its face value or par value. Yield (interest rate) on a pure discount bond is the annualized rate of return to investors who buy it and hold it until it matures. Bahattin Buyuksahin, Derivatives Pricing

  25. Example Bahattin Buyuksahin, Derivatives Pricing

  26. Bond Pricing • To calculate the cash price of a bond we discount each cash flow at the appropriate zero rate • The theoretical price of a two-year bond providing a 6% coupon semiannually is Bahattin Buyuksahin, Derivatives Pricing

  27. Bond Yield • The bond yield is the discount rate that makes the present value of the cash flows on the bond equal to the market price of the bond • Suppose that the market price of the bond in our example equals its theoretical price of 98.39 • The bond yield is given by solving to get y = 0.0676 or 6.76%. Bahattin Buyuksahin, Derivatives Pricing

  28. Par Yield • The par yield for a certain maturity is the coupon rate that causes the bond price to equal its face value. • In our example we solve Bahattin Buyuksahin, Derivatives Pricing

  29. Par Yield (continued) In general if m is the number of coupon payments per year, d is the present value of $1 received at maturity and A is the present value of an annuity of $1 on each coupon date Bahattin Buyuksahin, Derivatives Pricing

  30. Bootstrap Method to calculate discount factor • A discount function is a set of discount factors, where each discount factor is just a present value multiplier. For example, d(1.0) is the present value of $1 dollar received in one year. The key idea is that each d(x) can be solved as one variable under one equation because we already solved for shorter-term discount factors. • The most popular approach is to use bootstrap method Bahattin Buyuksahin, Derivatives Pricing

  31. Bootstrap : Example Bahattin Buyuksahin, Derivatives Pricing

  32. Discount Factor Bahattin Buyuksahin, Derivatives Pricing

  33. Determining Treasury Zero Rates Bahattin Buyuksahin, Derivatives Pricing

  34. Treasury Zero Rate Curve Bahattin Buyuksahin, Derivatives Pricing

  35. Figure 14.4 Bond Prices: Callable and Straight Debt Bahattin Buyuksahin, Derivatives Pricing

  36. Example 14.4 Yield to Call Bahattin Buyuksahin, Derivatives Pricing

  37. Realized Yield versus YTM • Reinvestment Assumptions • Holding Period Return • Changes in rates affect returns • Reinvestment of coupon payments • Change in price of the bond Bahattin Buyuksahin, Derivatives Pricing

  38. Figure 14.5 Growth of Invested Funds Bahattin Buyuksahin, Derivatives Pricing

  39. Figure 14.6 Prices over Time of 30-Year Maturity, 6.5% Coupon Bonds Bahattin Buyuksahin, Derivatives Pricing

  40. Holding-Period Return: Single Period HPR = [ I + ( P0 - P1 )] / P0 where I = interest payment P1= price in one period P0 = purchase price Bahattin Buyuksahin, Derivatives Pricing

  41. Holding-Period Return 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)] / 1000 HPR = 10.85% (semiannual) Bahattin Buyuksahin, Derivatives Pricing

  42. Figure 14.7 The Price of a 30-Year Zero-Coupon Bond over Time at a Yield to Maturity of 10% Bahattin Buyuksahin, Derivatives Pricing

  43. Default Risk and Ratings • Rating companies • Moody’s Investor Service • Standard & Poor’s • Fitch • Rating Categories • Investment grade • Speculative grade/Junk Bonds Bahattin Buyuksahin, Derivatives Pricing

  44. Figure 14.8 Definitions of Each Bond Rating Class Bahattin Buyuksahin, Derivatives Pricing

  45. Factors Used by Rating Companies • Coverage ratios • Leverage ratios • Liquidity ratios • Profitability ratios • Cash flow to debt Bahattin Buyuksahin, Derivatives Pricing

  46. Table 14.3 Financial Ratios and Default Risk by Rating Class, Long-Term Debt Bahattin Buyuksahin, Derivatives Pricing

  47. Figure 14.9 Discriminant Analysis Bahattin Buyuksahin, Derivatives Pricing

  48. Protection Against Default • Sinking funds • Subordination of future debt • Dividend restrictions • Collateral Bahattin Buyuksahin, Derivatives Pricing

  49. Figure 14.10 Callable Bond Issued by Mobil Bahattin Buyuksahin, Derivatives Pricing

  50. Default Risk and Yield • Risk structure of interest rates • Default premiums • Yields compared to ratings • Yield spreads over business cycles Bahattin Buyuksahin, Derivatives Pricing