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L Pch13

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  • 1. Investments Chapter 13: Interest Rates and Bond Valuation
  • 2. Definition: Bonds and Yields
    • Bonds
    • Represent a claim on future cash flows (coupon payments and par value).
    • Yield to Maturity
    • The annualized discount rate that makes the present value of the future cash flows equal to the current price of the bond.
  • 3. Other Measures of Bond Yields
    • Coupon yield / nominal yield.
    • Current yield.
    • Yield to call.
    • Realised yield.
  • 4. Yield Curve: I
    • Bond prices are related inversely to market interest rates.
    • This relation is NOT tautological, however:
    • bond prices and market interest rates are determined simultaneously by the underlying economic forces that drive the supply and demand for money.
  • 5. Yield Curve: II
    • The market generally has various interest rates for various maturities.
    • The relationship between the market interest rate and the time to maturity is known as the yield curve.
  • 6. Yield Curve: III Exhibit 13.1 Examples of actual yield curves
  • 7. Spot and Forward Rates
    • The Spot Rate
    • The yield to maturity of a zero-coupon bond that has a stated maturity.
    • The Forward Rate
    • The yield to maturity of a zero-coupon bond that an investor agrees to purchase at some future specified date.
  • 8. Spot- & forward rates for pure discount bonds Spot rate is the yield (return) of a pure discount bond, which is sold att discount, since discount bonds, P < F. If a one-year pure discount bond, just issued, is sold at P = €90.9 and has an F = €100, the spot rate is :
  • 9. Spot & forward rates for pure discount bonds Forward rate is the interest rate an investor will pay to buy a bond in the future , no matter its true interest rate (or its bond price), that date. If I sign a forward contract to buy next year a two-years bond at a P = SEK892.9 (with F = SEK1000, to be paid in two years from now), the forward rate is : If the interest rate next year becomes 10%, the price of the bond will be SEK909. In that case, I gain since I buy the bond at SEK892.9 .
  • 10. Spot- & forward rates for pure discount bonds Forward rates are derived from spot rates and provide a good information on the expected interest rates in the future. Maturity (n) Spot (R m ) Forward (f n ) 1 5 - 2 5.8 6.606 3 6.3 7.307 4 6.4 6.701 5 6.45 6.65
  • 11. Spot- & forward rates for pure discount bonds If we graph the spot yield curve, it is 5 % for 1-year and 6.45 % for 5-years. But why is it f 2 = 6.606 % ? Strategy 1 : Save 1 $ directly in 2-years and get: 1(1 + R 2 ) 2 = 1(1.058) 2 = 1.11936. Strategy 2 : (a) Save first 1 $ for 1-year, and (b) sign a contract to invest your $ and its return in an implied rate , (i.e. f 2 ), in order to get the same as in strategy 1.
  • 12. Spot- & forward rates for pure discount bonds [1(1.05)]*[1 + r impl ] = 1.11936 , i.e. 1 + r impl = 1.11936 / 1.05, => r impl = f 2 = 0.06606. Alternatively, R 2 = (R 1 + f 2 ) / 2. The Formula to estimate implied forward rates (f n ) from one periods’ spot rates (R n ) is:
  • 13. Calculating Spot and Forward Rates Exhibit 13.2 Spot and forward rates for annually compounded, zero-coupon bonds Source: From Introduction to Investments , 2nd edn, by Levy. © 1999. Reprinted with permission of South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730-2215.
  • 14. Explaining Yield Curves
    • The Expectations Hypothesis:
    • - The Local Expectations Hypothesis.
    • - The Unbiased Expectations Hypothesis.
    • The Liquidity Preference Hypothesis.
    • The Market Segmentation Hypothesis.
    • - The Preferred Habitat Hypothesis.
  • 15. Credit Risk
    • The risk that a company issuing bonds fails to pay the coupon payments or par value in a timely manner.
    • Firms that assess the credit risk of bonds are known as credit rating agencies.
  • 16. Bond Ratings Exhibit 13.4 Bond rating categories by company Source: From Introduction to Investments , 2nd edn, by Levy. © 1999. Reprinted with permission of South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730-2215.
  • 17. Junk Bonds
    • Bonds rated below BBB or Baa (speculative-grade bonds).
    • Junk bonds have two attractive features:
    • 1. They offer relatively high yields (if bankruptcy does not occur).
    • 2. They have low correlations with changes in overall interest rates.
  • 18. Embedded Options in Bonds
    • The Call Feature
    • The bond issuer has the right to buy bonds back at a stated redemption price.
    • The Conversion Feature
    • The bond issuer has the right to convert bonds in common or preferred stocks.
  • 19. Convertible Bonds
    • A convertible bond is similar to a bond with warrants.
    • The most important difference is that a bond with warrants can be separated into different securities and a convertible bond cannot.
    • Recall that the minimum (floor) value of convertible:
      • Straight or “intrinsic” bond value
      • Conversion value
    • The conversion option has value.
  • 20. The Value of Convertible Bonds
    • The value of a convertible bond has three components:
      • Straight bond value
      • Conversion value
      • Option value
  • 21. Convertible Bond Problem
    • Litespeed, Inc., just issued a zero coupon convertible bond due in 10 years.
    • The conversion ratio is 25 shares.
    • The appropriate interest rate is 10%.
    • The current stock price is $12 per share.
    • Each convertible is trading at $400 in the market.
      • What is the straight bond value?
      • What is the conversion value?
      • What is the option value of the bond?
  • 22. Convertible Bond Problem (continued)
      • What is the straight bond value?
      • What is the conversion value?
      • 25 shares × $12/share = $300
      • What is the option value of the bond?
      • $400 – 385.54 = $14.46
  • 23. The Value of Convertible Bonds Convertible Bond Value Stock Price Conversion Value Straight bond value = conversion ratio floor value floor value Convertible bond values Option value