week 6

• Fixed Income Security


  Financial claims with promised cashflows of known fixed amount paid at fixed dates
• Fixed-income securities


  • Treasury Securities
  • Federal Agency Securities
  • Corporate Securities
  • Municipal Securities
  • Mortgage-backed Securities
  • Derivatives (CDO's, CDS's, etc.)
• Total value of US Fixed Income Securities Q1 2017 = USD 39.7tn
• Fixed-Income Market Participants


  • Issuers: Governments, Corporations, States, Municipalities, SPVs
  • Intermediaries: Primary Dealers, Other Dealers, Investment Banks, Credit-rating Agencies, Credit Enhancers, Liquidity Enhancers
  • Investors: Governments, Pension Funds, Insurance Companies, Commercial Banks, Mutual Funds, Hedge Funds, Foreign Institutions, Individuals
• Bonds


  Debt obligations of issuers (borrowers) to bondholders (creditors)
• When the bond matures, the issuer repays the debt by paying the bond's par value
• The coupon rate of the bond determines the interest payment: The annual payment is the coupon rate times the bond's par value
• Treasury notes are issued with original maturities ranging between 1 and 10 years, while Treasury bonds are issued with maturities ranging from 10 to 30 years
• Bond example


  • Par value of $1,000, coupon rate of 8%, 30-year maturity

  
• Bond types based on coupon or cash flow pattern

  • Straight-bond
  • Zero-coupon bond
  • Deferred-coupon bond
  • Perpetuity bond
• Foreign bonds


  Bonds issued by a borrower from a country other than the one in which the bond is sold
• Eurobonds


  Bonds denominated in one currency, but sold in other national markets
• Inverse Floaters


  Bonds where the coupon rate falls when the general level of interest rates rises
• Asset-Backed Bonds


  Bonds where the payments are tied to the performance of a particular asset
• Catastrophe Bonds


  Bonds that transfer "catastrophe risk" from the firm to the capital markets
• Indexed Bonds


  Bonds where payments are tied to a general price index or the price of a particular commodity
• Example 1: 3-year coupon bond

  • Principal of $1,000, annual coupon payment of 5%
• Valuation components


  • Time value of principal and coupons
  • Risks: Inflation, Credit, Timing (callability), Liquidity, Currency
• Valuation of discount bonds


  1. P0 = F / (1 + r)^T

  2. P0 = Present value

  3. F = Face value

  4. r = Interest rate

  5. T = Maturity

  
• Valuation of coupon bonds


  1. Discount the cashflow by the opportunity cost of capital

  2. P0 = C1 / (1 + y)^1 + C2 / (1 + y)^2 + ... + (C + F) / (1 + y)^T

  3. P0 = Present value

  4. C = Coupon payment

  5. y = Yield to maturity

  6. T = Maturity

  7. F = Face value
• Example 2: IBM bond

  • Pays $115 every September 30 for 5 years, plus $1,000 in September 2025
  • Yield to maturity is 7.5%

  
• Example 2 continued


  • Another bond: $100 interest payment per year, 5 year maturity, $1,000 face value, 12% yield to maturity

  
• Coupon bond

  Bond that pays a coupon (interest payment) annually
• Valuation of Coupon Bonds


  1. Discount the cashflow by the opportunity cost of capital (normally government bill rate)

  2. Calculate the present value of the bond
• P0


  Present value of the bond
• y


  Yield to maturity
• F


  Face value of bond
• For pure discount bonds, the YTM's are the current spot rates
• (P0, y, C) is over-determined; any two determines the third
• Valuation of Coupon Bonds

  • Example 2
  • Example 3
• As interest rates rise and fall

  Bondholders experience capital losses and gains

  
• Bond prices and yields


  • Negative relationship: larger yields mean lower bond prices
  • Non-linear relationship: progressive increases in the interest rate result in progressively smaller reductions in the bond price

  
• Yield to maturity (YTM)


  The interest rate that makes the present value of the bond's payments equal to its price

  
• Interest rate risk


  • As interest rates rise, bondholders experience capital losses
  • As interest rates fall, bondholders experience capital gains
  • These gains or losses make fixed-income investments risky, even if the coupon and principal payments are guaranteed

  
• Duration


  The weighted average term to maturity (or the times to each of the cash payments)
• Modified duration


  Sensitivity of bond prices to yield changes = Duration/(1+yield)

  
• Measures of Interest rate risk

  • Example 5
• Duration decreases with coupon rate
• Duration decreases with YTM
• Duration usually increases with maturity