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Bonds, Arbitrage

types of bonds -  

  • issued by gov't >> gov't bonds
  • issued by firms >> corporate bonds
  • risk premium - difference between interest rate paid and interest rate paid on best rated bond
  • junk bond - high default risk
  • discount bond - offers single payment (face value) at maturity
  • coupon bond - offers multiple payments before maturity, another payment at maturity
    • coupon payments - payments before maturity
    • face value - final payment at maturity
    • coupon rate - ratio of payments to face value
    • current yield - ratio of payment to price of bond
  • treasury bills (T-bills) - gov't bonds w/ maturity of 1 year
    • price equal to payment in terms of present values
    • $Pt = payment / (1+it)
  • treasury notes - maturity of 1 to 10 years
  • treasury bonds - maturity of 10 or more years
  • indexed bonds - payments adjusted for inflation

bond characteristics -  

  • default risk - risk that firm issuing bond will not pay full amount
  • maturity - length of time over which bond makes payments
  • yield curve (term structure of interest rates) - relation between maturity and yield of bond

arbitrage - comparing expected returns  

  • 1 year bond >> worth $M (1+it) next year
  • 2 year bond >> worth $M (Pt+1/P2t)
    • Pt+1 = price expected to be sold next year
    • P2t = price of 2 year bond
  • same expected 1 year return >> (1+it) = (Pt+1/P2t)
    • P2t = Pt+1 / (1+it)
    • price of 2 year bond equal to expected bond price next in present values
    • Pt+1 = (final payment) / (1+it+1)
    • expected bond price relates to expected interest rate
    • P2t = (final payment) / [(1+it)(1+it+1)]
    • P2t = (final payment) / (1+i2t)2
  • (1+i2t)2 = (1+it)(1+it+1)
    • i2t ~ (1/2)(it + it+1)
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