on-year zero rate???

Discussion in 'Fixed Income (P1.T4 or P2.T5)' started by dandy, Feb 21, 2010.

  1. dandy

    dandy New Member

    Hello
    please can you help me
    because there is quite a difficult task for me

    zero-coupon government bonds with maturities ranging 1-5 years now have the following yields: 6%, 7%, 8%, 8,5%, 10,5%. using the expectations theory of the term structure what will you say the market expects the on-year zero rate to be one year from now???

    Thanks in advance
     
  2. structurer

    structurer New Member

    around 8%
     
  3. afterworkguinness

    afterworkguinness Active Member

    The solution is interest rate parity; the relationship between current spot rates and forward rates.
    Firstly, let's clarify that the rate your trying to solve for is a forward rate - the 1 year forward rate maturing in 2 years (forward rate that starts in 1 year and goes for 1 year).
    To prevent arbitrage, the 1 year forward rate, maturing in 2 years must equal :

    (assuming annual compounding)

    (1 + 2 year spot rate)^2 = (1 + 1 year spot rate)^1 * (1 +1 year forward rate maturing in 2 years)^1

    Note the pattern of (1 + r)^t to calculate future values.

    The logic behind this is that we should be indifferent if we invest now for 2 years at the 2 year spot, or invest for 1 year at the 1 year spot and roll over after 1 year for another 1 year (total time in the investment is still 2 years) at the 1 year forward rate agreed upon at time 0;
     
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