It fails to recognize the uncertainty related to long

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short term rates. It fails to recognize the uncertainty related to long term bond. Local expectation theory: Return of the bonds with different maturities is same over short term horizons. Return to maturity theory: Rolling over short term bond gives the same return as a long term zero coupon bond. 2/11/17 Fixed Income Securities 38
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Expectation theory o Liquidity theory: The forward rate reflect both expectation about the future short term rate plus a liquidity premium due to risk associated with bonds (price + reinvst. risk). The risk premium rises uniformly with maturity. The curve can only be upward sloping. 2/11/17 Fixed Income Securities 39
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Expectation theory o Preferred Habitat theory The risk premium is a function of the preferred habitat of the investors (missmatch of demand and supply). It reflects the compensation for the risk aversion of the participants to price/reinvestment risk. It does not necessarily increases with the maturity, ie can be positive or negative. 2/11/17 Fixed Income Securities 40
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Market Segmentation theory 2. Market Segmentation theory o Investor have their preferred habitat due to the nature of their asset-­‐liabilities structure. They are not willing to shift from one segment to the other to take advantage of the market opportunities. 2/11/17 Fixed Income Securities 41
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Conclusion The government yield curve is good for benchmarking, but cannot be used for pricing. Term structures of interest rates based on the spot rates is the correct one. The spot rate is the yield of zero-coupon of a government bond. Spot rates are derived either from forward rates or par rates. 2/11/17 Fixed Income Securities 42
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Appendix 2/11/17 43 Fixed Income Securities
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Bootstrapping the Yield Curve To find the spot rates we have to start for the 1 st period par bond and then work out the discount factor df 1 and the spot rate r 1 . We then proceed to the 2 nd period par bond and calculate the df 2 and spot rate r 2. 2/11/17 Fixed Income Securities 44 Period Years Par coupon Spot rate 1 0.5 5.25% 5.25% 2 1 5.50% 5.50% 3 1.5 5.75% 5.76% 4 2 6.00% 6.02% 5 2.5 6.25% 6.28% 6 3 6.50% 6.55%
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Bootstrapping the Yield Curve % 76 . 5 ? 2 0275 . 0 2 02625 . 0 2 % 875 . 2 2 % 75 . 5 2 2 1 100 2 2 1 2 2 1 2 100 3 3 2 1 5 . 1 3 3 5 . 1 2 2 5 . 1 1 5 . 1 = = = = = = Ο Π Ξ Μ Ν Λ + + + Ο Π Ξ Μ Ν Λ + + Ο Π Ξ Μ Ν Λ + = r result r r r c r c r c r c 2/11/17 Fixed Income Securities 45 The 6mnth UST Bill and 1 yr UST are the spot rates already. Need to calculate the spot rate for 1.5y UST. Given that it trades at par the following relationship holds:
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Bootstrapping the Yield Curve Follow the same procedure to get the implied spot rate curve. o Meaning we now need to calculate a 2yr bond with par coupon of 6%. The implied spot rate will be 6.02%. o Continue with the 2.5yr, 3yr bonds and so on until the end of the curve.
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