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BOND MATH: The Theory Behind the Formulas by Donald J. Smith

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Money Market Implied Forward Rates

Suppose that 90-day LIBOR is 1.00% and 180-day LIBOR is 2.00%. What rate would a true believer in the expectations theory of the yield curve anticipate for 90-day LIBOR, 90 days into the future? That is, what's the 90 × 180 day forward LIBOR—3.00%, calculated as a simple average? Unfortunately, you cannot use the approximation formula or even the accurate formula with money market instruments because their rates have different periodicities. 90-day LIBOR has a periodicity of 4 and 180-day LIBOR a periodicity of 2, assuming a 360-day year. equations 5.2 and 5.4 simply do not apply.

Our true believer could delve back into Chapters 1 and 2 and retrieve the correct procedures to deal with the periodicity problem. ...

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