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101 Concepts for the Level I Exam

Essential Concept 77: Fixed-Income Forward and Futures Contracts


Unique issues:

  • Quoted priced, accrued interest and full price: The quoted price is the clean price without the interest accrued since the last coupon date. The full price is the quoted price plus interest accrued since the last coupon date.
  • Conversion factor: Fixed-income futures contracts often have more than one bond that can be delivered by the seller. Because bonds trade at different prices based on their maturity and stated coupon, an adjustment known as the conversion factor is used to make all deliverable bonds roughly equal in price.
  • Cheapest to deliver bonds: However, even after applying the conversion factor there will be a bond that is the cheapest to deliver.

The fixed-income forward or futures price can be expressed as:

\mathrm{F}}_0\left(\mathrm{T}\right)\mathrm{=}{\mathrm{FV}}_{\mathrm{0,T}}\mathrm{(}{\mathrm{B}}_0\mathrm{+}{\mathrm{AI}}_0\mathrm{)-}{\mathrm{AI}}_{\mathrm{T}}\mathrm{-}{\mathrm{FVCI}}_{\mathrm{0,T}}

 

The quoted price which includes the conversion factor is:

\mathrm{QF}}_0\mathrm{=}{\mathrm{F}}_0\mathrm{(T)/CF}

 

 

Example: Suppose T = 0.25, CF = 0.8,  = 107 (quoted price),  (meaning no accrued interest over the life of the contract),

r = 0.2\%, {\mathrm{AI}}_0\mathrm{=0.07\ and\ }{\mathrm{AI}}_{\mathrm{T}}\mathrm{=0.20}

 

 

The futures price is:

\mathrm{F}}_0\left(\mathrm{T}\right)\mathrm{=}{\mathrm{FV}}_{\mathrm{0,T}}\mathrm{(}{\mathrm{B}}_0\mathrm{+}{\mathrm{AI}}_0\mathrm{)-}{\mathrm{AI}}_{\mathrm{T}}\mathrm{-}{\mathrm{FVCI}}_{\mathrm{0,T}}

\mathrm{F}}_0\left(\mathrm{T}\right)\mathrm{=}\left(\mathrm{107+0.07}\right){\left(\mathrm{1+0.002}\right)}^{\mathrm{0.25}}\mathrm{-}\mathrm{0.20-0.0=106.9235}

 

The quoted futures price is:

\mathrm{QF}}_0\mathrm{=}{\mathrm{F}}_0\mathrm{(T)/CF}

\mathrm{QF}}_0\mathrm{=}\frac{\mathrm{106.9235}}{\mathrm{0.8}}\mathrm{=133.6544.}