# Number of futures contracts to modify a bond portfolio duration given a cheapest-to-deliver bond value (formula)

NF = (((MDURt – MDURi) * Portfolio Value)/(MDURctd * Pctd)) * Conversion Factor

MDURt = the target modified duration for the portfolio

MDURi = initial modified duration of the portfolio

MDURctd = the modified duration of the cheapest-to-deliver bond

Pctd = the price of the cheapest to deliver bond

Conversion Factor of the cheapest-to-deliver bond

It seems this formula is actually identical to another one involve bond yield and thus I didn’t include it immediately but if you just put cheapest-to-deliver where futures go and conversion factor when bond yield goes in the other formula you should get the same number as using this, the brackets are wash mathematically.