Use 2 of Futures Contracts - Hedging Interest-rate Risk Bond Portfolio P, hedge it with futures contract dP+qx dH = 0 (1) The underlying bond on Futures contract is fictive, so cheapest-to-deliver bond is selected and delivered. dHcTD = CF x dH, that is dH q = dPxCF dHcTD = Since $Durp = -MDP X Vp dHCTD plug into (1) CF " dP + q x $DurpXdy $Dur HCTDXdy1 dHcTD CF = 0 (2) CF =-MDHCTD X NH X PCTD, where PCTD = F CF $Dur HCTD = -MDHCTD XVHCTD Substitute into equation (2), dy 9 = MDP X Vp MDHCTD X NH XPCTD CF X dy1 or q= MDHCTD MDP X VP NH FT CF dy CF X dy1 Example 7: consider now an investor who holds a bond portfolio whose principal value, price (%) and modified duration are, respectively, $10,000,000, 102 and 8. He wishes to be hedged against a rise in interest rates. He uses a future contract as hedging instrument whose features are the following: o Future price of the contract is 103 o Future contract size is $100,000 O O The MD of bond B delivered (contained in the grades of the underlying assets) is 7.6024 Bond B conversion factor is 112.74% Then what is the hedge ratio of such future contract (assuming a parallel shift in yield term structure)?