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Suppose we have a portfolio of i terest rate swaps that we wish to delta hedge. we build a delta ladder by shocking the instruments used to build the forecasting and discouting curves (Eurodollar futures, par swaps etc...)

Suppose we wish to hedge by using key par swaps identified from the delta ladder. Im confused about the proper hedge ratio to be used. Do we need to calculate the delta of the par swaps or is the hedge ratio simply the value i. the delta ladder for those instruments?

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What you are probably looking for is DV01 based hedging. Let's suppose your delta risk strip is defined as the market value impact of +1bp shift in the par instruments. As an example, suppose you have a risk of -5k DV01 in the 5Y bucket.

In order to completely hedge this -5k DV01 risk, your hedge needs to have +5k DV01 risk. Assuming zero interest rates, your hedge would be to pay 5Y IRS with 10MM of notional. In the general case (nonzero flat IR curve) your hedge ratio is defined as the ratio of the corresponding DV01's.

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