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Is the Protection Buyer Hedged?

Upon default, the protection buyer

receives $10m from the protection seller

and (assuming 40% recovery)

delivers defaulted debt worth $4m.

At the inception of the contract, the GMAC note was only worth $9.3m.

So the buyer receives a net of $6m from the CDS,

but has really lost only 9.3-4=$5.3m. So the buyer has too much CDS.

The correct hedge ratio is given by

In this case the protection buyer should buy $10m x (.93-.4)/(1-.4)=$8.9m notional CDS to be hedged.

(Note the assumption of the recovery rate!)

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