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Good evening,

I try to compute the performance of a portfolio of a CDS. I already know how to mark-to-market a CDS but typically, the first time you enter a CDS, you invest zero as the mark-to-market of a CDS is zero at t=0, so that the value of the portfolio is still zero. So when you exit the CDS, you do a non-zero P&L. But how to compute the return in this case, because in the usual definition of a return, it would imply a division by zero, right? I'm pretty confused on the subject, do you have any clue?

Cheers!

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There are a number of ways you might consider it:

1) As an investor (speculator) you may be required to post collateral that permits the holding of the position. What is your return relative to the invested collateral (and/or possibly expected collateral if the trade moves adversely)

2) This is one of the performance metrics measured in an investment bank. Every position requires an amount of capital to be held as a regulated percentage of its market risk (see Basel III capital rules), as well as other capital rule considerations as part of the wider portfolio. The return is therefore the pnl recouped relative to the amount of regulatory capital exposed (possibly time weighted).

3) A common method, and my preferred method for personal risk management is to define a nominal capital and allocate it to that product. Say you sell an equity future. You don't need to invest capital in that but the return is fairly obvious; it matches the index on the underlying notional of the contract (you may be using futures to gain leverage in which case your returns are amplified). For CDS it might or might not make sense to use the notional of the contract, but for personal trading you might choose to allocate an amount of secured collateral to a position and measure the return against that.

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Usually when you invest in a CDS you rarely pay zero as the CDS coupons, unlike textbooks CDS and rates swaps, are standardized to 25bp, 100bp or 500bp. To compensate for the difference with the quoted spread, you receive/pay an upfront. So in practice you invest the upfront.

Also in practice, if you are running a mutual fund, you will never find a bank to enter a CDS with you if you don't hold cash in your fund ptf as they will be exposed to a huge counterparty risk.

All in all, If you are able to invest in a CDS at zero upfront and without holding cash (or capital if you are a bank) to metigate your counterparty risk than you have an infinite leverage. So don't be surprized to have infinite return.

Finally if you insist to to calculate a return on such textbook portfolio I suggest to divid by gross notionals.

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