Say I buy a 10-year bond with a notional of 100k. To hedge my credit risk entirely I could buy a 10-year CDS, also on a notional of 100k.
Now, if there are only 5-year CDS trading and no 10-year CDS, then I could still hedge the first 5 years of my bond, assuming that I do not "care" about the years 5 till 10 right now.
But the question is, on which notional should I buy the 5-year CDS. Intuitively I would say it should also be 100k. But I heard the following reasoning which I do not fully understand:
Making the simplying assumption that the risky annuities (RA) of the two CDS contracts are 5 and 10 respectively one would need to buy a 5-year CDS with a notional of 200k. The reason being that (in its first five years) a 5-year CDS with 2*100k notional and RA of 5 acts like a 10-year CDS with notional 100k and RA 2*5.
Could somebody explain this behaviour? Is the reasoning right or wrong? Basically, how would one try to cope with the fact that 10-year CDS are not currently traded, but 5-year CDS are?