I am trying to determine the effect of recovery rate on the Kth-to-default CDS Basket made up of 5 names (all major investment bank names). I repeatedly change the recovery rate assumption from 0 to 1.0 on the Markit provided spreads when building my credit curve and re-value the fair spread on kth-to-default basket. If I plot the fair spread vs recovery rate, I get something like below.
I can probably explain the plot for first-to-default (k=1). As the RR increases, the protection seller has less to pay in case of first default, so the spread decreases (?) However, I am struggling to explain the apparent no effect of RR on second and third to default.
Would like to get your opinion on if this plot looks good to you? Any idea how it can be explained?
Thank you for your time.