# Optimising PnL on an interest rate swap

"You are about to execute a zero fixed rate vs. Float rate swap under daily cash margining with a client in a normal swap rate curve environment. The Bank is receiving fixed. Just before execution, you get an opportunity to either change the collateral rate or the client all-in rate to increase PnL for the bank. Which one would you choose and why? You can only change either of the 2 rates by 1bp."

• The use of the phrase "client all in rate" Is a bit puzzling. Usually it refers to the sum of all rates paid/received by the client in a complex deal involving a swap among other things. But here they only mention the swap and not the other cash flows in the deal. So how to understand this phrase "client all in rate"? Are there other aspects to the question? – noob2 Jul 28 '20 at 20:10
• All-in rate in this case means the final rate that the client would be charged after taking into account the hedge costs and normal PnL – acchan94 Jul 28 '20 at 21:02

If you change the collateral rate, that would not increase PnL. If market moves against the bank, no collateral will be posted and the increased collateral rate will be irrelavante (assuming one way CSA), and if the market moves in favour of the bank, the client will post collateral that will be payed by the higher rate.

If you change the fixed rate, that would directly reflect in an increase of PnL, roughly 1bp times the PV01, so I would go with the higher client rate.

Update: Considering that at the moment you trade the derivative should be close to fair value, I would assume the initial MtM is close to zero for a zero fixed rate. After that it depends on the direction of the market, and even then, both rates would affect your PnL differently.

Changing the swap rate would affect the PnL directly (1 x PV01) but changing the collateral rate would have a much lower impact.

Consider a notional of 10Mln on a 5y swap, the PV01 would be roughly 5k, so if you increase the swap rate by 1bp the PnL will be 5k. If market moved 1bp the posted collateral would be 5k and the daily marginal return on the collateral after changing the collateral rate would be 5000 x 0.0001 / 360 = 0.001389

• I was thinking that, since this a zero coupon fixed leg swap, the rate would be higher that on a vanilla IRS. . . so there would be more implied forward rates that are lower than the fixed rate. Consequently, the probability of the swap MtM being in favour of the bank is higher, and so client will post margin more frequently. So a higher rate on funding would create more PnL. This would also apply if it was a 2-way CSA – acchan94 Jul 28 '20 at 21:08
• Thanks, David! I do agree with your logic here! – acchan94 Jul 29 '20 at 17:20