How Swap Rate and Collateral Rate Changes Affect PnL
Summary
The document compares two possible ways for a bank receiving fixed on a daily margined interest rate swap to increase its PnL: raising the client’s fixed rate or changing the collateral rate. It argues that a higher fixed rate has a direct valuation effect, roughly proportional to the swap’s PV01, while a collateral rate change affects returns on posted collateral over time.
The example considers a five-year swap with a notional of 10 million and estimates a PV01 of about 5,000. A one basis point increase in the fixed rate therefore adds about 5,000 to PnL. By contrast, if a one basis point market move leads to 5,000 of collateral, a one basis point change to its rate produces only a small daily return difference. The comparison assumes a one-way CSA and notes that the collateral-rate effect depends on the direction of market moves and whether collateral is posted. It is an illustrative, simplified estimate rather than a full valuation of funding, margin, or counterparty effects.
Key ideas
- Changing the client’s fixed swap rate affects the trade’s value directly through its PV01.
- Changing the collateral rate affects PnL through interest earned or paid on posted collateral.
- The collateral-rate impact depends on whether collateral is posted and on the market move’s direction.
- The numerical comparison is illustrative and does not model every funding or margin effect.
Tags
Full text
# Optimising PnL on an interest rate swap # Optimising PnL on an interest rate swap I recently just got asked the below question. Please help. "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." ## Answer by David Duarte (score 2) https://quant.stackexchange.com/a/55969 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
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.