On a plain vallia pay fixed rec float SOFR swap, the question is where the risk lies.

Floating leg or fixed leg?

My answer is the floating leg but the interviewer kept insisting it was the fixed leg.

Makes me wonder and hope someone could help clarify.

I have two thoughts on my answer assuming upward sloping SOFR discount curve:

1. In principle, when the SOFR curve reprices, the forward curve will change much more than the discount curve.

Let's say we have 1bps shock on the SOFR curve, the forward curve will need to move more.

forward curve 1Y move by 1bps is 2Y move by 2bps etc

This changes the cashflow on the floating side significantly.

2. Consider a realistic scenario of asset swap.

For example, buy 5Y UST and pay fixed swap.

The risk on the 5Y UST and the swap should be similar.

If curve move 1bps up parallel, the UST will suffer a 1bps loss.

On the swap fixed leg, there will be a tiny pnl due to the curve change on discounting the fixed coupons.

So the offsetting pnl doesn't come from the fixed leg, then it must come from the floating leg.

Not sure what's the standard convention but let's say the following.

Currency USD

Discount curve SOFR OIS

Forward curve: SOFR forward curve

Payment Freq: 6M Floating leg and fixed leg

Floating index: SOFR 180 day published by NY Fed

Term: 5Y

Happy if you could share any readings.

Thanks in advance,