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kfcnhl
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Joined: July 28th, 2009, 3:56 pm

sofr swap risk interview question

March 3rd, 2023, 11:30 pm

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,
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Re: sofr swap risk interview question

March 4th, 2023, 7:55 pm

The correct way to answer the question (I occasionally ask some variation of this in interviews myself) is “what do you mean with ‘risk’?” That being said, we typically associate risk with short term price volatility (although usually in terms of contribution to the volatility of a portfolio of sorts. But, in that context, you’ve pretty much got everything wrong. If the discount (I guess you mean spot) curve changes in parallel by one bp, so does the forward curve. The price of a 5Y UST will move slightly less than 5 bps when the curve moves by 1 bp. The fixed leg of the swap will do the same (if you include a terminal payment of the notional; with this convention the floating leg value will remain essentially constant). The standard convention is annual payments of both legs: fixed against daily compounded SOFR.
 
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kfcnhl
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Joined: July 28th, 2009, 3:56 pm

Re: sofr swap risk interview question

March 5th, 2023, 3:42 am

Thanks for your response.
I do like the fact that you are asking the question of definition of risk in the discussion.

Essentially, the fixed leg is the same as a fixed coupon bond and the floating leg is FRN.
Therefore, all the risk lies in the fixed leg.

I am considering the following though:
Let's say I enter into a 2Y swap today at 2% interest.
The curve move up parallel by 1%.
There is actually $2 of loss on the floating leg not on the fixed leg.
Please have a look at the excel attached

Let me know if you see any errors please.

 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Re: sofr swap risk interview question

March 5th, 2023, 8:06 pm

OK - I think you got it pretty much right. There is probably some slight inconsistency in your compounding (otherwise your initial swap value should be exactly zero), but you are correct that when not including the terminal notional amounts on each leg, then most of the value change does indeed come from the floating leg. As you experienced in your interview, that is not the typical way to think about vanilla swap pricing, but that doesn’t make it wrong. At this level, if you have a general interest in derivatives, John Hull’s book is a pretty standard reference.
 
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kfcnhl
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Joined: July 28th, 2009, 3:56 pm

Re: sofr swap risk interview question

March 7th, 2023, 4:14 pm

Appreciate your quick response.

My current desk is in the bank ALM capacity and has a portfolio of swaps of various tenors.
For example we will have a lot of non standard terms given rolling (5Y-> 4.6Y etc).
We typically think a lot about the aggregated risk of the portfolio by various fixings.
As such, we view the floating side as the risky side.
If we feel compiled, we will change the portfolio profile by targeting a specific tenor.