I had an interview question couple weeks ago as below, what is the best way to go about answering it (obviously i didn’t get the job! )
“I have a $10m 10% 10Year receiver interest rate swap, if the rate changes to 11% tomorrow, what is my P&L?”
Don’t be so hard on yourself. I’m guessing this is a floating to fixed swap? This turns a variable into a fixed certainty. So you pay a fee of some sort to ensure that your interest rate will remain at 10% on the 10m. If the interest rate goes to 11%, you essentially miss out on additional interest income. 1%*10m = 100k.
its a fair question… if you ever worked with credit instruments you should know this.
Receiver swap means you receive fixed and pay floating, so if rates go up to 11% you will be losing on the trade. Other variables you would need to know in order to be accurate you be time to next payment date, discount rate and time to maturity of the swap.
I think of a swap as a pairs trade. But since I don’t deal with swaps regularly, I have to disentangle all the words carefully.
having a 10 year receiver swap = you receive fixed, pay floating. So you’re basically long a fixed 10y bond and short a floating 10y bond.
Duration of the reciever swap = duration of equivalent fixed bond - duration of equivalent floating bond
Duration of a 10y bond at 10%: I don’t know this number but would guess it’s around 8
Duration of 10y floating bond: Somewhere between 0 and 0.5, depending on next floating reset date. 0.25 is not a bad estimate.
Duration of swap = 8 - 0.25 = 7.75
EDIT: It turns out that a 10y bond at 10% coupon interest and trading at par has a duration of about 6.5. So the duration of the swap is 6.25, and the P&L for the swap is about a 625k LOSS.
Change in interest rate = 1% higher
Change in swap value = 1% * (-7.75) = -7.75%
Notional value of swap = $10MM
P&L after interest rate change = $10MM * (-7.75%) = -750k
i.e. to create a reverse swap that would neutralize all future swap liabilities on this would cost you about 750k.
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I’m trying to square this with CFAvMBA’s number of 100k. I think my number is correct because you’d be missing out on 100k for 10 years, or $1MM total. When you discount that for the TVM, you get something less than $1MM which would be about 750k.
There’s also a convexity calculation, but I wouldn’t know how to do that part without someone telling me what C is.
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This question might well throw me in an interview though, because swap language gets very easy to confuse (a bit like options language) if you’re not used to dealing with it frequently. Plus there’s the stress of the interview messing with your mind.
dvictr is right that if you deal with credit regularly, you probalby just know a lot of this because you’ve seen the numbers, or know a bunch of mental shortcuts to get to the answer. So it depends on whether your interviewer is asking to see if you know why it’s priced that way or just that you know how it’s priced.
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EDIT: It turns out that the duration of a 10y 10% T-note trading at par is about 6.5. So the swap duration would be about 6.25, and the P&L would be a 625k LOSS.
I would fail this question so hard. The little information I picked up on swaps ran screaming from my skull the moment I walked out of level 3, I think.
just came out of another interview where they asked me a similar Q…i think my thought process was correct although my arithmetic skills were worse than a 5 year old’s under interview pressure!
I did as bchadwick mentioned and split it into a floater and a fixed and tried working out the values. fingers crossed it went okay!
in terms of a held for trading portfolio… (100k) is the “daily P&L loss” in terms of mark to market.
This is an aspect I’m not familiar with. You mean the value of the security declines by 625k but you only have to mark 100k to market?
That’s presumably because you already budgeted for a 10% coupon payment and now you have to budget 1% more, so that’s an extra 1% * 10MM = 100k.
But your portfolio P&L is still down by 625k, because there’s no way to shut off the remaining stream of $100k you’re going to owe on the swap without either 1) interest rates going back down to their original value, or 2) buying an offsetting swap which is going to cost you the same amount (625k) to set up.