Can someone please explain how with a receive-fixed/pay-floating position in a swap, you are short a floating-rate bond and long a fixed-rate bond? With receive fixed, you benefit if I.R decreases (bond price goes up), so you are long the bond. With pay floating, you benefit if I.R decreases (bond price goes up), so aren’t you long the bond?
I’m not clear on how this is meant to be short a floating-rate bond and long a fixed-rate bond
First of all you got to look at total returns. (Coupon + Counpon reinvestment returns)
The only point CFAI is trying to make is that the cashflow of receive fixed is fixed - hence representing a long position in FRB. Similarly with Pay floating, you are shorting a floating rate bond with respect to the cash flow.
Hope this helps.
If you’re long a fixed rate bond, you’re the bondholder, so you receive fixed-rate coupon payments.
If you’re short a floating-rate bond, you’re the issuer, so you make floating-rate coupon payments.
This bond equivalent approach was the basis for pricing a plain vanilla interest rate swap at Level II. Surely you remember Level II.
But why does receive fixed-rate payments/make floating-rate payments equate to positive (increased) duration?
When you buy a 10-year fixed-rate bond you have, say +7.5 years (effective) duration.
When you sell a 10-year floating-rate bond you have, say, −0.25 years (effective) duration.
The net (assuming the same principal) is +7.25 years.
And so: receive fixed-rate payments benefits when rates go down since still receive same fixed rate. pay floating-rate payments benefits when rates go down since only have to pay lower rate. So we only benefit when rates go down, no protection when rates increase?
We lose when rates increase: +7.25 years duration.
Sorry, i’m still confused by this: If you are short a floating-rate bond, you want the price to decrease (interest rates subsequently increase). But when making floating-rate payments, you want interest rates to decrease so that you pay a lower rate. So i’m confused as to why these are conflicting. In other words, normally when short something you want price to decrease, but with short floating-rate payments, we want price to increase (rates to decrease)?
If I’m short a floating-rate bond, I want rates to decrease so I pay less interest.
Nevertheless, we’re talking about duration here: if I’m short a bond, I’m short duration.
And is short duration the same as negative duration? So that if rates decrease and you are short/negative duration, your portfolio increases in value?
nightmares… this is giving me nightmares
Yes.
No.
With positive duration, when interest rates decrease your portfolio increases in value. Think of buying a bond.
With negative duration, when interest rates decrease your portfolio decreases in value.
s2000magician thank you, i feel like i am understanding it better. So is the below correct?: When interest rates are falling, want to be long (positive) duration, assets gain more than liabilities (portfolio gains value). But if rates increase while you are long (positive) duration, assets lose more than liabilities (portfolio loses value). When interest rates are rising, want to be short (negative) duration, liabilities lose more than assets (portfolio gains value). But if rates decrease while you are short (negative) duration, liabilities gain more than assets (portfolio loses value).
Man. You are mixing different cases. What am going to recommend is not 100% right, but close.
Think of coupons only and the impact of interest rates (opportunity cost, and exposure) on those coupons.
For swaps (vanilla) look at everything from the perspective of the fixed rate, even when comparing to bonds:
Long position means Pay Fixed, Rec Float (In a bond you pay fixed cpn if you issued/sold a fixed rate bond)
Long Swap DV01 = Duration of Asset minus Duration of Liability = What you Receive minus What you pay
= Receive Float DV01 minus Pay Fixed DV01 results in a negative value (i.e. less than zero as Fixed DV01 is greater than Float DV01 by definition) = -DV01. Hence you hedge a Pay Swap by buying a bond.
If you Pay Fixed and Rec Float, then if interest rates go down, you lose - you are paying a fixed rate (say 5%) when the market rate has gone down to 3%. In order to profit, you need rates to go up.
Short position means Rec Fixed, Pay Float (In a bond you rec fixed cpn if you bought a fixed rate bond)
Short Swap DV01 = Duration of Asset minus Duration of Liability = What you Receive minus What you pay
= Receive Fixed DV01 minus Pay Float DV01 results in a positive value (i.e. greater than zero as Fixed DV01 is greater than Float DV01 by definition) = +DV01. Hence you hedge a Rec swap by selling a bond.
If you Rec Fixed and Pay Float, then if interest rates go up, you lose - you are receiving a fixed rate (say 5%) when the market rate has now gone up to 8%. In order to profit, you need rates to go down.
Good to hear.
Yes.
Yes.
One clarification: being short or long duration isn’t enough; you want to be short or long _ dollar duration_. The relative value of the assets and liabilities matters, too.
Why we’re talking about assets and liabilities in here. It’s relevant, but at one step farther than fixed/floating swaps; UNLESS:
OP. By assets and liabilities, do you mean swap legs ?
If this is the case, I hope this doesn’t confuse you in other readings.
It is not a step further, it is part of understanding a swap (especially its DV01). Since a vanilla swap has two legs: one being pay, one being rec, the former will be a liability and the latter an asset. On our trading desk, it is common to hear “paying 3m liabilities, receiving the asset, etc.” between different desks and other shops.
I agree on the technical term. The issue is that in other readings they calculate net value of assets/liabilities dollar duration . In principles they’re similar, but it needs experience or comprehensive reading to grasp the whole idea . If the concepts are clear, there’s no problem.
Thanks everyone for the input. And yes we have combined a few (related) topics. But going back to my original question, i still don’t see why with a swap: -if you are receiving fixed coupons you are long a fixed-rate bond. -if you are paying floating coupons you are short a floating-rate bond.