Someone who knows Duration of Interst Rate Swaps... PLEASE HELP

The following capitalized #'d quotes are straight from Schweser book 5 pages 92 to 95 ( Duration of Interst rate Swaps. I will explain my way of thinking about the stated schweser excerpt and I need someone to confirm my way of thinking or provide further explanation if needed. #1)SCHWESER- YOU SHOULD RECALL THAT DURATION IS THE SENSITIVITY OF AN ASSET’S PRICE TO CHANGES IN A RELEVANT INTEREST RATE, FOR FIXED RATE INSTRUMENTS, DURATION WILL BE HIGHER, SINCE THE CHANGE IN INTEREST RATES WILL CHANGE THE PRESENT VALUE OF FIXED CASH FLOWS, AND FOR FLOATING RATE INSTRUMENTS, DURATION IS CLOSE TO 0. Me- Ok , the above makes sense, and this is the thinking I was going in with in regards to the rest of the reading… #2) BECAUSE HE RECEIVES FIXED CASH FLOWS, TAKING THE RECEIVE-FIXED/PAY FLOATING POSITION IN A SWAP INCREASES THE DOLLAR DURATION OF A FIXED INCOME PORTFOLIO. Me - ok, so that would mean then someone taking the pay-fixed/receive floating position in a swap would DECREASE the dollar duration of a fixed income portfolio. ----This is where i start getting a little confused… #3) THE SIGN OF THE DURATION OF THE SWAP DEPENDS UPON WHICH SIDE OF THE SWAP YOURE ON. THE PAY FIXED SIDE OF THE SWAP HAS EFFECTIVELY ADDED A FIXED-RATE LIABILITY, SO THE DURATION FOR THE SWAP IS -.85, WHICH REDUCES THE DURATION OF THE OVERALL PORTFOLIO. Me- Ok , so why is the duration of the swap negative? As i am under the impression, is it because we shorted a fixed rate bond which means normally a fixed rate bond is an asset with positive duration, but since we shorted it it now has negative duration? #4) ASSUME THAT THE FIRMS EQUITY IS POSITIVE AND THE DURATION OF THE FIRMS ASSETS IS GREATER THAN THAT OF ITS LIABILITES SUCH THAT THE NET DURATION OF THE FIRMS EQUITY IS POSITIVE. Me- I think this is my main point of confusion. So when doing these examples, I am to assume that “equity” in this case is the fixed income portfolio, and that assets are instruments which we receive payments such as long bonds and liabilities are those where we owe money such as shorting bonds ? #5) NOW WE’LL ASSUME THAT MANAGEMENT ENTERS A PAY-FIXED, RECEIVE FLOATING SWAP TO CHANGE THE NATURE OF THE LIABILITY…SINCE FIXED RATE INSTRUMENTS HAVE A LONGER DURATION THAN FLOATING RATE INSTRUMENTS, THE ADDITION OF THE SWAP HAS INCREASED THE DURATION OF THE FIRMS LIABILITIES AND NARROWED THE DIFFERENCE BETWEEN THE ASSET AND LIABILITY DURATIONS. THE BOTTOM LINE IS THAT THE FIRMS EQUITY WITH A SHORTENED DURATION IS NOW LESS SENSITIVE TO CHANGES IN INTEREST RATES THAN BEFORE MANAGEMENT ENTERED THE SWAP. Me - Ok - When they say Firms equity, do we mean the fixed income portfolio of the firm? -If yes, does this mean that equity refers to us having more assets such as long bonds than we do liabilities such as short bonds? - So when it says “addition of the SWAP has increased the duration of the firms Liabilities” this simply means that since we are now paying fixed, this is like our liabilities. But when it says it has narrowed the duration, dfoes this mean that its beacuse the assets duration has decreased more since we had to short a bond, and shorting a bond means adding a negative duration to the portfolio?

You have to add one more concept to the picture. As a corporation with a balance sheet, the firms Assets, Liabilities and Equity have their respective durations. Duration of Assets = Duration of Liabilities + Duration of Equity. Initially the way you can caliculate the Duration of the Firms Equity = Duration of Assets - Duration of Liabilities. By entering into a Pay Fixed - Recieve floating swap, you are reducing the Duration of your firms equity, and the firm valuation’s interest rate sensitivity. Your thinking is 99% correct, you just need to broaden it a bit to include the overall firm duration and Equity duration concepts and not just its fixed income portfolio.

One more thing to add. Firm would preferr to have the Duration of firm equity to be close to 0; why? Because they want firm’s equity to be less senentative to overall intereste rate environment. So, as managment, you looks at your asset and liablity to see its duration, and find a SWAP to manage the duration of your asset and liablity.

SO being Long on a Fixed Rate bond is considered a Firm ASSET, while being SHORT a Fixed Rate bond as in the case of PAY Fixed Swap is considered a Liability. ???

Yes, Being long a fixed rate asset, adds to firms asset duration and subsequently firms equity duration. Being short a fixed rate bond adds to firms liability duration and subsequently reduces firms equity duration. Asset duration - liability duration = equity duration.

IH8FSA Wrote: ------------------------------------------------------- >while being SHORT a Fixed Rate bond as > in the case of PAY Fixed Swap is considered a > Liability. > > ??? Look the firm’s balance sheet, what falls under long-term liablility? Bonds. Shorting a Fix rate bond is like issuing fix rate bonds. A Pay Fix Swap is paying fix rate interest (issuing/short fix-rate bond also need to pay fix interest rate) becomes a liability for the firm.

" Look the firm’s balance sheet, what falls under long-term liablility? Bonds " When you say Bonds you mean when you issue bonds correct ?

Yeah. When you are long a fixed rate bond you are LENDING your cash to someone else. When you are short you are borrowing someone else cash. So, as ws said, when you are short a fixed rate bond you are essentially issuing a fixed rate bond.

Thanks Guys ! This makes a little bit more sense to me. Even though I h8 fsa, at least I was good at it. I was always weak when it came to fixed income stuff. Thanks again!