# duration schweser practive exam vol 1; exam 2 q. 17.4

Schweser answer “Anderson’s position in the swap will have a net positive duration” I think this should be NEGATIVE position. Issuing a bond gives you a positive duration. To take advantage of decreasing interest rate one want to decrease duration so the total result of the swap should be NEGATIVE SITUATION I Pay fixed duration 4.0 (pos) SITUATION II Swap receive fixed/pay floatingduration - 3.75 + 0.25 = -3.50. Mentioned swap plus bond issued 4.0 – 3.50 = 0.5 (end position) The end position is what he wanted to achieve; lower duration to take advantage of decrease interest rates what am I doing wrong?

Issuing a bond gives you a positive duration. >> gives you a negative duration.

Long bond means lose money when interest rate go up and therefore you are negative duration. Issuing fixed bond you make money when IR go up and therefore you have POSITIVE DURATION. This is what I learned in the Level I and II so that is why I am confused

the questions just asked for the net duration of just the swap not the total position.

Even so its Should be stated NEGATIVE. If the net psoition is positive that that will INCREASE the duration position which is contrary to the purpose when you see that interests rates are increasing. you want DURATION to come DOWN.

If you Pay Fixed in a SWAP your are NEGATIVE Duration If you Pay Floaitng ina SWAP your are POSITIVE Duration

pay swap means, issue fixed bonds (=long duration) and receive float (negative duration). fixed income durations is larger than float durations. So how can you be NEGATIVE DURATION?

no i think it just said semiannual pay bonds which does not imply paying fixed. the questions said like they want to take advantage of decreasing rates so they would be the floating rate payer. I got confused on it too, it’s a dumb question.

The fixed side of the swap has a net positive duration. If you own a fixed-coupon 5-yr bond and issue a floating rate 5-yr bond, this is analogous to being the rec fix/pay float side of a swap because you are long the fixed side and short the floating side. The fixed side has a duration of say 3.5. The floating side has a duration of say 0.25 (this is assuming semi-annual payments). Your total duration is +3.5 - 0.25 = +3.25. This is why the rec fix (or receiver) swap has a positive duration. If you owned a floating rate bond and issued a fixed-rate bond, your duration would be the exact reverse: -3.5 + 0.25 = -3.25.

n_ganpat Wrote: ------------------------------------------------------- > pay swap means, issue fixed bonds (=long duration) > and receive float (negative duration). fixed > income durations is larger than float durations. > So how can you be NEGATIVE DURATION? Remember, if you issue the bond, you are short the bond so you have negative duration from this position. If you are receiving a payment from a floating bond, you are long that payment so you have positive duration. Both the fixed and floating sides have positive duration, but the fixed side has a much larger duration. If you receive fix/pay float, your net duration is positive since you are long the higher fixed duration and short the smaller floating duration. If you receive floating/pay fixed, your net duration is negative since you are long the smaller floating duration and short the higher fixed duration.

NO, If you pay fixed you are Negative Duration. This is because when Interest Rates Decrease, your position decreases b/c you are stuck paying a higher rate and receiving a lower rate, so your value decreases. Remember Duration typically moves in the opposite direction, so when Interest Rates Decrease your position Increases. But you are opposite or Negative Duration. So you Benefit from a rise in interest rates and lose from a decrease in interest rates. Remember if you Receive you are Long if you Pay you are Short. So you are Short Fixed, Long Floating… Does that help?

I think n_ganpat is confused with the structure of the swap, it is receive fix pay floating.

Well if yo Pay floating and receive fixed, then YES it is Positive

how can you have negaive duration ??

Rudeboi, If your long position has a smaller duration than your short position, your net duration is negative.

recieve floating pay fixed = lower net duration or possibly negative duration ? Since the duration is really defines by the fixed side - Did i get that right ?

Receive say Semi-Annual Floating = +0.25 Duration Pay say Semi-Annual Fixed = -3.5 Net Duration: -3.5+0.25 = -3.25 Duration.

Rudeboi Wrote: ------------------------------------------------------- > recieve floating pay fixed = lower net duration > or possibly negative duration ? Since the > duration is really defines by the fixed side - Did > i get that right ? Yes. Rec Float/Pay Fix will have a negative net duration. Both Floating and Fixed sides have positive durations by themselves, but the Fixed side has the higher duration. If you are long (receiving) the fixed side and short (paying) the floating side, your net duration will be positive since you are long a bigger duration than you are short.

Just remember the equation: D(fixed) - D(float) > 0, or D(fixed) > D(float). If you pay fixed, you are swapping a higher duration and receiving a lower duration. Your net duration is what you receive - what you pay = negative.