Reading 29- EOC 2B is to increase the duration of portfolio. and below is the answer.
Duration of four -year = 2.875 (higher)
duration of three year = 2.0 (lower)
Because the objective is to increase the duration of the bond portfolio, the four -year pay-floating, receive-fixed swap is the better choice.
Does this mean if we were to reduce the duration of portfolio, we would use three year swap?
Thanks
No. If we use the three year swap, pay float receive fixed, our duration still increases but not as much as it would have increased had we used the four year.
If we want to reduce duration we need to enter into a pay fixed receive float swap. The fixed portion of the swap determines whether or not you are increasing or decreasing your duration.
If you want more duration => You get paid fixed. E.g. I own fixed rate bonds.
If you want less duration => You pay fixed. E.g. I make payments on fixed rate bonds.
CFA Institute’s position seems to be that you always choose the swap that will give you the lowest notional value; thus, you always pick the swap with the highest (net) duration.
sachin, i’ve copied and pasted below my post to another swap-related thread this morning… hope it helps.
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some tricks for solving all swap duration questions, and some detail so you could understand it conceptually….
1. duration of fixed = 0.75 X maturity of the bond (i.e 3yr fixed… 0.75 x 3 = 2.25)
duration of floating = 0.50 x pmt interval (i.e. semiannual pmts… 0.50 x 0.50 = 0.25)
2. the equation is Duration(swap) = D(fixed or floating) - D(floating or fixed). Whatever the swap is (fixed or floating) will go SECOND in the equation. For example, if it is a FIXED swap, you will line it up as Duration(fixed swap) = Duration(floating) - Duration(fixed), and vice versa.
3. when calculating the duration of the swap, you want to first figure out what YOU will be RECEIVING (think “asset - liability”). if you are receiving fixed, it will go first… if you are receiving floating, it will go first.
4. the key to figuring out what TYPE of swap you need (fixed or floating) depends on your interest rate expecations and/or if you want to increase or decrease duration. Obviously, if you want to increase your duration, that means you think interest rates will decline, so you would want to RECEIVE fixed rates and pay floating (think asset - liability, so you will want a swap that is fixed - floating, which is a FLOATING rate swap).
Junior, thanks for your post. Just to extend on it…
Applying these two rules has always helped me with these questions:
Use “Duration of Asset minus Duration of Liability” for either type of interest rate swap. Asset is what you receive, liability is what you pay. Thats it.
Duration of FIXED = 0.75% * maturity and duration of FLOAT = half of reset period, i.e semi-annual reset = 0.5/2 and quarterly reset = 0.25/2
3 Year Pay fixed swap: (Pay Fixed, Rec Semi-Annual Libor)
Duration of Asset is (Libor) minus Duration of Liability (Pay Fixed):
0.5/2 = 0.25 minus 0.75 * 3 years = 1.5 = -1.25 duration (Pay Fixed, -DV01)
3 Year Rec fixed swap: (Rec Fixed, Pay Semi-Annual Libor)
Duration of Asset is (Rec Fixed) minus Duration of Liability (Pay Semi-Annual Libor)
0.75 * 3 years = 1.5 minus 0.5/2 = 0.25 = +1.25 duration (Rec Fixed, +DV01)
great… thanks for the explanation.
is it always the case that duration of fixed is 0.75*maturity? I am asking because in all problems they gave it to us. we never had to assume it.
also from what I understood this thread is, we always pick the swap with higher absolute duration.
we just switch the sides based on if we want to increase the duration or decrease the duration
is that correct?
BTW thank you chuck, magician, junior and arigolden
For CFAI purposes, and from what I have seen, yes the duration for the fixed is 0.75 * maturity and the duration for float is half of the reset period. Whether given or not, just remember those two, they’re not that bad to remember.
In terms of increasing or decreasing duration, just apply my logic above. If you know that a PAY Fixed Swap is a -DV01 swap and a REC Fixed Swap is a +DV01 swap, then to increase duration/DV01, you have to choose the REC Fixed Swap position and to decrease duration/DV01, you have to choose the PAY Fixed Swap position.