# CFAI Reading 40 P270, Q2 B

The Question exactly says that " you wish to increase duration to 3.5". current bond duration is 1.5. YOu have two choices either use 1) four year / qtly payments or 2) use 3 year / semianual payments/ 1) has duration of 2.875 2) has duration of 2.0 so my ans was 2) to make 3.5 the desired duration but the ans said 1) and the reason given was always use longer duration. But if you use 1) you dont get your targeted duration of 3.5. Any thoughts ???

I thought there was more to this question… 3.5-1.5/2.875 = 0.695652 3.5-1.5/2 = 1.000 Anyways, #1 would be cheaper to implement b/c the ratio is 0.69 vs 1.0. So if the Notional was \$1,000,000 and the Futrues contract was 100,000 you would only have to buy 6.9 ~7 contracts vs 10 using option #2.

Like i said above, i thought that there were mroe specifics to this case that might make it mroe reasonable. What was CFAI’s answer? Sorry dont’ have my book.

your target duration can be adjusted (remember duration in the portfolio is weighted by its components ) - so you can buy less of longer bond, and increase duration using up less cash … w*1.5+(1-w)*2.875= total portfolio duration not sure if this is the logics the CFAI wants to follow, but this would be how I approach it.

But eliappa, When you are adding swap into your portfolio, and you want to add duration, you do not have to do weighted average like your formula. you do not need to 1.5 or (1-w) . bigwilly, thanks for replying but the ans given in the text book only said use longer duration (just that) but if you use longer duration swap, you get more than your desired duration.

No you don’t, you will need less of the Higher duration Futures than you will if you had Lower Duration futures.

But this is not futures but swap… If it is Futures, we can use higher duration Futures and increase/decrease the port Duration. But if it is swap, already the Duration is calculated using Fixed side and floating side. it would be either 2.875 or 2.5. And you have to use either of them. Then why don’t you go with 2.5 ? 2.5 + 1 = 3.5 ( voila, you get 3.5 ! not 3.875 ) WOOOOOOh.

If it’s a swap, then there is the notional principal to worry about. I’m thinking the notional will be lower if you were to use a longer duration swap. Which is supported by the calculations you guys did.

OK, I also started to think of that after reading the post by bigbrother bigwilly, but for swap, how ever big it is, you are swapping the fix and floating so the duration is same. of course if you change the amount for each side, it would be a different story, like you suggested. But in the Q, it is not giving the notional amount for this swap. Why ? because for swap, amount is irrelevant ! Amount is importatnt wheather that amount would cover or hedge the original trade that he has. Am I right ?

Read page 226 and 227. The reason a longer duration is used is to lower the notional principal which is calculated as: NP = Vp * (Target Dur. - Current Dur.) / Dur. of Swap As Dur. of Swap rises, the NP falls. Execution is easier for a smaller swap than for a larger swap.

ymmt, thanks for the follow up. i don’t have book w/ me now, so I will check later, but if what you said is right, swap is easier with smaller swap (small means duration i think, correct me if I am wrong,) then the ans given in the text is STILL wrong ! because they chose the longer duration of 2.875. not the smaller duration swap of 2 !!! OHHHHH after REreading your post, I think I got the clue. small did not mean duration small meant the amount, right? OK !!! ! I do not have the book but I think I understood with your explanation. Great! Thanks !!

small means, smaller notional amount on which swap is based