# CFAI Swaps question - WTF

swaps - CFAI book 5, page 530, question 2, part B. portf dur = 1.5. we wanna extend portf dur to 3.5. ques asks which swap would we rather - the one that has net dur of 2 or net dur of 2.875, and answers say we want the one that’s 2.875. What??? is this a mistake???

You want to go as close to 3.5 as possible , so you you can insure with lower notional. The choices are 2 and 2.875 . Choose.

isn’t the swap dur added to the portf dur we still have? as opposed to replacing it? 1.5 + 2 = 3.5

The swap notional is not same as the portfolio notional. Your equation is not valid as you are not weighting swap notional correctly. (3.5-1.5)*100k=NPofSwap*2.875 NP of swap=69.565k If you use Swap Dur of 2.0 then you get NP of swap = 100k. You’d prefer to insure with lower notional to reduce different kinds of risk

if seeking to adjust duration with a swap, always use the swap with the highest duration because it allows you to have a lower notional principal. Formula to determine Notional Principal of Swap (somebody correct me here) (Target Duration - Current duration)/Swap Duration x Portfolio Value = Notional Principal

So… the answer is always to select the lowest swap duration to have minmum NP. Great! No calculation required!

I think you got that wrong bell99,… lower swap has higher notional. but the more important thing is that you need the duration to increase to 3.5 years … selecting anything less - like the 3 year swap – will require you to enter into ONE more swap to achieve the necessary increase in duration. The notional principal being smaller for the 4 year swap is an added bonus. …

Bell99, I think it should be “highest swap duration” rather than “lowest…”. Right?

Oh ya, good point. Getting confused.

According to CFAI Text Vol 5 P.487~488, the main purpose of using higher durations (absolute value) shall be to keep the notional principal as small as possible. Am I missing something ?

AMA I don’t have this year’s book, but I assume it is the same as last year. There is an example about QAM. In there, you’ll find the following quote “It would probably be best for the swap to have a maturity at least as long as the period during which the duration adjustment applies. Otherwise, the swap would expire before the bond matures, and QAM would have to initiate another swap.” There is an example about choosing between a 3B swap and 464M swap and the text says that the 3B may be too big to implement, but it does not specific say keep the notional amount as small as possible. I could not find any explicit text saying that the main purpose of using higher durations (absolute value) shall be to keep the notional principal as small as possible, but the text may have changed this year. The end result is however identical: Choose the longest and (thus smallest notional) swap. At least, choose the one lasting longer than desired duration which is the key reason for choosing the longer swap in this example.

elcfa, Yes, it is true that there are those statements on P.486 as indicated by you. And on P.487, as you said, there is an example on P.487 about choosing between a 3B swap and 464M swap and the text says that the 3B may be too big to implement, and it also said “464M, a much more reasonable amount, although “STILL” A FAIRLY LARGE AMOUNT”. Doesn’t this mean the smaller the notional principal the better ? So, what shall we say ?

elcfa, Correction to my previous massage, it also said "464M, a much more reasonable amount, although “STILL” A FAIRLY LARGE SAWP (not AMOUNT). On the other hand, in the same one example, if a swap with duration of - 7.00 is available, which one (- 3.50 with NP of 464M & -7.00 with NP of 262M) shall be used ? Since it is said that “It would probably be best for the swap to have a maturity AT LEAST AS LONG AS the period during which the duration adjustment applies. Otherwise, the swap would expire before the bond matures, and QAM would have to initiate another swap.” I think there is no change in 2011 text concerning this portion.

As indicated earlier and as alluded by CP earlier: choose the one(s) with duration lasting longer than desired duration. Ignore the minimum notional requirement since if you choose the longest one(s), it would normally be the minimum notional amount anyway. A tricky CFAI multi-choice question could be to give you a choice between a combo of 2 swaps both with duration lasting longer than desired duration and a combo with one lasting longer and one shorter than desired duration, BUT the total notional amount for the last combo (say 2+2= 4 million) is smaller than the notional amount of the first combo (say 1.8+2.7=4.5 million). In this case, choose the first combo, not the second combo.

elcfa, OK, Thank you very much !

thanks.