Calculation of Duration by Long hand method

[jyothi1965]

A trader executes a $300 million 5-year receive fixed swap with one client and a $180 million
10-year pay fixed swap with another client shortly afterwards. Assuming that the 5-year rate is
3.25 percent and 10-year rate is 6.05 percent and that all contracts are transacted at par, how
can the trader hedge his net delta position?

A. Sell 175 Eurodollar contracts.
B. Buy 175 Eurodollar contracts.
C. Sell 10,745 Eurodollar contracts.
D. Buy 10,745 Eurodollar contracts.

Solution

Given the rates of 3.25% and 6.05%, the dollar durations of the 5-year and 10-year par swaps
are approximately 4.55 and 7.34. Therefore, the trader has the following DVBP positions
First swap DVBP = $300 million x 4.55 x 0.0001 = -$136,500.
Second swap DVBP = $180 million x 7.34 x 0.0001 = $132,120.
Net DVBP position = -136,500 + 132,120 = -4,380.

Since the trader has a long position he needs to sell the futures. The DVBP or a Eurodollar
future is $25. Therefore, the number of contracts required = 4,380 / 25 = 175.


David... the question is again from the PRM set. There are no issues here.

Your Tutorial on calculator (duration calculation) is very heplful but we can't apply it here (shocking by xx bp method) we need to calculate the durations by long hand (4.55 and 7.34 as above)

Any guidance on this?

Thanks

J

 

[David Harper CFA FRM]

Jyothi,

Interesting, but an FRM wouldn't get this question because the SWAP coverage is not this deep. (This is typical CFA question)

Specifically, you'd need to know that an interest rate swap deconstructs into two bonds: long (short) a fixed plus short (long) a floater. That's the easier part. The harder part is seeing that the floater has a duration near enough to ZERO that it can be (assumptionally) eliminated. That may be common CFA/PRM but Hull/Tuckman do not cover this, to my knowledge. So, if you are a fixed rate receiver, your duration is about the same (not exactly) as the duration on a fixed rate bond.

Given that, I do think the "manual" duration works. If I had the TI BA II+ and not the professional, I would not know any other way to do it.

I tried the 10-year 6.05% bond and i do get a MODIFIED duration of 7.34 (they really should say 'modified'). In fact, frankly, if there is a shortcut to shocking (i.e., repricing the bond at +/- basis points) in order to get the modified duration, I don't know it. You could be given the Macaulay, that would be easier; but calculating the Macaulay would be more difficult. (as Telon explains in his comment here which i did not know, you can use the TI BA II+ PROFESSIONAL's bond worksheet and have it perform the duration calculation...)

David