Help needed, swap valuation BETWEEN payment dates, two methods?

I wanted to get into details regarding this topic and since in the CFAI books the valuation of a swap (for example pay fix receive floating) is done only on settlement date I wanted to value one between payment dates. (apparently schweser cancelled this section in the errata).

Nothing special, but using the two methods explained in the CFAI books (equation 12 and equation 14 pag.308 and 310) I don’t get it right.

I take the example from the Schweser notes:

1-year LIBOR with quarterly payments

Fix rate at initiation: 6.052%

at initiation 90-day LIBOR 5.5%.

Notional: 30mio

Value after 30days? Here the new libors:

60-day LIBOR 6.0% 0.99010 150-day LIBOR 6.5% 0.97363 240-day LIBOR 7.0% 0.95541 330-day LIBOR 7.5% 0.93567

Method 1 equation 12: FB=Cn∑i=1PV0,ti(1)+PV0,tn(1)

just value the cash flow of a fixed rate bond:

0.06052/4 = 0.01513

Fixed side : 0.01513*(0.99010+0.97363+0.95541+0.93567)+0.93567 = 0.993993

Floating side: 0.055/4 (first payment in 90days, given at initiation) + 1 (which is the principal, since at 90days the bond is reset) = 1.01375

Obviously we have to discount it back to today (60days): 1.01375*0.99010 = 1.003714

Value of the swap (fix rate payer) = Floating - Fix = (1.003714 - 0.993993) *30mio = 291’6302

Method 2 V=NA(FS0−FSt)n′∑i=1PVt,ti

New fix rate = (1-0.93567)/(0.9901+0.97363+0.95541+0.93567)= 0.016688

applying equation 14: (0.016688 - 0.01513)*(0.9901+0.97363+0.95541+0.93567)*30mio = 180’73

Why this difference? I am missing something? Does equation 14 works only on settlment date?

This Method 2 annoys me a bit, because I find the first one clearer.

In the CFAI curriculum BB 14 values swap at settlement date with the method 2, but method 1 gives the same result (except for rounding).

Blue boxes 15 and 16 in the curriculum value swaps between settlement dates, only for these check the errata on the website because they contain a mistake.

Hopefully this helps, and I would like to mention it is out of the scope of the curriculum as I know it. I figured it might help you understand that there is a bit more and really valuing between payment periods is far to complex to do on this exam with all the variables. Everything I am saying is strictly my opinion so take it with a grain of salt. I work on derivative valuations (Not a quant nor an expert by any means just have a lot of exposure to derivatives) and what schweser and the CFA teach is a very condensed version of the metrics that actually go into valuing an interest rate swap. For starters the floating rate note is an approximation attempt. The cash flows based on libor are actually projected for the pay frequency of the swap with the appropriate aggregation factor and discounted. The fixed and float cashflows are summed and netted which is then used to value most swaps on a par adjusted basis (at least on most accounting platforms). As to the meat of your question, I think the confusion pops up because of the fact they are approximations with one method being a bit more accurate than the other IMO. Method 1 is being valued as if it were a fixed rate bond under a new rate environment but it truly doesn’t capture the net value actually inherent in the swap as the PV fo the float leg value won’t really be par and the final payment won’t include principle. Hopefully that makes a bit of sense. When is comes down to it I feel like a piece of the answer to your question is that valuing between payment dates is much more complex due to the forecasting component on the LIBOR leg and not something the canceled material could accomplish for this exam IMO. I think the best way is what the revised material is suggesting which is to look at the fixed component and adjust the cashflows accordingly by the new libors. Hopefully I didn’t miss the ball with what you were trying to get at and please remember I am just making an educated guess as to why the above is causing an issue. Good luck

Thank you ACDC for your clear answer. I thought there could be some difference but wanted to have an opinion from others who maybe now mre than me on this topic.

I agree that the first method “makes more sense” or is easier to understand because it’s calculation it’s based on cashflow. On the other side, also method 2 makes completely sense from an operational point of view, to unwind the swap, just enter in the opposite position and discount the difference of the two rates.