Hedging floating rate - An update

A reader has been looking in detail at my posting of regarding hedging floating rate interest into fixed using swaps or FRAs and sent me a question.

The most important thing the question reminds me of is how dangerous spreadsheets can be. Leaving out the final quarter's tax refund was simply a mistake.  I normally have spreadsheets checked by a colleague, but after five years cannot recall how this one slipped through.

The attached spreadsheet is basically the one I used for the article in 2000.  The tab ""Article yield curve" uses the same numbers as in the original article, but corrects the summation of the tax savings.  The NPV benefit of using FRAs disappears, and in fact there is a small NPV benefit from using a swap.  While the FRAs give you earlier tax relief, they also give you less aggregate tax relief as less interest is paid overall.  This reduction in overall interest expense wipes out the benefit of getting tax relief earlier.  As the pre-tax NPVs of the FRA and swap payments is identical (by definition) I think it is valid to compute the NPV of the tax savings as done in the spreadsheet; the conclusion is that there is nothing in it, indeed a small detriment with the humped yield curve assumed.

As a check, I then took the yield curve expected to be most favourable to using FRAs, which is one that slopes steadily downwards.  See tab "Steady downwards slope."  This also showed a benefit from using swaps rather than FRAs, exactly the opposite of what I expected. The impact is small, 49p of NPV for £10,000 of loan, but still counterintuitive.

One point affecting the conclusion is that tax relief is given for the interest paid in each accounting year, not by reference to the interest actually paid on each quarterly interest payment date.  With a yield curve sloping downwards, this accounts for a major part of the actual disadvantage of the FRA route, as illustrated in columns "Q" to "T" of the spreadsheet.  I think the rest of the disadvantage arises from the fact that the FRA route involves paying interest earlier, but the tax relief is delayed slightly compared with the interest payment dates.  Obviously, if the tax relief was an instantaneous 30% of each interest payment, the NPV of the tax relief columns would be identical just like the NPV of the gross interest columns.

Apart from the vital importance of applying "four eyes" to every spreadsheet, the other point this brings out is how often one gets counter-intuitive answers when building financial models.  It demonstrates why it is always essential to build them, rather than relying on one's intuition with cash flows and net present values.

Download Hedging with swaps and FRAs 3 with corrected summation.pdf

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Mohammed Amin