Hi

@kausthub It's a good question, I have the benefit (curse?

) of having much opportunity to think about this ... first, we might distinguish between spreadsheet implementation, which of can vary, and

*textual notation*, which (in my opinion) should aspire to consistency, especially for exam candidates, but unfortunately has two versions.

In terms of textual notation, we use and I prefer

**F(start, end)** **rather than F(start, tenor) or start_F_tenor** such that for example,

**F(1.5, 2.0) refers to the six-month forward rate beginning in 1.5 years**; or F(2.0, 3.0) refers to the one-year forward rate starting in two years. Admittedly we do this because it follows the conventional approach to fixed rate agreements (FRA) where (eg) a 3.0 × 3.25 FRA would refer to Hull's Example 4.3 where we "suppose that a company enters into an FRA that is designed to ensure it will receive a fixed rate of 4% on a principal of $100 million

**for a 3-month period starting in 3 years**." ... that's my notation applied to his example. (Some would assume that 3 × 4 FRA refers to a 30-day rate starting in three months, but I'm not a fan of switching to months unless explicit. If we aren't told otherwise, inputs should always be in per annum terms).

Now, while we use F(1.5, 2.0) to refer to a six month rate starting in eighteen months (1.5 years), it is absolutely true that many authors instead would refer to this as F(1.5, 0.5) so that the second value refers to the

*tenor *of the loan/rate which, in fact, the rate. Related, it's event to refer to this as 1.5y0.5y. There is just no way around the fact that we can be referring either to the tenor of the forward rate (six months) or the end of the forward rate from the perspective of today, time zero, which is how I notate a forward.

With respect to the spreadsheet, it also can be tricky but I *always* have the forward rate in the column that marks the end of the loan/rate period. So if we are painting a term structure with six-month periods, the first column contains the six-month spot rate, S(0.5), which can also be said to be the six month forward rate starting immediately; i.e. F(0, 0.5). The next column contains the six-month forward rate starting in six months; i.e., F(0.5, 1.0), and so if that value in the cell is 2.0% then header timeline will be 1.0 years; in this way, on the XLS, the timeline of 1.0 years corresponds to the end of the rate period. This has a key advantage of "matching" my notation; i.e., the F(X.0, Y.0) rate should be aligned under Time = Y.0 years. I hope that's helpful!

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