Mark Hendricks’ lecture on Fixed Income introduced a nice, simplified methods of looking at many important mathematical rules of thumb on the yield curve.
We used only
zero coupon government bonds without any call feature.
We used log yield, log fwd rate, log spot rate, log return, log price (usually negative) etc. This reduces compounding to addition! There’s no “1+r” factor either.
As much as possible we use one-period (1Y) loans. All the interest rates quoted are based on some hypothetical (but realistic) loan, and the loan period is for one-period, though it can forward-start 3 periods from time of observation. One of the common exceptions — 5Y point on the yield curve is the yield on a bond with 5Y time to live, so this loan period is 5Y, not one-period.
If the shortest unit of measurement is a month, then that’s the one-period, otherwise, 1Y is the one-period. All the rates and yields are annualized.
Perhaps the best illustration is the rule on fwd curve vs YC, on P4.12.