Lesson 14 of 25 · 7 min
What is already priced into a rate, and what a surprise is
Deliver a quarter-point cut into a market expecting three of them, and the borrower's accrual runs above what the forward number implied.
The level of a rate and the change in a rate are different objects, and confusing them produces the most reliably counter-intuitive result in this track. A term rate already contains the market's expected path. Only deviations from that path move anything.
Set it up with illustrative numbers. The overnight rate is 4.94 percent and the twelve-month term index is 4.31. That 0.63 gap is not a discount anyone is offering. It is the market's expectation that the average overnight rate across the coming year will run 0.63 below today's — roughly two and a half quarter-point cuts.
Now suppose the policymaker delivers one cut, of 0.25, at the six-month mark. The realised average overnight rate for the year is (4.94 × 6 + 4.69 × 6) ÷ 12 = 4.815 percent. That is 0.505 of a point above the 4.31 the market priced at the start. A facility indexed to a compounded backward-looking rate therefore accrued at 4.815 across a year in which the policy rate fell.
Price it. On a $1,845,000 balance across 365 days, Act/360, accruing at 4.815 percent costs $90,070.59 against $80,623.94 at the priced 4.31. A cut was delivered, and the borrower paid $9,446.66 more than the forward-looking number implied twelve months earlier.
A cut can be a tightening. What matters is the cut measured against the cuts already sitting in the price, not the cut measured against nothing.
Key terms
- Priced-in path
- The sequence of future rates a term rate already reflects. It is the baseline everything is measured against, and it is not zero.
- Surprise
- The gap between what happened and what was priced. The only quantity that moves anything, and it can be positive when the level fell.
- Realised average
- The actual average of the daily rates across a period. What a backward-looking index reports, and what is actually charged.
Worked example
A year with one cut, and a bill that went up
Overnight rate 4.94 percent and twelve-month term index 4.31 percent at the start. Balance $1,845,000, Act/360, 365 days.
- Cuts embedded in the gap
- 0.63 of a point
- Cuts delivered
- One, of 0.25, at the six-month mark
- Realised average overnight rate
- 4.815%
- Surprise
- +0.505 of a point
- Interest accrued
- $90,070.59
- Interest the priced path implied
- $80,623.94
4.94 less 4.31; about two and a half quarter points.
(4.94 × 6 + 4.69 × 6) ÷ 12.
4.815 less the priced 4.31.
$1,845,000 × 0.04815 × 365 ÷ 360.
A difference of $9,446.66.
The policy rate ended the year a quarter point lower and the facility cost $9,446.66 more than the market's own forward number implied. Both statements are true and neither is a paradox.
Check yourself
The twelve-month index is 3.88 percent while the overnight rate is 4.66 percent. The policymaker then makes no change at all for the whole year. What was the surprise, and what did it cost on a $2,240,000 balance over 365 days, Act/360?
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.