Lesson 3 of 25 · 7 min

From an overnight market to a term index

A one-month rate is built in one of two ways, and the choice decides whether your cost lags the cycle or leads it.

Your facility is not priced off an overnight rate. It is priced off a term index covering one month or three. Getting from a one-day market to a one-month number requires a construction, and there are two of them in common use.

The first is backward-looking. Take the overnight rates that actually occurred across the period and compound them together, then annualise. The answer is a realised average, and it is not known until the period has ended. The second is forward-looking. Take the rate at which participants will commit today to lend for the whole month. That number contains the market's expectation of what the overnight rate will do, which means it moves before a policy decision rather than after it.

compounded index = (product of (1 + overnight rate ÷ 360) over all days − 1) × 360 ÷ days

compounded index: The annualised term rate produced by the backward-looking construction.
overnight rate: The published fixing for one particular day, as a decimal.
360: The day-count divisor the money market uses, as Track 1 lesson 15 set out.
days: The number of calendar days in the period being annualised.

The compounding is small and it is real. Over a 30-day period in which the overnight rate was 4.33 percent for eighteen days and 4.58 percent for twelve, the compounded index comes to 4.4379 percent while the simple weighted average of the two segments is 4.4300 percent. The 0.0079 gap is worth $10.80 over the month on a $1,640,000 balance. Not a large number, and it is the reason a reader reproducing the index by averaging will always be slightly low.

The construction decides when in a cycle your cost rises. A backward-looking index peaks after the policy rate does, because it is reporting what already happened. A forward-looking one peaks before, because it is pricing what is expected. Your collateral, meanwhile, always reprices on expectations, because a market price is a forward-looking object by nature. A backward-looking index therefore puts the two legs of your exposure on different clocks — a point lesson 22 returns to with numbers.

Key terms

Term index: A rate covering a period longer than a day, built from an overnight market. What a facility is actually priced against.
Backward-looking index: A term rate made by compounding the overnight rates that already occurred. Known only at the end of the period it describes.
Forward-looking index: A term rate quoted today for committing money over the whole period. It contains expectations, so it moves ahead of the events it anticipates.

Worked example

Compounding thirty days of overnight into one number

A 30-day period containing one mid-period decision. Illustrative rates throughout.

Overnight rate, first 18 days: 4.33%
Overnight rate, last 12 days: 4.58%
Compounded index: 4.4379%
Simple weighted average: 4.4300%
Gap: 0.0079 of a point
Cost of the gap, 30 days on $1,640,000: $10.80

Compounding added eight ten-thousandths of a point. The figure matters less than the fact that the index is a construction, not an observation, and reproducing it requires the construction.

Check yourself

A facility uses a backward-looking index that compounds realised overnight rates across the calendar month. A decision on the 24th of a 31-day month raises the overnight rate by 0.40 of a point. Roughly how much of that decision is in this month's index?

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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.