Lesson 4 of 25 · 7 min
What an index actually is, mechanically
It is the output of a published procedure run over other people's trades, not a quote, a forecast or an opinion.
An index is not a price anyone offered you and not a view anyone holds. It is the result of running a stated procedure over a stated set of transactions and publishing the answer at a stated hour, whether or not the day produced anything interesting.
The procedure has four parts. It defines which transactions are eligible — by counterparty type, by term, by whether collateral was involved. It filters the day's eligible trades, usually discarding the extreme tails. It takes a statistic, most often a volume-weighted mean or a volume-weighted median. And it names a publication time, along with a fallback for days when the market was too thin to produce a reliable figure.
Volume weighting is the part that changes answers. Take five eligible trades on one day: $14.2 billion at 4.28 percent, $31.6 billion at 4.31, $47.9 billion at 4.33, $22.4 billion at 4.35 and $9.3 billion at 4.41, for $125.4 billion in total. The unweighted mean of those five rates is 4.336 percent. The volume-weighted mean is 4.3288 percent, because the small trade at the high rate carries one fifth the weight of the large trade in the middle. The volume-weighted median is 4.33 percent, because the halfway point of the volume, $62.7 billion, falls inside the third bucket.
Two consequences follow for a borrower. The index that priced your day is a fact about a market you are not in, produced from trades between parties you will never identify. And on a day when nothing traded, the fallback publishes something anyway — commonly the previous value — and that value accrues on your balance exactly as a live one would.
Nothing in an index responds to your account, your collateral, or anything you did. That is what makes the index leg impersonal, and it is also what makes it impossible to negotiate.
Key terms
- Volume-weighted mean
- An average in which each rate counts in proportion to the size of the trade that produced it. Large trades dominate; small outliers barely register.
- Eligible transaction
- A trade that meets the index's stated criteria for inclusion. Everything outside the definition is invisible to the published number.
- Fallback value
- What the procedure publishes when the day produced too little activity to compute a figure. Usually the previous value, and it accrues like any other.
Worked example
One day of trades, one published number
Five eligible transactions totalling $125.4 billion. Illustrative volumes and rates.
- The trades
- $14.2bn at 4.28%, $31.6bn at 4.31%, $47.9bn at 4.33%, $22.4bn at 4.35%, $9.3bn at 4.41%
- Unweighted mean of the five rates
- 4.3360%
- Volume-weighted mean
- 4.3288%
- Halfway point of the volume
- $62.7bn
- Volume-weighted median
- 4.3300%
- Gap between the two means
- 0.0072 of a point
The sum of five rates ÷ 5.
Sum of volume × rate, ÷ $125.4bn.
Falls inside the $47.9bn bucket at 4.33%.
Three defensible statistics on one day's trades gave three different numbers. Which one your rate uses is a definition in a document, not a property of the market.
Check yourself
A day's eligible volume is $88.0 billion: $12.0bn at 4.19 percent, $40.0bn at 4.24 percent and $36.0bn at 4.27 percent. What is the volume-weighted mean, and how far is it from the unweighted mean of the three rates?
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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.