Reading an index price-to-earnings or price-to-book ratio against its own ten-year record is the cheapest gauge on the dashboard, and it carries a trap that almost nobody adjusts for. The index is not the same set of businesses it was ten years ago.
The index multiple is a market-value-weighted harmonic mean of its constituents' multiples, because it is total capitalisation divided by total earnings. Which means a shift in weight toward a high-multiple sector raises the index multiple even when no company's own multiple moves at all. Take a market with a high-multiple sector at a price-to-earnings ratio of 45 and everything else at 18. At a 12 percent weight the index multiple is 19.40. Lift the weight to 26 percent, change nothing else, and it is 21.33. That is 1.93 points, a 9.95 percent rise, all of it composition.
So an index multiple two points above its ten-year average is not evidence of anything until you have asked whether the index is two points more expensive or simply two points more weighted toward software. The repair is a constant-weight recalculation: hold the sector weights at their ten-year average and recompute the index multiple from current sector multiples. The gap between that and the reported figure is the composition effect, and reporting the two separately is what turns the gauge from an anecdote into a measurement.
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Why can price to book mislead at index level?
Price-to-book carries a different distortion that runs the same way. Book value counts capital that passed through an asset account and misses capital that was expensed. A company spending 150 a year on research from revenue of 1,000, with a five-year useful life, carries an unrecorded net research asset of 450 in steady state, three times annual spend. Reported book equity of 800 against a market capitalisation of 4,800 shows a price-to-book of 6.00. Add the 450 and the adjusted figure is 3.84. The reported ratio overstates by 56.25 percent.
The consequence at index level is that a market whose composition has shifted toward research-intensive and brand-intensive businesses shows a rising price-to-book that is partly an accounting artefact of expensing. Comparing today's index price-to-book with its 1995 counterpart is comparing two different measurement conventions applied to two different economies.
Does survivorship bias affect index multiples?
Survivorship works on the index too, though more gently than in fund databases. Constituents that fail are removed and replaced, so the index's own multiple history is a history of the companies that were in it at each date, not of a fixed set. That is the right construction for an investable index and the wrong one for inferring anything about the survival characteristics of the average listed company.