Lesson 1 of 7
Choosing the window
Nine filed years of what, exactly. Why the window decides every average computed inside it, and what half a swing does to a normalised figure.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- At a cyclical business the window decides every average computed inside it, so it is chosen first and defended in writing.
- A window that contains half a swing produces a normalised figure that is neither a peak nor a trough nor a cycle.
- The filed record you can get is rarely the window you want, and saying which you have is part of the work.
Before any figure is computed, one decision is made and written down. At a stable business it barely matters. Here it determines everything.
One filer's revenue, nine filed fiscal years
- Revenue
Show the numbers
| Revenue | |
|---|---|
| FY17 | 5,815$m |
| FY18 | 7,143$m |
| FY19 | 7,224$m |
| FY20 | 7,078$m |
| FY21 | 8,790$m |
| FY22 | 10,276$m |
| FY23 | 9,995$m |
| FY24 | 10,847$m |
| FY25 | 10,967$m |
Why the window comes first
Because a normalised figure is an average, an average is taken over a window, and at a business whose result swings the window contains more of the answer than the arithmetic does.
Average the nine years above and you get one number. Average the last four and you get a considerably higher one. Neither is wrong. They answer different questions, and a reader who does not say which window they used has published a number nobody can check.
What this window contains, and what it does not
Nine fiscal years, 2017 through 2025, from nine separate annual reports. Revenue rises from 5,815 million dollars to 10,967 million, with two down years in the middle: a fall of 2.03 percent in fiscal 2020 and one of 2.73 percent in fiscal 2023.
Two shallow down years is not a housing cycle. The filer's own record reaches further back and contains a much larger contraction, and the second lesson of the boom course used it: homebuilding revenue as reported in the annual report for fiscal 2010 fell from 3,148 million dollars for fiscal 2008 to 1,495 million for fiscal 2010, a fall of 52.5 percent across two fiscal years.
So the honest statement about this window is that it contains an expansion with two pauses in it, and that a full contraction lies outside it. Anything normalised over these nine years is normalised over a period in which the industry did not have a bad one.
Why not simply extend the window
Three reasons, and all three are ordinary.
The figures before fiscal 2017 come from filings that reported a different revenue line, so extending the window means comparing two definitions. Accounting standards changed inside the longer period, most visibly the lease standard. And a company that was one shape in 2008 is not the same company in 2025, so an average spanning both is an average over two businesses.
None of that is a reason to ignore the earlier record. It is a reason to read it separately, as evidence about how far this industry can fall, rather than to blend it into an average.
What to write down before going further
The window, in years. What it contains and what it does not. Why the boundaries are where they are. And the definitional breaks inside it, so that any average computed later carries them.
Four sentences. They are the difference between a normalised figure and a number.
Check yourself
Why is the window chosen before any figure is computed?
- Because the data has to be downloaded first
- Because a normalised figure is an average over a window, and at a swinging business the window contains more of the answer than the arithmetic
- Because filings are published annually
Show the answer
Answer: B.
Three windows on the same nine filings gave mean operating margins of 9.83, 13.04 and 16.61 percent. None is an error and the choice is what has to be defended.What does this nine-year window contain?
- A complete cycle for this industry
- An expansion with two shallow down years, with a much larger contraction lying outside it
- Two full contractions
Show the answer
Answer: B.
The two down years were falls of 2.03 and 2.73 percent. The company's own earlier record contains a fall of 52.5 percent across two fiscal years.Why not simply extend the window back to include the larger contraction?
- Because the older filings are unavailable
- Because the revenue line was defined differently, standards changed inside the longer period, and the company is not the same shape
- Because older data is less accurate
Show the answer
Answer: B.
The earlier record is read separately, as evidence about how far the industry can fall, rather than blended into an average over two businesses.Sources
- Toll Brothers, Inc., annual reports on Form 10-K for fiscal years 2017 through 2025, for revenue and operating income: accessions 0000794170-17-000065, 0000794170-18-000055, 0000794170-19-000067, 0000794170-20-000066, 0000794170-21-000079, 0000794170-22-000049, 0000794170-23-000066, 0000794170-24-000051 and 0000794170-25-000112.
- Toll Brothers, Inc., annual report on Form 10-K for the fiscal year ended 31 October 2010, accession 0000950123-10-115566, filed 22 December 2010, for homebuilding revenue for fiscal 2008 and fiscal 2010 as reported in that filing.
What this leaves out
- Nine fiscal years is the window this course uses and it is stated for that reason. It is not the company's whole filed history and it is not a cycle.
- The fiscal 2008 and 2010 figures are taken from a later filing's comparatives, which is why the accession is named. They are a different revenue line from the one in the nine-year table.
- The three averages are arithmetic means of annual margins, which weights each year equally regardless of size. A revenue-weighted average would give different numbers.
- Nothing here is a view on Toll Brothers or on any security, and none of it describes what any figure will do next.