Roth Ledger

A ledger of what a strategy did to your exposure, period by period, beside where it ended up. The claim this instrument makes is about time, so the record it keeps is per period rather than at the end.

Helps you decide: whether to hold the same exposure steadily, or to hold more of it early and less of it later. You will have: a per-period record of the share of your balance held in each year, beside the total it adds up to — and, named rather than filled in, the balance behind each row that would turn those shares into money.

Walk not started — every stop is readable, and the walk becomes interactive once the module for this page runs.

The walk

1 of 9 stops open so far. The next one opens when you reach it. Stop 1 of 9.

This stop

Some numbers on this page are not shown yet — here is why (5 notes)

Some numbers here are missing, and are left missing rather than guessed.

Which ones: the balances themselves — what any of this is worth, year by year and at the end; the historical figures — what this strategy actually returned in past 30-year windows; what the choice costs — the gap between getting it right and getting it wrong; the two searches themselves, and whether they agree.

Why they are not filled in with plausible-looking figures: they come from running the plan, and this page will not print a number it has not run; a backtest is a record of what happened, and inventing one would be inventing history; a cost shown without the calculation behind it is a claim rather than a finding; agreement is the evidence here, so asserting it without running both would be asserting the evidence.

What will fill them: the run this instrument is built on, once it can be reached from here; the measured history this instrument reads from; the calculation that turns a goal and a plan into a banded answer; the search this instrument runs over the plan.

Each stop says which of its own numbers are missing, at the point where they would be.

Stop 1 of 9

What this is, and what it is for

You already diversify across assets. This instrument is about diversifying across TIME — spreading the same exposure over more years rather than more holdings.

The rest of what this stop says (1)

The gap is that a single number at the end cannot show you what time did. A record per period can, which is what this page is built around.

Every stop, in order (9 stops — reference, not the walk)

Stop 1

You are on this stop — it is shown in full beside this.

What this is, and what it is for

You already diversify across assets. This instrument is about diversifying across TIME — spreading the same exposure over more years rather than more holdings.
The gap is that a single number at the end cannot show you what time did. A record per period can, which is what this page is built around.

Where the other frame holds all the way — 60%
5 holdings, each adding the same amount

Each holding adds 12% to what is already there, and the 5th arrives at 60% — the level the other frame holds all the way along, on the same axis at the same scale. How many holdings is this page’s own illustration of what you already do; nothing here knows what you hold.

The balance these shares are taken OF, and so the exposure in money that they multiply to is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (2 lines)

the baseline this page starts from, drawn here as the level being arrived at — Where the other frame holds all the way — 60%
this page’s own illustration of holding-by-holding spread — 5 holdings, each adding the same amount

Where each line comes from (2 lines) — in the record, under this stop.

A constant allocation, held throughout
The same share, spread across TIME — more early, less late

Both hold the same average — 60% against 60% — and differ only in WHEN. The same total again, spread across TIME rather than across holdings. Neither is a result.

Where each line comes from (2 lines)

the baseline this page starts from — A constant allocation, held throughout
the exposure control on this page, at the shape it starts in — The same share, spread across TIME — more early, less late

Where each line comes from (2 lines) — in the record, under this stop.

What is missing here is marked on the drawing it belongs to.

Stop 2

You are on this stop — it is shown in full beside this.

Which of these three is closest to you?

Pick the one whose length of time is nearest yours. You do not have to be one of them, and nothing here is typed in.
Each line starts at the exposure that person holds today and runs as far right as the years they have. Two things differ between them, and only one of the two can never be topped up.

Early career, long horizon — 40 years
Mid career, balance building — 25 years
Near the goal, short horizon — 8 years

Each line starts where that person is today and eases to the same late floor.

What the other two end up with is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (3 lines)

this page’s own three people — Early career, long horizon — 40 years
this page’s own three people — Mid career, balance building — 25 years
this page’s own three people — Near the goal, short horizon — 8 years

Where each line comes from (3 lines) — in the record, under this stop.

The numbers behind the three (4 rows)

	Early career	Mid career	Near the goal
Years to the goal	40 yrs	25 yrs	8 yrs
Already invested	~$15K	~$300K	~$900K
Added each year	~$10K	~$25K	~$30K
Exposure held today	90%	70%	50%

What is missing here is marked on the drawing it belongs to.

Stop 3

You are on this stop — it is shown in full beside this.

What actually happened

Every replay leaves a record with one row per year: 30 years each, overlapping, walked forward rather than cut into blocks. The published record runs 1970 to 2024, so it holds 26 of them — every one is drawn, each starting a year later than the last.
The strategy each of them replays is the tilted exposure path this page starts from. A window covers more time than the shortest horizon here and less than the longest, so for a short plan no single record is a run of the whole thing.
What a record of the past is for is the shape of the rows rather than the number at the end of them — which is the same reason this page keeps a row per period for the future it cannot yet run.
Every row here is a year that happened. This stop is a record rather than a forecast, and nothing on it runs forward.

Where each window starts
Where it ends, 30 years later

Real years along the bottom, one row per window: 26 of them, each starting a year after the one above, because the record is walked forward rather than cut into blocks. The record runs 1970 to 2024, and these are years that happened. Nothing on this stop runs forward.

What the strategy actually RETURNED in each of these windows — the measured history itself is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (2 lines)

the first year of every window the published record supports, one year apart — Where each window starts
the last year of each of those windows, which is its start plus the replay length — Where it ends, 30 years later

Where each line comes from (2 lines) — in the record, under this stop.

What is missing here is marked on the drawing it belongs to.

Stop 4

You are on this stop — it is shown in full beside this.

The rule, and what it costs when it misses

The rule is drawn here: hold more exposure early than late.
The upright line is where holding it that way stops meaning more exposure and starts meaning less. It is computed from the two paths rather than stated, so it moves when they move. What is not drawn is what being on the wrong side of it costs you, which is the miss.
A rule shown without its miss is an instruction rather than a decision, which is why the two are one stop and not two.
When the cost arrives it will arrive as a range: one number with no spread around it claims to be more exact than it can be.

A constant allocation, held throughout
The tilted path — more exposure early, less late — the rule this instrument recommends
The hinge — where which one holds more exposure flips

Left of the upright line the sloping path holds MORE exposure than the flat one; right of it, less. That line is the hinge, computed from where the two cross rather than stated. The tilted path is the one this instrument recommends, marked as such in the key.

WHERE YOU SIT on this boundary, and what being on the wrong side of it costs is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (3 lines)

the baseline this page starts from — A constant allocation, held throughout
the exposure control on this page, at the shape it starts in — The tilted path — more exposure early, less late
computed from the two paths above, not asserted — The hinge — where which one holds more exposure flips

Where each line comes from (3 lines) — in the record, under this stop.

What is missing here is marked on the drawing it belongs to.

Stop 5

You are on this stop — it is shown in full beside this.

Two searches, side by side

Two frames, set up identically on purpose.
The same family of shapes, the same starting point, the same draws — which is what makes a difference between the searches a difference of method rather than of luck. The first picks one shape and commits to it before anything happens. The second picks a rule and re-decides as things happen, so what it holds late depends on what happened early.
Where they agree, the agreement is the evidence — two methods that share no assumption landing in the same place is worth more than either alone. Where they disagree, that is a finding, shown rather than resolved, with neither presented as the one to take.

Widest the family goes — most early
Widest the other way — most late
One shape, chosen at the start and held to

One shape, chosen before anything happens and held all the way along. The outer lines are the family both searches are given.

Which shape this search returns, and how it scored is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (3 lines)

the edge of what the control admits — Widest the family goes — most early
the edge of what the control admits — Widest the other way — most late
a shape out of that family — One shape, chosen at the start and held to

Where each line comes from (3 lines) — in the record, under this stop.

Widest the family goes — most early
Widest the other way — most late
A rule, re-decided at 3 moments — each upright is one

A rule rather than a shape: the path holds between the uprights and changes AT them. Same family and axes as the other frame.

Which rule this search returns, and whether the two agree is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (3 lines)

the edge of what the control admits — Widest the family goes — most early
the edge of what the control admits — Widest the other way — most late
the same family, held between re-decisions rather than gliding through them — A rule, re-decided at 3 moments — each upright is one

Where each line comes from (3 lines) — in the record, under this stop.

What is missing here is marked on the drawing it belongs to.

Stop 6

You are on this stop — it is shown in full beside this.

The same decision, where the assumption was wrong

The assumption being changed is how long you have: one arm keeps the horizon you planned against, the other finds out it is shorter.
Both arms leave the same point and are identical up to the upright line. Everything else is held — the same rule, the same draws, the same decision — so the gap after the line is the assumption and nothing else.
This is the stop a book cannot do for you: being wrong on purpose, and seeing where that lands.

The plan as made — the same tilt spread over 40 years
The same plan, where the horizon turned out to be 28 years
Where the assumption changed — year 16

Drawn at 40 years, which is early career, long horizon. Pick a different one at the locating stop and this is redrawn at yours. After the upright line one arm still has 40 years to reach its floor and the other has 28, so the same rule has to come down faster.

What each arm is WORTH — the two runs whose difference is the whole finding here is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (3 lines)

the exposure control on this page, over the horizon this version is drawn at — The plan as made — the same tilt spread over 40 years
the same control and the same rule, over a horizon that turned out shorter — The same plan, where the horizon turned out to be 28 years
the point this page states the two arms are identical up to — Where the assumption changed — year 16

Where each line comes from (3 lines) — in the record, under this stop.

The plan as made — the same tilt spread over 25 years
The same plan, where the horizon turned out to be 18 years
Where the assumption changed — year 10

Drawn at 25 years, which is mid career, balance building. Pick a different one at the locating stop and this is redrawn at yours. After the upright line one arm still has 25 years to reach its floor and the other has 18, so the same rule has to come down faster.

What each arm is WORTH — the two runs whose difference is the whole finding here is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (3 lines)

the exposure control on this page, over the horizon this version is drawn at — The plan as made — the same tilt spread over 25 years
the same control and the same rule, over a horizon that turned out shorter — The same plan, where the horizon turned out to be 18 years
the point this page states the two arms are identical up to — Where the assumption changed — year 10

Where each line comes from (3 lines) — in the record, under this stop.

The plan as made — the same tilt spread over 8 years
The same plan, where the horizon turned out to be 6 years
Where the assumption changed — year 3

Drawn at 8 years, which is near the goal, short horizon. Pick a different one at the locating stop and this is redrawn at yours. After the upright line one arm still has 8 years to reach its floor and the other has 6, so the same rule has to come down faster.

What each arm is WORTH — the two runs whose difference is the whole finding here is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (3 lines)

the exposure control on this page, over the horizon this version is drawn at — The plan as made — the same tilt spread over 8 years
the same control and the same rule, over a horizon that turned out shorter — The same plan, where the horizon turned out to be 6 years
the point this page states the two arms are identical up to — Where the assumption changed — year 3

Where each line comes from (3 lines) — in the record, under this stop.

What is missing here is marked on the drawing it belongs to.

Stop 7

You are on this stop — it is shown in full beside this.

Change one thing that matters

The parameter here is the exposure path: not how much, but when.
Every position holds the same average across the horizon and spreads it differently.
Press one and the ladder marks it; the per-period record is redrawn at that position.
What it is WORTH has to be run — a change re-runs the whole thing rather than re-scaling the last answer. That run is not available from this page yet.

Level — same all the way
Gentle — a little more early
Tilted — clearly more early
Steep — as much as possible early

Every line holds the same average — 60% — and differs only in WHEN.

What each tilt is worth is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (4 lines)

a position of the exposure control on this page — Level — same all the way
a position of the exposure control on this page — Gentle — a little more early
a position of the exposure control on this page — Tilted — clearly more early
a position of the exposure control on this page — Steep — as much as possible early

Where each line comes from (4 lines) — in the record, under this stop.

A constant allocation, period after period
Level — same all the way, period after period

One value per year rather than one number at the end, at the level setting. Drawn over the full 40 years rather than one horizon, because the four positions are only comparable on one axis. At this setting the two rows are one row — the honest picture of not tilting at all.

The balance behind each row is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (2 lines)

the baseline this page starts from — A constant allocation, period after period
the exposure control on this page, at the position chosen, averaged over each year — Level — same all the way, period after period

Where each line comes from (2 lines) — in the record, under this stop.

A constant allocation, period after period
Gentle — a little more early, period after period

One value per year rather than one number at the end, at the gentle setting. Drawn over the full 40 years rather than one horizon, because the four positions are only comparable on one axis. The steps are the periods.

The balance behind each row is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (2 lines)

the baseline this page starts from — A constant allocation, period after period
the exposure control on this page, at the position chosen, averaged over each year — Gentle — a little more early, period after period

Where each line comes from (2 lines) — in the record, under this stop.

A constant allocation, period after period
Tilted — clearly more early, period after period

One value per year rather than one number at the end, at the tilted setting. Drawn over the full 40 years rather than one horizon, because the four positions are only comparable on one axis. The steps are the periods.

The balance behind each row is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (2 lines)

the baseline this page starts from — A constant allocation, period after period
the exposure control on this page, at the position chosen, averaged over each year — Tilted — clearly more early, period after period

Where each line comes from (2 lines) — in the record, under this stop.

A constant allocation, period after period
Steep — as much as possible early, period after period

One value per year rather than one number at the end, at the steep setting. Drawn over the full 40 years rather than one horizon, because the four positions are only comparable on one axis. The steps are the periods.

The balance behind each row is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (2 lines)

the baseline this page starts from — A constant allocation, period after period
the exposure control on this page, at the position chosen, averaged over each year — Steep — as much as possible early, period after period

Where each line comes from (2 lines) — in the record, under this stop.

What is missing here is marked on the drawing it belongs to.

Stop 8

You are on this stop — it is shown in full beside this.

The ledger this page hands you

The rows the exposure control sets, added up as they go — at whichever position is showing.
Every position of the control banks the same total exposure by the close, and what a position changes is the pace of getting there — which is the whole claim this instrument makes, and it is a claim a closing number cannot show you, because at the close they all agree.
This is what the arrival promised you would have. The balance behind each row is the part that has to be run.

A constant allocation, added up
The level path, added up

Adding the rows up as they go, at the level setting, over the full 40 years rather than one horizon. At this setting the two are one line: choosing not to tilt is choosing to bank exposure at exactly the pace the baseline does. A single closing number would show the two ending together and say nothing at all about how they got there.

The balance behind each period, without which these are shares rather than money is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (2 lines)

the baseline this page starts from, accumulated period by period — A constant allocation, added up
the exposure control on this page, accumulated period by period — The level path, added up

Where each line comes from (2 lines) — in the record, under this stop.

A constant allocation, added up
The gentle path, added up

Adding the rows up as they go, at the gentle setting, over the full 40 years rather than one horizon. The gentle path banks its exposure earlier and the level one banks it steadily, and they close on the same total — which is the claim the per-period record is evidence for: the same exposure overall, arranged differently across time. A single closing number would show the two ending together and say nothing at all about how they got there.

The balance behind each period, without which these are shares rather than money is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (2 lines)

the baseline this page starts from, accumulated period by period — A constant allocation, added up
the exposure control on this page, accumulated period by period — The gentle path, added up

Where each line comes from (2 lines) — in the record, under this stop.

A constant allocation, added up
The tilted path, added up

Adding the rows up as they go, at the tilted setting, over the full 40 years rather than one horizon. The tilted path banks its exposure earlier and the level one banks it steadily, and they close on the same total — which is the claim the per-period record is evidence for: the same exposure overall, arranged differently across time. A single closing number would show the two ending together and say nothing at all about how they got there.

The balance behind each period, without which these are shares rather than money is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (2 lines)

the baseline this page starts from, accumulated period by period — A constant allocation, added up
the exposure control on this page, accumulated period by period — The tilted path, added up

Where each line comes from (2 lines) — in the record, under this stop.

A constant allocation, added up
The steep path, added up

Adding the rows up as they go, at the steep setting, over the full 40 years rather than one horizon. The steep path banks its exposure earlier and the level one banks it steadily, and they close on the same total — which is the claim the per-period record is evidence for: the same exposure overall, arranged differently across time. A single closing number would show the two ending together and say nothing at all about how they got there.

The balance behind each period, without which these are shares rather than money is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (2 lines)

the baseline this page starts from, accumulated period by period — A constant allocation, added up
the exposure control on this page, accumulated period by period — The steep path, added up

Where each line comes from (2 lines) — in the record, under this stop.

What is missing here is marked on the drawing it belongs to.

Stop 9

You are on this stop — it is shown in full beside this.

Now put it through a crisis

Three named episodes — a 2008-style crisis, a COVID-style disruption, an extended bear market — drawn as the falls they are stylized from.
Each carries in the key the published figure behind it. What one of them does to YOUR plan is the run this page cannot make yet, so these are the shocks rather than their consequences.
Worst first — by how deep the market fall each is stylized from was, which is the one thing about them that is a published measurement rather than this page's judgement. Every one is read against the same plan with no shock at all, because a number with nothing to compare it to says nothing.
The no-shock run is the thing being compared against rather than a fourth episode, so it is never offered as one to choose. It is the flat line along the bottom of the drawing.

2008-Style Crisis — drawn at a 50% fall, held 2 years (the episode itself fell −56.8%)
Extended Bear Market — drawn at a 45% fall, held 3 years (the episode itself fell −49.1%)
COVID-Style Disruption — drawn at a 34% fall, held 1 year (the episode itself fell −33.9%)
No shock at all — the run every one of them is read against

Worst first means the depth of the market fall each is stylized from: the deepest line is first. The flat line is the same plan with nothing applied — what the others are read against, not a fourth episode to choose.

What any of these regimes costs against that baseline is not shown here. Nothing here computes it or stands in for it.

Where each line comes from (4 lines)

stylized from Global financial crisis, 2007–2009, where the market actually fell S&P 500 peak-to-trough −56.8% (Oct 2007 → Mar 2009); duration from BLS, NBER — 2008-Style Crisis — drawn at a 50% fall, held 2 years (the episode itself fell −56.8%)
stylized from Dot-com unwind, 2000–2002, where the market actually fell S&P 500 −49.1% (Mar 2000 → Oct 2002); NASDAQ −78%; duration from BLS, NBER — Extended Bear Market — drawn at a 45% fall, held 3 years (the episode itself fell −49.1%)
stylized from COVID-19 market disruption, 2020, where the market actually fell S&P 500 −33.9% (Feb–Mar 2020); duration from BLS — COVID-Style Disruption — drawn at a 34% fall, held 1 year (the episode itself fell −33.9%)
the same plan with none of these applied — No shock at all — the run every one of them is read against

Where each line comes from (4 lines) — in the record, under this stop.

What is missing here is marked on the drawing it belongs to.

Nothing on this page is a forecast this page made up. Where a number is missing, it is missing and says so.

When the numbers do arrive they will come as ranges rather than single figures, and beside the shape they came from rather than on their own — said now so that what arrives can be held to it.

What is missing here is marked on the drawing it belongs to.