Chapters

Chapters

Lesson 04 / 05

In this lesson

Starting dates and cumulative results
The observed loss and recovery
Consistent rolling-period comparisons
The shared observation history
The goal’s own deadline

See how the chosen dates change the story

Inspect the dates and the path between them, then count how much independent history a set of rolling results actually contains.

The same ending value can support opposite headlines.

Fictional total-return levels; income reinvested, unchanged currency, no expenses, tax, contributions or withdrawals. Dots are annual endpoints; the intervening path is unknown.

Level · initial value = 100

150100500

100Start

140Y1

70Y2

105Y3

115.5Y4

Start → year 4 · +15.5% cumulative

Year 2 → year 4 · +65% cumulative

Year 1 → year 4 · −17.5% cumulative

Different lengths mean these are not comparable annual rates. Launch or reliable-data boundaries can justify a start; the reason should accompany the display, rather than follow whichever result looks best.

Calculate annual moves and selected returns

Annual moves: +40%, −50%, +50%, +10%. Selected returns: 115.5 ÷ 100 − 1 = 15.5%; 115.5 ÷ 70 − 1 = 65%; 115.5 ÷ 140 − 1 = −17.5%.

The SEC warns about choosing favourable dates after seeing results.

Recovery of which reference value?

The visible 140→70 decline is 50%. Within-year moves are unspecified; the deepest daily drawdown could be worse.

Year 3 exceeds the original 100; year 4 still misses the 140 peak. Starting capital, peak and purchasing power differ. Units sold for spending cannot participate in a later rebound.

Inflation and the path between observations

Purchasing-power recovery needs its inflation basis, as the Bank of England explains. FINRA encourages comparison across years, but sparse observations still cannot reveal intrayear losses; the same nominal level at different dates need not buy the same goods.

Move the start without changing the calculation.

Rolling analysis repeats a fixed holding period from successive starts, holding currency, income, inflation and cash-flow assumptions consistent. This reveals variation within available history; it adds no absent country, crisis or condition.

Many windows reuse the same months.

Complete thirty-year record, month-end values including the initial observation: 360 monthly returns. Each ten-year window contains 120 returns; starts move one month. The strips show only the first two windows on a shared 121-month scale.

First window: months 1–120

Next window: months 2–121

The hatched span is the same 119 monthly returns in both windows. Only one month leaves and one enters.

Complete rolling windows in the record: 241
Non-overlapping ten-year blocks: 3

More windows create no extra decades. Even non-overlapping blocks need not be independent or representative of future conditions. Every sampled window succeeding does not establish a 100% future success chance; worst observed loss or recovery time is no future bound.

Count starts, shared observations and non-overlapping blocks

360 − 120 + 1 = 241 complete windows. Moving one month drops one return and adds one, leaving 119 of their 120 shared. Three non-overlapping ten-year blocks use 360 returns without repetition, not with established economic independence.

The worst sampled loss/longest recovery remain observations under this record, not contractual limits.

A twenty-year record cannot postpone a five-year obligation.

Compare the path and access with your actual spending deadline. Nominal value, real value, prior peak and ability to pay are different success tests. Favourable results requiring more time than your bill allows leave that risk unresolved.

Check your understanding

Try each question, then check your answer.

Choose questions from another chapter

Many ten-year windows

A thirty-year record produces many ten-year windows by moving the start one month at a time. What should be remembered?

Annualising each window’s return makes the neighbouring outcomes independent observations.
Their historical success fraction supplies the future success probability once all windows have the same length.
Adjacent windows share most observations and are not independent ten-year histories.

Show the explanation

Correct answer: Adjacent windows share most observations and are not independent ten-year histories.

Rolling calculations reveal sensitivity to start dates within the same record. Most months overlap between neighbouring windows, so a large window count does not create an equally large set of independent decades. The available markets, events and assumptions still limit the evidence.

Return to the explanation

Year-end observations

A table of year-end values shows a largest peak-to-trough fall of 30%. What can be concluded about losses within those years?

The table alone cannot rule out a larger interim drawdown.
No investor could have experienced more than a 30% fall.
Recovery by a year-end observation establishes the maximum waiting time after each interim fall.