What did the chart actually measure?
A chart labelled “stocks” may cover only one country’s large companies. Read the complete fictional H-4 record below: its claimed +20% belongs to four specified accounts, not a market. The next lesson continues this same record to the owner’s result.
Bonds need currency, credit and maturity specified. More years add no missing countries. Identify universe, selection and weights, as in MSCI’s construction methodology.
A changing index differs from today’s winners traced backward
An evolving index differs from today’s winners traced backward. Even a century reflects that country’s institutions, access and economic outcomes.
Endpoint growth does not describe each intervening year.
A 20% cumulative gain over exactly two years has a compound annual equivalent of about 9.54%, not 10%. It need not have earned that rate in either year. Count elapsed intervals from exact dates, not table rows.
Year-end observations can also omit a severe fall and recovery inside a year.
Calculate the annual equivalent of the two-year gain
1.20^(1÷2)−1≈9.54%. Cumulative, calendar-year and annualised rates answer different questions. The annualised rate joins the endpoints without reconstructing the path.
The dollar gain can disappear in euro spending.
Complete chosen universe: four fund accounts, A/B/C/D; $2,500 each initially (25% initial-capital weights), no rebalancing, external flows or hedge. This is not a representative sample, a world market or an investable composite.
A / B / C$2,500 each → $3,250 eachCombined end value $9,750
D closes · 1 January 2025$2,500 → $2,250 proceedsProceeds retained at assumed 0% until 1 January 2026
Four starting accounts $10,000 → surviving accounts $9,750 + D's proceeds $2,250 = $12,000
Values already include reinvested distributions and underlying fund expenses through each account's end. No additional financing/derivative layer is modelled. Owner execution/account costs and personal tax are excluded. Annual account paths are not supplied.
Value index · start = 100 separately in each currency
1001 Jan 2024
Only endpoints are known. USD 100→120 is +20% cumulatively. EUR 100→100 is 0% before owner costs. Each index has its own starting currency base; the conversion is unhedged, not the return of a euro listing.
Invented euro spending basket: 100→110 over the same dates. €9,000 ÷ 1.10 ≈ €8,182 in initial euros: −9.09% before owner costs. The next lesson finishes this same record with its separately specified owner charge.
Before owner costs, nominal euro return is zero and real return about −9.09%. Check exchange-quote direction, dates and hedge; the fund name cannot establish them. Nothing in H-4 establishes an earlier bill’s funding, an intraperiod drawdown, omitted markets or a future rate.
Calculate the change in purchasing power
Real endpoint: €9,000 ÷ 1.10≈€8,182; (1÷1.10)−1≈−9.09%.
Which price basket was removed?
US inflation generally answers a different question from euro spending. Specify country, basket, dates and method; your housing, care or education costs may diverge from a national index.
A real return already includes its defined adjustment; subtracting inflation again counts it twice.
The national reference and long comparisons
The Bank of England calculator concerns UK purchasing power. Changing goods and measurement methods reduce very-long-period precision. A national basket is a population reference, not your personal spending guarantee; currency conversion and inflation adjustment remain separate steps.
Keep the definition beside the claim.
H-4’s sources explain the method; they do not supply its invented figures. Check the primary observations, construction and permitted use of any real chart.