C1T5L2 · Revised 2026-10-26

Decision and objectives

Practical task: Compare fictional fund histories without favoring one selected endpoint

Objectives: Calculate cumulative and annualized historical return; Compare rolling windows on common dates; Separate unit performance from investor cash-flow experience.

Required prior knowledge: C1T5L1. Classification: domestic. Revision: 2026-10-26. All fictional names, prices, rates, fees, calendars and tax schedules below are hypothetical unless explicitly identified as a dated document observation.

A fund's ranking can reverse when the start date moves. A single long return hides the path; a single recent return can reward an unusually favorable window. Compare cumulative, annualized and rolling outcomes for the same dates, currency and income treatment. Use unit-price performance to compare investment vehicles before adding the investor's own timing and taxes.

Mechanics

Cumulative return measures total growth between two dates. Annualized return expresses that same growth as a constant geometric yearly rate. A rolling return repeats a fixed-length window through a series, revealing sensitivity to entry date. Rolling observations overlap, so many observations do not necessarily mean many independent market experiences.

Use total-return data if distributions occur. A price drop on a distribution date can look like a loss if the paid cash is ignored. Check splits, mergers, mandate changes and missing values. A fund launched recently cannot fairly be assigned a longer history from another manager or predecessor without a documented continuity basis.

Price and return drivers

With no intervening external flows and appropriately adjusted units, cumulative return = ending unit value / starting unit value − 1. For a complete n-year period, annualized return = (ending / starting)^(1/n) − 1. With days, use the explicitly stated day basis as in C1T1L3. An arithmetic average of period returns differs from compound growth and should not replace it. Historical annualization is a description, not a forecast.

Worked case

Hypothetical adjusted year-end values are A: 100, 120, 108, 140.4; B: 100, 110, 121, 133.1. No distributions or external flows. A's three-year cumulative return is 40.4%; B's is 33.1%. Their annualized returns are 1.404^(1/3) − 1 ≈ 11.98% and 1.331^(1/3) − 1 = 10%.

A's successive one-year returns are +20%, −10% and +30%; B's are +10%, +10%, +10%. Two-year rolling returns for A are 108/100 − 1 = 8% and 140.4/120 − 1 = 17%. B's are 21% and 21%. The higher final cumulative return of A does not mean it provided the higher return in every holding window. The numbers are already after hypothetical fund expenses; investor charges and tax are excluded.

Adverse case

A learner selects only A's last year and describes its 30% as the expected next-year return. That ignores the earlier −10% and the two-year 8% outcome. Another investor adds money just before A's losing year, so the investor's money-weighted experience differs from the fund's three-year unit growth. The available data are insufficient to compute that experience without contribution amounts and dates. Do not invent them or call the fund's annualized return the investor's realized bank-account yield.

Practical use

Retrieve consistent historical data and the official fund disclosures. Record start/end dates, treatment of distributions, expenses and any series discontinuities. Ordinary or restricted access and redemption timing must be verified independently of performance. When converting a historical series into a personal net comparison, add actual investor fees and the correctly dated tax treatment; do not deduct embedded expenses again. This lesson applies no actual current tax rate and no assumption that any historical price is an executable quote.

Decision boundaries

Rolling analysis is useful when entry timing is uncertain and the horizon is known. It cannot demonstrate that future losses are bounded by the worst observed window. Short histories, changing mandates and overlapping samples limit conclusions. Decline a purchase justified only by a selected winning period; request the full common window and examine losses, cash needs and costs. A smooth history may be genuine, stale or too short to contain the relevant stress.

Practice and references

Exercise: hypothetical adjusted prices at successive year-ends are 50, 60, 54 and 64.8. Answer: cumulative three-year return = 64.8/50 − 1 = 29.6%; annualized = 1.296^(1/3) − 1 ≈ 9.03%; two-year rolling returns are 54/50 − 1 = 8% and 64.8/60 − 1 = 8%. The second year's loss is 54/60 − 1 = −10%. Explain why reporting only the final year's +20% changes the impression.

Takeaway: a matched return window is a measurement choice that can change the ranking.

Reference guide: mutual-fund; compound-return; annualized-return; holding-period-return; rolling-return; cumulative-return; total-return. Next: C1T5L3. Topic test.

Sources: SPK Mutual Funds Introduction Guide — What is a fund; fund expenses; fund types; founder and manager; recorded units; date not stated; retrieved 2026-10-26; checked 2026-10-26; TI1 Investor Information Form attached to KAP notification 1665983 — Pages 1–2: identity; risk profile; expenses; important information; date 2026-09-21; checked 2026-10-26. Source records: sources.json. Check the cited rule dates and confirm current dealing terms before any transaction.

Shared reference guide