C1T5L3 · Revised 2026-10-26

Decision and objectives

Practical task: Assess two hypothetical funds with the same final value but different paths

Objectives: Calculate sample return volatility; Measure peak-to-trough drawdown; Calculate the gain needed to recover a loss.

Required prior knowledge: C1T5L2. 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.

Ending return does not tell the investor how difficult the journey was. Volatility describes variation in measured returns; drawdown describes the decline from a previous peak; recovery shows the gain needed after a loss. These measures describe different features and can change with observation frequency. A daily series and a monthly series cannot be compared as if they see the same path.

Mechanics

Convert adjusted unit prices into consecutive returns first. Choose sample or population standard deviation and state the choice. Sample volatility divides squared deviations from the arithmetic mean by n − 1 before taking the square root. Drawdown at each observation compares current value with the highest previous value, including that date. Maximum drawdown is the most negative of those ratios over the observed window.

A fund with infrequent appraisal marks can appear less volatile than a traded portfolio while having substantial economic risk. Likewise, a month-end series misses a severe intra-month fall that later recovers. Neither volatility nor drawdown is a contractual loss boundary.

Price and return drivers

Sample volatility = square root of [sum of (return − mean)^2 / (n − 1)]. For comparable independent monthly observations under strong simplifying assumptions, multiplying monthly volatility by square root of 12 gives an annualized descriptive scale. Serial correlation and changing volatility can make that scaling unreliable. Recovery after loss L as a positive fraction is 1 / (1 − L) − 1: the reduced capital base requires a larger percentage gain.

Worked case

Hypothetical monthly returns are +1%, +3%, −1%, +1%. Arithmetic mean is 1%. Deviations in percentage points are 0, +2, −2, 0; squared deviations sum to 8. Sample volatility = sqrt(8/3) = 1.6330% per month. Under the simplified scaling assumption, annualized volatility is 1.6330% × sqrt(12) = 5.6569%. These four observations are too few for a dependable forecast.

A separate hypothetical adjusted-value path is 100, 120, 90, 108. The running peak becomes 120; the drop to 90 is 90/120 − 1 = −25%, the observed maximum drawdown. From 90, recovering to 120 requires 120/90 − 1 = 33.3333%. Ending at 108 gives a positive 8% return from inception but remains 10% below the previous peak.

Adverse case

An investor needs TRY 100,000 when that path is at 90 on a starting TRY 100,000 position. The cash shortfall is TRY 10,000 before exit costs. The 25% peak drawdown and 10% loss from original investment answer different questions; neither should replace the other. A larger stress of a 50% loss requires a 100% gain to recover. Historical low volatility can coexist with an unobserved gap risk, default event or redemption suspension.

Practical use

Use official adjusted unit histories with documented dates and consistent frequency. A risk indicator in an investor form is a summary under its method, not an exact future-loss limit; TI1's form makes that distinction explicit. Confirm access and dealing terms when relating drawdown to usable cash. Published prices already contain disclosed embedded expenses; investor exit charges and tax affect the realized result separately. This lesson excludes them from the statistical series and applies no current tax rule.

Decision boundaries

Use volatility for variation, drawdown for path loss and a cash stress for the liability. Do not choose a fund on one measure alone. The sample can be too short, stale or from a different strategy. Decline an allocation when the supplied adverse cash outcome breaches a hard spending need even if its measured volatility is lowest. A precise standard deviation cannot compensate for uncertain valuation inputs.

Practice and references

Exercise: hypothetical adjusted values are 100, 110, 88 and 105.6. Answer: the observed maximum drawdown is 88/110 − 1 = −20%; recovery from 88 to 110 needs 25%; ending return from 100 is +5.6%. Separately, two returns of 0% and 4% have mean 2%; sample volatility is sqrt((4+4)/(2−1)) = 2.8284 percentage points. Report the sample size alongside the estimate.

Takeaway: measure the path and the funding consequence, not only the endpoint.

Reference guide: mutual-fund; sample-volatility; maximum-drawdown; recovery-gain; volatility; maximum-drawdown; recovery. Next: C1T5L4. 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