C1T5L4 · Revised 2026-10-26

Decision and objectives

Practical task: Interpret fictional benchmark and risk-adjusted performance tables

Objectives: Choose a benchmark matching the mandate; Calculate a simplified Sharpe ratio and tracking difference; Distinguish average underperformance from tracking variability.

Required prior knowledge: C1T5L3. 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 return becomes meaningful relative to an objective and a comparable alternative. A benchmark should reflect the fund's mandate and data convention, rather than being chosen after seeing which comparison looks favorable. Risk-adjusted measures can help but compress many assumptions. Calculate the number, then state what it cannot establish.

Mechanics

A benchmark is a specified reference portfolio or index. Match currency, distributions, dates and expense treatment. A price index excluding dividends is not equivalent to an equity fund whose assets receive dividends. A mixed fund may need a disclosed blended reference. If the mandate changes, a full-period comparison can mix different responsibilities.

The Sharpe ratio compares average excess return over a specified cash reference with return volatility. Tracking difference is the fund return minus benchmark return over a stated period. Tracking error measures variability in periodic return differences. A fund can lag by a nearly constant amount, giving a negative tracking difference but small tracking error.

Price and return drivers

Use a simplified annual Sharpe illustration: (annual arithmetic mean fund return − annual cash-reference return) / annual standard deviation, with compatible measurement conventions. It does not mean “return per unit of maximum loss.” For actual multi-period data, compute periodic excess returns and their standard deviation consistently, stating annualization assumptions. Sample tracking error is the sample standard deviation of periodic active returns, where active return means fund minus benchmark for that period.

Worked case

Hypothetical same-year data: Fund A mean annual return 18%, cash reference 8%, annual return volatility 10%; Fund B 16%, 8% and 5%. Simplified Sharpe ratios are (18−8)/10 = 1.0 and (16−8)/5 = 1.6. B has the larger ratio despite the smaller return. These are supplied compatible summary estimates, not a guarantee or recommendation.

Independent tracking example: monthly active returns are −0.1%, +0.1%, −0.1%, +0.1%. Mean active return is zero; squared deviations sum to 0.04 in percentage-point-squared units. Sample tracking error = sqrt(0.04/3) = 0.1155 percentage points per month. Separately, a fund gaining 11% against a 12% annual benchmark has a −1 percentage point annual tracking difference. Do not confuse that one-year difference with monthly tracking variability.

Adverse case

Change B's valuation to a stale, infrequently updated series. Its measured volatility may fall, inflating its Sharpe ratio without reducing its true exit risk. A strategy with occasional large losses can show an attractive ratio before a rare adverse event. If the cash reference changes from 8% to 14% while supplied fund means and volatilities stay fixed, A's simplified ratio is 0.4 and B's also 0.4; the ranking depends on the defined reference and period. A denominator near zero can make ratios unstable or meaningless.

Practical use

Obtain official benchmark definitions and dated performance reports. SPK's BYF communique separately defines tracking difference and tracking error; the distinction is useful in ordinary-fund analysis too. Verify any benchmark amendments rather than using the current benchmark retroactively without explanation. Comparison returns should identify embedded expenses and investor taxes excluded. Actual investable alternatives may add spreads, fees and different settlement; a theoretical benchmark usually does not hand the investor cash. No current tax rate is applied in these statistical examples.

Decision boundaries

Use these measures to ask better questions, not to replace risk, liquidity and mandate analysis. Compare funds with similar exposures and reliable pricing. Defer a ranking when benchmark income treatment, cash-reference convention or valuation frequency is unknown. A fund can be the closest tracker yet unsuitable for a near cash liability; a high Sharpe ratio cannot grant access to a restricted fund.

Practice and references

Exercise: hypothetical annual mean return 15%, compatible cash reference 6%, volatility 9%. Calculate the simplified Sharpe ratio and interpret a 15% fund return against a 17% matched benchmark.

Answer: simplified Sharpe = (15−6)/9 = 1.0. If a matching benchmark returns 17% over the observed year while the fund's actual cumulative return is 15%, tracking difference is −2 percentage points. If monthly active returns are all exactly −0.2%, sample tracking error is zero despite persistent underperformance. The arithmetic mean averages periodic returns; geometric growth multiplies their growth factors. For two hypothetical one-year returns of +10% and −10%, the arithmetic mean is (10% − 10%)/2 = 0%, but cumulative growth is 1.10 × 0.90 − 1 = −1%. The geometric annualized return is (0.99)^(1/2) − 1 = approximately −0.5013%. Volatility creates this difference even when the arithmetic mean is zero; the arithmetic mean in the stated Sharpe convention must not be replaced silently by the compounded rate.

Takeaway: benchmark fit and data definitions determine what a performance ratio means.

Reference guide: mutual-fund; domestic-byf; sharpe-ratio; tracking-difference; tracking-error; benchmark; sharpe-ratio; tracking-difference; tracking-error. Next: C1T5L5. Topic test.

Sources: 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; SPK Communique III-52.2 — Articles 3–4 definitions; creation/redemption and index tracking sections; date 2013-11-27; checked 2026-10-26. Source records: sources.json. Check the cited rule dates and confirm current dealing terms before any transaction.

Shared reference guide