Identifier: C5T2L2 · Revision: 2026-10-26 · Classification: domestic

Decision and objectives

The practical task is to calculate sample volatility and correlation from a small dataset. Make the decision reproducible: name the exposure, time horizon, cash requirement and comparison baseline before selecting a product.

Objectives: Calculate sample volatility and correlation from a small dataset; Measure concentration independently of historical covariance; Explain annualization and sample limitations.

Prerequisite: C5T2L1; completed Classes 1–4 and the Stock Market School foundation or Forex School foundation. Every example is hypothetical. Prices, dates, rates, fees, contract factors, policies and tax schedules are supplied teaching inputs, not current offers or legal parameters. No live account is needed.

Mechanics

Volatility describes dispersion of returns under a stated observation period and estimator. Correlation describes co-movement after subtracting means; it is neither causal protection nor the fraction of losses hedged. A small sample can be calculated exactly yet tell little about an unobserved crisis. Concentration is a different property: a portfolio can have low measured volatility while depending on one issuer or funding source.

Price and return drivers

Sample variance = sum((return − sample mean)^2)/(n − 1); sample volatility is its square root. Use all returns in decimals or all in percentage points consistently. Sample correlation divides the sum of paired deviations by the square root of the two sums of squared deviations. A simple concentration index is sum(weight^2); its reciprocal is an effective number only under that particular measure, not an issuer default model.

Worked case

Hypothetical four daily returns in percent: A = −2, 0, 2, 4; B = 4, 2, 0, −2. Both means are 1%. For A squared deviations are 9, 1, 1, 9, sum 20; sample variance 20/3 = 6.6667 percentage-points squared, volatility 2.5820%. B has the same volatility; paired deviation sum −20 gives correlation −1. An equal-weight portfolio returns 1% each observed day, so sample volatility is zero. Separately, issuer weights 50%, 30%, 20% have concentration 0.25 + 0.09 + 0.04 = 0.38 and reciprocal 2.6316 effective holdings.

Adverse case

On an unobserved stress day both A and B lose 10%; the equal-weight portfolio loses 10% despite zero sample volatility. Annualizing A as 2.5820% × sqrt(252) gives about 40.99% only under a supplied 252-day, independent/stationary-return approximation. It is not a reliable annual forecast from four observations. Bid/ask noise, stale fund marks and nonmatching holidays can suppress or distort measured correlation.

Practical use

Use comparable total returns, synchronized dates and a transparent choice of sample/population estimator. Include cash and derivatives in portfolio weights with an explicit denominator. Check whether transaction costs and distributions are in the series; do not add an embedded fund expense twice. Translating asset returns into a common investor currency can change both volatility and correlation.

Use permitted domestic access routes and the actual instrument documents. Verify intermediary authority, investor eligibility, order/redemption terms, settlement, custody and executable size before implementation. Reconcile spread and commissions, funding, collateral, custody, product expenses, conversion and exit charges; an amount already embedded in a fill or fund unit price is not deducted again. A published mark or product description does not promise an executable price or liquidity.

Tax is excluded unless a numerical schedule is expressly supplied as hypothetical. For actual rules record income year, residence and individual/corporate status, instrument and acquisition/contract dates, taxable event and rule effective date. The GIB investment-income guide, checked 2026-10-26, covers 2025 individual income; its 2026 publication date alone cannot settle a 2026 liability.

Decision boundaries

Use statistics to summarize observed behavior and support, not replace, scenario analysis. A zero or negative estimated correlation does not prove a worst-case hedge. If conclusions change radically when one observation is removed, report the instability and avoid a precision-based allocation.

Practice and references

Exercise: hypothetical returns −1%, 1%, 3%. Solution: mean 1%; squared deviations 4, 0, 4; sample variance 8/(3 − 1) = 4, sample volatility 2%. Weights 60% and 40% have concentration 0.52. A larger number of wrappers does not necessarily reduce the underlying issuer concentration calculated in the previous lesson.

Takeaway: Explain annualization and sample limitations with the cash dates, costs and remaining risks stated.

Product card: portfolio-decision-record. Formula: Sample return volatility. Glossary: Sample volatility, Concentration index. Next lesson: C5T2L3. Topic test.

Sources checked 2026-10-26:

Additional formulas: sample-correlation, weight-concentration.

Shared reference guide