Identifier: C5T2L3 · Revision: 2026-10-26 · Classification: domestic

Decision and objectives

The practical task is to calculate a supplied historical percentile and tail average. Make the decision reproducible: name the exposure, time horizon, cash requirement and comparison baseline before selecting a product.

Objectives: Calculate a supplied historical percentile and tail average; Distinguish VaR, expected shortfall and a worst possible loss; Explain sample, horizon and liquidity limitations.

Prerequisite: C5T2L2; 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

Value at risk (VaR) is a loss threshold at a specified confidence, horizon and model. It does not describe the size of losses beyond that threshold. Expected shortfall (ES) summarizes the chosen tail average, but depends heavily on rare observations and the estimator. Different quantile/interpolation conventions can produce different small-sample numbers, so state the convention.

For this lesson, twenty equally weighted hypothetical one-day loss scenarios are ordered from smallest to largest. Use nearest-rank VaR and the average of the worst stated tail fraction for ES. This is an arithmetic teaching dataset, not a calibrated forecast or a banking capital implementation.

Price and return drivers

In twenty equal scenarios each has 5% weight. The 95% nearest-rank threshold is observation 19; the worst 5% tail contains one observation. At 90% the threshold is observation 18 and the worst 10% contains two. Losses are positive cash outflows. ES can be much larger than VaR, but neither imposes a contractual loss limit.

Worked case

Hypothetical ordered losses in TRY thousands: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 30, 40, 100. The 95% VaR is TRY 40,000 and worst-5% ES TRY 100,000. The 90% VaR is TRY 30,000 and worst-10% ES (40,000 + 100,000)/2 = TRY 70,000. A TRY 1,000,000 portfolio therefore has 4% reported 95% VaR and 10% ES under this dataset. A cash reserve TRY 50,000 exceeds the percentile but falls TRY 50,000 below the supplied tail loss.

Adverse case

Add an unobserved joint shock causing TRY 180,000 loss and TRY 80,000 same-day collateral demand. The original 95% figure remains a description of the old sample, not evidence the new state is impossible. Market loss and collateral need must be reconciled without counting a settlement loss twice; the additional TRY 80,000 is stated here as incremental required collateral, beyond loss settlement. Selling illiquid holdings to fund it can produce still different realized losses.

Practical use

Record dataset dates, confidence, horizon, loss definition, weighting, quantile and tail convention, price source and whether valuations assume executable exits. The official ACPR research highlights small-sample uncertainty; it does not supply a retail safety threshold. Include slippage, financing and operational freezes through separate scenarios when absent from the statistical series. Tax is outside these loss estimates unless expressly modeled.

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 VaR and ES as summaries beside stress losses and dated funding needs. Do not say a 95% VaR is the maximum loss or that ES forecasts a precise crisis debit. Defer a leveraged allocation if it survives only the reported percentile while the plausible adverse cash path is unfunded.

Practice and references

Exercise: supplied ten equal loss states in TRY thousands: 0, 1, 2, 3, 4, 5, 6, 7, 12, 30. Calculate nearest-rank 90% VaR, worst-10% ES and their fractions of TRY 200,000 wealth. Solution: VaR is TRY 12,000 and ES TRY 30,000. On TRY 200,000 wealth these are 6% and 15%. They are conditional dataset measures, not future loss guarantees.

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

Product card: portfolio-decision-record. Formula: Supplied equal-weight tail average. Glossary: Value at risk, Expected shortfall. Next lesson: C5T2L4. Topic test.

Sources checked 2026-10-26:

Shared reference guide