Use a risk quantile without calling it a maximum loss

Learning goals

• Calculate the normal one-day 95% VaR in currency.
• Explain why a model-based loss quantile, not the maximum loss applies to this case.
• Identify the case-specific assumption or failure mode before taking action.

Draft · approximately 30 minutes, excluding further revision.

Shared case and decision context

A 1 million portfolio has daily mean return zero and volatility 2%. For a one-day normal illustration use z=1.645 for a 95% lower-tail VaR. Positions include options in reality, so normal linear assumptions are questionable.

Economic or professional mechanism

VaR estimates a loss quantile over a defined horizon and confidence level. It does not describe the severity beyond the threshold or the largest possible loss. Expected shortfall averages losses in the tail under its definition. Parametric, historical and Monte Carlo approaches make different assumptions and remain vulnerable to model and data limitations.

Apply, challenge and communicate

The linear-normal one-day VaR is 32,900. Revalue nonlinear option positions under relevant shocks rather than assuming constant delta everywhere. Use stress tests, concentration limits, liquidity planning and backtesting alongside VaR; square-root-of-time scaling requires assumptions that can fail during serial dependence or changing volatility.

Limits, capital and institutional risk measures

A riskbudget allocates acceptable contributions to portfolio or activerisk; positionlimits cap concentrations, scenariolimits cap modeled stress losses, andstop-lossrules trigger review/trading after losses. A stop does not guarantee execution at its threshold through a gap or illiquid market. Test interactions rather than adding independent limits and assuming the whole is safe.

Capital allocation can consider incremental and marginal risk, expected return on economic capital and diversification, while acknowledging model uncertainty and regulatory constraints. Banks often combine market, credit, liquidity and capital measures; assetmanagers emphasize mandate tracking and redemption liquidity; pensions measure funded status and liability sensitivity; insurers combine asset risk with claim, underwriting and solvency exposures. A common VaR number does not make their objectives identical.

Formula and assumptions

One-day normal VaR≈portfolio value*(z*sigma−mu)

Case analysis with explicit assumptions

1. A 1 million portfolio has daily mean return zero and volatility 2%. For a one-day normal illustration use z=1.645 for a 95% lower-tail VaR. Positions include options in reality, so normal linear assumptions are questionable.
2. Method: One-day normal VaR≈portfolio value*(z*sigma−mu)
3. Case result: 32,900. The linear-normal one-day VaR is 32,900. Revalue nonlinear option positions under relevant shocks rather than assuming constant delta everywhere. Use stress tests, concentration limits, liquidity planning and backtesting alongside VaR; square-root-of-time scaling requires assumptions that can fail during serial dependence or changing volatility.

Errors to catch

• Do not replace the stated assumptions with an unstated shortcut. Reconcile units, timing and the claim being valued or duty being assessed.
• The logo of the fund is not a defensible conclusion for these case facts.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov