GARP FRM Part II Cheat Sheet: Measures and Risk Decisions

Market risk: measure the right tail

For a continuous, zero-mean normal loss distribution with standard deviation \(\sigma\):

\[ \mathrm{VaR}_c=z_c\sigma, \qquad \mathrm{ES}_c=\frac{\phi(z_c)}{1-c}\sigma \]

With \(\sigma=2\) million dollars, \(z_{0.99}=2.326\) and \(\phi(z_{0.99})=0.02665\), 99% VaR is $4.652 million and ES is $5.33 million. These are normal-model estimates, not bounds on all possible losses. Discrete empirical ES needs an explicit tail convention, especially at a quantile with tied observations.

• Square-root-of-time scaling requires appropriate independence, stationarity and portfolio assumptions. It does not add unobserved crisis tails or liquidation costs.
• Unconditional exception frequency, exception independence and conditional coverage answer different backtesting questions. A non-rejection does not prove the model is correct.
• Correlation can weaken a hedge without changing either leg’s standalone volatility. Copula dependence and marginal distributions play distinct roles.

For a small yield change under a first-order duration approximation:

\[ \Delta V\approx-D_{\mathrm{mod}}V\Delta y \]

A $20 million bond position with modified duration 4 and a 25 basis-point rise gives approximately −$200,000: \(-4\times20{,}000{,}000\times0.0025\). Convexity, nonparallel shifts, options and basis changes can matter beyond that approximation.

In a short-rate tree, discount expected continuation values using risk-neutral transition weights and the current node’s short rate. An issuer call caps continuation value at the immediate call payment when optimal exercise is assumed. Recombination is valid only when the retained state captures the future transitions, cash flows and exercise rights; a path-dependent contract may require more state.

Credit: distinguish forecasting from pricing

Under consistent exposure and horizon definitions:

\[ \mathrm{EL}=\mathrm{PD}\times\mathrm{LGD}\times\mathrm{EAD} \]

Annual PD of 2%, LGD of 40% and EAD of $2 million give $16,000 expected loss. That average is not unexpected loss or the capital required for every tail scenario. Recovery assumptions must state timing, costs, collateral and who receives or pays each cash flow.

A simplified unilateral CVA discretization sums discounted expected positive exposure, LGD and incremental risk-neutral default probabilities across intervals. Check survival, timing and dependence conventions before substituting a cumulative default probability at every date.

Operational risk and resilience

• Separate an event, its loss, the failed control, a leading indicator and its accountable owner. A better reporting system can increase observed incidents without increasing the underlying risk.
• Independence in an AND/OR fault calculation is an assumption. For events \(A\) and \(B\), \(P(A\cap B)=P(A)P(B\mid A)\); an OR calculation subtracts overlap.
• Scenario analysis, internal losses and external data serve different purposes. Tail estimates remain conditional on reporting, scaling, distribution and dependence choices.
• Keep historical BIA/TSA/AMA, later standardized capital methods and local implementation separate. Do not mix coefficients or claim a Basel publication is automatically binding national law.
• Model validation challenges design, data, implementation and use. A successful backtest does not replace governance or ongoing monitoring.

The assigned FDIC June 2017 model-risk framework is dated assessment material. For a current U.S. supervisory case, verify the applicable guidance: April 2026 SR 26-2 supersedes SR 11-7 and SR 21-8. The change in supervisory guidance does not erase the assigned historical reading or create a universal enforceable standard.

Liquidity and treasury

Using the relevant framework’s eligibility and cap rules:

\[ \mathrm{LCR}=\frac{\text{eligible HQLA}}{\text{30-day stressed net cash outflows}}, \qquad \mathrm{NSFR}=\frac{\text{available stable funding}}{\text{required stable funding}} \]

Illustrative LCR: gross outflows of $150 million and eligible inflows of $130 million, with a 75% inflow cap, give net outflows of \(150-\min(130,112.5)=37.5\) million dollars. Eligible HQLA of $45 million gives 120%. Apply required asset haircuts and composition caps before treating raw assets as eligible HQLA. A 120% ratio is not proof of survival under every stress.

LCR’s 30-day stress perspective differs from NSFR’s one-year structural funding perspective. Market liquidity, funding liquidity and solvency are connected but not interchangeable. Contractual ladders can differ from realized cash flows through withdrawals, prepayments and options.

Funding transfer pricing attributes tenor- and liquidity-consistent funding costs or benefits to business decisions. It is not an additional external cash flow. Net-interest-income sensitivity and economic-value sensitivity use different horizons and behavioural assumptions; neither can be inferred from a repricing gap without those conditions.

Investment risk and performance

For a differentiable, degree-one homogeneous portfolio risk measure:

\[ \text{component risk}_i=w_i\frac{\partial R}{\partial w_i}, \qquad \sum_i\text{component risk}_i=R \]

Marginal and component contributions are not identical; a diversifying position can have a negative contribution. Specify whether weights or dollar holdings define the derivative and denominator.

For average annual excess return of 6% and annual return volatility of 12%, a simple Sharpe ratio is 0.50. Dividing by 12 basis points instead would be a unit error. A high ratio does not establish causal manager skill, liquidity or future performance.

Private investments require actual cash-flow dates, fees, leverage and valuation conventions. Smoothed reported returns may understate observed volatility. A hedge-fund redemption promise and the liquidity of its assets can be mismatched.

Current Issues: mechanism, evidence, limitation

Use the eight assigned 2026 papers, not a news headline, as the scope. AI adoption can create concentration, common-model and governance risks; automation is not inherently safer. Private credit can change financing choices and bank/nonbank connections without eliminating credit risk. Geopolitical effects vary by country, sector and event. Rising government debt and monetary/fiscal tensions can push an economy outside a region of stability; the relevant constraints and policy interaction matter more than a universal debt threshold.

Tokenization can alter lifecycle frictions, coordination and settlement arrangements, but does not inherently resolve legal rights, liquidity or all counterparty risk. Unbacked crypto assets are not the same as tokenized claims on conventional assets. Digital resilience includes interconnected service dependencies, not only recovery at an isolated institution.

Before answering, identify the measure, decisive assumption, supported inference and remaining limitation. Check Official Resources and test the distinctions in free practice . This reference is original study support, not an official formula sheet or pass prediction.