FRM 2 Exam Questions with Complete Solutions 100% Verified| Latest Update Graded A+
Liquidity Risk Early Warning Indicators - An unusual growth in assets, particularly when
accompanied by volatile liabilities
- Debt (credit) spreads widen, and/or credit default swap (CDS) spreads widen
- Declining diversity in the makeup of assets and liabilities; Growing currency mismatches
- When the weighted average of liabilities' maturity declines;
- Positions going beyond or getting close to regulatory limits
- Certain product line experience negative trends; The financial condition of the bank weakens;
Public press that is negative
- A downgrade in the credit rating; A decline in the stock price; Debt costs increase; Retail
and/or wholesale funding costs increase
- Counterparties becoming nervous about the financial condition of the bank
- Credit lines are lowered
- Outflows of retail deposits at an increased pace; Certificates of deposit (CDs) are increasingly
redeemed;
- Longer-term funding opportunities become more difficult
- Placing short-term liabilities becomes more difficult
Techniques to Validate Rating Model PD - The binomial test can be applied to one rating
category at a time, but it assumes independence of default events
- The chi-square test can be used to check several rating categories simultaneously but assumes
independence and a normal approximation
- The normal test is a multi-period test of a default probability forecast for a single rating
category that allows for cross-sectional dependence
Contingent liquidity Short-term funding (cash or assets) that are available when a stressing
scenario materializes (Liquid asset buffer)
,Restricted Liquidity Longer-term funding set aside for specific purposes (like securing a
loan). Attributed to outfolws under stress but not for general obligations.
Operational Liquidity Short-term, day-to-day liquidity to cover operational tasks; not
available for drawdown during stress scenarios
Strategic Liquidity Longer-term funding for special initiatives/capital projects. Not for day-
to-day use or draw-down during liquidity crisis.
Deposit Tracker Report The deposit tracker is a simple report of the current size of deposits,
together with a forecast of what the level of deposits are expected to be going forward. This
report is tracked weekly and monthly because it provides an idea of the LTD ratio in the
immediate short term
Gaussian Copula Properties a) The Gaussian copula has low tail dependence which is a
weakness because dependencies (including correlations) increase in a crisis
b) The Gaussian copula is difficult to calibrate to market prices; for example, it is difficult to
calibrate CDO tranches with a single correlation model
c) The Gaussian copula is principally static and consequently allows only limited risk
management; i.e., there is no stochastic process for the critical underlying variables' default
intensity and default correlation
Empirical Properties of Correlation I. Equity correlation levels are lowest during economic
expansions (growth) and highest during recessions
II. Equity correlation volatility is generally high; i.e., above 70.0% during each of
growth/normal/recessionary periods
, III. There is a general, positive association between correlation level and correlation volatility
IV. Equity correlations exhibit high, strong mean reversion and, therefore, low (positive)
autocorrelation
Historical Simulation Decay Weights weight = (1 - lambda)*lambda^(n-1) / (1 - lambda^k)
Hazard Rate lambda = Spread / LGD
Currency Forward Formula F = S[f/d] * (1 + r[f]) / (1 + r[d])
Modified Duration of Perpetuity 1/y
Macauly Duration Modified Duration * (1 + ytm/2)
SMM 1 - (1-CPR)^(1/12)
Effective Duration Formula (PV[-] - PV[+]) / (2 * PV[0] * dr)
Effective Convexity Formula (PV[-] + PV[+] - 2*PV[0]) / (2 * PV[0] * dr^2)
Value of Subordinate Debt c(V, F, T, t) - c(V, F+U, T, t)
CreditRisk+ The CreditRisk+ model measures the credit risk of a portfolio using a set of
common risk factors for each obligor. Each obligor shows unique sensitivity to each of the
common risk factors. The model allows for only two outcomes for a loss of a fixed size: default
and no default. The probability of default for each obligor is a function of:
Liquidity Risk Early Warning Indicators - An unusual growth in assets, particularly when
accompanied by volatile liabilities
- Debt (credit) spreads widen, and/or credit default swap (CDS) spreads widen
- Declining diversity in the makeup of assets and liabilities; Growing currency mismatches
- When the weighted average of liabilities' maturity declines;
- Positions going beyond or getting close to regulatory limits
- Certain product line experience negative trends; The financial condition of the bank weakens;
Public press that is negative
- A downgrade in the credit rating; A decline in the stock price; Debt costs increase; Retail
and/or wholesale funding costs increase
- Counterparties becoming nervous about the financial condition of the bank
- Credit lines are lowered
- Outflows of retail deposits at an increased pace; Certificates of deposit (CDs) are increasingly
redeemed;
- Longer-term funding opportunities become more difficult
- Placing short-term liabilities becomes more difficult
Techniques to Validate Rating Model PD - The binomial test can be applied to one rating
category at a time, but it assumes independence of default events
- The chi-square test can be used to check several rating categories simultaneously but assumes
independence and a normal approximation
- The normal test is a multi-period test of a default probability forecast for a single rating
category that allows for cross-sectional dependence
Contingent liquidity Short-term funding (cash or assets) that are available when a stressing
scenario materializes (Liquid asset buffer)
,Restricted Liquidity Longer-term funding set aside for specific purposes (like securing a
loan). Attributed to outfolws under stress but not for general obligations.
Operational Liquidity Short-term, day-to-day liquidity to cover operational tasks; not
available for drawdown during stress scenarios
Strategic Liquidity Longer-term funding for special initiatives/capital projects. Not for day-
to-day use or draw-down during liquidity crisis.
Deposit Tracker Report The deposit tracker is a simple report of the current size of deposits,
together with a forecast of what the level of deposits are expected to be going forward. This
report is tracked weekly and monthly because it provides an idea of the LTD ratio in the
immediate short term
Gaussian Copula Properties a) The Gaussian copula has low tail dependence which is a
weakness because dependencies (including correlations) increase in a crisis
b) The Gaussian copula is difficult to calibrate to market prices; for example, it is difficult to
calibrate CDO tranches with a single correlation model
c) The Gaussian copula is principally static and consequently allows only limited risk
management; i.e., there is no stochastic process for the critical underlying variables' default
intensity and default correlation
Empirical Properties of Correlation I. Equity correlation levels are lowest during economic
expansions (growth) and highest during recessions
II. Equity correlation volatility is generally high; i.e., above 70.0% during each of
growth/normal/recessionary periods
, III. There is a general, positive association between correlation level and correlation volatility
IV. Equity correlations exhibit high, strong mean reversion and, therefore, low (positive)
autocorrelation
Historical Simulation Decay Weights weight = (1 - lambda)*lambda^(n-1) / (1 - lambda^k)
Hazard Rate lambda = Spread / LGD
Currency Forward Formula F = S[f/d] * (1 + r[f]) / (1 + r[d])
Modified Duration of Perpetuity 1/y
Macauly Duration Modified Duration * (1 + ytm/2)
SMM 1 - (1-CPR)^(1/12)
Effective Duration Formula (PV[-] - PV[+]) / (2 * PV[0] * dr)
Effective Convexity Formula (PV[-] + PV[+] - 2*PV[0]) / (2 * PV[0] * dr^2)
Value of Subordinate Debt c(V, F, T, t) - c(V, F+U, T, t)
CreditRisk+ The CreditRisk+ model measures the credit risk of a portfolio using a set of
common risk factors for each obligor. Each obligor shows unique sensitivity to each of the
common risk factors. The model allows for only two outcomes for a loss of a fixed size: default
and no default. The probability of default for each obligor is a function of:
