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FRM Part II study materials
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FRM Part II practice questions

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Question 1Market Risk Measurement and Management

A portfolio reports a one-day 99% VaR of USD 2 million. Which statement best describes this measure?

  1. The maximum one-day loss the portfolio can experience is USD 2 million.
  2. There is a 1% chance that the one-day loss exceeds USD 2 million under normal market conditions. Correct answer.
  3. The average loss on the worst 1% of trading days is USD 2 million.
  4. The portfolio will lose exactly USD 2 million on one day out of every 100.

Explanation

VaR is a quantile of the loss distribution: at 99% confidence, losses exceed the VaR threshold with 1% probability over the holding period. It is not a worst-case loss, nor an average of tail losses.

Question 2Market Risk Measurement and Management

Which property distinguishes expected shortfall from VaR at the same confidence level?

  1. It satisfies subadditivity, so combining portfolios cannot increase measured risk. Correct answer.
  2. It is always smaller than VaR for the same confidence level.
  3. It depends only on the single maximum possible loss.
  4. It can be computed only when returns are normally distributed.

Explanation

Expected shortfall averages losses beyond the VaR threshold and is a coherent risk measure, which includes subadditivity. VaR can violate subadditivity because diversification can increase the VaR of combined positions.

Question 3Market Risk Measurement and Management

In an exponentially weighted moving average volatility model, lowering the decay factor from 0.94 to 0.90 causes the volatility estimate to:

  1. place more weight on the long-run average variance and revert faster.
  2. place more weight on the most recent return and become more responsive. Correct answer.
  3. remain unchanged because the decay factor affects only the mean return.
  4. place more weight on distant observations and become smoother.

Explanation

In the EWMA recursion, the weight on the latest squared return is (1 minus lambda). A lower lambda increases that weight, so the volatility estimate reacts more strongly to recent market moves.

Question 4Market Risk Measurement and Management

For a GARCH(1,1) model with variance equation sigma-squared(t) = omega + alpha times epsilon-squared(t-1) + beta times sigma-squared(t-1), the long-run variance is:

  1. omega divided by (1 minus alpha).
  2. omega divided by (1 minus alpha minus beta). Correct answer.
  3. (omega + alpha) divided by (1 minus beta).
  4. omega divided by (alpha + beta).

Explanation

Setting expected future variance equal to current variance and solving gives the unconditional variance omega divided by (1 minus alpha minus beta), provided alpha plus beta is less than one. This is the level to which the variance forecast mean-reverts.

Question 5Market Risk Measurement and Management

Delta-normal VaR provides a reasonable approximation for a portfolio composed primarily of:

  1. deep out-of-the-money options.
  2. portfolios of barrier options.
  3. large long positions in short-dated straddles.
  4. linear FX forward contracts. Correct answer.

Explanation

Delta-normal VaR assumes linear payoffs and normally distributed risk-factor returns. Linear instruments such as forwards have payoffs well approximated by their delta, so the method works reasonably well.

Question 6Market Risk Measurement and Management

What is a main advantage of historical simulation for estimating VaR?

  1. It produces a closed-form VaR estimate that requires no historical data.
  2. It guarantees that future losses will not exceed the largest historical loss.
  3. It always produces the same VaR as the variance-covariance method.
  4. It makes no parametric distributional assumption and can reflect fat tails in observed returns. Correct answer.

Explanation

Historical simulation revalues the portfolio under past risk-factor changes, so it does not impose normality and can capture fat tails and empirical correlations. Its accuracy still depends on the historical window being representative of the future.

Question 7Market Risk Measurement and Management

Under the Basel backtesting framework for a 99% one-day VaR over 250 trading days, the green zone corresponds to how many exceptions?

  1. 5 to 9 exceptions
  2. 0 to 1 exceptions
  3. 0 to 4 exceptions Correct answer.
  4. 0 to 9 exceptions

Explanation

The Basel traffic-light approach places 0 to 4 exceptions in the green zone, 5 to 9 in the yellow zone, and 10 or more in the red zone. The zone determines the plus factor added to the minimum capital multiplier.

Question 8Market Risk Measurement and Management

Equity index options typically exhibit which implied volatility pattern across strikes?

  1. A downward skew, with higher implied volatility at low strikes. Correct answer.
  2. No systematic relationship between strike and implied volatility.
  3. A flat surface, because index options are priced with constant volatility.
  4. An upward slope, with higher implied volatility at high strikes.

Explanation

Equity index implied volatility usually slopes downward: low-strike puts trade at higher implied volatility because investors pay for downside crash protection. This produces the well-known equity skew rather than a symmetric smile.

Question 9Market Risk Measurement and Management

A one-day 99% VaR is estimated at USD 1.2 million. Assuming independent and identically distributed normal returns, the approximate 10-day 99% VaR is:

  1. USD 12.0 million.
  2. USD 3.79 million. Correct answer.
  3. USD 1.2 million.
  4. USD 2.40 million.

Explanation

Under the square-root-of-time rule, VaR scales with the square root of the holding period when returns are i.i.d. normal. Multiplying USD 1.2 million by the square root of 10 gives approximately USD 3.79 million.

Question 10Market Risk Measurement and Management

Two trading desks have 99% one-day VaRs of USD 3 million and USD 4 million, and their returns have a correlation of 0.5. Using the variance-covariance approach, the combined VaR is closest to:

  1. USD 5.00 million
  2. USD 4.00 million
  3. USD 7.00 million
  4. USD 6.08 million Correct answer.

Explanation

For two positions, combined VaR equals the square root of VaR1 squared plus VaR2 squared plus twice the correlation times VaR1 times VaR2. Here this is the square root of 9 plus 16 plus 12, which is the square root of 37, or about 6.08 million.

Question 11Market Risk Measurement and Management

A GARCH(1,1) model has omega = 0.000002, alpha = 0.08, and beta = 0.90. The previous day's squared return was 0.0009 and the previous variance forecast was 0.0004. The one-day-ahead variance forecast is:

  1. 0.000500
  2. 0.000362
  3. 0.000400
  4. 0.000434 Correct answer.

Explanation

The forecast is omega plus alpha times the previous squared return plus beta times the previous variance. Substituting gives 0.000002 plus 0.000072 plus 0.000360, which equals 0.000434.

Question 12Market Risk Measurement and Management

An EWMA model uses lambda = 0.94. Yesterday's variance forecast was 0.0001 and yesterday's return was minus 2%. The updated daily volatility is closest to:

  1. 1.09% Correct answer.
  2. 1.20%
  3. 1.00%
  4. 0.94%

Explanation

The EWMA variance update is lambda times the previous variance plus (1 minus lambda) times the previous squared return. This gives 0.000094 plus 0.000024, or 0.000118, whose square root is about 1.09%.

Question 13Market Risk Measurement and Management

A historical simulation uses 500 daily scenarios to estimate a one-day 99% VaR. The VaR estimate corresponds to:

  1. the fifth-largest loss in the sample. Correct answer.
  2. the largest loss in the sample.
  3. the average of the ten largest losses.
  4. the 25th-largest loss in the sample.

Explanation

With 500 observations and a 99% confidence level, the tail contains 1% of 500, or 5 observations. The VaR is therefore read at the fifth-largest loss when losses are ordered from largest to smallest.

Question 14Market Risk Measurement and Management

A portfolio has a large short-option position, giving it negative gamma. Compared with a full revaluation, delta-normal VaR will tend to:

  1. be independent of the size of the market move.
  2. understate risk for large market moves because losses grow faster than the linear approximation. Correct answer.
  3. equal the true risk because delta captures all option sensitivities.
  4. overstate risk because it ignores time decay.

Explanation

Negative gamma means the portfolio's loss accelerates as the underlying moves against it. Delta-normal VaR uses a fixed linear exposure, so it misses this convexity and understates tail risk for large moves.

Question 15Market Risk Measurement and Management

Vega, the sensitivity of an option's value to implied volatility, is largest for an option that is:

  1. deep out of the money with a short time to maturity.
  2. deep in the money with a short time to maturity.
  3. at the money with a long time to maturity. Correct answer.
  4. at the money with one day to maturity.

Explanation

Vega is greatest when the option is at the money because the value is most sensitive to volatility there. Vega also increases with time to maturity, so a long-dated at-the-money option has the highest vega.

Question 16Market Risk Measurement and Management

Compared with a Gaussian copula, a Student-t copula is characterized by:

  1. tail dependence in the lower tail only.
  2. zero tail dependence in both tails.
  3. tail dependence that disappears as the degrees of freedom increase.
  4. positive tail dependence in both tails. Correct answer.

Explanation

The Student-t copula exhibits symmetric positive tail dependence, meaning extreme joint losses occur more often than under the Gaussian copula. As degrees of freedom increase, the t-copula approaches the Gaussian copula and tail dependence vanishes in the limit.

Question 17Market Risk Measurement and Management

In cash-flow mapping for fixed-income VaR, each bond cash flow is represented as:

  1. a credit spread exposure with no interest rate sensitivity.
  2. an equivalent position in zero-coupon bonds at standard maturity vertices. Correct answer.
  3. a floating-rate note resetting at the next coupon date.
  4. a position that ignores all cash flows beyond one year.

Explanation

Cash-flow mapping decomposes a bond into zero-coupon exposures at standard vertices so that interest rate risk can be aggregated and VaR computed. The mapped portfolio should match the value and risk of the original cash flows.

Question 18Market Risk Measurement and Management

A bond portfolio has a modified duration of 5 and a market value of USD 100 million. Daily yield volatility is 10 basis points and the 99% normal quantile is 2.33. The duration-based one-day 99% VaR is closest to:

  1. USD 0.23 million
  2. USD 1.17 million Correct answer.
  3. USD 5.00 million
  4. USD 2.33 million

Explanation

The duration approximation gives a price change of duration times market value times yield change. Multiplying 5 by USD 100 million by 0.0010 by 2.33 gives approximately USD 1.17 million.

Question 19Market Risk Measurement and Management

Under the Basel FRTB internal models approach, the market risk capital measure is based on:

  1. 97.5% expected shortfall. Correct answer.
  2. 99% variance-covariance VaR.
  3. 99.9% stressed VaR.
  4. 95% expected shortfall.

Explanation

FRTB replaces 99% VaR with a 97.5% expected shortfall measure, calibrated to capture tail risk at a comparable level. The measure is computed using stressed calibration and liquidity-adjusted horizons.

Question 20Market Risk Measurement and Management

Under the Basel market risk framework, the capital multiplier applied to VaR is determined as:

  1. 2 plus the plus factor.
  2. 3 plus the plus factor. Correct answer.
  3. 3 minus the plus factor.
  4. 1 plus the number of backtesting exceptions.

Explanation

The Basel multiplier has a minimum of 3 and increases by a plus factor that depends on the number of backtesting exceptions. The plus factor is zero in the green zone and rises for yellow-zone and red-zone exception counts.

Question 21Market Risk Measurement and Management

In a principal component analysis of the yield curve, the second principal component typically represents:

  1. idiosyncratic noise unrelated to the yield curve.
  2. a parallel shift of all rates by the same amount.
  3. a slope shift that moves short and long rates in opposite directions. Correct answer.
  4. a curvature shift concentrated in medium maturities.

Explanation

The first principal component is usually a level shift, the second is a slope or steepening factor, and the third is a curvature factor. The slope component affects short and long maturities in opposite directions.

Question 22Market Risk Measurement and Management

Under the FRTB internal models approach, liquidity risk is addressed by:

  1. applying a common 10-day horizon to every risk factor.
  2. applying a liquidity horizon only to credit spread risk factors.
  3. assigning risk factors to liquidity horizons and aggregating expected shortfall across those buckets. Correct answer.
  4. ignoring liquidity horizons because expected shortfall is coherent.

Explanation

FRTB assigns different liquidity horizons to risk factors according to how quickly they can be hedged or liquidated. Expected shortfall is then aggregated across liquidity buckets using a prescribed overlapping-horizon formula.

Question 23Market Risk Measurement and Management

A GARCH(1,1) model estimates alpha plus beta equal to 0.99. The half-life of a variance shock is closest to:

  1. 69 days Correct answer.
  2. 100 days
  3. 25 days
  4. 50 days

Explanation

The half-life for a persistence of 0.99 is the natural logarithm of 0.5 divided by the natural logarithm of 0.99. This equals approximately 69 days.

Question 24Market Risk Measurement and Management

To generate correlated normally distributed risk-factor scenarios in a Monte Carlo simulation, the standard approach is to:

  1. invert the correlation matrix and multiply it by its eigenvalues.
  2. multiply a vector of independent standard normal draws by the lower-triangular Cholesky factor of the correlation matrix. Correct answer.
  3. use only the diagonal of the correlation matrix to scale the draws.
  4. sort the independent draws and apply the inverse normal distribution.

Explanation

The Cholesky decomposition produces a lower-triangular matrix L such that L times its transpose equals the correlation matrix. Multiplying independent standard normal draws by L introduces the desired correlation structure.

Question 25Market Risk Measurement and Management

If current volatility is above its long-run mean and volatility is mean-reverting, the volatility term structure is typically:

  1. downward sloping. Correct answer.
  2. upward sloping.
  3. increasing at the long end.
  4. flat at the current volatility level.

Explanation

Mean reversion implies that future volatility is expected to move toward its long-run average. When current volatility is above that average, expected future volatility declines, producing a downward-sloping term structure.

Question 26Market Risk Measurement and Management

Which property distinguishes expected shortfall from value at risk as a risk measure?

  1. Translation invariance, which only VaR satisfies
  2. Positive homogeneity, which neither measure satisfies
  3. Subadditivity, which expected shortfall satisfies but VaR can violate Correct answer.
  4. Monotonicity, which expected shortfall violates in the tails

Explanation

A coherent risk measure satisfies monotonicity, translation invariance, positive homogeneity and subadditivity. Expected shortfall is coherent, whereas VaR can violate subadditivity when payoffs are non-linear or tails are fat, so the VaR of a combined portfolio may exceed the sum of standalone VaRs.

Question 27Market Risk Measurement and Management

A portfolio's VaR is decomposed into risk contributions using Euler (marginal) allocation. The sum of the component VaRs equals:

  1. Zero whenever the portfolio is fully hedged
  2. The portfolio's total VaR Correct answer.
  3. The portfolio's undiversified VaR
  4. The average of the positions' standalone VaRs

Explanation

Euler allocation is a complete decomposition of a homogeneous risk measure, so each position's component VaR (marginal VaR times position value) adds up exactly to the total portfolio VaR. The diversification benefit is then the difference between the sum of standalone VaRs and total VaR.

Question 28Market Risk Measurement and Management

In the peaks-over-threshold approach to extreme value theory, the distribution of losses that exceed a high threshold is modeled with:

  1. A binomial distribution of VaR exception counts
  2. A normal distribution fitted to all observed losses
  3. A generalized Pareto distribution Correct answer.
  4. A GARCH process with a unit root

Explanation

The peaks-over-threshold method fits a generalized Pareto distribution to the excesses above a sufficiently high threshold. The shape parameter governs tail thickness: a positive value implies a fat, power-decaying tail.

Question 29Market Risk Measurement and Management

A portfolio has a 99% one-day VaR of USD 10 million. A trader holds a position worth USD 5 million whose marginal VaR, measured as the change in portfolio VaR per unit change in the position's value, is 0.20. The incremental VaR attributable to that position is closest to:

  1. USD 0.5 million
  2. USD 10.0 million
  3. USD 2.0 million
  4. USD 1.0 million Correct answer.

Explanation

Multiplying the marginal VaR by the size of the position gives the position's contribution: 0.20 x USD 5 million = USD 1.0 million. This is the component VaR under the marginal (Euler) allocation, and such components sum to the total portfolio VaR of USD 10 million.

Question 30Market Risk Measurement and Management

A USD 100 million equity portfolio has a beta of 1.2 relative to a broad index. The index's annual volatility is 20%. Using beta mapping, 250 trading days per year and a 95% normal quantile of 1.645, the one-day 95% VaR is closest to:

  1. USD 39.5 million
  2. USD 2.1 million
  3. USD 3.5 million
  4. USD 2.5 million Correct answer.

Explanation

Beta mapping converts the position into an equivalent index exposure of 1.2 x USD 100 million = USD 120 million, whose daily volatility is 20%/sqrt(250) = 1.265%. Applying the 1.645 quantile gives 120 million x 0.01265 x 1.645, approximately USD 2.5 million.

Question 31Market Risk Measurement and Management

A fund holds a USD 50 million position in a stock quoted with a bid-ask spread of 0.40% of the mid price. Assuming the position is liquidated at the mid price less half the spread and ignoring all other costs, the liquidity add-on to the one-day VaR is closest to:

  1. USD 100,000 Correct answer.
  2. USD 400,000
  3. USD 200,000
  4. USD 20,000

Explanation

The exogenous liquidity cost is half the quoted spread applied to the position value: 0.5 x 0.0040 x USD 50 million = USD 100,000. This amount is added to the plain VaR to obtain the liquidity-adjusted VaR.

Question 32Market Risk Measurement and Management

A risk manager backtests a 99% one-day VaR model over 250 trading days and observes 4 exceptions, close to the 2.5 expected under a correct model. Which statement best describes the statistical power of this test?

  1. Power is high because 250 observations constitute a large sample
  2. Power rises as the VaR confidence level is increased from 99% to 99.9%
  3. Power is irrelevant because the test rejects a correct model with certainty
  4. Power is limited, so a model that moderately understates risk would often go undetected Correct answer.

Explanation

Power depends on the number of expected tail events, not just on the sample size. With a 99% VaR over 250 days only about 2.5 exceptions are expected, so a model that understates risk somewhat produces a distribution of exceptions that still overlaps heavily with the correct-model distribution, making Type II errors common.

Question 33Market Risk Measurement and Management

Portfolio losses are modeled with the peaks-over-threshold method. The threshold is 4.0% of portfolio value, 10% of observations exceed it, and the excesses follow a generalized Pareto distribution with shape parameter 0.3 and scale parameter 1.0% (in the same units). The 99% VaR is closest to:

  1. 3.3%
  2. 5.7%
  3. 7.3% Correct answer.
  4. 4.8%

Explanation

The peaks-over-threshold VaR is u + (beta/xi) x [((n/Nu)(1-p))^(-xi) - 1]. Here (10)(0.01) = 0.1, so 0.1^(-0.3) - 1 = 0.995, and (1.0/0.3)(0.995) = 3.32; adding the 4.0% threshold gives about 7.3%.

Question 34Market Risk Measurement and Management

Under the FRTB internal models approach, capital for non-modellable risk factors is determined by:

  1. Assigning them the longest available liquidity horizon bucket used for modellable factors
  2. A stressed calibration applied without diversification benefit across such factors Correct answer.
  3. Scaling the modellable expected shortfall by the share of notional they represent
  4. Running them through the same expected shortfall model with full diversification

Explanation

Because non-modellable risk factors lack sufficient observable data for a validated expected shortfall model, each is capitalized with a stressed-scenario measure calibrated to a period of stress, and these amounts are added without recognizing diversification benefits across the non-modellable factors.

Question 35Credit Risk Measurement and Management

Under the standard credit risk framework, the expected loss on a single credit exposure is calculated as:

  1. probability of default multiplied by loss given default multiplied by exposure at default Correct answer.
  2. probability of default multiplied by exposure at default
  3. loss given default multiplied by exposure at default
  4. probability of default multiplied by loss given default divided by exposure at default

Explanation

Expected loss is the product of three components: the likelihood of default, the fraction of the exposure lost if default occurs, and the size of the exposure at the time of default. Each component is measured over the same horizon, typically one year.

Question 36Credit Risk Measurement and Management

In credit portfolio management, economic credit capital is held primarily to absorb:

  1. expected losses over a one-year horizon
  2. market risk losses on trading-book bond positions
  3. unexpected losses above the expected loss up to a target confidence level Correct answer.
  4. losses arising solely from rating downgrades

Explanation

Expected loss is treated as a cost of doing business and is covered by pricing and provisions. Capital protects the institution against the volatility of losses beyond that mean, measured as the tail of the loss distribution at a chosen confidence level.

Question 37Credit Risk Measurement and Management

In the Merton structural model, the equity of a levered firm is best characterised as:

  1. a risk-free bond plus a short credit default swap on the firm
  2. a forward contract on the firm's assets struck at the face value of debt
  3. a call option on the firm's assets with strike equal to the face value of debt Correct answer.
  4. a put option on the firm's assets with strike equal to the face value of debt

Explanation

Shareholders receive the residual value of assets after debt is repaid, so their payoff is max(asset value minus debt face value, 0), which is the payoff of a European call on the assets. Debt holders correspondingly hold a risk-free bond plus a short put.

Question 38Credit Risk Measurement and Management

A protection buyer in a single-name credit default swap:

  1. is short the credit risk of the reference entity
  2. pays a periodic premium and receives the loss given default amount on a default Correct answer.
  3. receives periodic premium and pays par on a default
  4. receives a fee for assuming the reference entity's credit risk

Explanation

The protection buyer pays a running spread and, if a covered credit event occurs, receives a payment equal to par minus the recovered value of the reference obligation. Economically the buyer is long protection, that is, short the reference entity's credit risk.

Question 39Credit Risk Measurement and Management

A subordinated bond has an estimated recovery rate of 45%. The corresponding loss given default is:

  1. 45%
  2. 145%
  3. 55% Correct answer.
  4. 100%

Explanation

Loss given default is one minus the recovery rate, since whatever fraction of the claim is recovered is not lost. With a 45% recovery rate, the loss fraction is 55%.

Question 40Credit Risk Measurement and Management

In a cash securitisation structured with senior, mezzanine and equity tranches, credit losses are first absorbed by:

  1. the equity (first-loss) tranche Correct answer.
  2. the senior tranche
  3. the tranche carrying the highest rating
  4. the mezzanine tranche

Explanation

The waterfall allocates losses bottom-up: the equity tranche absorbs losses first, then mezzanine, and senior last. This subordination is what allows the senior tranche to earn a high rating despite exposure to sub-investment-grade collateral.

Question 41Credit Risk Measurement and Management

A credit-linked note is best described as:

  1. an option on a credit spread
  2. a repo transaction collateralised by corporate bonds
  3. a funded note whose principal or coupon is written down when a specified credit event occurs Correct answer.
  4. a swap exchanging fixed and floating interest payments

Explanation

A credit-linked note embeds a credit derivative in a funded security: the investor provides principal and receives an enhanced coupon, but suffers a writedown or coupon reduction if the referenced credit event occurs. The issuer is effectively buying protection through the note.

Question 42Credit Risk Measurement and Management

Under Altman's Z-score model applied to manufacturing firms, a lower Z-score indicates:

  1. a higher recovery rate in default
  2. a higher probability of bankruptcy Correct answer.
  3. a higher distance to default
  4. greater financial strength

Explanation

The Z-score combines liquidity, profitability, leverage, solvency and activity ratios into a single discriminant score, with lower values associated with greater financial distress. Firms below the lower cut-off are classified as likely to fail.

Question 43Credit Risk Measurement and Management

A firm has asset value of 500, default point of 400, asset volatility of 20% per year and expected asset return of 5%. Using the Merton distance-to-default formula with a one-year horizon, the distance to default is closest to:

  1. 1.12
  2. 0.85
  3. 1.37
  4. 1.27 Correct answer.

Explanation

The numerator is ln(500/400) plus the drift term (0.05 minus one half of 0.20 squared), giving 0.2231 + 0.03 = 0.2531; dividing by the annual asset volatility of 0.20 gives approximately 1.27 standard deviations.

Question 44Credit Risk Measurement and Management

A credit has a constant default intensity of 3% per year. The probability that it survives the next two years is closest to:

  1. 0.9139
  2. 0.9409
  3. 0.9700
  4. 0.9418 Correct answer.

Explanation

With a constant hazard rate, survival probability over horizon t is the exponential of minus the hazard rate times t. For a 3% intensity over two years, exp(-0.06) equals approximately 0.9418.

Question 45Credit Risk Measurement and Management

A five-year single-name credit default swap trades at 180 basis points per year and the assumed recovery rate is 40%. Using the standard credit-triangle approximation with a flat hazard rate, the implied annual default intensity is closest to:

  1. 3.00% Correct answer.
  2. 7.20%
  3. 1.08%
  4. 4.50%

Explanation

The credit triangle states that the spread approximates the hazard rate multiplied by one minus the recovery rate. Dividing 1.80% by the loss given default of 0.60 gives an implied intensity of 3.00% per year.

Question 46Credit Risk Measurement and Management

A bank has two trades with the same counterparty, marked at +80 and -30, covered by an enforceable bilateral netting agreement. Compared with no netting, the netted exposure and the percentage reduction in exposure are:

  1. exposure of 110 and no reduction
  2. exposure of 50 and a reduction of 30.0%
  3. exposure of 50 and a reduction of 37.5% Correct answer.
  4. exposure of 30 and a reduction of 62.5%

Explanation

Without netting only the positive mark-to-market counts, giving exposure of 80. Netting allows the negative trade to offset it, leaving exposure of 50, a reduction of 30 on a base of 80, or 37.5%.

Question 47Credit Risk Measurement and Management

CreditMetrics estimates the distribution of portfolio credit value changes primarily by:

  1. bootstrapping default intensities from observed credit default swap quotes
  2. modelling default as the first passage of asset value through a barrier
  3. simulating Poisson default arrivals with stochastic sector default rates
  4. applying a rating transition matrix and revaluing exposures at the spreads of the migrated rating Correct answer.

Explanation

CreditMetrics is a mark-to-market migration model: it uses historical transition probabilities to generate end-of-horizon rating states and revalues each exposure using forward spread curves for those states, including the default state with a recovery assumption.

Question 48Credit Risk Measurement and Management

A bank's mark-to-market exposure to a counterparty rises sharply at the same time as the counterparty's probability of default increases. This condition is known as:

  1. right-way risk
  2. migration risk
  3. wrong-way risk Correct answer.
  4. sovereign risk

Explanation

Wrong-way risk arises when exposure and counterparty credit quality are positively related, so that losses are largest exactly when the counterparty is most likely to fail. It makes standard CVA calculations that assume independence understate the true charge.

Question 49Credit Risk Measurement and Management

From a bank's perspective, credit value adjustment on a derivative portfolio is best described as:

  1. the regulatory capital allocated to counterparty credit risk
  2. the market value of the counterparty credit risk borne by the bank Correct answer.
  3. the value of collateral posted against derivative exposure
  4. the gain recognised when a counterparty is upgraded

Explanation

CVA is the difference between the risk-free value of a derivative portfolio and its value allowing for the possibility of counterparty default, so it is a reduction in value that reflects expected loss from counterparty credit risk.

Question 50Credit Risk Measurement and Management

A one-year rating transition matrix is most directly used to estimate:

  1. the hazard rate implied by credit default swap quotes
  2. the recovery rate on defaulted debt
  3. the probability of a downgrade and the associated mark-to-market loss Correct answer.
  4. the loss given default of a secured lending facility

Explanation

Transition matrices give the probability of moving between rating grades over a horizon, including default. Applied to exposure values repriced at the new grades' spreads, they produce the distribution of migration-driven credit losses.