A bank expects the error rate in transaction data entry for a particular business process to be 0.005%. What is the range of expected errors in a day within +/- 2 standard deviations if there are 2,000,000 such transactions each day?
A Bank Holding Company (BHC) is invested in an investment bank and a retail bank. The BHC defaults for certain if either the investment bank or the retail bank defaults. However, the BHC can also default on its own without either the investment bank or the retail bank defaulting. The investment bank and the retail bank's defaults are independent of each other, with a probability of default of 0.05 each. The BHC's probability of default is 0.11.
What is the probability of default of both the BHC and the investment bank? What is the probability of the BHC's default provided both the investment bank and the retail bank survive?
Monte Carlo simulation based VaR is suitable in which of the following scenarios:
I. When no assumption can be made about the distribution of underlying risk factors
II. When underlying risk factors are discontinuous, show heavy tails or are otherwise difficult to model
III. When the portfolio consists of a heterogeneous mix of disparate financial instruments with complex correlations and non-linear payoffs
IV. A picture of the complete distribution is desired in addition to the VaR estimate
If an institution has $1000 in assets, and $800 in liabilities, what is the economic capital required to avoid insolvency at a 99% level of confidence? The VaR in respect of the assets at 99% confidence over a one year period is $100.
For a US based investor, what is the 10-day value-at risk at the 95% confidence level of a long spot position of EUR 15m, where the volatility of the underlying exchange rate is 16% annually. The current spot rate for EUR is 1.5. (Assume 250 trading days in a year).
As part of designing a reverse stress test, at what point should a bank's business plan be considered unviable (ie the point where it can be considered to have failed)?
Which of the following belong to the family of generalized extreme value distributions:
I. Frechet
II. Gumbel
III. Weibull
IV. Exponential
Which of the following are considered properties of a 'coherent' risk measure:
I. Monotonicity
II. Homogeneity
III. Translation Invariance
IV. Sub-additivity
Which of the following was not a policy response introduced by Basel 2.5 in response to the global financial crisis:
What would be the correct order of steps to addressing data quality problems in an organization?
A derivative contract has a negative current replacement value. Which of the following statements is true about its loan equivalent value for credit risk calculations over a 2-year horizon?
Which of the following losses can be attributed to credit risk:
I. Losses in a bond's value from a credit downgrade
II. Losses in a bond's value from an increase in bond yields
III. Losses arising from a bond issuer's default
IV. Losses from an increase in corporate bond spreads
Ex-ante VaR estimates may differ from realized P&L due to:
I. the effect of intra day trading
II. timing differences in the accounting systems
III. incorrect estimation of VaR parameters
IV. security returns exhibiting mean reversion
Which of the following statements are true with respect to stress testing:
I. Stress testing results in a dollar estimate of losses
II. The results of stress testing can replace VaR as a measure of risk as they are better grounded in reality
III. Stress testing provides an estimate of losses at a desired level of confidence
IV. Stress testing based on factor shocks can allow modeling extreme events that have not occurred in the past
Which of the following statements is true in relation to a normal mixture distribution:
I. Normal mixtures represent one possible solution to the problem of volatility clustering
II. A normal mixture VaR will always be greater than that under the assumption of normally distributed returns
III. Normal mixtures can be applied to situations where a number of different market scenarios with different probabilities can be expected
If A and B be two uncorrelated securities, VaR(A) and VaR(B) be their values-at-risk, then which of the following is true for a portfolio that includes A and B in any proportion. Assume the prices of A and B are log-normally distributed.
An asset has a volatility of 10% per year. An investment manager chooses to hedge it with another asset that has a volatility of 9% per year and a correlation of 0.9. Calculate the hedge ratio.
The Options Theoretic approach to calculating economic capital considers the value of capital as being equivalent to a call option with a strike price equal to:
There are three bonds in a diversified bond portfolio, whose default probabilities are independent of each other and equal to 1%, 2% and 3% respectively over a 1 year time horizon. Calculate the probability that exactly 1 of the three bonds will default.
The unexpected loss for a credit portfolio at a given VaR estimate is defined as:
The 99% 10-day VaR for a bank is $200mm. The average VaR for the past 60 days is $250mm, and the bank specific regulatory multiplier is 3. What is the bank's basic VaR based market risk capital charge?
A loan portfolio's full notional value is $100, and its value in a worst case scenario at the 99% level of confidence is $65. Expected losses on the portfolio are estimated at 10%. What is the level of economic capital required to cushion unexpected losses?
Pick underlying risk factors for a position in an equity index option:
I. Spot value for the index
II. Risk free interest rate
III. Volatility of the underlying
IV. Strike price for the option
Which of the following statements are true:
I. Capital adequacy implies the ability of a firm to remain a going concern
II. Regulatory capital and economic capital are identical as they target the same objectives
III. The role of economic capital is to provide a buffer against expected losses
IV. Conservative estimates of economic capital are based upon a confidence level of 100%
Which of the following formulae describes CVA (Credit Valuation Adjustment)? All acronyms have their usual meanings (LGD=Loss Given Default, ENE=Expected Negative Exposure, EE=Expected Exposure, PD=Probability of Default, EPE=Expected Positive Exposure, PFE=Potential Future Exposure)
The difference between true severity and the best approximation of the true severity is called:
The cumulative probability of default for a security for 4 years is 11.47%. The marginal probability of default for the security for year 5 is 5% during year 5. What is the cumulative probability of default for the security for 5 years?
Which of the following statements are correct in relation to the financial system just prior to the current financial crisis:
I. The system was robust against small random shocks, but not against large scale disturbances to key hubs in the network
II. Financial innovation helped reduce the complexity of the financial network
III. Knightian uncertainty refers to risk that can be quantified and measured
IV. Feedback effects under stress accentuated liquidity problems
Which of the following is not a permitted approach under Basel II for calculating operational risk capital
If the returns of an asset display a strong tendency for mean reversion, what is the relationship between annualized volatility calculated based on daily versus weekly volatilities (using the square root of time rule)?
Which of the following cannot be used to address the issue of heavy tails when modeling market returns
The principle underlying the contingent claims approach to measuring credit risk equates the cost of eliminating credit risk for a firm to be equal to:
The daily VaR of an investor's commodity position is $10m. The annual VaR, assuming daily returns are independent, is ~$158m (using the square root of time rule). Which of the following statements are correct?
I. If daily returns are not independent and show mean-reversion, the actual annual VaR will be higher than $158m.
II. If daily returns are not independent and show mean-reversion, the actual annual VaR will be lower than $158m.
III. If daily returns are not independent and exhibit trending (autocorrelation), the actual annual VaR will be higher than $158m.
III. If daily returns are not independent and exhibit trending (autocorrelation), the actual annual VaR will be lower than $158m.
Which of the following statements are true:
I. Credit VaR often assumes a one year time horizon, as opposed to a shorter time horizon for market risk as credit activities generally span a longer time period.
II. Credit losses in the banking book should be assessed on the basis of mark-to-market mode as opposed to the default-only mode.
III. The confidence level used in the calculation of credit capital is high when the objective is to maintain a high credit rating for the institution.
IV. Credit capital calculations for securities with liquid markets and held for proprietary positions should be based on marking positions to market.
A stock's volatility under EWMA is estimated at 3.5% on a day its price is $10. The next day, the price moves to $11. What is the EWMA estimate of the volatility the next day? Assume the persistence parameter λ = 0.93.
Which of the following statements is the most appropriate description of feedback effects:
If X represents a matrix with ratings transition probabilities for one year, the transition probabilities for 3 years are given by the matrix:
Which of the following is not a tool available to financial institutions for managing credit risk:
Under the basic indicator approach to determining operational risk capital, operational risk capital is equal to:
Which of the following statements are true in relation to Monte Carlo based VaR calculations:
I. Monte Carlo VaR relies upon a full revalution of the portfolio for each simulation
II. Monte Carlo VaR relies upon the delta or delta-gamma approximation for valuation
III. Monte Carlo VaR can capture a wide range of distributional assumptions for asset returns
IV. Monte Carlo VaR is less compute intensive than Historical VaR
Company A issues bonds with a face value of $100m, sold at issuance at $98. Bank B holds $10m in face of these bonds acquired at a price of $70. What is Bank B's exposure to the debt issued by Company A?
Which of the following statements are true:
I. Top down approaches help focus management attention on the frequency and severity of loss events, while bottom up approaches do not.
II. Top down approaches rely upon high level data while bottom up approaches need firm specific risk data to estimate risk.
III. Scenario analysis can help capture both qualitative and quantitative dimensions of operational risk.
Which of the following are valid approaches to leveraging external loss data for modeling operational risks:
I. Both internal and external losses can be fitted with distributions, and a weighted average approach using these distributions is relied upon for capital calculations.
II. External loss data is used to inform scenario modeling.
III. External loss data is combined with internal loss data points, and distributions fitted to the combined data set.
IV. External loss data is used to replace internal loss data points to create a higher quality data set to fit distributions.
Which loss event type is the loss of personally identifiable client information classified as under the Basel II framework?
Which of the following techniques is used to generate multivariate normal random numbers that are correlated?
Which of the following statements is true:
I. If the sum of its parameters is less than one, GARCH is a mean reverting model of volatility, while EWMA is never mean reverting
II. Standardized returns under both EWMA and GARCH show less non-normality than non standardized returns
III. Steady state variance under GARCH is affected only by the persistence coefficient
IV. Good risk measures are always sub-additive
Which of the following contributed to the systemic failure during the credit crisis that began in 2007?
Which of the following statements is true?
I. It is sufficient to ensure that a parent entity has sufficient excess liquidity to cover a liquidity shortfall for a subsidiary.
II. If a parent entity has a shortfall of liquidity, it can always rely upon any excess liquidity that its foreign subsidiaries might have.
III. Wholesale funding sources for a bank refer to stable sources of funding provided by the central bank.
IV. Funding diversification refers to diversification of both funding sources and funding tenors.
The frequency distribution for operational risk loss events can be modeled by which of the following distributions:
I. The binomial distribution
II. The Poisson distribution
III. The negative binomial distribution
IV. The omega distribution
The VaR of a portfolio at the 99% confidence level is $250,000 when mean return is assumed to be zero. If the assumption of zero returns is changed to an assumption of returns of $10,000, what is the revised VaR?
Which of the following introduces model error when basing VaR on a normal distribution with a static mean and standard deviation?
Which of the following are measures of liquidity risk
I. Liquidity Coverage Ratio
II. Net Stable Funding Ratio
III. Book Value to Share Price
IV. Earnings Per Share
Which of the following is true in relation to a Contingency Funding Plan (CFP)?
I. A CFP is like a disaster recovery plan to deal with a liquidity crisis
II. A CFP should consider market stress conditions, but failures of payment systems are not relevant as they fall under the remit of operational risk
III. Reputational damage may result if the market finds out that a firm has had to execute its CFP
IV. Sources of emergency funding considered in the CFP should include the role of the central bank as the lender of last resort
Which of the following are valid techniques used when performing stress testing based on hypothetical test scenarios:
I. Modifying the covariance matrix by changing asset correlations
II. Specifying hypothetical shocks
III. Sensitivity analysis based on changes in selected risk factors
IV. Evaluating systemic liquidity risks
The probability of default of a security over a 1 year period is 3%. What is the probability that it would not have defaulted at the end of four years from now?
If the systematic VaR for an equity portfolio is $100 and the specific VaR is $80, then which of the following is true in relation to the total VaR:
Which of the following statements are true:
I. Stress testing, if exhaustive, can replace traditional risk management tools such as value-at-risk (VaR)
II. Stress tests can be particularly useful in identifying risks with new products
III. Stress testing is distinct from a bank's ICAAP carried out periodically
IV. Stress testing is a powerful communication tool that can convey risks to decisionmakers in an organization
Under the credit migration approach to assessing portfolio credit risk, which of the following are needed to generate a distribution of future portfolio values?
A bank prices retail credit loans based on median default rates. Over the long run, it can expect:
A statement in the annual report of a bank states that the 10-day VaR at the 95% level of confidence at the end of the year is $253m. Which of the following is true:
I. The maximum loss that the bank is exposed to over a 10-day period is $253m.
II. There is a 5% probability that the bank's losses will not exceed $253m
III. The maximum loss in value that is expected to be equaled or exceeded only 5% of the time is $253m
IV. The bank's regulatory capital assets are equal to $253m
The Basel framework does not permit which of the following Units of Measure (UoM) for operational risk modeling:
I. UoM based on legal entity
II. UoM based on event type
III. UoM based on geography
IV. UoM based on line of business
Company A issues bonds with a face value of $100m, sold at $98. Bank B holds $10m in face of these bonds acquired at a price of $70. Company A then defaults, and the recovery rate is expected to be 30%. What is Bank B's loss?
If a borrower has a default probability of 12% over one year, what is the probability of default over a month?
Which of the following statements are true in relation to Historical Simulation VaR?
I. Historical Simulation VaR assumes returns are normally distributed but have fat tails
II. It uses full revaluation, as opposed to delta or delta-gamma approximations
III. A correlation matrix is constructed using historical scenarios
IV. It particularly suits new products that may not have a long time series of historical data available
If two bonds with identical credit ratings, coupon and maturity but from different issuers trade at different spreads to treasury rates, which of the following is a possible explanation:
I. The bonds differ in liquidity
II. Events have happened that have changed investor perceptions but these are not yet reflected in the ratings
III. The bonds carry different market risk
IV. The bonds differ in their convexity
Which of the following statements is true:
I. Basel II requires banks to conduct stress testing in respect of their credit exposures in addition to stress testing for market risk exposures
II. Basel II requires pooled probabilities of default (and not individual PDs for each exposure) to be used for credit risk capital calculations
For the purposes of calculating VaR, an interest rate swap can be modeled as a combination of:
If the annual default hazard rate for a borrower is 10%, what is the probability that there is no default at the end of 5 years?
In respect of operational risk capital calculations, the Basel II accord recommends a confidence level and time horizon of:
Under the CreditPortfolio View approach to credit risk modeling, which of the following best describes the conditional transition matrix:
Which of the following statements are true:
I. It is usual to set a very high confidence level when estimating VaR for capital requirements.
II. For model validation, very high VaR confidence levels are used to minimize excess losses.
III. For limit setting for managing day to day positions, it is usual to set VaR confidence levels that are neither too low to be exceeded too often, nor too high as to be never exceeded.
IV. The Basel accord requirements for market risk capital require the use of a time horizon of 1 year.
A Monte Carlo simulation based VaR can be effectively used in which of the following cases:
The EWMA and GARCH approaches to volatility clustering can be applied to VaR calculations using:
Which of the following represents a riskier exposure for a bank: A LIBOR based loan, or an Overnight Indexed Swap? Which of the two rates is expected to be higher?
Assume the same counterparty and the same notional.
A long position in a credit sensitive bond can be synthetically replicated using:
Which of the following statements is true in relation to the Supervisory Capital Assessment Program (SCAP):
I. The SCAP is an annual exercise conducted by the Treasury Department to determine the health of key financial institutions in the US economy
II. The SCAP was essentially a stress test where the stress scenarios were specified by the regulators
III. Capital buffers calculated under the SCAP represented the amount of capital that the institutions covered by SCAP held in excess of Basel II requirements
IV. The SCAP focused on both total Tier 1 capital as well as Tier 1 common capital
What is the annualized steady state volatility under a GARCH model where alpha is 0.1, beta is 0.8 and omega is 0.00025?
Under the internal ratings based approach for risk weighted assets, for which of the following parameters must each institution make internal estimates (as opposed to relying upon values determined by a national supervisor):
Which of the following is not a possible early warning indicator in relation to the health of a counterparty?
Which of the following are true:
I. Delta hedges need to be rebalanced frequently as deltas fluctuate with fluctuating prices.
II. Portfolio managers are right to focus on primary risks over secondary risks.
III. Increasing the hedge rebalance frequency reduces residual risks but increases transaction costs.
IV. Vega risk can be hedged using options.
Which of the following statements are true:
I. A transition matrix is the probability of a security migrating from one rating class to another during its lifetime.
II. Marginal default probabilities refer to probabilities of default in a particular period, given survival at the beginning of that period.
III. Marginal default probabilities will always be greater than the corresponding cumulative default probability.
IV. Loss given default is generally greater when recovery rates are low.
When compared to a high severity low frequency risk, the operational risk capital requirement for a low severity high frequency risk is likely to be:
If E denotes the expected value of a loan portfolio at the end on one year and U the value of the portfolio in the worst case scenario at the 99% confidence level, which of the following expressions correctly describes economic capital required in respect of credit risk?
Which of the following are true:
I. Monte Carlo estimates of VaR can be expected to be identical or very close to those obtained using analytical methods if both are based on the same parameters.
II. Non-normality of returns does not pose a problem if we use Monte Carlo simulations based upon parameters and a distribution assumed to be normal.
III. Historical VaR estimates do not require any distribution assumptions.
IV. Historical simulations by definition limit VaR estimation only to the range of possibilities that have already occurred.
If F be the face value of a firm's debt, V the value of its assets and E the market value of equity, then according to the option pricing approach a default on debt occurs when:
If EV be the expected value of a firm's assets in a year, and DP be the 'default point' per the KMV approach to credit risk, and σ be the standard deviation of future asset returns, then the distance-to-default is given by:
A)
B)
C)
D)
There are two bonds in a portfolio, each with a market value of $50m. The probability of default of the two bonds over a one year horizon are 0.03 and 0.08 respectively. If the default correlation is zero, what is the one year expected loss on this portfolio?
For a corporate bond, which of the following statements is true:
I. The credit spread is equal to the default rate times the recovery rate
II. The spread widens when the ratings of the corporate experience an upgrade
III. Both recovery rates and probabilities of default are related to the business cycle and move in opposite directions to each other
IV. Corporate bond spreads are affected by both the risk of default and the liquidity of the particular issue