- •Var can apply to funding risk:
- •If the sample size is greater than 30 and population variance is unknown, the appropriate test for the sample mean is the:
- •If the variance of the sampling distribution of an estimator is smaller than all other unbiased estimators of the parameter of interest, the estimator is:
- •In the process of hypothesis testing, what is the proper order for these steps?
- •In using a log-likelihood ratio to backtest a var model, the reason to measure the conditional rather than the unconditional coverage of the model is to consider the:
Financial risk management:
A) is the process of detecting, assessing and managing financial risks
B) seeks to eliminate all financial risks
C) only focuses on managing market-related financial risks
D) is the process of reacting to financial losses in order to minimize losses
The correct answer is A) the process of detecting, assessing and managing financial risks
Reduction of risks not under management’s control:
A) may cause managers to overinvest.
B) makes stock options more valuable.
C) cannot improve management incentives.
D) can lead to lower incentive compensation
The correct answer was D) can lead to lower incentive compensation.
Risk management to reduce the probability of financial distress:
A) always increases firm value.
B) is easily replicated by individual shareholders.
C) cannot reduce the weighted average cost of capital.
D) can increase firm value because financial distress has measurable costs.
The correct answer was D) can increase firm value because financial distress has measurable costs.
The role of risk management does NOT involve performing which of the following tasks?
A) Assess all risks faced by the firm.
B) Communicate these risks to risk-taking decision makers.
C) Make sure that the firm takes greater than the necessary amount of risk.
D) Monitor and manage these risks
The correct answer was C) Make sure that the firm takes greater than the necessary amount of risk.
Operational risks include all of the following items except:
A) General business operations: risk of inefficiency and ineffectiveness.
B) Information technology: risk of obsolescence and inability of information technology to function in a changing operational environment.
C) Empowerment: risk of incompetent leadership/management at the top and throughout the organizational ranks.
D) Competition: risk of competitor developing a better product/service.
The correct answer was D) Competition: risk of competitor developing a better product/service.
The risk that a counterparty will fail to deliver its obligation is
people risk
settlement risk
delivery risk
model risk
The correct answer is B)
Political risk is most accurately defined as the:
A) risk that a foreign government, acting in concert with its central bank, will limit or prevent domestic borrowers from repaying debt.
B) economic and financial risk factors associated with a country as distinctly separate from those of the borrower.
C) relationship between the constitution of a country and the means by which it is enforced.
D) risk of loss due to inadequate monitoring systems, management failure, defective controls, fraud, and/or human errors
The correct answer was C) relationship between the constitution of a country and the means by which it is enforced.
Funding liquidity risk refers to the risk:
A) That an institution will not be able to raise cash necessary to make debt payments
B) That a counterparty to a financial transaction will default
C) That the government will decide to terminate a government-funded program
D) Resulting from a large position size in an asset relative to the asset’s typical trading lot size
The correct answer is A) that an institution will not be able to raise cash necessary to make debt payments
Which of the following statements regarding liquidity risk is correct?
a. Asset liquidity risk arises when a financial institution cannot meet payment obligations.
b. Flight to quality is usually reflected in a decrease in the yield spread between corporate and government issues.
c. Yield spread between on-the-run and off-the-run securities mainly captures the liquidity premium, and not the market and credit risk premium.
d. Funding liquidity risk can be managed by setting limits on certain markets or products and by means of diversification.
The correct answer is d.
Answer a) refers to asset liquidity risk.
Answers b) and c) refer to funding liquidity risk.
The risk of sustaining significant losses due to the inability to take or exit a position at a fair price is most likely
A) Market risk
B) Operational risk
C) Liquidity risk
D) Credit event risk
The correct answer was C) liquidity risk
A security’s systematic risk is proportional to
A) the covariance of its return with the return on the market portfolio
B) the standard deviation of its return
C) the variance of its return
D) its diversifiable risk
The correct answer is A) the covariance of its return with the return on the market portfolio
Which of the following strategies may increase firm value by decreasing the costs of bankruptcy and financial distress?
I. Reducing the potential costs of financial distress and bankruptcy.
II. Reducing the weighted average cost of capital.
III. Improving management incentives.
IV. Reducing information asymmetries
A) I and II only.
B) I only.
C) I and III only.
D) I, II, and IV only.
The correct answer was A) I and II only.
All of the following affect the role of operational risk management in preventing large trading losses EXCEPT:
A) the breadth of responsibilities and power given to traders.
B) the degree of supervision and oversight.
C) marked-to-market losses.
D) multiple approvals for large trades by senior management
The correct answer is C) marked-to-market losses.
Information systems at Barings Bank were deficient for all of the following reasons EXCEPT:
A) management’s failure to audit reporting quality.
B) incomplete account information on gains and losses.
C) technological limitations that hindered accurate financial reporting.
D) management’s inability to detect the inconsistency of Leeson’s trading strategy and profits.
The correct answer was C) technological limitations that hindered accurate financial reporting.
In general, the bankruptcy of Barings Bank might have been avoided with:
A) pricing models less vulnerable to model risk.
B) a more moderate use of leverage.
C) stronger reporting and control systems.
D) maturity matching between the hedging instrument and the asset being hedged.
The correct answer was C) stronger reporting and control systems.
Nicholas Leeson is identified with which of the following?
A) Commodity Futures Trading Commission.
B) Sumitomo.
C) Nikkei stock index futures.
D) Metallgesellschaft AG.
The correct answer is C) Nikkei stock index futures.
Which of the following factors contributed to the collapse of Barings Bank?
A) A maturity mismatch between the hedging instrument and the risk being hedged.
B) Basis risk.
C) Japanese financial reporting requirements.
D) A trader having authority in the settlement process
The correct answer is D) A trader having authority in the settlement process.
Which of the following choices is an example of operational risk in the collapse of Barings?
A) The Nikkei collapsed due to an earthquake.
B) Much of a company’s assets were in illiquid derivative products.
C) The default of Japanese industrial firms.
D) Failure to supervise the actions of its trader.
The correct answer was D) Failure to supervise the actions of its trader.
Metallgesellschaft could have addressed the cash flow crisis created by their stack-and-roll hedge strategy by:
I. Buying puts.
II. Selling puts.
III. Selling calls.
IV. Requiring periodic cash settlements from customers.
A) I only.
B) IV only.
C) I and IV only.
D) II and IV.
The correct answer was C) I and IV only.
Metallgesellschaft’s mismanagement in its long-term fixed contract strategy was evidenced by which of the following?
I. Refunding payments to customers who willingly paid to cancel their long-term obligations.
II. Canceling the program too soon while the positive legs of the contracts could have been sold at a profit or used to secure additional financing.
III. Not considering the sale of the program to another firm.
A) I, II, and III.
B) I only.
C) I and III.
D) II and III
The correct answer was A) I, II, and III.
The high degree of operational risk in the Sumitomo case was illustrated by which of the following?
I. Model risk.
II. Lack of informed supervisors to approve large trades.
III. High degree of autonomy, allowing the trader to execute highly levered positions.
IV. The trader’s ability to keep two sets of books trading books and hide trading losses.
A) I only.
B) I and IV only.
C) II, III, and IV.
D) II and III only.
The correct answer was C) II, III, and IV.
Which of the following are examples of model risk illustrated in the Long-Term Capital Management case?
I. Poor management oversight.
II. Financial reporting standards.
III. Ignoring autocorrelation of economic shocks.
IV. Underestimating correlations among asset classes during economic crises.
A) II, III, and IV only.
B) III and IV only.
C) I, II, III, and IV.
D) I only.
Answer B is correct!
All of the following are reasons that Nick Leeson engaged in aggressive speculative trading in the Barings Bank collapse EXCEPT
A) he was attempting to recover previous trading losses.
B) Barings’ risk management models were flawed.
C) Barings’ lack of risk management oversight.
D) his authority over settlement operations allowed him to hide trading losses
Your answer: B was correct!
The type of capital used to buffer a bank from unexpected losses is known as:
A) regulatory capital.
B) economical capital.
C) unexpected capital.
D) risk-adjusted capital.
Answer B is correct!
The type of capital used to buffer a bank from unexpected losses is known as:
A) regulatory capital.
B) economical capital.
C) unexpected capital.
D) risk-adjusted capital.
The answer B is correct!
Which of the following statements does NOT adequately describe economic capital?
I. It is always less than regulatory capital.
II. It differs depending on the type of borrower, independent of borrower risk.
III. It must be considered along with regulatory capital when making allocation decisions.
IV. It is the amount of capital that management determines to be necessary to cushion losses from an asset or business line.
A) II only.
B) I and II.
C) I and III.
D) IV only
The answer B is correct!
The primary purpose of operational risk economic capital is to:
A) protect the company against insolvency due to unexpected operational losses.
B) protect the company against insolvency due to expected and unexpected operational losses.
C) meet financial reporting requirements.
D) meet regulatory guidelines
The correct answer was A) protect the company against insolvency due to unexpected operational losses.
Economic capital protects the company against insolvency due to unexpected operational losses. In identifying the appropriate level of economic capital, a bank should focus on the part of the loss probability distribution represented by losses
A) in excess of the loss at a given level of confidence.
B) between the loss at a given level of confidence and the expected loss.
C) below the loss at a given level of confidence.
D) greater than the expected loss
The answer B is correct!
How many of the following statements about economic capital are CORRECT?
Banks set aside economic capital in anticipation of expected losses.
Banks keep reserves to provide a cushion against unexpected losses.
Banks should set economic capital at 100% confidence level.
Economic capital provides various stakeholders of an institution with a degree of confidence that their invested funds are safe
A) 2. B) 1. C) 3. D) 4.
The answer B is correct!
What is the major source of market risk for a bank?
A) Credit risk.
B) Gap risk.
C) Operational risk.
D) Exchange rate risk
The answer B is correct!
Which of the following is TRUE about economic capital?
I. For most financial institutions, economic capital held exceeds regulatory capital.
II. It protects financial institutions from expected and unexpected losses
III. It is the capital required to keep the banking system safe.
IV. It is a function of the risk of the financial institutions and inversely related to performance.
A) I and II. B) II and III.
C) I and IV. D) II and IV
The correct answer was C) I and IV.
Consider the following information pertaining to a loan:
Revenue: $4 million.
Expected loss: $200,000.
Interest expense: $2.5 million.
Economic capital: $6.25 million with a return of $200,000.
What is the risk-adjusted return on capital (RAROC)?
A) 20%.
B) 18%.
C) 14%.
D) 24%.
The correct answer was D) 24%.
= ($4 − 0.2 − 2.5 + 0.2) / 6.25
= 24%
The flaw in the first-generation risk-adjusted return on capital (RAROC) approach is that it:
A) attempts to align the risk of the business with the firm’s equity.
B) assumes that the default probability remains constant.
C) only estimates the RAROC hurdle rate.
D) is poorly understood by investors and directors
The answer B is correct!
Given the following information, calculate the RAROC.
Gross revenue: $8 million.
Interest expense: $4 million.
Economic capital: 10 million.
Return on invested economic capital: 500,000.
Operating costs associated with making the loan: $1.5 million.
Expected loss on the loan: 300,000.
A) 42%. B) 40%. C) 5%. D) 27%.
The correct answer was D) 27%.
RAROC = (8 - 0.3 – 4 + 0.5 - 1.5) / 10 = = 27%.
A bank loan has
expected gross revenue of $300,000,
interest expense of $200,000,
expected return on the $200,000 of economic capital of $20,000,
expected loss on the loan of $10,000
and operating costs associated with the loan of $70,000.
What is the risk adjusted return on capital (RAROC) for this loan?
A) 10%. B) 20%. C) 30%. D) 55%.
The answer B is correct!
RAROC = (300 − 200 − 10 + 20 − 70) / 200 = 20%.
What is the adjusted RAROC for a business if
its RAROC is 22%,
the company’s beta is 1.1,
and the risk-free rate is 5%?
A) 15.45%.
B) 17%.
C) 4.84%.
D) 24.2%.
The correct answer was A) 15.45%.
ARAROC = (RAROC – Rf) / Beta
ARAROC = (22 – 5) / 1.1 = 15.45%.
Assume that the risk-adjusted return on capital (RAROC) is equal to 15%.
If the risk-free rate is equal to 3% and the company's equity beta is 1.5, what is the adjusted RAROC?
A) 4.5%.
B) 18%.
C) 8%.
D) 12%.
The correct answer was C) 8%.
Adjusted RAROC =
= (RAROC − Rf) / Beta =
=(15% − 3%) / 1.5= 8%
Assume RAROC is 10%, the risk free rate is 4%, the market return is 10%, the firm’s required return on equity is 12%, and the firm’s beta is 1.1.
What is the ARAROC and should the project be accepted?
A) 5.5%; reject.
B) 5.5%; accept.
C) 10%; accept.
D) 7.3%; accept
The correct answer was A) 5.5%; reject.
ARAROC = (RAROC − Rf) / beta =
= (10% − 4%) / 1.1 = 5.4545%;
Accept when ARAROC > (Rm − Rf);
10% - 4% = 6%;
Reject since 5.5% < 6%.
Which of the following is a property of a coherent risk metric?
A) Sub-Monotonic.
B) Sub-Additive.
C) Positive Heterogeneous.
D) All of these.
The answer B is correct!
Only Sub-Additive is a coherent risk metric
Which of the following is NOT a correct description of a coherent risk measure property?
I. Homogeneity – the size of a portfolio will impact the size of its risk.
II. Monotonicity – a portfolio with greater future returns will likely have less risk.
III. Subadditivity – the risk of a portfolio is always more than the risk of the assets within the portfolio.
IV. Translation invariance - the risk of a portfolio is independent of the assets within the portfolio.
A) I and II. B) I and III.
C) II and III. D) III and IV.
The correct answer was D) III and IV.
Which of the following are properties of a Coherent risk metric?
A) Positive homogeneous.
B) Monotonicity.
C) All of these.
D) Sub-additivity.
The correct answer was C) All of these.
Value at risk (VAR) is a benchmark associated with a given probability. The actual loss:
A) cannot exceed this amount
B) may be much greater
C) is expected to be the average of the expected return of the portfolio and VAR
D) will have an inverse relationship with VAR
The answer B is correct!
The minimum amount of money that one could expect to lose with a given probability over a specific period of time is a definition of
A) value at risk (VAR)
B) delta
C) the hedge ration
D) the coefficient of variation
The correct answer was A) value at risk (VAR).
Which of the following statements about value at risk (VAR) is TRUE?
A) VAR increases with longer holding periods.
B) VAR decreases with lower probability levels.
C) VAR is not dependent on the choice of holding period.
D) VAR is independent of probability level
The correct answer was A) VAR increases with lower probability levels.
Which of the following statements about value at risk (VAR) is TRUE?
A) VAR decreases with lower confidence level.
B) VAR decreases with longer holding periods.
C) VAR is not dependent on the choice of holding period.
D) VAR is independent of probability level
The correct answer was A) VAR decreases with lower confidence level.
The accuracy of a value at risk (VAR) measure:
A) is included in the statistic.
B) is complete because the process is deterministic.
C) is one minus the probability level.
D) can only be ascertained after the fact
The correct answer was D) can only be ascertained after the fact.
The difference between a Monte Carlo simulation and a historical simulation is that a historical simulation uses randomly selected variables from past distributions, while a Monte Carlo simulation:
A) uses randomly selected variables from future distributions.
B) uses a computer to generate random variables.
C) uses variables based on roulette odds.
D) projects variables based on a priori principles
The answer B is correct!
If the one-day value at risk (VaR) of a portfolio is $50,000 at a 95% probability level, this means that we should expect that in one day out of:
A) 20 days, the portfolio will decline by $50,000 or less.
B) 20 days, the portfolio will decline by $50,000 or more.
C) 95 days, the portfolio will lose $50,000.
D) 95 days, the portfolio will increase by $50,000 or more
The answer B was correct!
vFor a $1,000,000 stock portfolio with an expected return of 12 percent and an annual standard deviation of 15 percent, what is the VAR with 95 percent confidence level?
A) $120,000.
B) $127,500.
C) $150,000.
D) $247,500
The answer B is correct!
VAR = Portfolio Value [E(R)-zσ]= 1,000,000[0.12 – (1.65)(0.15)] =
=-$127,500
A hedge fund portfolio has an expected return of 0.1 percent per day and a 5 percent probability 1-day value at risk (VAR) of $909. Which of the following statement is the best descriptor of this information?
A) The minimum loss for the worst 5% of the days is $909.
B) The maximum daily loss on the portfolio is $909.
C) The portfolio will earn more than $909 only 5% of the time.
D) The minimum daily loss on the portfolio is $909.
The correct answer was A) The minimum loss for the worst 5% of the days is $909.
If the expected change in a fixed income portfolio is $520,000 and the standard deviation of the estimated change in the portfolio is $2,275,500, the 95 percent value-at-risk (VAR) for this portfolio is closest to:
A) $855,400.00.
B) $3,223,197.50.
C) $3,743,197.50.
D) $4,598,597.50
The answer B is correct!
VAR for this portfolio would be
–[$520,000 – 1.645($2,275,500)] = $3,223,197.50.
A large bank currently has a security portfolio with a market value of $145 million. The daily returns of the bank’s portfolio are normally distributed with 80% of the distribution lying within 1.28 standard deviations above and below the mean and 90% of distribution lying within 1.65 standard deviations above and below the mean. Assuming the standard deviation of the bank’s portfolio returns is 1.2%, calculate the VAR (5%) on a one-day basis.
A) $2.87 million
B) $2.23 million
C) $2.04 million
D) cannot be determined from information given
The correct answer was A) $2.87 million.
The 10-Q report of Global Bank states that the monthly VAR of ABC Bank is $10 million at 95% confidence level. What is the proper interpretation of this statement?
There is a 95% probability that the bank will lose less than $10m over a month
If we collect 100 monthly gain/loss data of Global Bank, we will always see five months with losses larger than$10m
There is a 5% probability that the bank will gain less than $10m each month
There is a 95% probability that the bank will lose less than $10m over month
The correct answer was A) There is a 95% probability that the bank will lose less than $10m over a month.
Hugo Nelson is preparing a presentation on the attributes of value at risk. Which of Nelson’s following statements is not correct?
VAR can account for the diversified holdings of a financial institution, reducing capital requirements
VAR(10%)=$0 indicates a positive dollar return is likely to occur on 90 of 100 days
VAR(1%) can be interpreted as the number of days that a loss in portfolio will exceed 1%
VAR was developed in order to more closely represent the economic capital necessary to ensure commercial bank solvency
The correct answer was C) VAR(1%) can be interpreted as the number of days that a loss in portfolio value will exceed 1%
The profit/loss distribution for Morozov Inc. (Morozov) is normally distributed with an annual mean of $20 million and a standard deviation of $13 million. Which of the following amounts is closest to VAR at the 99% confidence level using a parametric approach?
A) $13.54 million.
B) $10.29 million.
C) $5.48 million.
D) $1.45 million
The answer B is correct!
If a 10-day VAR is $15,000,000, the 250-day VAR, assuming no change in confidence level, would be:
A) $237,000,000.
B) $23,700,000.
C) $75,000,000.
D) $7,500,000
The correct answer was C) $75,000,000.
The most important way in which the Monte Carlo approach to estimating operational VAR differs from the historical method and variance-covariance method is:
A) it involves repeatedly shocking a model of risk data to produce a range of potential losses.
B) its heavy dependence on historical data.
C) its computational simplicity.
D) its inability to account for non-linear risk structures
The correct answer was A) it involves repeatedly shocking a model of risk data to produce a range of potential losses.
There are several different methods commonly used to compute value at risk (VAR). Which of the following statements best describes historical VAR? It is:
A) a method that computes VAR by assuming that losses in the future will occur with the same frequency and magnitude as they have in the past.
B) an analysis that looks for trends in VAR from period to period to predict future VAR.
C) an analysis used by regulators that compares current market risks to historical market risks.
D) an analysis used by investors that compares current market risks to historical market risks
The correct answer was A) a method that computes VAR by assuming that losses in the future will occur with the same frequency and magnitude as they have in the past.
Derivation Inc. has a portfolio of $100 MM. The expected return over one year is 6 percent, with a standard deviation of 8 percent. What is the VAR for this portfolio at the 99 percent confidence level?
A) $2.0 MM.
B) $12.6 MM.
C) $7.2 MM.
D) $12.1 MM
The answer B is correct!
VAR = $100 MM [0.06 – (2.326)(0.08)] = $12.608 MM
In the presence of fat tails in the distribution of returns for a linear portfolio, VAR based on the delta-normal method would:
A) be the same as the true VAR.
B) underestimate the true VAR.
C) overestimate the true VAR.
D) cannot be determined from the information provided.
The answer B is correct!
The VAR would be underestimated because of the greater frequency of losses in the tails of the distribution
Which of the following statements regarding value at risk (VAR) and expected shortfall (ES) is least accurate?
The ES provides an estimate of the tail loss by averaging the VARs for increasing confidence levels in the tail.
B) The calculation of lognormal VAR and normal VAR will be similar when dealing with long-time periods.
C) As the number of VAR observations increases, the ES will increase.
D) The calculated VAR amount is always negative.
The answer B is correct!
The calculation of lognormal VAR and normal VAR will be similar when dealing with short time periods.
If a 1-day 95 percent VAR is $5 million, the 250-day 99 percent VAR level would be closest to:
A) $55.89 million.
B) $83.84 million.
C) $21.00 million.
D) $111.79 million
The correct answer was D) $111.79 million.
First it is necessary to adjust for confidence levels (2.326/1.645), then by days (√250). In this case, ($5 million) (2.326/1.645)(√250) = $111.79 million
Which of the common methods of computing value at risk relies on the assumption of normality?
A) Historical.
B) Variance/covariance.
C) Monte Carlo simulation.
D) Rounding estimation
The answer B is correct!
The variance/covariance method relies on the assumption of normality.
On December 31, 2006, Portfolio A had a market value of $2,520,000. The historical standard deviation of daily returns was 1.7%. Assuming that Portfolio A is normally distributed, calculate the daily VAR(2.5%) on a dollar basis and state its interpretation. Daily VAR(2.5%) is equal to:
A) $83,966, implying that daily portfolio losses will only exceed this amount 2.5% of the time.
B) $83,966, implying that daily portfolio losses will fall short of this amount 2.5% of the time.
C) $70,686, implying that daily portfolio losses will only exceed this amount 2.5% of the time.
D) $70,686, implying that daily portfolio losses will fall short of this amount 2.5% of the
The correct answer was A) $83,966, implying that daily portfolio losses will only exceed this amount 2.5% of the time.
Which of the following characterize extreme value theory (EVT)?
I. Focuses on catastrophic losses that are more likely than standard distributions suggest.
II. Uses a different distribution to describe losses in the left tail.
III. Most commonly uses a lognormal distribution in the tails.
IV. Estimates expected losses beyond an established confidence interval.
A) I and III only.
B) I, II, and IV only.
C) I and IV only.
D) II and III only.
Your answer: B was correct!
The primary focus of Extreme Value Theory (EVT) is the notion that:
A) large losses occur more frequently than many assumed distributions suggest.
B) low frequency, high severity losses are more common than losses of more moderate magnitude.
C) the risk of extreme events is defined by the percentile established by a predetermined confidence interval.
D) the possibility of extreme events is sufficiently small that it can safely be ignored.
The correct answer was A) large losses occur more frequently than many assumed distributions suggest.
Assume that the value at risk (VAR) over a 1-day time horizon for an $80 million equity portfolio at the 95 percent confidence level is calculated to be $792,000. Which of the following is a drawback to this VAR calculation?
A) Increasing the time period used in the calculation will increase the VAR.
B) The interpretation of the VAR measure would be different for a fixed-income portfolio.
C) The measure is backward looking.
D) The actual loss in a time of extreme market stress could be much greater than $792,000.
The correct answer was D) The actual loss in a time of extreme market stress could be much greater than $792,000.
Var can apply to funding risk:
A) by calculating the fall in surplus when the portfolio’s VAR loss occurs.
B) in no way, funding risk is not a type of risk to which VAR can apply.
C) by showing how to construct the surplus so that it goes up when the VAR loss occurs.
D) by calculating the level of VAR associated with a zero surplus
The correct answer was A) by calculating the fall in surplus when the portfolio’s
Which of the following statements is not a limitation of the value at risk (VAR) measure in capturing the spectrum of hedge fund risks?
A) Hedge funds exhibit a wide spectrum of risks.
B) VAR is a conditional measure of risk.
C) VAR does not capture unique risks associated with different underlying economic structures.
D) VAR is difficult to estimate due to the uncertainty of tail exposure for differing economic structures
The answer B is correct!
Under the Extreme Value Theorem (EVT), which of the following is (are) TRUE regarding the modeling of market risk?
I. The three key resulting distributions are: Gumbel, Weibull, and Frechet.
II. EVT permits the analysis of maxima and minima distributions.
III. EVT is does not account for “heavy” tails observed in the market place.
IV. EVT is dependent upon the normal distribution
A) I and III only.
B) I and II only.
C) I only.
D) None of these
The answer B is correct!
When ξ = 0, the generalized extreme value distribution (GEV) becomes which of the following distributions?
A) Gaussian distribution.
B) Frechet distribution.
C) Gumbel distribution.
D) Weibull distribution
The correct answer was C) Gumbel distribution.
Extreme value theory (EVT) helps quantify two key measures of risk. The magnitude of:
A) VAR and the level of risk obtained from scenario analysis.
B) market risk and the magnitude of operational risk.
C) an X year return in the loss in excess VAR.
D) market risk and the magnitude of credit risk.
The correct answer was C) an X year return in the loss in excess VAR.
Extreme value theory (EVT) looks at the value of losses beyond an identified cutoff point
Extreme value theory (EVT) can assist with value at risk (VAR) calculations by providing better probability estimates of observing extreme losses than that indicated by a standard normal distribution because empirical distributions exhibit fat tails. If one uses the generalized Pareto distribution (GPD) method to generate parameter estimates for the shape parameter, fat tails will indicate a:
A) positive parameter estimate and VAR calculations that are too large.
B) negative parameter estimate and VAR calculations that are too small.
C) positive parameter estimate and VAR calculations that are too small.
D) negative parameter estimate and VAR calculations that are too large.
The correct answer was C) positive parameter estimate and VAR calculations that are too small.
Extreme value theory can assist with VAR calculations by providing better probability estimates of extreme losses than those indicated by a standard normal distribution. Using the generalized Pareto distribution (GPD), the parameter that indicates the fatness of tails is the:
A) shape parameter, ξ.
B) threshold level, μ.
C) scaling parameter, β.
D) slope coefficient, b.
The correct answer was A) shape parameter, ξ.
Which of the following statements is (are) FALSE concerning extreme value distributions?
I. Using block maxima, local maxima may not resemble extreme observations.
II. Small tails reduce the variance of the estimator in cluster analysis.
III. The two classes of EVT models are block maxima and generalized extreme value distribution.
A) I and II only.
B) II and III only.
C) I and III only.
D) I, II, and III
The answer B is correct!
Given a VAR equal to 2.26, a threshold of 1%, a shape parameter of 0.2, and a scale parameter of 0.3, what is the expected shortfall?
A) 2.85.
B) 2.75.
C) 2.65.
D) 2.95
The correct answer was D) 2.95.
The generalized extreme value (GEV) distribution is useful for:
I. estimating VAR.
II. stress testing.
III. Estimating correlation.
IV. backtesting
A) I, II, III, and IV.
B) I and III only.
C) II only.
D) I only.
The correct answer was C) II only.
Extreme value theory (EVT) can assist with value-at-risk (VAR) calculations by providing better probability estimates of observing extreme losses than that indicated by a standard normal distribution because:
A) the observed empirical distribution of most asset returns tends to be platykurtic*.
B) extreme losses appear to occur more frequently than indicated by a normal distribution.
C) extreme losses appear to occur less frequently than indicated by a normal distribution.
D) EVT is the most efficient method for estimating extreme losses.
platykurtic* - имеющий отрицательный эксцесс (меньший эксцесса нормального распределения)
The answer B is correct!
Which of the following statements about extreme value theory (EVT) is FALSE?
A) Cluster analysis is appropriate for financial data with time dependency.
B) EVT can be used to model everyday occurrences.
C) POT models determine the cut-off between typical and extreme values.
D) EVT focuses on data that is generally considered outliers.
The answer B is correct!
The Peaks Over Threshold (POT) approach serves as a basis for an expanded model of risk estimation. Which of the following statements are false regarding POT?
I. Under the POT method, in the case of “fat” tails, not all moments are defined.
II. POT is often estimated with a Generalized Pareto Distribution.
A) Both I and II.
B) Neither I nor II.
C) I only.
D) II only
The answer B is correct!
Which of the following most accurately describes the parameters of a generalized Pareto distribution (GPD)?
A) The scale parameter: 0 < β. The shape (tail) index: ξ, can be any real number.
B) β The scale parameter: 0 > β. The shape (tail) index: ξ, can be any real number.
C) The scale parameter: β, can be any real number. The shape (tail) index: ξ, can be any real number.
D) The scale parameter: β, which can be any real number. The shape (tail) index: ξ > 0.
The correct answer is A) The scale parameter: 0 < β. The shape (tail) index: ξ, can be any real number.
Which of the following is TRUE comparing VAR and extreme value theory (EVT)?
A) VAR and EVT assume normality of the return distribution.
B) The generalized Pareto distribution is fully parameterized by the mean and variance.
C) EVT focuses exclusively on the upper half of the return distribution.
D) Only EVT considers losses beyond a specified threshold
The correct answer was D) Only EVT considers losses beyond a specified threshold.
Which of the following statements regarding generalized extreme value (GEV) and peaks-over-threshold (POT) is CORRECT?
A) Only one of the approaches has a tail parameter denoted ξ.
B) Both POT and GEV focus on the distributions of extremes.
C) POT approach may introduce additional uncertainty.
D) POT requires the estimation of one more parameter than GEV
The correct answer was C) POT approach may introduce additional uncertainty.
The first step in the process of hypothesis testing is:
A) the collection of the sample.
B) the calculation of sample statistics.
C) to state the hypotheses.
D) selecting the test statistic
The correct answer was C) to state the hypotheses.
If the sample size is greater than 30 and population variance is unknown, the appropriate test for the sample mean is the:
A) t-test.
B) z-test.
C) t-test or z-test.
D) p-test or F-test.
The correct answer was C) t-test or z-test.
Which of the following would result in a wider confidence interval? A:
A) higher alpha level.
B) higher point estimate.
C) greater level of significance.
D) higher degree of confidence.
The correct answer was D) higher degree of confidence.
A goal of an “innocent until proven guilty” justice system is to place a higher priority on:
A) avoiding type II errors.
B) avoiding type III errors.
C) avoiding type I errors.
D) the null hypothesis.
The correct answer was C) avoiding type I errors.
Which of the following statements is FALSE?
A) A Type I error is rejecting the null when it is actually true.
B) Failing to reject the null when it is false is an example of a Type II error.
C) The probability of committing a Type I error is the significance level of the test.
D) If a person is presumed innocent unless proven otherwise, finding a guilty person innocent is an example of a Type I error
The correct answer was D) If a person is presumed innocent unless proven otherwise, finding a guilty person innocent is an example of a Type I error.
A Type I error:
A) rejects a false null hypothesis.
B) fails to reject a false null hypothesis.
C) rejects a true null hypothesis.
D) fails to reject a true null hypothesis
The correct answer was C) rejects a true null hypothesis.
A Type I error occurs when the null hypothesis
A) fails to be rejected when it is false.
B) is rejected when it is false.
C) fails to be rejected when it is true.
D) is rejected when it is true.
The correct answer was D) is rejected when it is true.
Which of the following statements about hypothesis testing is most accurate?
A) The probability of a Type I error is equal to the significance level of the test.
B) If you can disprove the null hypothesis, then you have proven the alternative hypothesis.
C) To test the claim that X is greater than zero, the null hypothesis would be H0: X > 0.
D) The power of a test is one minus the probability of a Type I error.
The correct answer was A) The probability of a Type I error is equal to the significance level of the test.
Which of the following statements about hypothesis testing is least accurate?
A) If the alternative hypothesis is Ha: μ > μ0, a two-tailed test is appropriate.
B) The null hypothesis is a statement about the value of a population parameter.
C) A Type II error is failing to reject a false null hypothesis.
D) A Type I error is rejecting the null hypothesis when it is actually true.
The correct answer was A) If the alternative hypothesis is Ha: μ > μ0, a two-tailed test is appropriate.
If the variance of the sampling distribution of an estimator is smaller than all other unbiased estimators of the parameter of interest, the estimator is:
A) efficient.
B) reliable.
C) unbiased.
D) consistent
The correct answer was A) efficient.
Which of the following statements about testing a hypothesis using a Z-test is least accurate?
A) A Type I error is rejecting the null hypothesis when it is actually true.
B) If the calculated Z-statistic lies outside the critical Z-statistic range, the null hypothesis can be rejected.
C) The calculated Z-statistic determines the appropriate significance level to use.
D) The confidence interval for a two-tailed test of a population mean at the 5% level of significance is that the sample mean falls between ±1.96 σ/√n of the null hypothesis value
The correct answer was C) The calculated Z-statistic determines the appropriate significance level to use.
Which of the following statements about hypothesis testing is most accurate?
A) A Type I error is rejecting the null hypothesis when it is true, and a Type II error is accepting the alternative hypothesis when it is false.
B) When the critical Z-statistic is greater than the sample Z-statistic in a two-tailed test, reject the null hypothesis and accept the alternative hypothesis.
C) A hypothesized mean of 3, a sample mean of 6, and a standard error of the sampling means of 2 give a sample Z-statistic of 1.5.
D) A two-tailed test on a large sample with a significance level of 0.01 has confidence intervals of ±1.96 standard errors.
The correct answer was C) A hypothesized mean of 3, a sample mean of 6, and a standard error of the sampling means of 2 give a sample Z-statistic of 1.5.
In the process of hypothesis testing, what is the proper order for these steps?
A) Specify the level of significance. State the hypotheses. Make a decision. Collect the sample and calculate the sample statistics.
B) State the hypotheses. Collect the sample and calculate the sample statistics. Make a decision. Specify the level of significance.
C) State the hypotheses. Specify the level of significance. Collect the sample and calculate the test statistics. Make a decision.
D) Collect the sample and calculate the sample statistics. State the hypotheses. Specify the level of significance. Make a decision.
The correct answer was C) State the hypotheses. Specify the level of significance. Collect the sample and calculate the test statistics. Make a decision.
The process of comparing losses predicted by a VAR model to those actually experienced over the test period is called:
A) validation.
B) authentication.
C) backtesting.
D) verification
The correct answer was C) backtesting.
Comparison analyses on backtesting methods indicate that the most powerful verification test of VAR is the:
A) unconditional parametric test statistic.
B) Kuiper test statistic.
C) conditional non-parametric test statistic.
D) Basel committee test statistic
The answer B is correct!
In using a log-likelihood ratio to backtest a var model, the reason to measure the conditional rather than the unconditional coverage of the model is to consider the:
A) timing of exceptions.
B) number of assets in the portfolio tested.
C) size of the portfolio.
D) the influence of the positions of individual traders
The correct answer was A) timing of exceptions.
The Kupiec log-likelihood ratio is used for:
A) backtesting VAR models.
B) estimating interest-rate spread volatility.
C) estimating the delta-normal VAR of option portfolios.
D) stress-testing VAR models
The correct answer was A) backtesting VAR models.
Which of the following causes for exceptions established by the Basel Committee would be considered more serious so that a penalty should apply?
I. Model accuracy needs improvement.
II. Intraday trading activity.
III. Basic integrity of the model is lacking.
A) I and III.
B) I only.
C) II only.
D) II and III.
The correct answer was A) I and III.
The International Bank has backtested its VAR models and has found four exceptions. Under the Basel Committee Penalty Zone rules, how would this be classified and what would be the associated VAR multiplier?
Classification VAR multiplier
A) Green zone Multiplier of 3
B) Green zone Multiplier greater than 3
C) Yellow zone Multiplier of 3
D) Yellow zone Multiplier greater than 3
The correct answer was A)
You are backtesting a VAR model using analysing exceptions using failure rates. Which of the following statements is (are) CORRECT?
I. The probability of rejecting an accurate VAR model is a Type II error.
II. The probability of accepting an inaccurate model is a Type I error.
A) Neither I nor II.
B) Both I and II.
C) I only.
D) II only.
The correct answer was A) Neither I nor II.
The Basel market risk charges require VAR to be computed over a horizon of:
A) at least one year.
B) at least three months.
C) one month or 21 trading days.
D) two calendar weeks or ten trading days.
The correct answer was D) two calendar weeks or ten trading days.
A Type I error occurs when a risk model is:
A) accepted when it is accurate.
B) accepted when it is inaccurate.
C) rejected when it is accurate.
D) rejected when it is inaccurate.
The correct answer was C) rejected when it is accurate.
Within the Basel penalty zones, which of the following multipliers would most likely apply to a yellow zone with five to nine exceptions?
A) 4.00.
B) 3.35.
C) 3.00.
D) 3.65
The correct answer was D) 3.65.
Comparison analyses on backtesting methods indicate that the most powerful verification test of VAR is the:
A) unconditional parametric test statistic.
B) Kuiper test statistic.
C) conditional non-parametric test statistic.
D) Basel committee test statistic
The answer B is correct!
A Type I error occurs when a risk model is:
A) accepted when it is accurate.
B) accepted when it is inaccurate.
C) rejected when it is accurate.
D) rejected when it is inaccurate
The correct answer was C) rejected when it is accurate.
The mean monthly return for an equity portfolio over 60 months is 1.5%. The standard deviation is 3.0%. The value of the test statistic to test the hypothesis that mean monthly return is equal to zero is closest to:
A) 30.00
B) 0.50.
C) 3.87.
D) 2.19.
The correct answer was C) 3.87.
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The GARCH model is useful for simulating asset returns. Which of the following statements about this model is false ?
a. The Exponentially Weighted Moving Average (EWMA) approach of RiskMetrics is a particular case of a GARCH process.
b. The GARCH allows for time-varying volatility.
c. The GARCH can produce fat tails in the return distribution.
d. The GARCH imposes a positive conditional mean return.
The correct answer is d) The GARCH imposes a positive conditional mean return.
The current estimate of daily volatility is 1.5 percent. The closing price of an asset yesterday was $30.00. The closing price of the asset today is $30.50.
Using the EWMA model with λ = 0.94, the updated estimate of volatility is
a. 1.5096
b. 1.5085
c. 1.5092
d. 1.5083
Using log-returns, we find R = 1.653% and σt = 1.5096%.
With discrete-returns, we find R = 1.667% and σt = 1.5105%.
Until January 1999 the historical volatility for the Brazilian real versus the U.S. dollar had been very small for several years.
On January 13, 1999, Brazil abandoned the defense of the currency peg.
Using the data from the close of business on January 13th, which of the following methods for calculating volatility would have shown the greatest jump in measured historical volatility?
a. 250-day equal weight
b. Exponentially weighted with a daily decay factor of 0.94
c. 60-day equal weight
d. All of the above
The correct answer was b) Exponentially weighted with a daily decay factor of 0.94
When using an EWMA model to estimate portfolio volatility, the method used to estimate the portfolio covariance matrix should be the:
A) EWMA method.
B) historical method.
C) GARCH(1,1).
D) hypergeometric method
The correct answer was A) EWMA method.
GARCH(1,1) (generalized autoregressive conditional heteroskedastic) models of volatility may be useful for option traders because they:
A) are useful in forecasting future volatility
B) provide efficient estimates of past volatility.
C) are the simplest volatility models to estimate.
D) are used in the Black-Scholes option pricing model
The correct answer was A) are useful in forecasting future volatility
A portfolio manager is using an exponentially weighted moving average (EWMA) model to forecast volatility for a particular market parameter.
What is the implication of an EWMA weighting parameter value of 0.84?
A) A greater weight is placed on the most recent change in parameter value than on the previous volatility estimate.
B) A greater weight is placed on the previous volatility estimate than on the most recent change in parameter value.
C) An equal weight is placed on the previous volatility estimate as on the most recent change in parameter value.
D) More information is required to determine the implication
The answer B is correct!
You estimate the following GARCH model:
If the most recent volatility estimate and error term are 0.15 and 0.02, respectively, the long-run average variance is closest to:
A) 0.16.
B) 0.20.
C) 0.23.
D) 0.04.
The answer B is correct!
Which of the following is (are) a shortcoming(s) when using the normal distribution for estimating GARCH(1,1) parameters?
I. Parameters such as volatility often exhibit mean reverting characteristics.
II. Maximum likelihood estimation with a normal distribution is not tractable.
III. Financial and economic data series often do not follow a normal distribution.
IV. Maximum likelihood estimation with a normal distribution will never generate a local maxima.
A) I, III, and IV only. B) II and IV only.
C) III only. D) I and II only
The correct answer is C) III only.
Which of the following are true about the RiskMetrics, GARCH, and historical standard deviation approaches to estimate conditional volatility?
I. RiskMetrics and historical standard deviation assume equal weights on all observations.
II. RiskMetrics and GARCH are parametric models: historical standard deviation is not.
III. Increasing λ suggests a higher relative weight on the most recent data for exponential smoothing models.
IV. The most recent weight for GARCH exceeds the most recent weight for historical standard deviation, assuming the same high number of observations.
A) II, III, and IV only. B) II and III only.
C) I, II, and IV only. D) III and IV only
The correct answer is D) III and IV only.
The historical standard deviation approach differs from the RiskMetrics TM and GARCH approaches for estimating conditional volatility, because it:
A) is a parametric method.
B) places a lower weight on more recent data.
C) uses recent historical data.
D) applies a set of weights to past squared returns.
The answer B is correct!
RiskMetrics uses the following value for the decay factor of daily data:
A) 0.92.
B) 0.95.
C) 0.94.
D) 0.97.
The correct answer was C) 0.94.