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8008 Dumps 2021 - New PRMIA 8008 Exam Questions
NEW QUESTION 141
For a hypotherical UoM, the number of losses in two non-overlapping datasets is 24 and 32 respectively. The Pareto tail parameters for the two datasets calculated using the maximum likelihood estimation method are 2 and 3. What is an estimate of the tail parameter of the combined dataset?
- A. 2.57
- B. 2.23
- C. Cannot be determined
- D. 0
Answer: A
Explanation:
Explanation
For a number of processes, including many in finance, while a distribution such as the normal distribution is a good approximation of the distribution near the modal value of the variable, the same normal distribution may not be a good estimate of the tails. For this reason, the Pareto distribution is one of the distributions that is often used to model the tails of another distribution. Generally, if you have a set of observations, and you discard all observations below a threshold, you are left with what are called 'exceedances'. The threshold needs to be reasonably far out in the tail. If from each value of the exceedances you subtract the threshold value, the resulting dataset is estimated by the generalized Pareto distribution.
The Pareto distribution has a 'shape parameter'. The average of two Pareto distributions with tail parameters 1 and 2 ( is a Greek character, pronounced as 'sai' (saa-eee)), is the weighted average of 1 and 2 with weights proportional to the number of observations in the datasets underlying the distributions.
NEW QUESTION 142
Which of the following statements are true:
I. Heavy tailed parametric distributions are a good choice for severity modeling in operational risk.
II. Heavy tailed body-tail distributions are a good choice for severity modeling in operational risk.
III. Log-likelihood is a means to estimate parameters for a distribution.
IV. Body-tail distributions allow modeling small losses differently from large ones.
- A. I and IV
- B. II and III
- C. All of the above
- D. II, III and IV
Answer: C
Explanation:
Explanation
When modeling for operational risk, we are generally concerned with tail losses - this is because the horizon for operational risk is 1 year at the 99.9th percentile. Since the 99.9th percentile is in the tail region, we would like to ensure that the tails are modeled as accurately as possible. Operational risk distributions are modeled using heavy tailed distributions.
Heavy tailed parametric distributions such as log-normal, pareto and others are therefore a good choice for modeling risk severity, therefore statement I is correct.
Body-tail distributions are combinations of parametric distributions, with different types of distributions being used to model the body and the tail - this provides flexibility because small and medium losses upto a threshold can be modeled using one distribution, and losses beyond the threshold can be modeled using a different distribution that is a better estimate of the tail. Statement II is therefore correct.
A log-likelihood function simplifies the optimization of a regular likelihood function. We generally maximize (or minimize the risk functional) a likelihood function with a view to estimating the parameters of the underlying distribution. If the likelihood function is complex, it may sometimes make it mathematically easier to optimize the log of the function - as that changes exponents and multiplications to additions, while behaving in the same way as the underlying function. Therefore statement III is correct, log-likelihood is a means to estimate parameters for a distribution.
Statement IV is correct as body-tail distributions allow modeling different parts of the distribution differently from each other.
NEW QUESTION 143
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
- A. I and IV
- B. II and III
- C. II
- D. A
- E. All of the above
Answer: D
Explanation:
Explanation
Historical Simulation VaR is conceptually very straightforward: actual prices as seen during the observation period (1 year, 2 years, or other) become the 'scenarios' forming the basis of the valuation of the portfolio. For each scenario, full revaluation is performed, and a P&L data set becomes available from which the desired loss quantile can be extracted.
Historical simulation is based upon actually seen prices over a selected historical period, therefore no distributional assumptions are required. The data is what the data is, and is the distribution. Statement I is therefore not correct.
It uses full revaluation for each historical scenario, therefore statement II is correct.
Since the prices are taken from actual historical observations, a correlation matrix is not required at all.
Statement III is therefore incorrect (it would be true for Monte Carlo and parametric Var).
Historical simulation VaR suffers from the limitation that if enough representative data points are no available during the historical observation period from which the scenarios are drawn, the results would be inaccurate.
This is likely to be the case for new products. Therefore Statement IV is incorrect.
NEW QUESTION 144
Which of the following are valid methods for selecting an appropriate model from the model space for severity estimation:
I. Cross-validation method
II. Bootstrap method
III. Complexity penalty method
IV. Maximum likelihood estimation method
- A. I and IV
- B. II and III
- C. I, II and III
- D. All of the above
Answer: D
Explanation:
Explanation
Once we have a number of distributions in the model space, the task is to select the "best" distribution that is likely to be a good estimate of true severity. We have a number of distributions to pick from, an empirical dataset (from internal or external losses), and we can estimate the parameters for the different distributions.
We then have to decide which distribution to pick, and that generally requires considering both approximation and fitting errors.
There are three methods that are generally used for selecting a model:
1. The cross-validation method: This method divides the available data into two parts - the training set, and the validation set (the validation set is also called the 'testing set'). Parameter estimation for each distribution is done using the training set, and differences are then calculated based on the validation set. Though the temptation may be to use the entire data set to estimate the parameters, that is likely to result in what may appear to be an excellent fit to the data on which it is based, but without any validation. So we estimate the parameters based on one part of the data (the training set), and check the differences we get from the remaining data (the validation set).
2. Complexity penalty method: This is similar to the cross-validation method, but with an additional consideration of the complexity of the model. This is because more complex models are likely to produce a more exact fit than simpler models, this may be a spurious thing - and therefore a 'penalty' is added to the more complex models as to favor simplicity over complexity. The 'complexity' of a model may be measured by the number of parameters it has, for example, a log-normal distribution has only two parameters while a body-tail distribution combining two different distributions may have many more.
3. The bootstrap method: The bootstrap method estimates fitting error by drawing samples from the empirical loss dataset, or the fit already obtained, and then estimating parameters for each draw which are compared using some statistical technique. If the samples are drawn from the loss dataset, the technique is called a non-parametric bootstrap, and if the sample is drawn from an estimated model distribution, it is called a parametric bootstrap.
4. Using goodness of fit statistics: The candidate fits can be compared using MLE based on the KS distance, for example, and the best one selected. Maximum likelihood estimation is a technique that attempts to maximize the likelihood of the estimate to be as close to the true value of the parameter. It is a general purpose statistical technique that can be used for parameter estimation technique, as well as for deciding which distribution to use from the model space.
All the choices listed are the correct answer.
NEW QUESTION 145
Which of the following statements are true?
I. Retail Risk Based Pricing involves using borrower specific data to arrive at both credit adjudication and pricing decisions II. An integrated 'Risk Information Management Environment' includes two elements - people and processes III. A Logical Data Model (LDM) lays down the relationships between data elements that an organization stores IV. Reference Data and Metadata refer to the same thing
- A. I and III
- B. I, II and III
- C. II and IV
- D. All of the above
Answer: A
Explanation:
Explanation
Statement I is correct. Retail Risk Based Pricing (RRBP) involves the use of borrower specific data (such as FICO scores, average balances etc) to arrive at credit decisions. These 'retail' credit decisions may include decisions on whether to grant a line of credit, a mortgage, issue a credit card, or any of the various other retail activities a bank may be dealing with. At the same time, this data can also be used to price the product, in addition to providing a yes or no credit decision so that risky borrowers are charged more than less risky borrowers.
Statement II is not correct, because an integrated Risk Information Management Environment includes three elements - people, processes and technology (and not just people and processes).
Statement III is correct. An LDM is a blue print of an organization's data, and describes the relationships between the various data elements.
Statement IV is not correct because reference data and metadata are not the same thing. Reference data refers to relatively static data, such as customer name (while actual transactions may not be so static). Metadata refers to data about data, and is stored in a data dictionary.
Therefore Choice 'b' is the correct answer and the rest are incorrect.
NEW QUESTION 146
A bank prices retail credit loans based on median default rates. Over the long run, it can expect:
- A. Correct pricing of risk in the retail credit portfolio
- B. Overestimation of risk and overpricing, leading to loss of market share
- C. Underestimation and therefore underpricing of risk in it retail portfolio
- D. A reduction in the rate of defaults
Answer: C
Explanation:
Explanation
The key to pricing loans is to make sure that the prices cover expected losses. The correct measure of expected losses is the mean, and not the median. To the extent the median is different from the mean, the loans would be over or underpriced.
The loss curve for credit defaults is a distribution skewed to the right. Therefore its mode is less than its median which is less than its mean. Since the median is less than the mean, the bank is pricing in fewer losses than the mean, which means over the long run it is underestimating risk and underpricing its loans. Therefore Choice 'd' is the correct answer.
If on the other hand for some reason the bank were overpricing risk, its loans would be more expensive than its competitors and it would lose market share. In this case however, this does not apply. Loan pricing decisions are driven by the rate of defaults, and not the other way round, therefore any pricing decisions will not reduce the rate of default.
NEW QUESTION 147
An equity manager holds a portfolio valued at $10m which has a beta of 1.1. He believes the market may see a dip in the coming weeks and wishes to eliminate his market exposure temporarily. Market index futures are available and the current futures notional on these is $50,000 per contract. Which of the following represents the best strategy for the manager to hedge his risk according to his views?
- A. Liquidate his portfolio as soon as possible
- B. Sell 220 futures contracts
- C. Buy 220 futures contracts
- D. Sell 200 futures contracts
Answer: B
Explanation:
Explanation
The number of futures contracts to sell are equal to $10m x 1.1/$50,000 = 220. Liquidating his portfolio would reduce the beta to zero, but would also get rid of the bets he wants to play on. Therefore Choice 'c' is the correct answer.
(Note that futures and spot prices generally move together allowing futures positions to be used for hedging the risk against movement in spot prices. However there is a basis risk between spot and futures, therefore the a perfect hedge is never possible with futures. If interest rates move a great deal, spot and futures prices may diverge. Of course, this risk is generally quite low but may become amplified with large leveraged portfolios.
Just something to be aware of.)
NEW QUESTION 148
In January, a bank buys a basket of mortgages with a view to securitize them by April. Due to an unexpected lack of investors in the securitization market, it is unable to do so and is left with the exposure to the mortgages on its books. This is an example of:
- A. Pipeline and warehousing risk
- B. Basis risk
- C. Market risk
- D. Wrong-way risk
Answer: A
Explanation:
Explanation
This is an example of pipeline and warehousing risk. Generally there is a lag between acquiring assets and securitizing them due to the legal work to be done, the work to be done by the ratings agencies and in finding investors. During this period, the bank is exposed to the underlying assets purchased, and this is the 'pipeline and warehousing' risk as these assets are in the pipeline and warehoused for intended subsequent sale.
Generally this period tends to be short. However, during the credit crisis this became a significant source of risk as many banks were left exposed to risk they had intended to get rid of, but could not do so as the market dried up. The other choices are all incorrect.
Note that pipeline and warehousing risk is also known as 'securitzation risk'. It means that funding from securitization cannot be relied upon as a matter of fact.
NEW QUESTION 149
As the persistence parameter under EWMA is lowered, which of the following would be true:
- A. The model will react slower to market shocks
- B. High variance from the recent past will persist for longer
- C. The model will react faster to market shocks
- D. The model will give lower weight to recent returns
Answer: C
Explanation:
Explanation
The persistence parameter, , is the coefficient of the prior day's variance in EWMA calculations. A higher value of the persistence parameter tends to 'persist' the prior value of variance for longer. Consider an extreme example - if the persistence parameter is equal to 1, the variance under EWMA will never change in response to returns.
1 - is the coefficient of recent market returns. As is lowered, 1 - increases, giving a greater weight to recent market returns or shocks. Therefore, as is lowered, the model will react faster to market shocks and give higher weights to recent returns, and at the same time reduce the weight on prior variance which will tend to persist for a shorter period.
NEW QUESTION 150
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?
- A. Since the derivatives contract has a negative current replacement value, exposure will be zero.
- B. The credit exposure will be a given quintile of the expected distribution of the value of the derivatives contract in the future.
- C. The current exposure can be used for loan equivalence calculations as that is an unbiased proxy for the future value.
- D. The notional value of the derivatives contract should be used for loan equivalence calculations.
Answer: B
Explanation:
Explanation
The current exposure is negative, so there is no immediate credit exposure. However, since the price of the derivative is volatile, we can reasonably expect the value to be greater than zero sometime in the future. This is a stochastic variable which will have a distribution, and not just a unique value, in the future that will represent the credit exposure. Since there is no unique value, a conservative approach is to pick a quintile of the distribution, and use that as the future value of the derivative contract, with the assurance that the probability of the credit exposure exceeding that quintile is known and has been consciously selected. This number can then be converted to a loan equivalent amount for credit risk purposes. Therefore Choice 'b' is the correct answer. Choice 'a', Choice 'd' and Choice 'c' are incorrect for these reasons.
NEW QUESTION 151
Financial institutions need to take volatility clustering into account:
I. To avoid taking on an undesirable level of risk
II. To know the right level of capital they need to hold
III. To meet regulatory requirements
IV. To account for mean reversion in returns
- A. I, II and IV
- B. I, II and III
- C. I & II
- D. II, III and IV
Answer: C
Explanation:
Explanation
Volatility clustering leads to levels of current volatility that can be significantly different from long run averages. When volatility is running high, institutions need to shed risk, and when it is running low, they can afford to increase returns by taking on more risk for a given amount of capital. An institution's response to changes in volatility can be either to adjust risk, or capital, or both. Accounting for volatility clustering helps institutions manage their risk and capital and therefore statements I and II are correct.
Regulatory requirements do not require volatility clustering to be taken into account (at least not yet).
Therefore statement III is not correct, and neither is IV which is completely unrelated to volatility clustering.
NEW QUESTION 152
Which of the following describes rating transition matrices published by credit rating firms:
- A. Expected ex-ante frequencies of migration from one credit rating to another over a one year period
- B. Probabilities of ratings transition from one rating to another for a given set of issuers
- C. Realized frequencies of migration from one credit rating to another over a one year period
- D. Probabilities of default for each credit rating class
Answer: C
Explanation:
Explanation
Transition matrices are used for building distributions of the value of credit portfolios, and are the realized frequencies of migration from one credit rating to another over a period, generally one year. Therefore Choice
'd' is the correct answer.
Since they represent an actually observed set of values, they are not probabilities nor are they forward looking ex-ante estimates, though they are often used as proxies for probabilities. Choice 'a' and Choice 'c' are not correct. They include more than information on just defaults, therefore Choice 'b' is not correct.
NEW QUESTION 153
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%
- A. I and III
- B. III
- C. I
- D. I, III and IV
Answer: C
Explanation:
Explanation
Statement I is true - capital adequacy indeed is a reference to the ability of the firm to stay a 'going concern'.
(Going concern is an accounting term that means the ability of the firm to continue in business without the stress of liquidation.) Statement II is not true because even though the stated objective of regulatory capital requirements is similar to the purposes for which economic capital is calculated, regulatory capital calculations are based upon a large number of ad-hoc estimates and parameters that are 'hard-coded' into regulation, while economic capital is generally calculated for internal purposes and uses an institution's own estimates and models. They are rarely identical.
Statement II is not true as the purpose of economic capital is to provide a buffer against unexpected losses.
Expected losses are covered by the P&L (or credit reserves), and not capital.
Statement IV is incorrect as even though economic capital may be calculated at very high confidence levels, that is never 100% which would require running a 'risk-free' business, which would mean there are no profits either. The level of confidence is set at a level which is an acceptable balance between the interests of the equity providers and the debt holders.
NEW QUESTION 154
Which of the following formulae describes Marginal VaR for a portfolio p, where V_i is the value of the i-th asset in the portfolio? (All other notation and symbols have their usual meaning.) A)
B)
C)
D)
All of the above
- A. Option B
- B. Option C
- C. Option A
- D. Option D
Answer: D
Explanation:
Explanation
Marginal VaR of a component of a portfolio is the change in the portfolio VaR from a $1 change in the value of the component. It helps a risk analyst who may be trying to identify the best way to influence VaR by changing the components of the portfolio. Marginal VaR is also important for calculating component VaR (for VaR disaggregation), as component VaR is equal to the marginal VaR multiplied by the value of the component in the portfolio.
Marginal VaR is by definition the derivative of the portfolio value with respect to the component i. This is reflected in Choice 'a' above. Using the definitions and relationships between correlation, covariance, beta and volatility of the portfolio and/or the component, we can show that the other two choices are also equivalent to Choice 'a'.
Therefore all the choices present are correct.
NEW QUESTION 155
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:
- A. Total VaR is $20
- B. Total VaR is greater than $180
- C. Total VaR is less than $180
- D. Total VaR is $180
Answer: C
Explanation:
Explanation
Choice 'd' is correct because VaR is sub-additive in cases where correlation is less than one.
Specific VaR refers to the risk in the portfolio from security selection, ie the risk from holding the specific equities in the portfolio, while systematic risk refers to the market risk. Definitionally, specific risk and systematic risk are uncorrelated, ie their correlation is zero. Since their correlation is zero, combining them will produce a VaR number lower than their stand alone aggregate. Total risk includes both specific risk and systematic risk, and can be calculated taking into account the specific and systematic VaRs and their correlation.
All other answers are therefore incorrect.
NEW QUESTION 156
Under the contingent claims approach to measuring credit risk, which of the following factors does NOT affect credit risk:
- A. Volatility of the firm's asset values
- B. Maturity of the debt
- C. Leverage in the capital structure
- D. Cash flows of the firm
Answer: D
Explanation:
Explanation
Under the contingent claims approach, credit risk is modeled as the value of a put option on the value of the firm's assets with a strike equal to the face value of the debt and maturity equal to the maturity of the obligation. The cost of credit risk is determined by the leverage ratio, the volatility of the firm's assets and the maturity of the debt. Cash flows are not a part of the equation. Therefore Choice 'a' is the correct answer.
NEW QUESTION 157
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