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NEW QUESTION 176
Which of the following statements is true:
I. Recovery rate assumptions can be easily made fairly accurately given past data available from credit rating agencies.
II. Recovery rate assumptions are difficult to make given the effect of the business cycle, nature of the industry and multiple other factors difficult to model.
III. The standard deviation of observed recovery rates is generally very high, making any estimate likely to differ significantly from realized recovery rates.
IV. Estimation errors for recovery rates are not a concern as they are not directionally biased and will cancel each other out over time.
- A. I, II and IV
- B. II and III
- C. II and IV
- D. III and IV
Answer: B
Explanation:
Explanation
Recovery rates vary a great deal from year to year, and are difficult to predict. Therefore statement III is true.
Similarly, any attempt to predict these is hamstrung by a high standard error, which can be as high as the historical mean itself. The error does not cancel itself out due to the effect of the business cycle making the error directionally biased. Thus statement IV is false.
Statement II is true as these are all factors that make forecasting recovery rates for any credit risk model rather difficult. Statement I is false because recovery rates are difficult to predict and assumptions are not easy to make.
NEW QUESTION 177
The diversification effect is responsible for:
- A. the super-additivity property of market risk VaR assessments
- B. the sub-additivity property of market risk VaR assessments
- C. total VaR numbers being greater than the sum of the individual VaRs for underlying portfolios
- D. VaR being applicable only to short term horizons
Answer: B
Explanation:
Explanation
Any good risk measure has the property that it is sub-additive, which means the whole is less than the sum of the parts. In the case of VaR, sub-additivity arises due to the diversification effect, or said differently, due to the correlation between different assets being less than one. Therefore Choice 'd' is the correct answer.
Super-additivity is just the opposite of sub-additivity, ie, the whole is greater than the sum of the parts. Good risk measures do not have super-additivity. Therefore Choice 'b' is incorrect.
Choice 'c' states the same thing as Choice 'b' in different words, and is incorrect. Choice 'a' is non-sensical and incorrect.
NEW QUESTION 178
The 10-day VaR of a diversified portfolio is $100m. What is the 20-day VaR of the same portfolio assuming the market shows a trend and the autocorrelation between consecutive periods is 0.2?
- A. 0
- B. 141.42
- C. 1
- D. 154.92
Answer: D
Explanation:
Explanation
The square root of time rule cannot be applied here because the returns across the periods are not independent.
(Recall that the square root of time rule requires returns to be iid, independent and identically distributed.) Here there is a 'autocorrelation' in play, which means one period's returns affect the returns of the other period.
VaR is merely a multiple of volatility, or standard deviation, using the factor for the desired confidence level.
VaR across time periods can be combined using the square root of time rule, in fact if returns were independent we could have easily calculated the VaR for the 20-day period as equal to $100m*SQRT(20/10) =
$141.4m
But in this case we need to account for the autocorrelation. We can do this akin to the way we combine the VaR of different assets that have a given correlation. Since we know that:
Variance (A + B) = Variance(A) + Variance(B) + 2*Correlation*StdDev(A)*StdDev(B).
The standard deviation, which the VaR is a multiple of, can be calculated by taking the square root of the variance.
Therefore the combined VaR over the two months will be equal to =SQRT( (100^2) + (100^2) +
2*0.2*100*100 )= $154.92m. All other answers are incorrect.
NEW QUESTION 179
Which of the following is not a limitation of the univariate Gaussian model to capture the codependence structure between risk factros used for VaR calculations?
- A. It cannot capture linear relationships between risk factors.
- B. Determining the covariance matrix becomes an extremely difficult task as the number of risk factors increases.
- C. A single covariance matrix is insufficient to describe the fine codependence structure among risk factors as non-linear dependencies or tail correlations are not captured.
- D. The univariate Gaussian model fails to fit to the empirical distributions of risk factors, notably their fat tails and skewness.
Answer: A
Explanation:
Explanation
In the univariate Gaussian model, each risk factor is modeled separately independent of the others, and the dependence between the risk factors is captured by the covariance matrix (or its equivalent combination of the correlation matrix and the variance matrix). Risk factors could include interest rates of different tenors, different equity market levels etc.
While this is a simple enough model, it has a number of limitations.
First, it fails to fit to the empirical distributions of risk factors, notably their fat tails and skewness. Second, a single covariance matrix is insufficient to describe the fine codependence structure among risk factors as non-linear dependencies or tail correlations are not captured. Third, determining the covariance matrix becomes an extremely difficult task as the number of risk factors increases. The number of covariances increases by the square of the number of variables.
But an inability to capture linear relationships between the factors is not one of the limitations of the univariate Gaussian approach - in fact it is able to do that quite nicely with covariances.
A way to address these limitations is to consider joint distributions of the risk factors that capture the dynamic relationships between the risk factors, and that correlation is not a static number across an entire range of outcomes, but the risk factors can behave differently with each other at different intersection points.
NEW QUESTION 180
If X represents a matrix with ratings transition probabilities for one year, the transition probabilities for 3 years are given by the matrix:
- A. P ^ (-3)
- B. 3 [P]
- C. 3 [P ^ (-1)]
- D. P x P x P
Answer: D
Explanation:
Explanation
Assuming time invariance and the Markov property, it is easy to calculate the transition matrix for any time period as P^n, where P is the given transition matrix for one period and n the number of time periods that we need to compute the new transition matrix for. Thus Choice 'b' is the correct answer.
NEW QUESTION 181
An investor holds a bond portfolio with three bonds with a modified duration of 5, 10 and 12 years respectively. The bonds are currently valued at $100, $120 and $150. If the daily volatility of interest rates is
2%, what is the 1-day VaR of the portfolio at a 95% confidence level?
- A. 115.51
- B. 163.11
- C. 0
- D. 1
Answer: A
Explanation:
Explanation
The total value of the portfolio is $370 (=$100 + $120 + $150). The modified duration of the portfolio is the weighted average of the MDs of the different bonds, ie =(5 * 100/370) + (10 * 120/370) + (12 * 150/370) =
9.46.
This means that for every 1% change in interest rates, the value of the portfolio changes by 9.46%. Since the daily volatility of interest rates is 2%, the 95% confidence level move will be 1.65 * 2% = 3.30%. Thus, the VaR of the portfolio at the 95% confidence level will be 3.3 * 9.46% * $370 = $115.51.
All other answers are incorrect.
NEW QUESTION 182
Which of the following are valid approaches for extreme value analysis given a dataset:
I. The Block Maxima approach
II. Least squares approach
III. Maximum likelihood approach
IV. Peak-over-thresholds approach
- A. I and IV
- B. All of the above
- C. I, III and IV
- D. II and III
Answer: A
Explanation:
Explanation
For EVT, we use the block maxima or the peaks-over-threshold methods. These provide us the data points that can be fitted to a GEV distribution.
Least squares and maximum likelihood are methods that are used for curve fitting, and they have a variety of applications across risk management.
NEW QUESTION 183
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?
- A. 0.0475 and 0.10
- B. 0.08 and 0.0475
- C. 0.05 and 0.0125
- D. 0.11 and 0
Answer: C
Explanation:
Explanation
Since the BHC always fails when the investment bank fails, the joint probability of default of the two is merely the probability of the investment bank failing, ie 0.05.
The probability of just the BHC failing, given that both the investment bank and the retail bank have survived will be equal to 0.11 - (0.05+0.05-0.05*0.05) = 0.0125. (The easiest way to understand this would be to consider a venn diagram, where the area under the largest circle is 0.11, and there are two intersecting circles inside this larger circle, each with an area of 0.05 and their intersection accounting for 0.05*0.05. We need to calculate the area outside of the two smaller circles, but within the larger circle representing the BHC).
Refer diagram below, please excuse the awful colors.
NEW QUESTION 184
The sensitivity (delta) of a portfolio to a single point move in the value of the S&P500 is $100. If the current level of the S&P500 is 2000, and has a one day volatility of 1%, what is the value-at-risk for this portfolio at the 99% confidence and a horizon of 10 days? What is this method of calculating VaR called?
- A. $14,736, historical simulation VaR
- B. $14,736, parametric VaR
- C. $4,660, parametric VaR
- D. $4,660, Monte Carlo simulation VaR
Answer: B
Explanation:
Explanation
If the current level of the S&P 500 is 2000, and a single day volatility is 1%, and the delta (ie change in portfolio value from a one point change) is $100, then the 1 day volatility for the portfolio in dollars is 2000 *
1% * $100 = $2,000.
At the 99% confidence level, the value of the inverse cumulative density function for the normal distribution is
2.33 (=NORMSINV(99%), in Excel). Therefore the 1 day VaR will be 2.33 * $2000 = $4,660. Extending it to
10 days using the square root of time rule, we get the 10 day VaR as equal to SQRT(10)*4660 = $14,736.
Since this method of calculating VaR relies upon a delta approximation of a risk factor (in this case the S&P500), it is the parametric approach to calculating VaR (the other methods being historical simulation, and Monte Carlo simulation).
The
2015 Handbook provides an excellent example of parametric (and other) VaR calculations in Chapter 3 of Volume III of Book 3. The spreadsheet used for the illustration can be downloaded from
http://www.prmia.org/prm-exam/handbook-resources.
NEW QUESTION 185
Under the CreditPortfolio View approach to credit risk modeling, which of the following best describes the conditional transition matrix:
- A. The conditional transition matrix is the transition matrix adjusted for the risk horizon being different from that of the transition matrix
- B. The conditional transition matrix is the unconditional transition matrix adjusted for the state of the economy and other macro economic factors being modeled
- C. The conditional transition matrix is the unconditional transition matrix adjusted for probabilities of defaults
- D. The conditional transition matrix is the transition matrix adjusted for the distribution of the firms' asset returns
Answer: B
Explanation:
Explanation
Under the CreditPortfolio View approach, the credit rating transition matrix is adjusted for the state of the economy in a way as to increase the probability of defaults when the economy is not doing well, and vice versa. Therefore Choice 'a' is the correct answer. The other choices represent nonsensical options.
NEW QUESTION 186
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. A LIBOR based loan; OIS rate will be higher
- B. Overnight Index Swap; LIBOR rate will be higher
- C. A LIBOR based loan; LIBOR rate will be higher
- D. Overnight Index Swap; OIS rate will be higher
Answer: C
Explanation:
Explanation
A LIBOR based loan requires cash to move from the lender to the borrower in the amount of the notional. The Overnight Index Swap requires only the exchange of interest payments, and therefore represents less risk.
Therefore the LIBOR based loan is a riskier exposure.
The LIBOR is generally higher than the OIS. In fact, the difference between the two, the LIBOR-OIS spread, is a standard measure of the risk premium in the market that goes up when the risk of default by counterparty banks is considered high. This is because when the market perceives the risk of default to be high, the participants need a risk premium to take on the default risk which is considerably lesser with the OIS.
NEW QUESTION 187
For a security with a daily standard deviation of 2%, calculate the 10-day VaR at the 95% confidence level.
Assume expected daily returns to be nil.
- A. 0.1471
- B. 0.104
- C. None of the above.
- D. 0.02
Answer: B
Explanation:
Explanation
If the daily standard deviation is 2%, the 10-day standard deviation will be 2%* 10 = 0.063245. The value of Z at the 95% confidence level is 1.64485. Therefore the VaR value is 1.64485 * 0.063245 = 10.4%. The other choices are incorrect.
NEW QUESTION 188
Which of the following are considered properties of a 'coherent' risk measure:
I. Monotonicity
II. Homogeneity
III. Translation Invariance
IV. Sub-additivity
- A. I and III
- B. II and IV
- C. All of the above
- D. II and III
Answer: B
Explanation:
Explanation
All of the properties described are the properties of a 'coherent' risk measure.
Monotonicity means that if a portfolio's future value is expected to be greater than that of another portfolio, its risk should be lower than that of the other portfolio. For example, if the expected return of an asset (or portfolio) is greater than that of another, the first asset must have a lower risk than the other. Another example:
between two options if the first has a strike price lower than the second, then the first option will always have a lower risk if all other parameters are the same. VaR satisfies this property.
Homogeneity is easiest explained by an example: if you double the size of a portfolio, the risk doubles. The linear scaling property of a risk measure is called homogeneity. VaR satisfies this property.
Translation invariance means adding riskless assets to a portfolio reduces total risk. So if cash (which has zero standard deviation and zero correlation with other assets) is added to a portfolio, the risk goes down. A risk measure should satisfy this property, and VaR does.
Sub-additivity means that the total risk for a portfolio should be less than the sum of its parts. This is a property that VaR satisfies most of the time, but not always. As an example, VaR may not be sub-additive for portfolios that have assets with discontinuous payoffs close to the VaR cutoff quantile.
NEW QUESTION 189
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. All of the above
- B. The forward yield curve
- C. A specified risk horizon
- D. A rating migration matrix
Answer: A
Explanation:
Explanation
The credit migration approach to assessing portfolio credit risk involves obtaining a distribution of future portfolio values from the ratings migration matrix. First, the frequencies in the matrix are used as probabilities, and expected future values of the securities belonging to each rating category are calculated. These are then discounted to the present using the discount rate appropriate to the 'future' rating category. This gives us a forward distribution of the value of each security in the portfolio. These are then combined using the default correlations between the issuers. The default correlation between the issuers is often proxied using asset returns, and recognizing that default occurs when asset values fall below a certain threshold. A distribution for the future value of the portfolio is generated using simulation, and from this distribution the Credit VaR can be calculated.
Thus, we need the migration matrix, the risk horizon from which the present values need to be calculated, and the forward yield curve or the discount curve for each rating category for the risk horizon. Thus, Choice 'd' is the correct answer.
NEW QUESTION 190
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
- A. I and III
- B. I and IV
- C. II and IV
- D. III only
Answer: D
Explanation:
Explanation
Statement I is not correct as VaR does not set an upper limit on losses. In this case, the bank expects the losses to exceed $253m 5% of the times, and the VaR number does not indicate any theoretical maximum amount of losses.Statement II is incorrect as there is a 95% (and not 5%) probability that the bank's losses will not exceed
$253mStatement III is correct and describes VaR.Statement IV is incorrect, as regulatory capital is a more complex computation for which VaR is only one of the various input.Therefore Choice 'b' is the correct answer.
NEW QUESTION 191
Which of the following best describes a 'break clause ?
- A. A break clause gives either party to a transaction the right to terminate the transaction at market price at future date(s)
- B. A break clause sets out the conditions under which the transaction will be terminated upon non-compliance with the ISDA MA
- C. A break clause determines the process by which amounts due on early termination will be determined
- D. A break clause describes rights and obligations when the derivative contract is broken
Answer: A
Explanation:
Explanation
A break close, also called a 'mutual put', gives either party the right to terminate a transaction at market price at a given date, or dates in the future. These are usually availed of in longer dated transactions, eg 10 years and over. For example, a 15-year swap might have a mutual put in year 5, and every 2 years thereafter.
All other choices are incorrect.
NEW QUESTION 192
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.
- A. I and III
- B. I and IV
- C. II and III
- D. II and IV
Answer: C
Explanation:
Explanation
In the case of mean reversion, the actual VaR would be lower than that estimated using the square root of time rule. This is because gains over a period would be followed by losses so that the price can revert to the mean.
In such cases, the autocorrelation between subsequent periods is effectively negative. This means the combined VaR over the periods would be lower.
In the case of positive autocorrelation, the actual VaR would be higher than that estimated using the square root of time rule for exactly the opposite reason than that described for the mean-reverting case.
(Recall that Variance (A + B) = Variance(A) + Variance(B) + 2*Correlation*StdDev(A)*StdDev(B). In cases where correlation is zero, the variance can simply be added together (which is the case for iid observations). In cases where the correlation is negative, the combined variance (and therefore standard deviation and also VaR) will be lower; and where correlation is positive, the combined variance (and therefore standard deviation and also VaR) will be higher.) Therefore statement II is correct, and so is statement III. Choice 'c' is the correct answer.
NEW QUESTION 193
If the annual variance for a portfolio is 0.0256, what is the daily volatility assuming there are 250 days in a year.
- A. 0.4048
- B. 0.0016
- C. 0.0006
- D. 0.0101
Answer: D
Explanation:
Explanation
If annual variance is 0.0256, then annual volatility (ie standard deviation) is 0.0256. Therefore the daily volatility will be 0.0256/250 = 1.01%. The other choices are not correct.
NEW QUESTION 194
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
- C. A
- D. All of the above
- E. II and III
Answer: C
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 195
For a FX forward contract, what would be the worst time for a counterparty to default (in terms of the maximum likely credit exposure)
- A. Roughly three-quarters of the way towards maturity
- B. At maturity
- C. Indeterminate from the given information
- D. Right after inception
Answer: B
Explanation:
Explanation
With the passage of time, the range of possible values the FX contract can take increases. Therefore the maximum value of the contract, which is when the credit risk would be maximum, would be at maturity. (Note that this is different than an interest rate swap whose value at maturity approaches zero.) Therefore Choice 'a' is the correct answer and the others are incorrect.
NEW QUESTION 196
Which of the following statements is true?
I. Real Time Gross Systems (RTGS) for large value payments consume less system liquidity than Deferred Net Systems (DNS) II. The US Fedwire is an example of a Real Time Gross System III. Current disclosure requirements in relation to liquidity risk as laid down in the Basel framework require banks to disclose how liquidity stress scenarios were formulated IV. A CFP (Contingency Funding Plan) provides access to Central Bank financing
- A. I and III
- B. I, II, III and IV
- C. II and IV
- D. II
Answer: D
Explanation:
Explanation
The correct answer is choice 'd'
For settlement of interbank payments, there are broadly two kinds of systems: RTGS (Real Time Gross Systems) and Deferred Net Systems (DNS). RTGS process payments in real time, settlement by settlement, and each transaction is settled by the a clearing institution (mostly the central bank) on a gross basis without regard for other settlements affecting the counterparty. DNS systems, on the other hand, allow for debiting or crediting the accounts of counterparties at periodic intervals after netting all payments paid or received since the last settlement. The exact timing of the payments does not matter so long as a bank has sufficient funding on a net basis at settlement time. Implicit in the DNS system is the extension of credit and liquidity by the central bank to the participating banks as it is possible for a bank to issue payment instructions even without having funds so long as they can arrange for such funds prior to settlement at the end of the day. In RTGS, a bank needs to have funds to make a payment at any point, and cannot make a payment against moneys expected to be received later intra-day. RTGS systems therefore need more liquidity on the part of the participants, and consume far more liquidity than DNS arrangements. Of course, the 'liquidity' of the DNS arrangement has a cost - which is that someone is taking up settlement risk, and invariably it is the central bank. If a bank under DNS fails to settle, its transactions have to be 'unwound', ie all payments made by it have to be rolled back. This can cause other banks to trip, causing further unwinding transactions. RTGS systems do not carry this risk. Therefore statement I is not correct as RTGS consume more liquidity than DNS arrangements.
Statement II is correct. US Fedwire or European TARGET are RTGS while CHIPS is a DNS based payment system.
Statement III is not correct. Current Basel requirements do not require any disclosure in respect of liquidity risk management. A consultative paper was issued by BIS in Dec 2009 for comments from members, but it is far from final. The BIS is still reacting to the liquidity issues that arose during the 2007-09 credit crisis.
Statement IV is not correct as a CFP is like a disaster recovery plan for liquidity, ie it helps a bank plan for and think about what steps would be taken to deal with a liquidity disaster situation. It does not provide any access to central bank financing.
NEW QUESTION 197
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
- A. II
- B. Neither statement is true
- C. I
- D. I & II
Answer: D
Explanation:
Explanation
The correct answer is choice 'b'
Both statements are accurate. Basel II requires pooled probabilities of default to be applied to risk buckets that contain similar exposures. Also, stress testing is mandatory for both market and credit risk.
NEW QUESTION 198
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