According to the Basel II framework, subordinated term debt that was originally issued 4 years ago with amaturity of 6 years is considered a part of:
According to the Basel II framework, Tier 1 capital, also called core capital or basic equity, includes equity capital and disclosed reserves.
Tier 2 capital, also called supplementary capital, includes undisclosed reserves, revaluation reserves, general provisions/general loan-loss reserves, hybrid debt capital instruments and subordinated term debt issued originally for 5 years or longer.
Tier 3 capital, or short term subordinated debt, is intended only to cover market risk but only at the discretion of their national authority. This only includes short term subordinated debt originally issued for 2 or more years.
An interesting thing to note is the difference between 'subordinated term debt' under Tier 2 and the 'short term subordinated debt' under Tier 3. The distinction is based upon the years to maturity at the time the debt was issued. The remaining time to maturity is not relevant. For the subordinated term debt included under Tier 2, the amount that can be counted towards capital is reduced by 20% for every year when the debt is due within 5 years. This takes care of the time to maturity problem for Tier 2subordinated debt. For Tier 3 short term subordinated debt, this is not an issue because debt will only qualify for Tier 3 if it has a lock-in clause stipulating that the debt is not required to be repaid if the effect of such repayment is to take the bank below minimum capital requirements.
Which of the following statements is true:
I. When averaging quantiles of two Pareto distributions, the quantiles of theaveraged models are equal to the geometric average of the quantiles of the original models based upon the number of data items in each original model.
II. When modeling severity distributions, we can only use distributions which have fewer parameters thanthe number of datapoints we are modeling from.
III. If an internal loss data based model covers the same risks as a scenario based model, they can can be combined using the weighted average of their parameters.
IV If an internal loss model and a scenario based model address different risks, the models can be combined by taking their sums.
Statement I is true, the quantiles of the averaged models are equal to the geometric average of the quantiles of the original models.
Statement II is correct, the number of data points from which model parameters are estimated must be greater than the number of parameters. So if a distribution, say Poisson, has one parameter, we need at least two data points to estimate the parameter. Other complex distributions may have multiple parameters for shape, scale and other things, and the minimum number of observations required will be greater than the number of parameters.
Statement III istrue, if the ILD data and scenarios cover the same risk, they are essentially different perspectives on the same risk, and therefore should be combined as weighted averages.
But if they cover completely different risks, the models will need to be added together, not averaged - which is why Statement IV is true.
Which of the following will be a loss not covered by operational risk as defined under Basel II?
Operational risk isdefined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk.
Therefore any losses from poor strategic planning will not be a part of operational risk. Choice 'd' is the correct answer.
Note that floods, earthquakes and the like are covered under the definition of operational risk as losses arising from loss or damage to physical assets from natural disaster orother events.
The generalized Pareto distribution, when used in the context of operational risk, is used to model:
Some risk experts have suggested the use of extreme value theory to model tail risk or extreme events for operational risk. The generalized Pareto model or the Peaks-over-Threshold (POT) model are often used to model extreme value distributions, and therefore Choice 'a' is the correct answer.
Which of the following losses can be attributed to credit risk:
I. Losses in a bond's value from a credit downgrade
II. Losses in a bond's value from an increase in bond yields
III. Losses arising from a bond issuer'sdefault
IV. Losses from an increase in corporate bond spreads
Losses due to credit risk include the loss of value from credit migration and default events (which can be considered a migration to the 'default' category). Therefore Choice 'd' is the correct answer. Changes in spreads or interest rates are examples of market risk events.
[Discussion: It may be argued that losses from spreads changing could be categorized as credit risk and not market risk. The distinction between credit and market risk is never really watertight.
The reason I have called it market risk in this question is because spreads can change due to two reasons: first, due to the individual issuer going down in their credit rating (whether issued or perceived, as we have witnessed in Europe sovereign debt), and second due to the spread for the overall category changing due to macro fundamentals with nothing changing for the individual issuer. For example the spread between municipal bonds and treasuries may be small during boom times and may expand during recessions - regardless of how the individual issuer has been doing. Clearly, the first case is credit risk and the second is probably market risk.
A changein overall corporate bond spreads is something I would consider akin to a rate change - which is why I have called it as not a part of credit risk. But an alternative perspective may not be incorrect either.]
When modeling severity of operational risk losses using extreme value theory (EVT), practitioners often use which of the following distributions to model loss severity:
I. The 'Peaks-over-threshold' (POT) model
II. Generalized Pareto distributions
III. Lognormal mixtures
IV. Generalized hyperbolic distributions
The peaks-over-threshold model is used when lossesover a given threshold are recorded, as is often the case when using data based on external public sources where only large loss events tend to find a place. The generalized Pareto distribution is also used when attempting to model loss severity using EVT.Lognormal mixtures and generalized hyperbolic distributions are not used as extreme value distributions.
Choice 'd' is the correct answer.
Which of the following cannot be used as an internal credit rating model to assess an individual borrower:
Altman's Z-score, the Probit and the Logit models can all be used to assess the credit rating of an individual borrower. There is no such model as the 'distance todefault model', and therefore Choice 'a' is the correct answer.
Conditional default probabilities modeled under CreditPortfolio view use a:
Conditional default probabilitiesare modeled as a logit function under CreditPortfolio view. That ensures the resulting probabilities are 'well behaved', ie take a value between 0 and 1. The probability may be expressed as = 1/ (1 + exp(I)), where I is a country specific index taking various macro economic factors into account.
For a FX forward contract, what would be the worst time for a counterparty to default (in terms of the maximum likely credit exposure)
With the passage of time, the range of possible values the FX contract can take increases. Therefore the maximumvalue 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.
For a 10 year interest rate swap, what would be the worst time for a counterparty to default (in terms of the maximum likely credit exposure)
Right after inception' is incorrect as the interest rate swap (IRS) would be valued at close to zero right after inception and the credit risk would be minimum. Choice 'a' (ie 10 years, at maturity) is incorrect as at maturity there would be no more cash flows to exchange, and the replacement value of the contract would again be close to zero.
Therefore the worst time for the counterparty to default is somewhere between inception and maturity - in fact the range of possible outcomes for the contract increases with the passage of time, and we should find the worst time to default to be a later date. However, towards maturity, the value of the contract starts to go towards zero again, and the maximum value is reached around 7 years. 2 years is too early for the maximum to be reached for the10 year IRS, and therefore choice a is the correct answer.
Which of the following steps are required for computing the aggregate distribution for a UoM for operational risk once loss frequency and severity curves have been estimated:
I. Simulate number of losses based on the frequency distribution
II. Simulate the dollar value of the losses from the severity distribution
III. Simulate random number from the copula used to model dependence between the UoMs
IV. Compute dependent losses from aggregate distribution curves
A recap would be in order here: calculating operational risk capital is a multi-step process.
First, we fit curves to estimate the parameters to our chosen distribution types for frequency (eg, Poisson), and severity (eg, lognormal). Note that these curves are fitted at the UoM level - which is the lowest level of granularity at which modeling is carried out. Since there are many UoMs, there are are many frequency and severity distributions. However what we are interested in is the loss distribution for the entire bank from which the 99.9th percentile loss can be calculated. From the multiple frequency and severity distributions we have calculated, this becomes a two step process:
- Step 1: Calculate the aggregate loss distribution for each UoM. Each loss distribution is based upon and underlying frequency and severity distribution.
- Step 2: Combine the multiple loss distributions after considering the dependence between the different UoMs. The 'dependence' recognizes that the various UoMs are not completely independent, ie the loss distributions are not additive, and that there is a sortof diversification benefit in the sense that not all types of losses can occur at once and the joint probabilities of the different losses make the sum less than the sum of the parts.
Step 1 requires simulating a number, say n, of the number of losses that occur in a given year from a frequency distribution. Then n losses are picked from the severity distribution, and the total loss for the year is a summation of these losses. This becomes one data point. This process of simulating the number of losses andthen identifying that number of losses is carried out a large number of times to get the aggregate loss distribution for a UoM.
Step 2 requires taking the different loss distributions from Step 1 and combining them considering the dependence between the events. The correlations between the losses are described by a 'copula', and combined together mathematically to get a single loss distribution for the entire bank. This allows the 99.9th percentile loss to be calculated.
Credit exposure for derivatives is measured using
Current replacement values are a very poor measure of the credit exposure from a derivative contract, because the future value of these instruments is unpredictable, ie is stochastic, and the range of values it can take increases the further ahead in the future we look. Therefore it is common for credit exposures for derivatives to be measured using forward looking exposure profiles, which are distributions of the expected value of the derivative at the time horizon for which credit risk is being measured. To be conservative, a high enough quintile of this distribution is taken as the 'loan equivalent value' of the derivative as the exposure.Choice 'c' is the correct answer.
The notional value of derivative contracts generally tends to be quite high and unrelated to their economic value or the counterparty exposure. Therefore notional value is irrelevant.
Under thebasic indicator approach to determining operational risk capital, operational risk capital is equal to:
Choice 'a' is the correct answer. According to theBasel II document, banks using the Basic Indicator Approach must hold capital for operational risk equal to the average over the previous three years of a fixed percentage (denoted alpha, and currently 15%) of positive annual gross income. Figures for anyyear in which annual gross income is negative or zero should be excluded from both the numerator and denominator when calculating the average.
Random recovery rates in respectof credit risk can be modeled using:
The beta distribution is commonly used to model recovery rates. It is a distribution forvariables whose values lie between 0 & 1, and the parameters of the distribution can be estimated using the mean and standard deviation of the data. Therefore Choice 'a' is correct and the others are wrong.
Refer to the tutorial on distributions for an Excel model of the beta distribution.
Which of the following credit risk models includes a consideration of macro economic variables such asunemployment, balance of payments etc to assess credit risk?
The correct answer is Choice 'd'. The following is a brief description of the major approaches available to model credit risk, and the analysis that underlies them:
1. CreditMetrics: based on the credit migration framework. Considers the probability of migration to other credit ratings and the impact of such migrationson portfolio value.
2. CreditPortfolio View: similar to CreditMetrics, but adds the impact of the business cycle to the evaluation.
3. The contingent claims approach: uses option theory by considering a debt as a put option on the assets of the firm.
4. KMV's EDF (expected default frequency) based approach: relies on EDFs and distance to default as a measure of credit risk.
5. CreditRisk+: Also called the 'actuarial approach', considers default as a binary event that either happens or does not happen. Thisapproach does not consider the loss of value from deterioration in credit quality (unless the deterioration implies default).
If the default hazard rate for a company is 10%, and the spread on its bondsover the risk free rate is 800 bps, what is the expected recovery rate?
The recovery rate, the default hazard rate (also called the average default intensity) and the spread on debt arelinked by the equation Hazard Rate = Spread/(1 - Recovery Rate). Therefore, the recovery rate implicit in the given data is = 1 - 8%/10% = 20%.
A zero coupon corporate bond maturing in an year has a probability of default of 5% and yields 12%. The recovery rate is zero. What is the risk free rate?
The probability of default would make the expected value of the future cash flows from both the corporate bond and the risk free bond identical. If p be the probability of default, the cash flows from the risky corporate bond would be
= (cash flows in the event of default x probability of default) + (cash flows without default x (1 - probability of default))
=> 5%*0 + (1 - 5%)*(1 + 12%) = (1 + Rf).
therefore Rf = 6.4%
(In reality investors would demand a 'credit risk premium' over and above the expected default loss rate. They are unlikely to be happy with just being compensated with exactly the expected default loss rate plus the risk-fre rate because the expected default loss rate itself is uncertain. They would demand some premium over and above what the default rate alone might mathematically imply above the risk free rate. In this question, this credit risk premium is ignored.)
A stock that follows the Weiner process has its future price determined by:
The change in the price of a security that follows a Weiner process isdetermined by its standard deviation and expected return. To get the price itself, we need to add this change in price to the current price. Therefore the future price in a Weiner process is determined by all three of current price, expected return and standard deviation.
Under the CreditPortfolio View approach to credit risk modeling, which of the following best describes the conditional transition matrix:
Under theCreditPortfolio 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.
Pick underlying risk factors for a position in an equity index option:
I. Spot value for the index
II. Risk free interest rate
III. Volatility of the underlying
IV. Strike price for the option
The index option is affected by the spot value for the underlying index, as also the risk free interest rate, or the zero rate for the duration of the option. It is also affected by the volatility of the underlying.The 'strike price' is set and is fixed at the time the option is purchased, and therefore is not a risk factor.
Therefore other than IV, all other choices are valid risk factors that underlie an equity index option.
Other instruments may have other risk factors - for example, a long forex position will have the spot exchange rate as the only risk factor.
Which of the following statements are true:
I. Pre-settlement risk is the risk that one of the parties to a contract might default prior to the maturity date or expiry of the contract.
II. Pre-settlement risk can be partly mitigated by providing for early settlement in the agreements between the counterparties.
III. The current exposure from an OTC derivatives contract is equivalent to its current replacement value.
IV. Loan equivalent exposures are calculated even for exposures that are not loans as a practical matter for calculating credit risk exposure.
Pre-settlement risk is the risk that one of the counterparties defaults prior to the date for the maturity of the transaction in question. This may be an unrelated default, in fact there may have been no default on that particular contract, but the party may have defaulted on its other obligations, or filed for bankruptcy. To deal with such cases and to protect the interests of both the parties, it is common toprovide for immediate termination of positions and settlement based on the current replacement value of the contracts. Therefore statements I and II are correct.
Statement III is correct as well - the exposure from an OTC derivative contract derives fromits current replacement value, and not the notional. If the current replacement value is negative, then the credit exposure is considered equal to zero.
Statement IV is correct as it is quite common to restate all exposures - those from credit lines, OTC derivatives etc - in loan equivalent terms prior to estimating credit risk.
There are two bonds in a portfolio, each with a market value of $50m. The probability of default of the two bonds are 0.03 and 0.08 respectively, over a one year horizon. If the default correlation is 25%, what is the one year expected loss on this portfolio?
We will need to calculate the joint probability distribution of the portfolio as follows.Probability of the joint default of both A and B =
The marginal probabilities (ie the standalone probabilities of default of the two bonds) are known, and if we can calculate the probability of joint defaults of the two bonds, we can calculate the rest of the entries. We thenmultiply the probabilities with the expected loss under each scenario and add them up to get the total expected loss.
The calculations are shown below. The expected loss is $5.5m, and therefore the correct answer is Choice 'd'.
Under the ISDA MA, which of the following terms best describes the netting applied upon the bankruptcy of a party?
Netting is the ability to set just the net balances when amounts are both owed and due. Netting can takemany forms. Payment netting is netting between counterparties that owe moneys to each other in the same currency under the same transaction (or master agreement). Closeout netting is when parties settle a net amount for the value of all outstanding transactions upon the occurrence of an event of default such as bankruptcy. Multiateral netting involves a third party that sets off exposures across counterparties that owe moneys to each other.
Closeout netting under the ISDA master agreement enables a party toterminate transactions early if an Event of Default or Termination Event occurs in respect of the other party. It involves the calculation and netting of the termination values of all transactions to produce a single amount payable between the parties. Closeout netting is therefore the correct answer.
Which of the following objectives are targeted by rating agencies when assigning ratings:
I. Ratings accuracy
II. Ratings stability
III. High accuracy ratio (AR)
IV. Ranked ratings
Rating agencies target both accuracy and stability when they assign ratings. These two objectives can sometimes conflict, so a balance needs to be struck between the two. Rating agencies do not target anyparticular 'accuracy ratio' or rankings. Therefore Choice 'c' is the correct answer.
A corporate bond maturing in 1 year yields 8.5% per year,while a similar treasury bond yields 4%. What is the probability of default for the corporate bond assuming the recovery rate is zero?
Theprobability of default would make the future cash flows from both the bonds identical. If p be the probability of default, the cash flows from the risky corporate bond would be
= (cash flows in the event of default x probability of default) + (cash flows without default x (1 - probability of default))
=> p*0 + (1 - p)*(1 + 8.5%) = (1 - p)*1.085.
The cash flows from the treasury bond would be 1.04. These two should be equal, ie,
1.04 = (1- p)*1.085, implying p = 4.15%.
(Note: The above is a simplification intended for the exam. In reality investors would demand a 'credit risk premium' for the corporate bond over and above the expected default loss rate. They are unlikely to be happy with just being compensated with exactly the expected default loss rate plus the risk-fre rate because the expected default loss rate itself is uncertain. They would demand some premium over and above what the default rate alone might mathematically imply above the risk free rate. In this question, this credit risk premium is ignored.)
Which of the following are true:
I. The total of the component VaRs for all components of a portfolio equals the portfolio VaR.
II. The total of the incremental VaRs for each position in a portfolio equals the portfolio VaR.
III. Marginal VaR and incremental VaR are identical for a $1 change in the portfolio.
IV. The VaR for individual components of a portfolio is sub-additive, ie the portfolio VaR is less than (or in extreme cases equal to) the sum of the individual VaRs.
V. The component VaR for individual components of a portfolio is sub-additive, ie the portfolio VaR is less than the sum of the individual component VaRs.
Statement I is true - component VaR for individual assets in the portfolio add up to the total VaR for the portfolio. This property makes component VaR extremely useful for risk disaggregation and allocation.
Stateent II is incorrect, the incremental VaRs for the positions in a portfolio do not add up to the portfolio VaR, in fact their sum would be greater.
Statement III is correct. Marginal VaR for an asset or position in the portfolio is by definition the change in the VaR as a result of a $1 change in that position. Incremental VaR is the change in the VaR for a portfolio from a new position added to the portfolio - and if that position is $1, it would be identical to the marginal VaR.
Statement IV is correct, VaR is sub-additive due to the diversification effect. Adding up the VaRs for all the positions in a portfolio will add up to more than the VaR for the portfolio as a whole (unless all the positions are 100% correlated, which effectively would mean they are all identical securities which means the portfolio has only one asset).
Statement V is in incorrect. As explained for Statement I above, component VaR adds up to the VaR for the portfolio.
Under the CreditPortfolio View model of credit risk, the conditional probability of default will be:
When the economy is expanding, firms are less likely to default. Therefore the conditional probability of default, given an economic expansion, is likely to be lower than the unconditional probability of default. Therefore Choice 'a' is the correct answerand the other statements are incorrect.
Which of the following are considered properties of a 'coherent' risk measure:
III. Translation Invariance
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 thatof 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 thanthe 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 thetime, 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.
What percentage of average annual gross income is to be held as capital for operational risk under the basic indicator approach specified under Basel II?
Banks using the basic indicator approach must hold 15% of the average annual gross income for the past three years, excluding any year that had a negative gross income.Therefore Choice 'd' is the correct answer.
The risk that a counterparty fails to deliver its obligation upon settlement while having received the leg owed to it is called:
Choice 'd' is the correct answer. Settlement risk, as the name suggests, arises upon settlement when one of the parties delivers its obligation under the transaction and the other does not. Consider a EUR/USD FX forward contract maturing in a month. At maturity, one of the parties will deliver EURs and the other USDs. If one party fails to deliver, then it constitutes a very large risk to the other party. This risk is much larger than pre-settlement risk, because the amount at risk is the entire notional and not just the replacement value. Of course, settlement risk exists for a very short period of time, no more than a number or hours or a day.
There is no such thing as 'replacement risk', and credit risk is a larger category of which settlement risks is one component. Settlement risk is the most appropriate answer.
Under the standardized approach to calculating operational risk capital under Basel II, negative regulatory capital charges for any of the business units:
According to Basel II, in any given year, negative capital charges(resulting from negative gross income) in any business line may offset positive capital charges in other business lines without limit. Therefore Choice 'b' is the correct answer.
Which of the following decisions need to be made as part of laying down a system for calculating VaR:
I. The confidence level and horizon
II. Whether portfolio valuation is based upon a delta-gamma approximation or a full revaluation
III. Whether the VaR is to be disclosed in the quarterly financial statements
IV. Whether a 10 day VaR will be calculated based on 10-day return periods, or for 1-day and scaled to 10 days
While conceptually VaR is a fairly straightforward concept, a number of decisions need to be made to select between the different choices available for the exact mechanism to be used for the calculations.
The Basel framework requires banks toestimate VaR at the 99% confidence level over a 10 day horizon. Yet this is a decision that needs to be explicitly made and documented. Therefore 'I' is a correct choice.
At various stages of the calculations, portfolio values need to be determined. The valuation can be done using a 'full valuation', where each position is explicitly valued; or the portfolio(s) can be reduced to a handful of risk factors, and risk sensitivities such as delta, gamma, convexity etc be used to value the portfolio. The decisionbetween the two approaches is generally based on computational efficiency, complexity of the portfolio, and the degree of exactness desired. 'II' therefore is one of the decisions that needs to be made.
The decision as to disclosing the VaR in financial filings comes after the VaR has been calculated, and is unrelated to the VaR calculation system a bank needs to set up. 'III' is therefore not a correct answer.
Though the Basel framework requires a 10-day VaR to be calculated, it also allows the calculation of the 1-day VaR and and scaling it to 10 days using the square root of time rule. The bank needs to decide whether it wishes to scale the VaR based on a 1-day VaR number, or compute VaR for a 10 day period to begin with. 'IV' therefore is a decision tobe made for setting up the VaR system.
The definition of operational risk per Basel II includes which of the following:
I. Riskof loss resulting from inadequate or failed internal processes, people and systems or from external events
II. Legal risk
III. Strategic risk
IV. Reputational risk
Operational risk as defined in Basel II specifically excludes strategic and reputational risk. Therefore Choice 'd' is the correct answer.
Note that Basel II defines operational risk as follows:
Operational risk is defined as the risk of lossresulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk.
Which of the following is a measure of the level of capital that an institution needs to hold in order to maintain a desired credit rating?
Economic capital is a measure of the level of capital needed to maintain adesired credit rating. Regulatory capital is the amount of capital required to be held by regulation, and this may be quite different from economic capital. Book value is an accounting measure reflecting the assets minus liabilities as measured per accounting rules, this is often expressed per share. Shareholders' equity is a narrow term which is the amount of capital attributable to the shareholders and includes paid up capital and reserves but not long term debt or other non-equity funding.
Therefore Choice 'b' is the correct answer.
For a back office function processing 15,000 transactions a day with an error rate of 10 basis points, what is the annual expected loss frequency (assume 250 days in a year)
An error rate of 10 basis points means the number of errors expected in a day will be 15 (recall that 100 basis points = 1%). Therefore the total number of errors expected in a year will be 15 x250 = 3750. Choice 'a' is the correct answer.
Which of the following formulae describes CVA (Credit Valuation Adjustment)? All acronyms have their usual meanings (LGD=Loss Given Default, ENE=Expected Negative Exposure, EE=Expected Exposure, PD=Probability of Default, EPE=Expected Positive Exposure, PFE=Potential Future Exposure)
The correct definition of CVA is LGD * EPE * PD. All other answers areincorrect.
CVA reflects the adjustment for counterparty default on derivative and other trading book transactions. This reflects the credit charge, that neeeds to be reduced from the expected value of the transaction to determine its true value. It is calculated as a product of the loss given default, the probability of default and the average weighted exposure of future EPEs across the time horizon for the transaction.
The future exposures need to be discounted to the present, and occasionally the equations for CVA will state that explicitly. Similarly, in some more advanced dynamic models the correlation between EPE and PD is also accounted for. The conceptual ideal though remains the same: CVA=LGD*EPE*PD.