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A forward rate agreement allows one of the parties to borrow an amount at a rate for a length of time, all of which are agreed in advance. Consider a "3 x 6" FRA. This allows a fixed rate borrowing starting at 3 months till the end of 6 months. This is economically equivalent to holding a zero coupon bond till the end of 6 months, and being short another zero coupon bond till the end of 3 months (or the other way round, depending upon which end of the FRA you are on). Therefore Choice 'c' is the correct answer.

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.

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.

This question is different in that it uses terminology you will not find in the PRMIA handbook. Yet it is important to understand these as there may be a question based on this slightly different terminology. (It is only the terminology that is different, the concepts are the same.)
If you read the PRMIA handbook, there are three methods of calculating VaR: Analytical or parametric, historical simulation and Monte Carlo simulations. There is one more way of categorizing the methods of calculating VaR, and these are as follows:
1. Local valuation: This refers to analytical or parametric VaR. This relies upon a neat statistical formula to calculate VaR and assumes a normal distribution. It also relies upon a known covariance matrix between the different components of VaR. Local valuation based VaR is further subdivided into two types:
a. Linear VaR: Linear VaR is calculated assuming the portfolio is linear, and its value changes just based upon the delta of the portfolio. In such cases, once a change (eg, in stock values) is known, that change is multiplied by the delta alone to get the VaR. Second order effects, such as gamma or convexity are ignored. b. Non-linear VaR: Non linear analytical VaR is calculated using both delta and the second derivative, ie gamma or the convexity. This is more accurate if the portfolio is non-linear. The key thing about 'local revaluation' VaR is that it does not require us to reprice or completely value all instruments in the portfolio. All we have to know is the delta (or the gamma and convexity as well) and multiply that with the number of standard deviations of change in the risk factor that we are interested in. So if we are considering a bond, we don't have to recalculate the new value of the bond as we can just use the delta.
This can be a significant computational advantage for a large financial institution where there may be a large number of positions.

2. Full revaluation: This refers to a VaR method where the asset in question is fully repriced based on the new value of the risk factor - and this includes both historical and Monte Carlo based VaR methods. Local revaluation, or analytical method based VaR is computationally easier to calculate, specially if based on just the delta-normal method (ie ignoring second order effects from convexity or gamma). But it will give incorrect results if the portfolio includes substantial non-linearity or other complexities. The full revaluation methods will always give the correct results, but they can be computationally difficult to arrive at. Statement
I is completely inaccurate - local revaluation methods do take correlations into account through the correlation or covariance matrices. Statement IV is false too - the 'delta normal' VaR refers to Var calculations based upon just the delta and do not account for the convexity or optionality.
Statements II and III are correct. Therefore Choice 'c' is the correct answer.

The VaR of a fixed income instrument is given by Duration x Volatility of the interest rate x z-factor corresponding to the confidence level. Therefore as the volatility of the yield goes up, the value at risk for the instrument goes up. At the same time, the value of the bond is given by the present value of its future cash flows using the current yield curve. This value is unaffected by the volatility of the underlying interest rates. Therefore a change in volatility of interest rates does not affect the value of the bond.
Therefore Choice 'd' represents the correct answer.

Using the beta for VaR calculations is a significant simplification based on the CAPM and the assumption that any specific risks are diversified away. The one thing a risk model based on the CAPM does not consider is the specific risk of individual stocks, because, as mentioned, these are considered to be offsetting each other so that the portfolio only carries market risk reflected in the beta. Therefore Choice 'c' is not true and therefore the correct answer.

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 migrations on 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. This approach does not consider the loss of value from deterioration in credit quality (unless the deterioration implies default).

Regardless of the approach being followed by a bank (ie, whether foundation IRB or advanced IRB), it must make its own estimates for the probability of default. Banks following the foundation IRB approach may use values set by the supervisor for the other three parameters, though those following the advanced IRB approach may use their own estimates for all four inputs. (This is also the difference between advanced IRB and the foundation IRB approaches.) Therefore Choice 'a' is the correct answer. Also note the four difference elements that go as inputs to the internal ratings based approach in the choices provided.

In an interest rate swap, the parties agree to exchanging interest rate payments, with one party being a fixed interest rate payer and the other paying floating rates. The party receiving fixed rates and paying floating can be considered to be long a fixed rate bond and short a floating rate note. Therefore an IRS can be modeled as a combination of a fixed coupon bond and a floating rate note. Choice 'b' is the correct answer.

Choice 'c' is the correct answer. Refer to the detailed loss event type classification under Basel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.

Parametric VaR relies upon reducing a portfolio's positions to risk factors, and estimating the first order changes in portfolio values from each of the risk factors. This is called the delta approximation approach.
Risk factors include stock index values, or the PV01 for interest rate products, or volatility for options. This approach can be quite accurate and computationally efficient if the portfolio comprises products whose value behaves linearly to changes in risk factors. This includes long and short positions in equities, commodities and the like.
However, where non-linear products such as options are involved and large moves in the risk factors are anticipated, a delta approximation based valuation may not give accurate results, and the VaR may be misstated. Therefore in such situations parametric VaR is not advised (unless it is extended to include second and third level sensitivities which can bring its own share of problems). Parametric VaR also assumes that the returns of risk factors are normally distributed - an assumption that is violated in times of market stress. So if it is known that the risk factor returns are not normally distributed, it is not advisable to use parametric VaR.

Model risk is the risk that a model built for estimating a variable will produce erroneous estimates. Model risk is caused by a number of factors, including: a) Misspecifying the model: For example, using a normal distribution when it is not justified. b) Model misuse: For example, using a model built to estimate bond prices to estimate equity prices c) Parameter estimation errors: In particular, parameters that are subjectively determined can be subject to significant parameter estimation errors d) Programming errors: Errors in coding the model as part of computer implementation may not be detected by end users e) Data errors: Errors in data used for building the model may also introduce model risk Therefore the correct answer is d, as all the choices are a source of model risk.

The major problem with using return on equity as a measure of performance is that return on equity is not adjusted for risk. Therefore, a riskier investment will always come out ahead when compared to a less risky investment when using return on equity as a performance metric.
Return on equity does not ignore the effect of leverage (though return on assets does) because it considers the income attributable to equity, including income from leveraged investments. Return on equity is generally measured after interest and taxes at the company wide level, though at business unit level it may use earnings before interest and taxes. However this does not create a problem so long as all performance being covered is calculated in the same way.
Cash flows being different from accounting earnings can create liquidity issues, but this does not affect the effectiveness of ROE as a measure of performance.

The bank will not be able to recover the principal advanced on this loan if both the home buyer defaults, and the house value falls to less than $1m, ie the price moves adversely by more than $500k, which is $- 500k/$150k = -3.33. (Note that 150k is the 1 year volatility in dollars, ie $1.5m * 10%).
The probability of both these things happening together is just the product of the two probabilities, one of which we know to be 5%. The other is also certainly a small number, and intuitively it is clear that the probability of both the things happening together will be less than 1%.

For a more precise answer, we can calculate the probability of the house price falling by 3.33 standard deviations by calculating the area under the standard normal curve to the left of -3.33. This indeed is a very small number (actually equal to NORMSINV(- 3.33)=0.00043), which when multiplied by the probability of default of the home buyer at 5% is certainly going to be less than 1%. Therefore Choice 'b' is the correct answer.

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.

Choice 'a' is the correct answer. The other choices represent non-sensical statements.

If the confidence levels for a VaR estimate are set too high, there may never be any exceedences, ie actual losses will never exceed VaR estimates. For limit setting, we want actual losses to exceed the VaR estimates enough number of times as during the year so that the limits are considered seriously. If the VaR estimate is exceeded too many times, or never, then it is unlikely to be considered seriously. Therefore Choice 'd' is the correct answer.

The other answers are incorrect as they either require the VaR to be too high (ie zero or rare excess loss situations) or too low (ie there will be too many cases of excess loss situations to be taken seriously).

Marginal probabilities of default are the probabilities for default for a given period, conditional on survival till the end of the previous period. Cumulative probabilities of default are probabilities of default by a point in time, regardless of when the default occurs. If the marginal probabilities of default for periods 1, 2... n are p1, p2...pn, then cumulative probability of default can be calculated as Cn = 1 - (1 - p1)(1-p2)...(1-pn). For this question, we can calculate the probability of default for year 3 as =1 - (1-2%)*(1-3%)*(1-4%) = 8.74%

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.

EDFs are derived from the distance to default. The distance to default is the number of standard deviations that expected asset values are away from the default point, which itself is defined as short term debt plus half of the long term debt. Therefore debt levels affect the EDF. Similarly, asset values are estimated using equity prices. Therefore market capitalization affects EDF calculations. Asset volatilities are the standard deviation that form a place in the denominator in the distance to default calculations. Therefore asset volatility affects EDF too. The risk free rate is not directly factored in any of these calculations (except of course, one could argue that the level of interest rates may impact equity values or the discounted values of future cash flows, but that is a second order effect). Therefore Choice 'b' is the correct answer.

Normal mixtures have higher peaks, and therefore higher kurtosis than a normal distribution with an equivalent mean and variance. Therefore statement I is correct. The term 'normal mixture' literally means that - the distribution is derived by summing two or more normal distributions. Statement II is correct. One interesting thing to note about normal mixtures is that their mean and variances are just the weighted averages of the means and variances of their underlying component normal distributions. But their kurtosis is higher than that of either of the components. They are more peaked, and have fatter tails, a property that makes them useful in finance. Unfortunately there is no analytical formula for calculating VaR based on normal mixtures. However, we can back solve for VaR (using Excel's Solver, for example), given we know the density functions for the underlying normal distributions. Statement III is not correct.

All product pricing should reflect the cost of maintaining the liquidity required to support a product. This is regardless of the accounting treatment for the product, ie irrespective of whether the product is on or off balance sheet. Therefore statement I is incorrect. The time horizon to consider for liquidity risk management is determined taking into account a number of factors, which include both the speed at which new sources of liquidity can be generated and any applicable regulatory requirements. Statement II is correct. Managing collateral, both collateral received and collateral posted with counterparties, is an important aspect of liquidity risk management as liquidity problems often manifest themselves in the form of margin calls requiring collateral to be posted. Statement III is therefore correct.
The maturity period of the different sources of capital funding for a bank, for example equity capital, preferred shares, long term debt etc quite clearly has a significant impact on liquidity needs. Stable sources of funds such as equity or preferred capital, or debt that is not maturing shortly help the liquidity position. Statement IV is therefore correct.
Choice 'b' is the correct answer.

EVT, when used in the context of operational risk measurement, focuses on tail events and attempts to build a distribution of losses beyond what is covered by VaR. Statements I, II and II are correct. Statement IV describes conditional VaR (CVAR) and not EVT.
Choice 'c' is the correct answer.

In December 2009 the BIS came out with a new consultative document on liquidity risk. Given the events of 2007 - 2009, it has been clear that a key characteristic of the financial crisis was the inaccurate and ineffective management of liquidity risk
The paper two separate but complementary objectives in respect of liquidity risk management: The first objective relates to the short-term liquidity risk profile of institution, and the second objective is to promote resiliency over longer-term time horizons. The paper identifies the following two ratios - you should be aware of these - though I am not sure if these will show up in the PRMIA exam:
1. Liquidity Coverage Ratio addresses the ability of an institution to survive an acute liquidity risk stress scenario lasting one month. It is calculated as follows:
Liquidity Coverage Ratio = Stock of high quality liquid assets/Net cash outflows over a 30- day time period 2. Net Stable Funding Ratio has been developed to capture structural issues related to funding choices.
Net Stable Funding Ratio = Available amount of stable funding/Required amount of stable funding Both ratios should be equal to or greater than 1. The statement contains detailed definitions of what is included or excluded from each of the terms used in the calculations for each of the ratios. In addition, the standard also describes the what the 'acute' scenario should include (things such as a 3 notch credit downgrade, reduction in retail deposits etc) Therefore Choice 'b' is the correct answer. Book Value to Share Price and Earnings Per Share are accounting measures unrelated to liquidity.

A computation of Altman's Z-score considers the following ratios:
- Working capital to total assets
- Retained earnings to total assets
- EBIT to total assets
- Market cap to debt
- Sales to total assets
It does not consider Net Income to total assets, therefore Choice 'c' is the correct answer. This makes sense as net income is after interest and taxes, both of which are not relevant for considering the cash flows for debt servicing.

Refer to the detailed loss event type classification under Basel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.

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 sort of 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 and then 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.

Normal mixtures, EVT and the t-distribution are all possible solutions addressing the issue of heavy tails in financial returns.
EWMA and GARCH address volatility clustering, which is the other problem when doing risk calculations.
Therefore Choice 'b' is the correct answer as EWMA is not used to address heavy tails but volatility clustering.

Hazard rate x Loss given default = CDS quote. In other words, Hazard rate x (1 - recovery rate) = CDS quote. We can therefore calculate the hazard rate for this problem as 200 bps/(1 - 40%) = 3.33%.

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. This problem can be solved by combining the variance of the returns from the two consecutive periods in the same way as one would combine the variance of different assets that have a given correlation. In such cases we know that: Variance (A + B) = Variance(A) + Variance(B) + 2*Correlation*StdDev(A)*StdDev(B). The standard deviation can be calculated by taking the square root of the variance. Therefore the combined volatility over the two months will be equal to =SQRT((5%^2) + (5%^2) + 2*0.3*5%*5%) = 8.062%. All other answers are incorrect.

The three pillars under Basel II are minimum capital requirements, supervisory review process and market discipline. Therefore statement I is false. The other two statements are accurate. Therefore Choice 'd' is the correct answer.

A situation where a firm has more liabilities than assets does not necessarily imply default, so long as the firm is able to pay its obligations when they come due. Therefore, short term debts have a greater bearing on a firm's default than longer term debt. However, this is not to say that merely having enough to pay off the short term debts (ie debts due within one year) is enough to avoid default. Over time, the long term debt will also be turning to short term debt, and it may not be possible for the firm to roll over its liabilities without lenders considering the long term debt. The KMV approach considers the entire short term debt and half of the long term debt as the critical value of assets below which default will be triggered. Therefore Choice 'c' is the correct answer.

High frequency and low severity risks, for example the risks of fraud losses for a credit card issuer, may have high expected losses, but low unexpected losses. In other words, we can generally expect these losses to stay within a small expected and known range. The capital requirement will be the worst case losses at a given confidence level less expected losses, and in such cases this can be expected to be low.
On the other hand, medium severity medium frequency risks, such as the risks of unexpected legal claims, 'fat-finger' trading errors, will have low expected losses but a high level of unexpected losses. Thus the capital requirement for such risks will be high. It is also worthwhile mentioning high severity and low frequency risks - for example a rogue trader circumventing all controls and bringing the bank down, or a terrorist strike or natural disaster creating other losses - will probably have zero expected losses & high unexpected losses but only at very high levels of confidence. In other words, operational risk capital is unlikely to provide for such events and these would lie in the part of the tail that is not covered by most levels of confidence when calculating operational risk capital. Note that risk capital is required for only unexpected losses as expected losses are to be borne by P&L reserves. Therefore the operational risk capital requirements for a low severity high frequency risk is likely to be low when compared to other risks that are lower frequency but higher severity.
Thus Choice 'c' is the correct answer.

A high score under the probit and logit models indicates a higher default risk, while under Altman's methodology it indicates a lower default risk. Therefore Choice 'd' is the correct answer.

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.

Normal mixtures address fat or heavy tails, not volatility clustering. Therefore statement I is not correct.
Statement II is not correct. Where VaR is calculated at low levels of confidence, VaR based on normal mixtures may be lower than that under a normal assumption. This is no different than for other fat tailed distributions. Statement III is correct. In situations where multiple market scenarios can unfold with a given probability, and each scenario is normal, we can express the result with a normal mixture where the underlying normal distributions have the probabilities of the different scenarios.

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 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.

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.

A bullet bond is a bond that pays coupons covering interest during the life of the bond and the principal at maturity. An amortizing loan pays the interest as well as a part of the principal with every payment.
Therefore, the exposure of the amortizing loan continually reduces, and approaches zero towards the end of its life. The bullet bond will always have a higher exposure at any time during its life when compared to an equivalent amortizing loan. Hence Choice 'd' is the correct answer.

Loss provisioning is intended to cover expected losses. Economic capital is expected to cover unexpected losses. No capital or provisions are set aside for losses in excess of unexpected losses, which will ultimately be borne by equity.
Choice 'd' is the correct answer.

The VaR in this case will be the top quintile of observations. In this case, since there are exactly 100 observations, this would mean the worst return would become the VaR. Therefore Choice 'b' is the correct answer. Choice 'a' and Choice 'c' make no sense. This highlights that at higher confidence levels, fewer and fewer observations impact the VaR if we are using historical simulation based VaR.

According to the option pricing approach developed by Merton, the shareholders of a firm have a put on the assets of the firm where the strike price is equal to the face value of the firm's debt. This is just a more complicated way of saying that the debt holders are entitled to all the assets of the firm if these assets are insufficient to pay off the debts, and because of limited liability of the shareholders of a corporation this part payment will fully extinguish the debt. A firm will default on its debt if the value of the assets falls below the face value of the debt. Therefore Choice 'a' is the correct answer. All other choices are incorrect. (There are two ways to consider this sort of optionality, and I have mentioned only one for this question: 1. The equity holders can sell the assets of the firm to the debt holders at a price equal to the face value of the debt, ie a put. (ie they can extinguish their liability to the debt holders in full by handing them the assets of the firm, effectively selling them the assets at the value of the debt)
2. The equity holders have a long position in a call option where they can keep the assets of the firm by paying a price equal to the face value of the debt (ie, they can pay off the debt holders and keep the assets) For this question, perspective 1 applies but you should be aware of the second one too as a question may reference that view point.)

Choice 'b' is the correct answer. All other answers are incorrect. Refer to the detailed loss event type classification under Basel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.

Suppose during a historical event interest rates rose from 2% to 2.25%. This can be understood as a change of either 25 basis points, or a change of 12.5%. When applied to the current portfolio when interest rates are 0.50%, we may model this 'shock' as either a rise to 0.75%, or 0.5625% (ie a rise of 12.5% over existing levels). The former is called an absolute shock, and the latter a relative shock. I is true as relative shocks can never change the sign of a risk factor. Yet interest rate changes are modeled as absolute changes as relative shocks can get artificially amplified or attenuated if the current level of interest rates is too different from those that existed during the crisis being modeled. Therefore II is true. III and IV are false as volatility is modeled as a relative shock and spreads are modeled as absolute shocks.

The difference between the yields on corporate bonds and the risk free rate is called the corporate bond spread. Widening of the spread means that corporate bonds yield more, and their yield curve shifts upwards, driving down bond prices. The increase in the spread is a consequence of the market risk from holding these interest rate instruments, which is a part of market risk. If the reduction in the value of the portfolio were to be caused by a change in the credit rating of the bonds held, it would have been a loss arising due to credit risk. Counterparty risk and liquidity risk are not relevant for this question. Therefore Choice 'c' is the correct answer.

High frequency and low severity risks, for example the risks of fraud losses for a credit card issuer, may have high expected losses, but low unexpected losses. In other words, we can generally expect these losses to stay within a small expected and known range. The capital requirement will be the worst case losses at a given confidence level less expected losses, and in such cases this can be expected to be low.
On the other hand, medium severity medium frequency risks, such as the risks of unexpected legal claims, 'fat-finger' trading errors, will have low expected losses but a high level of unexpected losses. Thus the capital requirement for such risks will be high. It is also worthwhile mentioning high severity and low frequency risks - for example a rogue trader circumventing all controls and bringing the bank down, or a terrorist strike or natural disaster creating other losses - will probably have zero expected losses & high unexpected losses but only at very high levels of confidence. In other words, operational risk capital is unlikely to provide for such events and these would lie in the part of the tail that is not covered by most levels of confidence when calculating operational risk capital. Note that risk capital is required for only unexpected losses as expected losses are to be borne by P&L reserves. Therefore the operational risk capital requirements for a low severity high frequency risk is likely to be low when compared to other risks that are lower frequency but higher severity.
Thus Choice 'c' is the correct answer.

Offsetting trades with other counterparties will not reduce credit exposure to a given counterparty. All other choices represent means of reducing credit risk. Therefore Choice 'c' is the correct answer.

Economic capital is a measure of the level of capital needed to maintain a desired 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.

The immediate impact of the default would be to improve the liquidity available in the short term due to the pay out from the CDSs. It is also important to consider the impact on liquidity from the occurence of a default even in situations where CDS protection may not have been purchased. In such cases, there may be a nearer term payout in the form of the recovery rate. Of course, recovery payments are generally not realized for longer periods of time as court cases linger on, but there is a good likelihood that a payment, albeit lower in total, is likely to be realized sooner than the maturity of the bond in cases where the bond is a longer term bond. At the same time, any interest payments, and the final principal payment, which may have been included in liquidity projections, will not occur.

The Earnings Volatility approach to calculating economic capital is a top down approach that considers economic capital as being the capital required to make for the worst case fall in earnings, and calculates EC as equal to the worst case decrease in earnings capitalized at the rate of return expected of the firm.

The worst case decrease in earnings, or the earnings-at-risk can only be stated at a given confidence level, and is equal to the Expected Earnings less Earnings under the worst case scenario.

Choice 'b', Choice 'c' and Choice 'a' correctly describe a bilateral close out netting as recommended by the ISDA. However Choice 'd' is not correct as it suggests individual settlement of transactions without netting which is the whole point of bilateral close out netting.

The binomial, Poisson and the negative binomial distributions can all be used to model the loss event frequency distribution. The omega distribution is not used for this purpose, therefore Choice 'a' is the correct answer. Also note that the negative binomial distribution provides the best model fit because it has more parameters than the binomial or the Poisson. However, in practice the Poisson distribution is most often used due to reasons of practicality and the fact that the key model risk in such situations does not arise from the choice of an incorrect underlying distribution.

Choice 'd' is the correct answer, as laid down in the Basel II document. The other choices are incorrect.

Statement I is true. According to the statement CP08/24: Stress and scenario testing (December 2008) issued by the FSA in the UK, an underlying objective of reverse stress tests is to ensure that a firm can survive long enough after risks have crystallized for one of the following to occur:
- the market decides that its lack of confidence is unfounded and recommences transacting with the firm;
- the firm down-sizes and re-structures its business;
- the firm is taken over, or its business is transferred in an orderly manner; or - public authorities take the firm over, or wind down its business in an orderly manner. Statement II and III
are true. The same statement clarifies the intention of the reverse stress testing requirement, which is to encourage firms to: explore more fully the vulnerabilities of theirbusiness model (including `tail risks');
make decisions that better integrate business and capital planning; and improve their contingency planning. Statement IV is incorrect. Since the question is asking for the statement which is NOT an objective for reverse stress tests, Choice 'b' is the correct answer. The same statement clarifies that the introduction of a reverse-stress test requirement should not be interpreted as indicating that the FSA is
pursuing a `zero-failure' policy. In the FSA's view, such a policy is neither possible, nor desirable.

First of all, if prices are lognormally distributed, that implies the returns (which are equal to the log of prices) are normally distributed. To say that prices are lognormally distributed is just another way of saying that returns are normally distributed. Since the correlation between the two securities is zero, this means their variances can be added. But standard deviations, or volatilities cannot be added (they will be the square root of sum of variances). VaR is nothing but a multiple of standard deviation, and therefore it is not additive if correlations are anything other than 1 (ie perfect positive, which would imply we are dealing with the same asset). Therefore VaR(A+B)=SQRT(VaR(A)^2 + VaR(B)^2). This implies the combined VaR of a portfolio with these two securities will be less than the sum of VaRs of the two individual securities.
Thus Choice 'c' is the correct answer and the other choices are wrong.