8005 Sample Questions Answers

A quanto is any instrument in which one asset is a foreign currency. Examples include any option on a foreign currency asset with the strike price in foreign currency, and an option on a foreign currency asset with the foreign currency risk hedged.

Correlation products refer to credit products on a basket of credits. Options on options represent an option to buy or sell an option in the future, and they are not 'quantos'. Similarly, not every two asset instrument is a quanto unless one of the two assets is a foreign currency.

The actuarial model considers defaults to follow a Poisson distribution with a given mean per period, and these are binary in nature, ie a default happens or it does not happen. The model does not consider the loss of value from credit downgrades, and focuses only on defaults. The model also does not consider default correlations between obligors. Therefore Choice 'c' is the correct answer.

The other choices are not true statements that would apply to the actuarial approach.

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.)

Forward premium or discount can be easily calculated as {(Forward rate - Spot rate) / Spot rate x 365/number of days]. In this case, it can be calculated as =((1.1652 - 1.1763) / 1.1763 ) * 365/91 = 3.785%, which is a discount as it is a negative number. It can also be interpreted as a discount as the forward price is lower than the spot price.

Convenience yield is the benefit from having access to the commodity - and if the convenience yield is very high, for example in a market where manufacturers must never run out of a particular raw material, then these can switch the total cost of carry (which include interest and storage costs, less convenience yields) to being negative. This causes forward prices to become lower than spot prices, a phenomenon known as backwardation.

Therefore Choice 'b' is the correct answer. If convenience yields are less than other carrying costs, then backwardation will not happen. The sign of convenience yields does not matter, what matters is their relative magnitude when compared to the other costs of carry.

To understand this in an intuitive way, consider that forward prices are nothing but spot prices, plus interest, plus storage costs, less convenience yields. If interest and storage costs are less than the convenience yield, the market will be backwarded.

Incremental capital (or incremental VaR, depending upon the context), is a measure of the change in the capital (or VaR) requirements if a certain change is made to a portfolio. It uses the 'before' and 'after' approach, ie find out what the capital requirement or VaR will be without the change, and what it will be after the change. The difference is the incremental capital or incremental VaR. It helps measure the change in risk as a result of a particular action, eg a change in a position.

Marginal capital or VaR on the other hand is a method to break down the capital requirement or the VaR so that it can be assigned to individual positions within the portfolio. The total of marginal capital or marginal VaR for all the positions in a portfolio adds up to the total capital requirements or total VaR. Note that marginal VaR is also called component VaR.

Therefore incremental capital is the correct answer to this question. The other choices are incorrect. In the exam, the question may be phrased differently, so try to keep in mind the different betweenincremental and marginal capital, which can be a bit confusing given what these terms mean in plain English.

There are multiple ways to incorporate scenario analysis for modeling operational risk capital - and the exact approach used depends upon the quantity of loss data available, and the quality of scenario assessments. Generally:

- If there is no past loss data available, scenarios are the only practical means to model operational risk loss distributions. Both frequency and severity estimates can be modeled based on scenario data.

- If there is plenty of past data available, scenarios can be used as a modifier for estimates that are based solely on data (for example, consider the MAX of the loss estimates at the desired quantile as provided by the data, and as indicated by scenarios)

- If high quality scenario data is available, and there is sufficient past data, one could mix scenario assessments with the loss data and fit the combined data set to create the loss distribution. Alternatively, both could be fitted with severity estimates and then the two severities could be parametrically combined.

In short, there is considerable flexibility in how scenarios can be used.

Statement I is therefore correct, and so is statement II as both indicate valid uses of scenarios.

Statement III is not correct because it may be okay to create severity estimates based on scenario data alone.

Statement IV is not correct because while using scenarios as modifiers to other means of estimation is acceptable, that is not the only use of scenarios.

A residential mortgage carries a prepayment option for the borrower, where in the event of a decrease in interest rates they are likely to repay the mortgage and refinance at the new lower rate. If rates go up, the bank does not have a similar option. If the volatility of the underlying interest rates increases, mortgage holders are more likely to be faced with new rates that are sufficiently lower to persuade them to refinance. This reduces the ability of the bank to continue to earn the higher interest rate it was earning before.

Therefore an increase in volatility of the mortgage interest rates decreases the value of the mortgage portfolio.

The same rationale applies to callable bonds, where the borrower has the option to call the bond.

There are two ways to think about this question: First, because the asset manager thinks that interest rates are going to decline, his profit will be maximized if he buys the bond with the greatest duration. The zero coupon bond has the greatest duration among the alternatives listed. Therefore Choice 'c' is the correct answer.

The second way to look at this question is to consider what is called 'reinvestment risk'. Yields to maturity calculations have an implicit assumption that any cash flows received prior to maturity are investible at the ytm rate. Thus, an yield to maturity calculation for a coupon bearing bond assumes that coupon payments get invested at the same rate as the calculated ytm from the time they are received till the time the bond matures. In an environment where interest rates fall, this assumption will not hold true. Reinvestment risk is the risk that coupons will not be able to earn the ytm that the bond was brought at - and the investor will be at a loss to the extent the money does not earn the ytm rate till the end of the investment. One way to reduce reinvestment risk is to minimize coupon receipts so the money stays invested as part of the bond, and the zero coupon bond helps to do exactly that.

Since AUD 1 = USD 0.6831, and USD 1 = SEK 8.1329, AUD 1 = SEK 8.1329*0.6831 = 5.5556.

It is important to remember how exchange rates are generally quoted. Most exchange rates are quoted in terms of how many foreign currencies does USD 1 buy. Therefore, a rate of 99 for the JPY means that USD 1 is equal to JPY 99. However, there are four major world currencies where the rate quote convention is the other way round - these are EUR, GBP, AUD and NZD. For these currencies, the FX quote implies how many US dollars can one unit of these currencies buy. So a quote of "1.1023" for the Euro means EUR 1 is equal to USD 1.1023 and not the other way round.

When calculating cross rates, it is important to pay attention to how the rates are quoted. This particular question is quoted in a very straightforward way because it specifies exactly what the rate means, eg by saying USD/AUD it clarifies that the rate is the number of USDs per AUD. If the question is not clear, remember how exchange rates are quoted - all are against 1 USD, except for EUR, GBP, AUD and NZD where it is the other way round.

For a number of processes, including many in finance, while a distribution such as the normal distribution is a good approximation of the distribution near the modal value of the variable, the same normal distribution may not be a good estimate of the tails. For this reason, the Pareto distribution is one of the distributions that is often used to model the tails of another distribution. Generally, if you have a set of observations, and you discard all observations below a threshold, you are left with what are called 'exceedances'. The threshold needs to be reasonably far out in the tail. If from each value of the exceedances you subtract the threshold value, the resulting dataset is estimated by the generalized Pareto distribution.

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The Pareto distribution has a 'shape parameter'. The average of two Pareto distributions with tail parametersξ1 andξ2 (ξis a Greek character, pronounced as 'sai' (saa-eee)), is the weighted average ofξ1 andξ2 with weights proportional to the number of observations in the datasets underlying the distributions.

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.

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.

Analytical methods are more 'efficient' than numerical methods in terms of computing power required, consistency of results and providing clarity on the inputs driving the results. Therefore 'efficient valuation' is not a reason to adopt numerical pricing methods over analytical methods.

It is much easier to incorporate changing stochastic volatility, discontinuous asset prices or other complex payoffs using numerical pricing methods. So these certainly represent good reasons to use numerical pricing methods for valuing exotics.

Therefore Choice 'b' is the correct answer.

Economic capital is sub-additive, ie, because of the correlation being less than perfect between the risks of the different business units, the total economic capital for the firm will be less than the sum of the EC for the individual business units. Therefore Choice 'b' is the correct answer.

In practice, correlations are difficult to estimate reliably, and banks often use estimates and corroborate their capital calculations with reference to a number of data points.

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 is true, 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.

Conditional default probabilities are 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.

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.

Commodity futures prices can be expressed as the summation of their spot prices and the carrying costs. Therefore any changes in either of these two would be a risk to the futures prices, and Choice 'b' is the correct answer. It is common to decompose complex commodity portfolios into underlying equivalent spot positions and the carrying costs, which includes interest, convenience yield and storage costs. For liquid commodities such as gold where changes of a short squeeze are low, interest costs dominate the carryings costs. Choice 'b' is the correct answer as it is most complete and covers the elements in the other choices. The 'lease rate' for a commodity is equivalent to (Fwd Price - Spot Price)/Spot Price, and comprises the interest and storage costs and the convenience yield. The other choices do not represent complete answers.

The distance to default is the number of standard deviations that expected asset values are away from the default point. The expression in Choice 'd' represents distance to default. Choice 'd' is the correct answer. The other choices are incorrect.

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.

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.

Choice 'a' is the correct answer. According to the Basel 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 any year in which annual gross income is negative or zero should be excluded from both the numerator and denominator when calculating the average.

This question requires a calculation of the present value of the future cash flows from the bond. The correct answer is $94.92, calculated as =(5/(1 + 5%)) + (5/(1+ 6%)^2) + (105/(1 + 7%)^3).

An out of the money convertible security behaves just like a regular debt security as the option isnear worthless. Therefore it is affected by changes in interest rates and the credit risk of the issuer, and unaffected by changes in the prices or volatility of the issuer's shares (the underlying).

Statement I is correct. Economic capital is the capital available to absorb unexpected losses, and credit ratings are also based upon a certain probability of default. Economic capital is often calculated at a level equal to the confidence required for the desired credit rating. For example, if the probability of default for a AA rating is 0.02%, then economic capital maintained at a 99.98% would allow for such a rating. Economic capital set at a 99.8% level can be thought of as the level of losses that would not be exceeded with a 99.8% probability.

Loss distributions are the product of the severity and frequency distributions, each of which are estimated separately. The total loss distribution is affected far more by the severity distribution than by the frequency distribution, therefore statement II is correct.

The Loss Distribution Approach (LDA) is one of the ways in which the requirements of the AMA can be satisfied, and not the other way round. Therefore statement III is incorrect.

Statement IV is correct as the total loss distribution is estimated using separate estimates of loss frequency and distributions.

Contingent premium options are options where no premiums are due upfront, and are due only at expiry and only if the option finishes in the money. (If this sounds too good to be true, remember that at expiry it is possible that the premiums due exceed the payoffs from the option. So there is no free lunch.) For this reason they are also called pay-later options.

They are simple combinations of a vanilla option and the 'right' number of cash-or-nothing options. The buyer of a contingent premium option has effectively purchased a vanilla option and sold enough number of cash-or-nothing options so that the net premium due at inception is zero.

Therefore statement I, II and III are correct and Choice 'b' is the correct answer.

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

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.

All the reasons and risks presented above are valid reasons for using scenario analysis, except V and VI - ie, the need to reduce the complexity of calculations is not a valid reason for using scenario analysis. Similarly, making operational risk capital estimates match management's desired capital allocation targets is also not a valid reason. Capital calculations are intended to provide adequate capital for managing the risk from operations, regardless of what management may desire them to be.

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.

Units of Measure for operational risk are homogenous groupings of risks to allow sensible modeling decisions to be made. For example, some risks may be fat-tailed, for example the risk of regulatory fines. Other risks may have finite tails - for example damage to physical assets risk (DPA) may be limited to the value of the asset in the question.

Additionally, risk reporting may need to be done at the line of business, legal entity or regional basis, and in order to be able to do, so the right level of granularity needs to be captured in the risk modeling exercise. The level of granularity applied is called the 'unit of measurement' (UoM), and it is okay to adopt all of the choices listed above as the dimensions that describe the unit of measure.

Note that it is entirely possible, even likely, to use legal entity, risk type, region, business and other dimensions simultaneously, though doing so is likely to result in an extremely large number of UoM combinations. That can be addressed by then subsequently grouping the more granular UoMs into larger UoMs, which may ultimately be used for frequency and severity estimation.

The London Interbank Offered Rate (LIBOR) is published by the British Bankers' Association (BBA). The BBA polls the rates offered by at least eight banks drops the top and bottom quartile, and averages the middle two quartiles of the rates to arrive at the LIBOR.

The peaks-over-threshold model is used when losses over 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.

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 answer and the other statements are incorrect.

In the Standardized Approach, banks’ activities are divided into eight business lines: corporate finance, trading & sales, retail banking, commercial banking, payment & settlement, agency services, asset management, and retail brokerage. Therefore Choice 'c' is the correct answer.

Futures contracts carry no gamma. Only options have gamma. Choice 'a' is the correct answer. Any instrument whose price varies in a linear fashion with respect to the underlying will have gamma equal to zero.

Choice 'd' represents the Basel II requirement, all other choices are incorrect.

Everything else remaining the same, an increase in the rate of dividends causes the value of call options to fall and the value of put options to rise. Therefore, Choice 'b' is the correct answer. (In the exam, the question could address either a call or a put option, so be aware of the answer in either case).

To understand this, consider how dividends are accounted for when valuing an option using the Black Scholes model. Future dividends are discounted to the present using the risk free rate andthis discounted value is reduced from the spot price used in the BSM valuation. Effectively, this reduces the spot price used in the BSM formula. When the spot price reduces, and the exercise price remains the same, then the value of the call option goes down. In the same way, when spot price is reduced by the present value of dividends (and the exercise price stays the same), obviously the put option becomes more valuable. Therefore an increase in the rate of dividends increases the value of the put option.

There is another intuitive way to think about this: A call option is like a long position in the stock, but the holder of the call option is not entitled to receive dividends (unlike the holder of the stock). Since the holder of the call option has to forego the dividends, he is willing to pay less for the option; or in other words, the value of the call reduces.

In the same way, a put option is like having a short position in the stock. The holder of the short position has to borrow the stock in order to get into the short position in the first place. When dividends are paid, the holder of the short stock position has to make good any dividends that might be paid to the lender of the stock. The holder of a put option does not have to make any such payments. Therefore the put option is more valuable, and the existence of dividends (or an increase in dividends) increases the value of the put option.

(Try this out using the Black Scholes Excel model given under the tutorials by varying the spot price.)

If capital calculations are done in a standard way regardless of risk (as reflected by credit ratings), then it creates a perverse incentive for the lenders' employees to lend to the riskiest borrowers that offer the highest expected returns as there is no incentive to 'save' on economic capital requirements that are equal for both safe and unsafe borrowers. Therefore statement I is correct.

Given that the portfolio of such an institution is likely to then comprise poor quality borrowers, and economic capital would be based upon 'average' expected ratings, it is likely to carry lower economic capital given its exposures. Therefore any such economic risk capital model is likely to understate economic capital requirements. Therefore statement IV is correct.

Statements II and III are incorrect and Choice 'b' is the correct answer.

When a operational loss frequency distribution (which, for example, may be based upon a Poisson distribution) and a loss severity distribution (for example, based upon a lognormal distribution), it is assumed that the frequency of losses and the severity of the losses are completely independent and do not impact each other. Therefore statement II is correct, and the others are not valid assumptions underlying the operational loss distribution.

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 Options Theoretic approach to calculating economic capital is a top-down approach that considers the value of capital as being equivalent to a call option with a strike price equal to the notional value of the debt - ie, the shareholders have a call option on the assets of the firm which they can acquire by paying the debt holders a value equal to their notional claim (ie the face value of the debt). Therefore Choice 'a' is the correct answer and the other choices are incorrect.

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.

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 or other events.

In a Dutch auction, the buyers put in their bids and the price at which the entire auction clears is the price at which each bidder receives the security. For example, if Bank A bids 5.5% for a bond, Bank B bids 5.6% and Bank C bids 5.7% and the total amounts bid by these three banks are enough to clear the auction, each of the banks will receive the bond at the price paid by the lowest successful bidder, ie Bank C. This is even though Banks A and B had bid higher (remember that bidding a higher yield means offering a lower price).

In a standard auction, every bidder pays the price they bid.

In a Dutch auction, there is an incentive to bid aggressively if a participant believes the final winning bid will be lower.

Each of the choices describes various scenarios related to the issue of bonds. A when-issued market is a market in government securities where securities are traded as forward contracts prior to their issue. Choice 'c' is the correct answer.

Choice 'd' refers to a 'bought deal'. Choice 'b' refers to the 'grey market', usually in corporate bonds. Choice 'a' refers to a fixed price re-offer mechanism.

An option on a futures contract is like any other option contract, and only the option premium is due upfront. If the option is exercised, then the futures contract comes into existence and futures margins become due in the normal way. Therefore Choice 'b' is the correct answer.

The exact formula for VaR is = -(Zασ+μ), where Zαis the z-multiple for the desired confidence level, andμis the mean return. Now Zαis always a negative number, or at least will certainly be provided the desired confidence level is greater than 50%, andμis often assumed to be zero because generally for the short time periods for which market risk VaR is calculated, its value is very close to zero.

Therefore in practice the formula for VaR just becomes -Zασ, and since Z is always negative, we normally just multiply the Z factor without the negative sign with the standard deviation to get the VaR.

For this question, there are two ways to get the answer. If we use the formula, we know that -Zασ= 250,000 (asμ=0), and therefore -Zασ-μ= 250,000 - 10,000 = $240,000.

The other, easier way to think about this is that if the mean changes, then the distribution's shape stays exactly the same, and the entire distribution shifts to the right by $10,000 as the mean moves up by $10,000. Therefore the VaR cutoff, which was previously at -250,000 on the graph also moves up by 10k to -240,000, and therefore $240,000 is the correct answer.

The other choices are intended to confuse by multiplying the z-factor for the 99% confidence level with 10,000 etc.

There are two main theories that explain an upward sloping yield curve. The first is the market expectations hypothesis (called 'pure expectations'). According to this explanation, the yield curve represents investor expectations of future yields, and forward rates are predictors of future interest rates. The yield curve slopes upwards when investors expect interest rates to go up in the future. Thus, statement I is correct. By the same logic, statement II is incorrect.

The second explanation for an upward sloping yield curve is the liquidity preference theory - according to which investors value liquidity and are prepared to pay more for instruments that mature earlier. Having their money tied up in longer maturity instruments increases all kinds of risks, and therefore longer term instruments are priced lower than instruments maturing earlier. Since the price of instruments that mature earlier is higher, their yield is lower than that of longer dated securities, thereby leading to an upward sloping yield curve. Therefore statement III is correct.

Statement IV actually explains why an yield curve may be downward sloping - in fact an inverted yield curve is considered an indicator of an upcoming recession. Therefore statement IV does not explain an upward sloping yield curve, and is therefore not a correct choice for the answer.

Thus statements I and III correctly explain an upward sloping yield curve. Other choices are incorrect.

Governance structures specify the policies, principles and procedures for making decisions about corporate direction. They distribute rights and responsibiliies among stakeholders that typically include executive management, employees, the board etc. Statement I is therefore correct.

"Cybernetics is a transdisciplinary approach for exploring regulatory systems, their structures, constraints, and possibilities. In the 21st century, the term is often used in a rather loose way to imply "control of any system using technology" (Wikipedia). Governance literature has been affected by cybernetics, which is not the same thing as information security or cyber security. Statement II is incorrect.

Corporate governance includes risk governance, and not the other way round. Therefore statement III is incorrect.

The Cadbury Report, titled Financial Aspects of Corporate Governance, was a report issued in the UK in December 1992 by "The Committee on the Financial Aspects of Corporate Governance". The report is eponymous with the chair of the committee, and set out recommendations on the arrangement of company boards and accounting systems to mitigate corporate governance risks and failures. Statement IV is therefore correct.

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.

Everything else remaining the same, an increase in the rate of dividends causes the value of call options to fall and the value of put options to rise. Therefore, Choice 'b' is the correct answer. (In the exam, the question could address either a call or a put option, so be aware of the answer in either case).

To understand this, consider how dividends are accounted for when valuing an option using the Black Scholes model. Future dividends are discounted to the present using the risk free rate and this discounted value is reduced from the spot price used in the BSM valuation. Effectively, this reduces the spot price used in the BSM formula. When the spot price reduces, and the exercise price remains the same, then the value of the call option goes down. In the same way, when spot price is reduced by the present value of dividends (and the exercise price stays the same), obviously the put option becomes more valuable. Therefore an increase in the rate of dividends increases the value of the put option.

There is another intuitive way to think about this: A call option is like a long position in the stock, but the holder of the call option is not entitled to receive dividends (unlike the holder of the stock). Since the holder of the call option has to forego the dividends, he is willing to pay less for the option; or in other words, the value of the call reduces.

In the same way, a put option is like having a short position in the stock. The holder of the short position has to borrow the stock in order to get into the short position in the first place. When dividends are paid, the holder of the short stock position has to make good any dividends that might be paid to the lender of the stock. The holder of a put option does not have to make any such payments. Therefore the put option is more valuable, and the existence of dividends (or an increasein dividends) increases the value of the put option.

(Try this out using the Black Scholes Excel model given under the tutorials by varying the spot price.)

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.

When modeling operational loss frequency distribution (which, for example, may be based upon a Poisson distribution) and a loss severity distribution (for example, based upon a lognormal distribution), it is assumed that the frequency of losses and the severity of the losses are completely independent and do not impact each other. Therefore Choice 'a' is correct, and the others are not valid assumptions underlying the operational loss modeling.

Once each of these distributions has been built, a random number is drawn from each to determine a loss scenario. The process is repeated many times as part of a Monte Carlo simulation to get a the loss distribution.

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 x 250 = 3750. Choice 'a' is the correct answer.

If the spot rate is 1.1010 and the forward is 1.1040, the swap rate is 30 "points" (= 1.1040 - 1.1010). The annualized swap premium is the swap premium divided by the spot rate, and therefore =0.0030/1.1010 =0.27%, or 27 basis points.