Three parameters define economic credit capital: the risk horizon, ie the time horizon over which the risk is being assessed; the confidence level, ie the quintile of the loss distribution; and the definition of credit losses, ie whether mark-to-market losses are considered in addition to default-only losses. The probability of default is not a parameter within the control of the risk manager, but an input into the capital calculation process that he has to estimate. Therefore Choice ' c ' is the correct answer.

Credit reserves are created in respect of expected losses, which are considered the cost of doing business. Unexpected losses are borne by economic credit capital, which is a part of economic capital. Therefore Choice ' c ' 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.

Note that events of default under the ISDA MA are caused by one of the parties that is considered ' at fault ' . In contrast, " termination events " are events for which no one is at fault, for example changes in legislation, illegality etc that still justify termination of the transactions under the contract.

The ISDA MA describes the following 8 types of events of default:

1. failure of pay or deliver

2. breach of agreement

credit support default

4. misrepresentation

5. default under specified transaction

6. cross default

7. bankruptcy

8. merger without assumption

All of the options presented in the question are events of default.

A standard model for representing asset returns in finance is the Geometric Brownian Motion process, and returns according to this model can be estimated by the expression given in Choice ' b ' . Note that prices according to this model are log-normally distributed, and returns are normally distributed.

All the factors listed above contributed to systemic failure. Liquidity risk was not on the radar of regulators, and was a second priority for risk managers, and most of the focus was on capital adequacy as liquidity was thought to be an unlikely problem. Liquidity, regardless of capital adequacy, was the primary cause of failure of a number of institutions during the crisis.

Similarly, stress tests proved to be much milder than the shocks that were actually experienced, and the strategy of ' originate and distribute ' implied that the mortgage and other debt originators had no interest in any due diligence as they intended to package and sell the debt to other investors.

Therefore Choice ' d ' is the correct answer.

Statement I is correct. The financial system proved to be stable against small shocks and disturbances, or shocks of a particular type (eg, the dotcom crash, the wars in the Persian Gulf); but rather fragile against other types of shocks, including disturbances to key market participants caused by a worsening of mortgage defaults. Statement II is incorrect. Financial innovation, in particular the slicing and dicing of ' risk ' through securitization, significantly increased interrelationships, dependence on the same risk factors, and the complexity of the system as a whole. Statement III is incorrect. A distinction is sometimes made between risk that is knowable, measureable, and quantifiable through parameters; and uncertainty, where the parameters are not known at all. The latter is called ' Knightian uncertainty ' after the name of the scholar who came up with the distinction between the two. Statement IV is correct. Feedback effects had the greatest impact on liquidity which was tended to be hoarded, and on asset prices that tumbled as market participants tried to sell assets to become more liquid. Thus, choice is a the correct answer.

Basel II requires financial institutions to compare their ex-ante VaR estimates to actual realized P & L. Therefore Choice ' d ' is the correct answer. A bank may use hypothetical P & L based upon constant positions to validate its model, but that is not required for Basel II.

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.)

The current Basel rules for the basic VaR based charge for market risk capital set market risk capital requirements as the maximum of the following two amounts:

1. 99%/10-day VaR,

2. Regulatory Multiplier x Average 99%/10-day VaR of the past 60 days

The ' regulatory multiplier ' is a number between 3 and 4 (inclusive) calculated based on the number of 1% VaR exceedances in the previous 250 days, as determined by backtesting.

- If the number of exceedances is < = 4, then the regulatory multiplier is 3.

- If the number of exceedances is between 5 and 9, then the multiplier = 3 + 0.2*(N-4), where N is the number of exceedances.

- If the number of exceedances is > =10, then the multiplier is 4.

So you can see that in most normal situations the risk capital requirement will be dictated by the multiplier and the prior 60-day average VaR, because the product of these two will almost often be greater than the current 99% VaR.

The correct answer therefore is = max(200mm, 3*250mm) = $750mm.

Interestingly, also note that a 99% VaR should statistically be exceeded 1%*250 days = 2.5 times, which means if the bank ' s VaR model is performing as it should, it will still need to use a reg multiplier of 3.