This questions deals with the appropriate levels of the holding period and confidence levels for VaR estimates. These depend upon the use the VaR estimate is intended to be put to - so when calculating VaR levels for capital requirements, or for maintaining credit ratings, very high levels of confidence are generally used. On the contrary, when setting limits or validating a model, a few excess loss situations are not only accept able but actually desirable, and therefore lower levels of confidence are used. When it comes to the holding period, that may be mandated, as it is under Basel II as being a 10 day period. For other cases, it may be a horizon roughly corresponding to a period in which positions may be liquidated in an orderly day, which could be just one day for highly liquid markets, or a week or more for larger positions in illiquid markets. Therefore statements I and III are true and the others are false. Therefore the only correct answer is Choice ' b ' .

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.

Assuming time invariance and the Markov property, it is easy to calculate the transition matrix for any time period as P^n, where P is the given transition matrix for one period and n the number of time periods that we need to compute the new transition matrix for.

However, when the new time period is less than the time period the matrix is available for, the only way to deriving a transition matrix for a partial period is to numerically calculate a matrix M such that M^n = P. Therefore Choice ' b ' is the correct answer. Taking cube roots of a matrix is not a possible operation, dividing by 3 gives a matrix meaningless in this context, and P x P x P will give us the transition matrix for 3 years, not 1/3rd of a year.

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.

Internal loss data is generally the highest quality as it is relevant, and is ' real ' as it has occurred to the organization. External loss data suffers from a significant limitation that the risk profiles of the banks to which the data relates is generally not known due to anonymization, and may likely may not be applicable to the bank performing the calculations. Therefore, replacing external loss data with external loss data is not a good idea. Statement IV is therefore incorrect.

All other approach described are valid approaches for the risk analyst to consider and implement. Therefore statements I, II and III are correct and IV is not.

Choice ' b ' is the correct answer. When two securities have a correlation of +1, they are effectively the same security. In such cases, the standard deviations of the two securities are additive, which means the VaRs can simply be added together to get the combined VaR. All the other choices are incorrect.

Choice ' c ' in particular would have been correct if the securities were completely uncorrelated, ie if they had a correlation of zero.

Choice ' a ' would have been correct if their correlation were -1.

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.

A default hazard rate is the rate of default in a continuous time setting. This question is asking for probability of survival at the end of 5 years. The formula to calculate the probability of survival at the end of t years where the default hazard rate is λ is e^(-λ *t) (or in Excel, =exp(-λ*t). Therefore the correct answer is Choice ' d ' .

(It may be tempting to infer that if the probability of survival at the end of 1 year is 90% (1 - 10%), then the probability of survival in 5 years would be 90%^5. However this reasoning is not correct for the reason that the given rate is not the discrete rate of default, but the hazard rate which is nothing but the continuously compounded rate of default.)