The actuarial or CreditRisk+ model considers default as an 'end of game' event modeled by a Poisson distribution. The annual number of defaults is a stochastic variable with a mean of μ and standard deviation equal to √ μ .

The probability of n defaults is given by ( μ ^n e^- μ ) /n!, and therefore in this case is equal to (=2^4 * exp(-2))/FACT(4)) = 0.0902.

Note that CreditRisk+ is the same methodology as the actuarial approach, and requires using the Poisson distribution.

This question emphasizes the difference between primary and secondary risks. Primary risks are the risks consciously undertaken, ie the risks whose premium the investor is trying to earn. Secondary risks are risks that accompany the primary risks that the investor will either hedge, or will ignore if they are small. It is important to watch out for secondary risks because they could become significant and offset the returns being sought even if the investor's market view is proved correct.

An investor in market index futures is betting that the index will rise. Index futures prices are largely driven by the spot value of the index, but are also affected by costs of carry. In particular, futures prices will be driven by interest rates, expected dividends, and any other factors that may cause the basis between spot and futures prices to diverge. These risks are secondary risks.

In this question, Choice 'd' represents the primary risk, and Choice 'a', Choice 'b' and Choice 'c' are all secondary risks. Therefore Choice 'd' is the correct answer.

Unexpected loss for a credit portfolio refers to the excess of the VaR estimate over the average expected loss. The term 'unexpected loss' has this specific meaning in the context of credit risk, and not any other intuitive meaning. So if for a portfolio worth $100m expected losses are 4%, and the credit VaR at 99% is $12m, then unexpected losses at that VaR quintile are $8m. This is unrelated to actual realized losses versus expected losses.

Therefore Choice 'd' is the correct answer and the others are not.

Unexpected loss is used to determine the capital reserves to be maintained against a credit portfolio at a certain level of confidence.

The bank paid $7m for the bonds, and expected recovery is $3m (30% x $10m face). Therefore Bank B's loss is $4m ($7m - $3m). Choice 'b' is the correct answer. All other answers are incorrect.

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.

Altman's Z-score, the Probit and the Logit models can all be used to assess the credit rating of an individual borrower. There is no such model as the 'distance to default model', and therefore Choice 'a' is the correct answer.

Some risk experts have suggested the use of extreme value theory to model tail risk or extreme events for operational risk. The generalized Pareto model or the Peaks-over-Threshold (POT) model are often used to model extreme value distributions, and therefore Choice 'a' is the correct answer.

The minimum variance hedge ratio answers the question of how much of the hedge to buy to hedge a given position. It minimizes the combined volatility of the primary and the hedge position. The minimum variance hedge ratio is given by the expression [ σ(x) / σ(y) ] * ρ(x,y)] . Effectively, this is the same as the beta of the primary position with respect to the hedge.

In this case, the hedge ratio is = 10%/9% * 0.9 = 1

The correct answer is choice 'd'

Marginal VaR is just the change in total VaR from a $1 change in the value of the asset in the portfolio. All other answers are incorrect. Mathematically, it is expressed as follows, where VaRp is the VaR for the portfolio, and Vi is the value of the asset in question.

A mathematical equation with numbers and symbols Description automatically generated

Other answers describe other VaR related concepts such as incremental VaR, Component VaR and Conditional VaR.

A non-financial firm such as a manufacturing company faces market risks similar to those faced by financial firms, except perhaps for not being exposed to risks from the equity markets. Non financial firms commonly face interest rate risks in respect of their debts, commodity price risks in respect of their inputs and products, and foreign currency risks in respect of their overseas operations. It is therefore not correct to say that the manufacturing firm does not face market risk because it does not take proprietary positions. While decisions on positions may not be actively taken, positions in foreign exchange (eg, through overseas debtors owing foreign currency, or liabilities in foreign currencies to overseas suppliers), commodities (through exposure to the need for raw material and inventory of finished goods) and interest rates (through debt financed, whether at fixed or floating rates) exist and create market risk much in the same way as they would for a proprietary position. Therefore statement I is incorrect.

While the firm faces market risks as an externality (as do financial firms for that matter, though often they seek such exposure to profit from their view on which way the externality will express itself), it is incorrect to say that these risks must be borne. They can be measured and hedged. Therefore statement II is incorrect.

The results of a manufacturing firm will include gains and losses arising from exposure to market risk, and will cloud the true profitability of the business. A firm with significant unhedged overseas sales may show vastly different results across time periods due to the FX gains and losses, making comparative assessment of profitability difficult. Therefore statement III is correct.

Market risks for a manufacturing firm may be directionally biased in terms of exposure, ie there may be a consistent 'long' position in a particular commodity that the firm produces, and a consistent 'short' position in the commodities consumed. In the same way, directional biases may exist in FX or interest rate exposures too. Regardless of the bias, the existence of market risk exposures increase the volatility of the income stream and make the firm more risky, even though the long term expected returns from such exposures is zero (ie, returns may be zero but standard deviation is not). Therefore statement IV is not correct as market risks form non financial firms do increase the overall risk of the firm.