Explanation
One may use separate UoMs for frequency and severity modeling, for example, a combined UoM may be used for estimating the frequency of cyber attacks in a scenario, while the severity may be modeled using a more granular line-of-business UoM. Therefore statement I is false, while statement IV is true.Statement II is correct, UoMs can be grouped together into larger units based on the facts relating to the business, controls and the business environment. Similarly, UoMs can be grouped together based on statistical clustering techniques using the 'distance' between the units of measure and combining UoMs that are closer to each other.
In addition, it is also possible to combine both business knowledge and statistical algorithms to combine UoMs.

Explanation
Other than Choice 'c', all others represent valid approaches to allocate economic capital to underlying business units. There is no such thing as 'fixed ratio economic capital contribution'

Explanation
This is a trick question, no great science to it. Remember that the 'present value of a basis point' refers to PV01, which is the same as BPV (basis point value) referred to in the PRMIA handbook. In other textbooks, the same term is also variously called 'DV01' (dollar value of a basis point). Remember these other terms too.
PV01, or the present value of a basis point, is the change in the value of a bond (or other fixed income security) from a 1 basis point change in the yield. PV01 is calculated as (Price * Modified Duration/10,000).
Therefore Choice 'a' is the correct answer.

Explanation
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 and standard deviation equal to .
The probability of n defaults is given by (^n e^-) /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.

Explanation
Component VaR measures the proportion of total VaR that can be allocated to each asset in the portfolio. It is based upon the covariance matrix multiplied by the weights, and each row represents the component VaR for the asset in question. Since the total of such a matrix is the total VaR, component VaR is additive. Component VaR is used to assess the contribution of each asset in the portfolio to total risk and has the useful property of being additive so some sense can be made of the contribution of each asset to total risk.
Incremental VaR, conditional VaR and VaR are sub-additive by definition, and therefore not the correct answer.