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Under the credit migration approach to assessing portfolio credit risk, which of the following are needed to generate a distribution of future portfolio values?
The credit migration approach to assessing portfolio credit risk involves obtaining a distribution of future portfolio values from the ratings migration matrix. First, the frequencies in the matrix are used as probabilities, and expected future values of the securities belonging to each rating category are calculated. These are then discounted to the present using the discount rate appropriate to the 'future' rating category. This gives us a forward distribution of the value of each security in the portfolio. These are then combined using the default correlations between the issuers. The default correlation between the issuers is often proxied using asset returns, and recognizing that default occurs when asset values fall below a certain threshold. A distribution for the future value of the portfolio is generated using simulation, and from this distribution the Credit VaR can be calculated.
Thus, we need the migration matrix, the risk horizon from which the present values need to be calculated, and the forward yield curve or the discount curve for each rating category for the risk horizon. Thus, Choice 'd' is the correct answer.
Which of the following are a CRO's responsibilities:
1. Statutory financial reporting
2. Reporting to the audit committee
3. Compliance with risk regulatory standards
4. Operational risk
Statutory financial reporting is the responsibility of the Chief Financial Officer, not the Chief Risk Officer. The head of internal audit reports to the audit committee of the board, not the CRO. Therefore statements I and II are incorect.
The CRO is generally expected to drive risk and compliance with related regulatory standards. Market risk, credit risk and operational risk groups report into the CRO, so statements III and IV are correct.
The unexpected loss for a credit portfolio at a given VaR estimate is defined as:
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.
A Bank Holding Company (BHC) is invested in an investment bank and a retail bank. The BHC defaults for certain if either the investment bank or the retail bank defaults. However, the BHC can also default on its own without either the investment bank or the retail bank defaulting. The investment bank and the retail bank's defaults are independent of each other, with a probability of default of 0.05 each. The BHC's probability of default is 0.11.
What is the probability of default of both the BHC and the investment bank? What is the probability of the BHC's default provided both the investment bank and the retail bank survive?
Since the BHC always fails when the investment bank fails, the joint probability of default of the two is merely the probability of the investment bank failing, ie 0.05.
The probability of just the BHC failing, given that both the investment bank and the retail bank have survived will be equal to 0.11 - (0.05+0.05-0.05*0.05) = 0.0125. (The easiest way to understand this would be to consider a venn diagram, where the area under the largest circle is 0.11, and there are two intersecting circles inside this larger circle, each with an area of 0.05 and their intersection accounting for 0.05*0.05. We need to calculate the area outside of the two smaller circles, but within the larger circle representing the BHC).
Refer diagram below, please excuse the awful colors.
An error by a third party service provider results in a loss to a client that the bank has to make up. Such as loss would be categorized per Basel II operational risk categories as:
Choice 'a' 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.
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