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NEW QUESTION 42
Which of the following is closest to the description of a 'risk functional'?

  • A. A risk functional is a model distribution that is an approximation of the true loss distribution of a risk
  • B. Risk functional refers to the Kolmogorov-Smirnov distance
  • C. A risk functional is the distribution thatmodels the severity of a risk
  • D. A risk functional assigns a penalty value for the difference between a model distribution and a risk's severity distribution

Answer: D

Explanation:
Explanation
For operational risk modeling, both frequency and severity distributions need to be modeled. Modeling severity involves finding an analyticaldistribution, such as log-normal or other that approximates the distribution best represented by known data - whether from the internal loss database, the external loss database or scenario data. A 'risk functional' is a measure of the deviation of the model distribution from the risk's actual severity distribution. It assigns a penalty value for the deviation, using a statistical measure, such as the KS distance (Kolmogorov-Smirnov distance).
The problem of finding the right distribution then becomes the problem of optimizing the risk functional. For example, if F is the model distribution, and G is the actual, or empirical severity distribution, and we are using the KS test, then the Risk Functional R is defined as follows:
8010-4ffe9f960baf10707469c7771694818e.jpg
Note that supx stands for 'supremum', which is a more technical way of saying 'maximum'. In other words, we are calculating the maximum absolute KS distance between the two distributions. (Note that the KS distance is the max of the distance between identical percentiles of the two distributions using the CDFs of the two.) Once the risk functional is identified, we can minimize it to determine the best fitting distribution for severity.

 

NEW QUESTION 43
Which of the following is a cause ofmodel risk in risk management?

  • A. All of the above
  • B. Programming errors
  • C. Incorrect parameter estimation
  • D. Misspecification of the model

Answer: A

Explanation:
Explanation
Model risk is the risk that a model built for estimating a variable will produce erroneous estimates. Model risk is caused by a number of factors, including:
a) Misspecifying the model: For example, using a normal distribution when it is not justified.
b) Model misuse: For example, using a model built to estimate bond prices to estimate equity prices c) Parameter estimation errors: In particular, parameters that are subjectively determined can be subject to significant parameter estimation errors d) Programming errors: Errors in coding the model as part of computer implementation may not be detected by end users e) Data errors: Errors in data used for building the model may also introduce model risk Therefore the correct answer is d, as all the choices are a source of model risk.

 

NEW QUESTION 44
An operational loss severity distribution is estimated using 4 data points from a scenario. The management institutes additional controls to reduce the severity of the loss if the risk is realized, and as a result the estimated losses from a 1-in-10-year losses are halved. The 1-in-100 loss estimate however remains the same.
What would be the impact on the 99.9th percentile capital required for this risk as a result of the improvement in controls?

  • A. The capital required will decrease
  • B. Can't say based on the information provided
  • C. The capital required will increase
  • D. The capital required will stay the same

Answer: C

Explanation:
Explanation
This situation represents one of the paradoxes in estimating severity that one needs to be aware of - the improvement in controls reduces the weight of the body/middle of the distribution and moves it towards the tails (as the total probability under the curve must stay at 100%) and the distribution becomes more heavy tailed. As a result, the 99.9th percentile loss actually increases. instead of decreasing, creating a counterintuitive result. Therefore the correct answer is that the capital required will increase.
If scenario analysis produces such a result, the analyst must question if the 1 in 100 year loss severity is still accurate. If the new control has reduced the severity in the body of the distribution, the question as to why the more extreme losses have not changed should be raised.

 

NEW QUESTION 45
A portfolio has two loans, A and B, each worth $1m. The probability of default of loan A is 10% and that of loan B is 15%. Theprobability of both loans defaulting together is 1%. Calculate the expected loss on the portfolio.

  • A. 0
  • B. 1
  • C. 2
  • D. 3

Answer: D

Explanation:
Explanation
The easiest way to answer this question is to ignore the joint probability of default as thatis irrelevant to expected losses. The joint probability of default impacts the volatility of the losses, but not the expected amount. One way to think about it is to think of asset portfolios, where diversification reduces risk (ie standard deviation) butthe expected returns are nothing but the average of the expected returns in the portfolio. Just as the expected returns of the portfolio are not affected by the volatility or correlations (these affect standard deviation), in the same way the joint probability of default does not affect the expected losses. Therefore the expected losses for this portfolio are simply $1m x 10% + $1m x 15% = $250,000.
This can also be seen from the lens of a joint probability distribution as follows:
8010-772e62c86ab3370eab0dcfd1f6d9460a.jpg
There are four possibilities for this portfolio:
- Only loan A defaults: loss of $1m: 9% probability
- Only loan B defaults: loss of $1m: 14% probability
- Both loan A and B default: loss of $2m: 1% probability
- Neither A nor B default: loss of $0m: 76% probability
Therefore the expected losses on the portfolio are ($1m x 9%) + ($1m x 14%) + ($2m x 1%) + ($0m x 76%) =
$250,000.
(Notes: How is the above table calculated? The totals (10%, 90%, 15% and 85%) are filled in first. The top left cell (both A & B default) is given as 1%. We can now calculate the rest of the cells as the totals are known.)

 

NEW QUESTION 46
If A and B be two debt securities, which of the following is true?

  • A. The probability of simultaneous default of A and B is greatest when their default correlation is negative
  • B. The probability of simultaneous default of A and B is greatest when their default correlation is 0
  • C. The probability of simultaneous default of Aand B is not dependent upon their default correlations, but on their marginal probabilities of default
  • D. The probability of simultaneous default of A and B is greatest when their default correlation is +1

Answer: D

Explanation:
Explanation
If the marginal probability of default of two securities A and B is P(A) and P(B), then the probability of both of them defaulting together is affected by the default correlation between them. Marginal probability of default means the probability of default of each security on a standalone basis, ie, the probability of default of one security without considering the other security.
The relationship that expresses the probability of joint default of the two is given by the following expression:
8010-a7c2750d0178656591c2f9075a9c59fa.jpg
It is easy to see that in a situation where the Default Correlation of A & B = 0, ie, the defaults are independent, the combined probability of default is P(A)*P(B), exactly what we would intuitively expect. Also in the other extreme case where the default correlation is equal to 1 and P(A) = P(B) = p, ie the securities behave in an identical way, the expression resolves to just p, which is what we would expect.
From the above relationship, it is clear that the probability of joint default of A and B is the greatest when default correlation between the two is equal to 1, ie the securities behave in an identical way. Therefore Choice
'a' is the correct answer.

 

NEW QUESTION 47
......

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