Which of the following statements are correct?
1. A reliance upon conditional probabilities and a-priori views of probabilities is called the 'frequentist' view
2. Knightian uncertainty refers to things that might happen but for which probabilities cannot be evaluated
3. Risk mitigation and risk elimination are approaches to reacting to identified risks
4. Confidence accounting is a reference to the accounting frauds that were seen in the past decade as a reflection of failed governance processes
In statistics, which is relevant to risk management, a distinction is often drawn between 'frequentists' and 'Bayesians'. Frequentists rely upon data to draw conclusions as to probabilities. Bayesians consider conditional probabilities, ie, take into account what things are already known, and inject sometimes subjective a-priori probabilities into the calculations. Statement I describes Bayesians, and not frequentists. In reality however, the difference is merely academic. Risk managers use whichever technique best applies to the given situation without making it about ideology.
The difference between 'Knightian uncertainty' and 'Risk' is similarly academic. Knightian uncertainty refers to risk that cannot be measured or calculated. 'Risk' on the other hand refers to things for which past data exists and calculations of exposure can be made. To give an example in the context of the financial world, the risk from a pandemic creating systemic failures from a failure of payment and settlement systems and the like is 'Knightian uncertainty', but the market risk from equity price movements can be modeled (albeit with limitations) and is calculable. Statement II is therefore correct.
Once a risk is identified, it can be mitigated, accepted, avoided or eliminated, or transferred by way of insurance. Therefore statement III is correct.
Confidence accounting is a conceptual idea that suggests that accounting statements make reference to ranges as opposed to point estimates in financial statements. For example, instead of saying that the pension obligation is $xx million, the company should say the pension obligation is in a range of $xx m - $yy m with a certain confidence level. Statement IV is therefore inaccurate.
Under the KMV Moody's approach to credit risk measurement, how is the distance to default converted to expected default frequencies?
KMV Moody's uses a proprietary database to convert the distance to default to expected default probabilities.
The probability of default of a security during the first year after issuance is 3%, that during the second and third years is 4%, and during the fourth year is 5%. What is the probability that it would not have defaulted at the end of four years from now?
The probability that the security would not default in the next 4 years is equal to the probability of survival at the end of the four years. In other words, =(1 - 3%)*(1 - 4%)*(1 - 4%)*(1 - 5%) = 84.93%. Choice 'd' is the correct answer.
The difference between true severity and the best approximation of the true severity is called:
This question relates to fitting a distribution to the true severity of the operational risk loss we are trying to model. The quality of the fit, or the precision of the fit, has two elements to the difference between the severity as represented by our model and the true severity. To understand this, consider the three data points below:
a. The true severity,
b. The best approximation of the true severity in the model space, and
c. The fit based on the dataset.
- True severity is what we are trying to model.
- The model space refers to the collection of analytical distributions (log-normal, burr etc) that we are considering to arrive at the estimate of the severity.
- The 'best approximation of the true severity in the model space' is reached by estimating the parameters of the distribution that optimizes the risk functional.
- The 'fit' is the actual parameter estimates we settle for with the distribution we have determined best fits the true estimate of our severity. When estimating parameters, we have various methods available for estimation - the least squares method, the maximum likelihood method, for example, and we can get different estimates depending upon the method we choose to use.
Our severity model will be different from the true severity, and the total difference can be split into two types of errors:
1. Fitting error, represented by 'c - b' above: The difference between the fit based on the dataset and the best approximation of the true severity is called 'fitting error', ie, a measure of the extent to which we could have estimated the parameters better.
2. Approximation error, represented by 'b - a' above: Approximation error is the difference between the true severity, and the best approximation of the true severity that can be achieved within the model space is called 'approximation error'.
One can reduce the approximation error by expanding the model space by adding more distributions. This will reduce the approximation error, but generally has the effect of increasing the fitting error because the complexity of the model space increases, and there are more ways to fit to the true severity.
For a group of assets known to be positively correlated, what is the impact on economic capital calculations if we assume the assets to be independent (or uncorrelated)?
By assuming the assets to be independent, we are reducing the correlation from a positive number to zero. Reducing asset correlations reduces the combined standard deviation of the assets, and therefore reduces economic capital. Therefore Choice 'b' is the correct answer.
Note that this question could also be phrased in terms of the impact on VaR estimates, and the answer would still be the same. Both VaR and economic capital are a multiple of standard deviation, and if standard deviation goes down, both VaR and economic capital estimates will reduce.
