I know they give marks for every reasonable point, and there are many "right" answers, but I disagree with the following point the examiners make on Q1: "Many candidates failed to note the two main points...that distinguishing between updise and downside risk is, in most circulmstances, not a particularly useful concept for stochastic modelling". I would have differently - if you are using an empirical distribution, OK, but if you are fitting, are you going to fit the model and/or parametres giving equal weight to all points of the distribution, or are you going to give more weight to how the model fits the "below average" points? e.g. use semi-variance rather than variance. Is my thinking off? Thanks,
Are the examiners not talking about the correlations and (co)variances between the different risks being modelled which, when modelled stochastically, begin to lose meaning if treated as individual risks and become a new distribution? Perhaps they are talking about upside and downside risks that could cancel out under certain correlations and distributions within a stochastic model? In other words just focussing on up or down risk misses the correlation effect between them. Just guessing though! Also I'm not quite sure what you mean by fitting the model. Do you mean deriving the distributions of the underlying risks and the joint distributions between the risks, or something completely different?
The point about stochastic model puzzled me in the first instance. At hindsight, would it be meant that, for stochastic model, you will simulate the outcomes of the risks tuning out to be positive or negative is a random variable; distinguishing upside and downside risk upfront will prevent the random feature of the model? In fact, the model answers didn't give the point that it is not important to distinguish upside and downside risk if the risk distribution is symmetrical.
Yeah, recently worked through April 2012, and I absolutely hated question #6. Same with question #1. It's like the examiners' strive to take seemingly basic concepts and construct questions in a way so as to test these concepts in the most obtuse way as possible. By the way: am I the only one who completely misinterpreted question #2(i), instead providing differences in types of regulation (e.g., principles-based vs. rules-based)? Yeah, that wasn't fun. Had to vent!
Here's my take on this one. I haven't looked at this question yet, so this is based on the comments below only. I agree that pointing out that "distinguishing between upside and downside risk is, in most circumstances, not a particularly useful concept for stochastic modelling" doesn't really sound like a "main point". I do think that it is a valid point however. A typical model will have a number of different risks each modelled stochastically, i.e. each with a distribution fitted. These will be joined together somehow (copulas or covariance matrix). We do a load of simulations each of which produces outputs. So we put these together to have a distribution of outputs. Look first at the individual risks (marginal distributions). If we're to get a realistic set of outputs then we need to ensure that we're sampling from the whole distribution. We might pay particular attention to the lower tail (the bottom 5% say) but I don't see that we would make any particular distinction between the upside risks (i.e. those more favourable than the 50th percentile) and the downside risks). So the median of the distribution doesn't really have a special significance. Looking next at the outputs (joint distribution). The midpoint of the distribution will be relevant, sure - this is best estimate liabilities, or expected loss, or whatever we're modelling. But otherwise, almost any metric we'll be interested in are either focussed on the lower tail (VaR, P(ruin), TVaR, ES) or don't distinguish between upside and downside (e.g. standard deviation). Again the distinction between upside and downside risks (say the 40th versus the 60th percentile) isn't particularly interesting. The only exception that comes easily to mind is skew - we might be interested in whether the mode point was on the upside or the downside. Hope that makes sense and I don't have to backtrack entirely once I get around to the April 2012 paper!
