Using simulations of asset returns have proved to be very useful in a large range of situations. They can give great insight into the asset and liability profile of a financial institution, or even for an individual.
They do, however, need to be used with caution. Some of the issues that need to be dealt with are:
- Is the asset model appropriate? Most asset models are mathematically quite complex, often based on some sophisticated statistical analysis. This complexity can make understanding what the underlying assumptions really are. Does the model make economic and mathematical sense? Does it break down in some situations?
- How are tail risks modeled? It seems likely that real life returns are, in fact, quite fat tails to their distribution. Using normal distributions will often underestimate tail risks.
- How does it work on a multi-year basis? A model with too high a degree of mean reversion can result in excessively low long term variance, understating the long term investment risks. I think this was a key problem with the Wilkie model which was widely used, but was poorly understood.
- Spurious precision. Running the model can give a result, for example a probability of ruin with a great deal of precision. We know that the distribution of the tails of the model are the least well understood parts of the models as the data is very scant. The tail probabilities are nearly entirely the result of the ultimate choice of model.
Often, the best insights come from following through the particular paths of returns where the company ends up in trouble and then thinking about what management actions could be taken to mitigate the problems. Useful tweaks to the basic strategy can also be derived.
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