Alternate title: Building a better Monte Carlo model.
Risk managers and investors will, of course, be familiar with Monte Carlo simulations — which are used in finance to value potential loan losses and things like portfolio risk or derivatives. The precise simulation varies from model to model but in general work something like this: define a domain of possible inputs, generate random inputs from the domain, apply some algorithms and then aggregate the results.
While Monte Carlo models haven’t been as lambasted as other methods of measuring risk (say for instance, the much-maligned Value at Risk) they are susceptible to the same shortcomings. Like VaR, they often miss so-called “fat tail” or outlier events, since they still rely on that domain of possible inputs and assumptions about the distribution of that domain.
Hence, it is with interest that we came across this press release (H/T Sam Jones):
New York, NY, October 06, 2009 — Investor Analytics, a global leader in risk measurement and risk management solutions for asset managers and asset owners, announces the release of SoFIE: Simulation of Financially Important Events. SoFIE is an implementation of advanced Monte Carlo that focuses on fat tails to significantly improve the accuracy, stability and speed of computing risk statistics as compared to traditional Monte Carlo approaches.
The techniques used by SoFIE, known collectively as “variance reduction”, target extreme values where the greatest financial risks arise. These techniques focus attention on critical areas of interest for each portfolio individually. In turn, the simulations highlight a portfolio’s unique material risks. Risk managers will immediately benefit by employing these techniques in three ways:
1. The fat-tailed characteristics of financial portfolios, especially those with any derivative securities, are better modeled;
2. The stability of the output is vastly improved compared to almost all other Monte Carlo simulations, and depending on the portfolio’s investments, the variance of the output can be improved by over a factor of 50;
3. Far fewer simulations are required to achieve a higher accuracy result, thereby improving speed and reducing computation time.
Adam Winik, Director of Financial Engineering at Investor Analytics said, “IA’s implementation of these innovative techniques, together with our flexible framework, allows for robust modeling of a wide range of asset classes. IA’s full re-valuation of derivative contracts in the simulation captures the true non-linearities that often times drive the risk of a portfolio.”
Variance reduction, as near as we can figure, involves changing the way the data is sampled so that `important’ datapoints are sampled more often, while less important ones are sampled less often. The press release is light on detail but it looks like what SoFIE does is attempt to flatten the overall distribution (towards fat tails, so to speak).
Will it improve the model?
We’re not sure. SoFIE might be able to capture more fat tail risk, but it will never predict say, a black swan-sized outlier event — by definition that event would lie outside the realm of defined possibilities. But perhaps that is asking too much of a model.
There is also the possibility, however, as some commentators have already pointed out, that the problem isn’t capturing more, or more of, the fat tails — it’s re-thinking Monte Carlo models’ (average) assumptions.
Here’s portfolio simulator TIP$STER on the subject:
How has the financial software services industry responded [to criticism of Monte Carlo simulations]? Predictably. Oh yes, the problem is in the tails. We’ll fatten those tails right up . . . Which misses the point. Unless those distributions are centered around realistic return expectations, fattening the tails will do as much good as putting lipstick on a pig. Models that use unrealistic return assumptions will continue to set up millions of advisor clients for disappointment.
Sure, minor improvements can be made to fatten the tails of conventional Monte Carlo distributions used to model equity returns. But tweaking the tails does not matter nearly as much, in the long run, as centering the distribution of returns about a reasonable expected mean.
Whatever the details of SoFIE, then, this is an interesting example of the kinds of the things people are doing in their attempt to build better models.
Be comforted or be scared.
Related links:
Gambling on Monte Carlo simulations - FT Alphaville
Finance and Monte Carlo simulation - Journal of Financial Planning
Of couples and copulas - FT
