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The Actuary The magazine of the Institute & Faculty of Actuaries


I was invited on behalf of The Actuary to the launch of Brunel University’s new research centre, CARISMA, the Centre for the Analysis of Risk and Optimisation Modelling Application.
Now shouldn’t that be CAROMA? Also, aren’t they optimising the risk of a bad reputation with spelling purists in the same way as Kwik-Fit and Supa-Snaps? They could have avoided this by making the centre a church, or a charity.
The launch took place at the Institute of Actuaries’ own Staple Inn. It consisted of two days of seminars separated by an evening reception. The crowd was predominantly academic, with a smattering of delegates from portfolio management companies. Speakers and delegates came from all over the world.
Right from the first seminar I was bombarded with statistical formulae the like of which I hadn’t seen since my university days. Do the earlier actuarial subjects cover this portfolio theory nowadays?

Risk measures
The first speaker was David Heath from Carnegie Mellon University in the USA. He was trying to find a good measure of risk. He provided a brief introduction to ‘coherent’ measures of risk and a taste of how these ideas can be extended to more complex stochastic processes.
Regulators of financial markets are concerned with the risks associated with large losses. To control these risks, you must be able to measure them. A ‘measure of risk’ is the minimum extra capital which, invested in a portfolio, makes the future value of the modified position become acceptable. There are four axioms that should hold for any risk measure that is to be used to regulate or manage risks effectively. Risk measures that satisfy the four axioms are called ‘coherent’.
Currently, many institutions use value-at-risk (VaR) as a measure of their exposure to risk. VaR is usually defined in terms of net wins, or profit or loss, and therefore ignores the timing of cashflows, which may be acceptable for small time periods and a single currency. Bankers in many countries use an amount based on VaR to decide whether the level of risk is too high, ie whether more risk capital is required. However, VaR has deficiencies as a risk measure: it doesn’t reflect the sizes of infrequent large losses and it doesn’t satisfy the principle that diversification reduces risk.
Another measure of risk is the standard portfolio analysis of risk (SPAN), developed by the Chicago Mercantile Exchange. This margin system is widely used in futures exchanges. The SPAN margin rules specify how much additional risk capital is required to hold a position involving futures contracts and options. It turns out to be a coherent measure of risk.
Clairvoyant costs
After coffee, Georg Pflug of the University of Vienna talked about ‘Risk measurement the primal and the dual view’. The quantification of risk is equivalent to the assessment of the degree of unforeseeability and its economic consequences. If everyone possessed full information, no risk would occur. Therefore, we measure risk by the value of full information for a particular decision. How much would we pay for a clairvoyant to reveal the future?

Su Doku
Over lunch I was introduced to a young lady who had given up the actuarial exams to start a PhD at Brunel University. I also got chatting to a Canadian chap who was on a quest to find a book about the history of Lloyd’s while he was in London. Nicely full, I made the most of the warm sunny day and did that day’s Su Doku in Staple Inn’s pretty garden.

Backtesting, backtesting
After lunch, Kevin Dowd from the University of Nottingham and Black Swan Risk Advisors talked about new developments in ‘backtesting’. Backtesting is the method of evaluating a model using quantitative methods. It might be statistical (is a model acceptable?) or it might involve ranking (is one model better than another?). There have been major advances in recent years.
Backtesting gives an indication of any possible problems such as mis-specification or the under-estimation of tails. It might be applied to the frequency of high losses, the size of high losses, or the distribution of profit and loss.
Mr Dowd described statistical backtests, which are based on the theory of hypothesis testing with a type I error of rejecting a good model and a type II error of accepting a bad one. There is a trade-off between these errors. The advantages of these basic frequency tests are that they are easy to carry out and don’t require much information. However, they are not reliable unless the sample size is large and information about the pattern and size of losses is ignored.
Distribution-equality tests, on the other hand, do not ignore the useful information about the size of tail losses. Such tests include the Chi-squared test and Kolmogorov-Smirnov test that I recall from my earlier actuarial exams. We need to test the difference between predicted and empirical observations, but this is difficult because we don’t have an empirical distribution to compare with the predicted one. Instead, we have a series of observations (eg of profit and loss), each drawn from a predicted distribution that changes daily. Hence, observations are not comparable from day to day. Mr Dowd went on to explain how to overcome this problem using ‘transformation’ models to map the observations onto a standard Normal distribution and then carrying out the Chi-squared and other tests.
Mr Dowd also described moments-based backtests, which he concluded are probably the best as they are powerful, flexible, and easy to use. However, he stressed the importance of not relying on one backtest and that backtests themselves should be backtested!

Risks you don’t know
The last talk of the day was by John Blin of APT inc. It was intriguingly called ‘The risks you know and the risks you don’t’. The first slide was a cartoon of a chap in his office saying into the ‘phone: ‘I was spreading some risk around and apparently it all wound up in your portfolio.’
Mr Blin used the analogy of good and bad cholesterol to help explain the difference between residual risk (risk you can diversify) and systematic risk (risk you can’t). An effective risk model must guarantee that the ‘bad’ risks won’t hide among the ‘good’ risks and that systematic risk won’t be mislabelled ‘residual’. The ‘mother’ of all risks, though, is model risk.

and relax
After a question and answer session with that day’s speakers, the party began. Unfortunately I had to miss it as I had a ballet class to go to. I hear that the wine was flowing though.

Greedy mortgagors
There were several late arrivals for the first talk of the second day. I obviously did miss a good party. Stanley Pliska of the University of Illinois in Chicago kicked off with ‘the valuation and optimal refinancing of mortgages’.
The typical approach to a mortgage valuation is to build a model of interest rates and possible early repayment. Then the expected discounted value of the cashflow is estimated through simulation.
Mr Pliska’s first approach was option-based. The idea is that the mortgagor’s decision to refinance is like the decision of an American option holder to exercise early. However, the analogy to an American option is flawed from the mortgagor’s standpoint because he or she has the opportunity to refinance more than once.
He also discussed a hazard rate model approach and endogenous mortgage rate models, using lots of statistical formulae. Some of the delegates were clearly following them, as there were many questions (shouldn’t that sigma be squared?).
Mr Pliska derived some optimal refinancing strategies by using his models. He concluded that the economic market is like a game. The market sets the mortgage rates; the mortgagors choose optimal refinancing strategies; the markets adjust the mortgage rates due to competitive forces; the mortgagors revise their optimal refinancing strategies; etc. Ultimately, there is equilibrium.
Interestingly, the mortgagor ends up paying more by trying to save money by re-financing when mortgage rates fall. Periodic payments will be smaller, but mortgage rates might fall even more. Also, if mortgage rates have fallen, then the short rate probably has too, which means that discounted values increase. Therefore, in the short run, greedy mortgagors choose refinancing strategies that minimise the cost of the loan but, in the long run, they might end up regretting their greed .
All in all, it was a gruelling two days . After one last coffee and a chat, I went home tempted to dust off my old statistics textbooks.