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The Actuary The magazine of the Institute & Faculty of Actuaries
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Modelling: Britain’s next top model?

Our office is based near Savile Row in London, sandwiched between the flagship stores of Ralph Lauren and Abercrombie & Fitch and overlooked by the statues of Galileo, Newton and Leibnitz behind the Royal Academy of Arts. While walking to work our thoughts are therefore naturally drawn to models — whether of the fashion variety or otherwise. One view of a model is that it is meant to be a perfect blank framework on which a designer can demonstrate the combined effects of different mixes of ideas. The difference between a model’s figure and the figures in real life is always a source of great attention. Models used to ‘optimise’ asset allocations are now under the spotlight more than ever.

In this article we discuss what the future may hold for such asset and liability models. The starting point for asset allocation is to consider the investor’s objectives, time horizon and tolerance for uncertainty of outcome (commonly termed ‘risk’). There are typically two common ways to allocate assets with the goal of increasing the value of an investor’s assets, while aiming for the least amount of fluctuation associated with that expected return. These are:

>> The ‘investment manager-type’ approach — ‘calling’ the market — buying when prices fall below a trigger level and selling when prices move above it

>> The ‘statistical type’ approach — holding a diversified mix — where the same factor affects the prices of different assets in different ways.

Calling the market, as suggested by some notable investment gurus, is based on the premise that good, solid investments can be underpriced because of heavy negative sentiment driving down all prices in the market. Though this method holds great attraction at the current time, modelling sentiment is rather difficult — we suggest that it is rather like trying to second-guess fashion trends — for each great fashion idea that succeeds, we are all usually aware of another embarrassing item that we thought looked good, but luckily managed to avoid. Even great investment gurus can follow the wrong fashion at the wrong time. Surely there is an approach to modelling that can help us?

The problem
In non-extreme conditions, the normal model market requires a balance of buyers and sellers in order to operate in the way that the model is designed. The real-life market is not like this (see box, below left). The speed at which the expectations of buyers or sellers change would steer market prices (and hence volatility) away from normal conditions. For example:

>> A lack of confidence in the future creates an excess of sellers
>> An expectation for strong growth creates an excess of buyers. In essence, the level of confidence or otherwise in the future amplifies the imbalance of buyers and sellers or, in other words, the market overreacts.

An increase in price suggests that buyers still see an investment as profitable at a higher price and they can achieve a profit from selling it within their time horizon. Therefore, for a portfolio of assets to gain value, for example, for the price of those assets to increase, someone else has to see further available profit at the higher price. However, if there is a majority consensus that there is no further profit, any existing profit is realised.

Nonetheless, if someone else always sees further available profit (and this information is perfect), would this not create a bubble? Considering the recent past, it is interesting to consider whether the recession was the trigger for bursting the bubble or if it happened the other way around. Would the recession have happened if Lehman Brothers was not allowed to fail? At what point was it the availability of credit-fuelled price increases rather than a combination of globalisation, innovation and improved efficiencies?

The next top model
So, what characteristics do we believe the next top model should display? Simplicity, simple scenarios and plain common sense. We suggest that trying to build an increasingly complex model to capture increasingly extreme events reduces understanding. But worse, such an approach can obscure or ‘average out’ the original views going into the model. Textbooks use words like ‘efficient’ and ‘optimal’ in a certain context, but these terms suggest a level of accuracy and sophistication that is just not possible and can be misleading.

On top of that, trying to fit a probability distribution can quickly confuse the message. If what we really mean is that the markets could either exhibit A (for instance, experience deflation) or B (say, high inflation), then we suggest telling people just that. It makes understanding the implications of an investment decision much clearer. Trying to combine views into a single model is likely to just obscure views, blur people’s understanding and cause original information to be lost — see figure 1.

“An investment in knowledge always pays the best interest” (Benjamin Franklin)
Our job as consultants is to help our clients make decisions and that means we need to get off the fence, say when models can help and also when they might not. We suggest that, rather than hiding behind complex models, we should discuss the views that would go into the model. Recipients of any advice will also have their own views — and we believe it is much easier for them to understand and use any advice if it is presented in this clear fashion.

In just the same way as a set of measurements tells us only so much about an item, actually asking ourselves the questions, “Does this feel right?” and, “What events would this be suitable for?” makes us likely to have a much greater feel for the appropriateness of a particular model. Rather than trying to distill the future into a mathematical best-guess, the model can only educate and forewarn the user by demonstrating clearly what could happen and why, using sensible scenarios.

Sensible solution
Can models really help? We suggest yes, but the model must be a simple collection of clear reactions to sensible scenarios so recipients of any advice understand the implications of their decisions. Creators of models, and hopefully users of models, understand that they are just models, but in trying to produce a single vital set of statistics that summarises the output, much of the understanding of the actual possible outcomes can be lost.

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The market
A market is formed when two parties come together to exchange goods or services at an agreed price. Investment can be thought of as deferring consumption today with the expectation of better return tomorrow. Market prices are determined by both current and future supply-and-demand expectations. Therefore, the inclusion of the future adds a whole new element to the original trade. If a price is agreed, based partially on hope or fear of the future, how is this equilibrium to be found? “One of the funny things about the stock market is that every time one person buys, another sells, and both think they are astute.” (William Feather, 1916)

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The model
On the premise that risk can be represented by some form of normal model statistic, and assets can be linked by an implicit character correlation, it is possible to create an asset allocation model. Pooling the daily fluctuations of an investment over the long term into a single statistic allows us to assess the impact of different combinations of asset classes without making exhaustive analysis of the basis of those fluctuations. If in the past, on balance, the value of an asset has behaved differently to that of another, then it is said to act as a diversifier.

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Ken Willis is a partner and head of the corporate investment practice and Jon Loach is an associate, both at Lane Clark & Peacock LLP

The views expressed in this article are those of the authors and not necessarily those of LCP. If you would like to comment on this article, please e-mail editor@the-actuary.org.uk