Maths is no surrogate for imagination

August 2013

Value at Risk (VaR) was devised to capture a bank’s exposure to risk, the taking of which is the engine of bank profits. That may not be so different from taking bets in a casino and is by no means the same thing as investing in a new business. Yet in modern finance this distinction is not only blurred but often reified, described in quasi-scientific language that leads one to think there must be hard facts behind or beneath it; that finance is as ‘hard’ as falling apples.

Consider this piece of jargon (from Wikipedia): ‘Value at Risk is a widely used measure of the risk of loss on a specific portfolio of financial assets … defined as a threshold value such that the probability that the mark-to-market loss on the portfolio over the given time horizon exceeds this value (assuming normal markets and no trading in the portfolio) is the given probability level. For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% probability).’ 

Naturally, if one analyses something from the physical world, it will exhibit stable and constant properties, which can also be expressed numerically. But the constancy comes from the physical world, not the maths; from the fact of gravity, for example, not the quantifying of it. The question is whether there is any such world behind financial maths. And also whether it is true that the future is discoverable in the past.

What the maths endeavours to do is to cast a net over the future, based on how things have been in the past. But is it really the case that the future derives from the past? Does my momentum cause me to catch a train, or my intent on achieving my destination, my image or expectation of the future? And can the future really be captured by maths? Is it not, rather, that the future is indeed unfolding from the future and has nothing to do with the past? In which case, maths may not be our best tool, other than as a way of imagining how things might be. VaR brings to mind John Nash’s equations on a saltwater library window. Using maths, he was trying ‘to get his head round’ the complexity of modern economic life, especially when it seeks to predict or gauge the future. But for this the right medium is imagination itself, reflective as it is of gut instincts and of what lives in our will.

Once perceived by or in the imagination, what to do or what will be done can be computed (for example, in a financial plan), but can one usurp or displace or even render imagination secondary by using maths? As Newton is reported, by Keynes, to have said when informing Halley of one of his most fundamental discoveries of planetary motion: “Yes,” replied Halley, “but how do you know that? Have you proved it?” Newton was taken aback: “Why, I've known it for years. If you'll give me a few days, I'll certainly find you a proof of it.”

Furthermore, if one begins in the realm of financial maths, instead of the ‘real’ world, the closest one gets to the real world is the world of stocks and bonds, money flows. But these to a certain extent these can be made to behave in the way one thinks they do or should behave. One can also go as far as changing governments to ensure that a country comports its economic behaviour (and thus its financial outcomes) with the pre-requirements of an investment strategy. 

If one is not to go the path of faux science (forcing the compliance of society in the process), how is one to understand economic life if not by imagination proper, true imagination? This takes us beyond the limits to knowledge set by brain-bound thinking, bringing the players together so that by sharing their knowledge and understanding of events, including their intentions, they together lift their understanding to an imaginative level. This level is not less real than mathematics, not less ‘physical’. The question is which better matches life.

Finally, when investing, is one merely betting one’s capital or is one seeking to underwrite the initiatives of other human beings? It is a moot point whether imaginative economics can be part of merely betting. If one is only concerned to know how much of one’s capital is at risk of being lost, how can one be concerned with the intuitions, endeavours and experiences of those, managers and workforce, who in fact create the extra value one is seeking to appropriate? Doubtless one can calculate the risk to one’s portfolio, even make this calculation close to certain. If to do so is to record typical investment patterns passively, that is one thing. For the investment is not then pulled by the investor (or his agent) when perhaps most needed by the entrepreneur. But if the aim is to ‘exit’ when profit falls or falters, what effect does such egotism have on the borrower and his objectives? In the alchemy of financial life, in confirmation of their own pessimism, such acts can kill the very forces needed to overcome the problem. 

'Value at risk' really means 'return to investor at risk'. The concept implicitly places the investor and his capital above or before the user of the capital, the entrepreneur – as if capital can grow of itself, merely by being lent. This is never the case. Capital 'grows' because it is lost into skills and initiative in order that they – if successful – can create new value. It is from this new money that the obligation to repay borrowings is paid. Economically speaking, therefore, it is nonsense to do otherwise than base repayment and interest on the actual performance of a business, not on the abstractly stated terms of borrowing.