# The Second Derivative Turns Down

‘The second derivative’ is not a Robert Ludlum novel, nor an element of Christian dogma. As described here back in mid-April, it is an algebraic concept that became hot in economic circles last spring. Now it looks as though it is making a comeback, but this time it will be much less popular — because in the spring the second derivative phenomenon was all about better news, whereas in the fall it looks like being about worse news.

Note the use of relative terms, ‘better’ and ‘worse’, rather than the absolutes, ‘good’ and ‘bad’. That’s the essence of the second derivative, both in its mathematical and economic applications. The easiest way to understand the concept is to think of speed (velocity) and acceleration. The first derivative of movement is velocity, measured (in cars) in miles or kilometers per hour; that’s how fast you are moving. The second derivative is acceleration/ deceleration, which measures the rate of change of the first derivative, velocity. When you decelerate from 150 to 100 you can’t be said to be going slow, but you are definitely going slower.

The same goes for economies. When an economy is in a severe recession, as virtually everyone was in the first part of this year, a deceleration in the speed of decline is an improvement: things are getting better because, to be precise, they are getting worse more slowly. In the second quarter of this year, virtually all developed economies were declining much more slowly than in the first. That meant that the rate of growth — the first derivative –– was still negative, but the rate at which the rate of growth was declining – ie the second derivative — was now positive. In some countries, even the first derivative turned positive in the April-June quarter; by July-September it had done so almost everywhere. We know this from the recent flow of monthly data, although the official GDP growth data for the quarter that ended on Wednesday will not be available for some weeks.

But we also know more than that. The flow of data began to improve in March, so that by April everyone was focused on the ‘green shoots’ and by May it was quite clear that the second quarter was going to show a big improvement over the first quarter (meaning a positive second derivative against a background of a negative first derivative). Now there are signs of a reverse process. Numerous items of economic data for August and September – by no means all, but quite a selection, both geographically and within economies – are proving to be worse than expected or even plain bad. ‘Worse than expected’ means the second derivative has turned negative, after a period (typically several months) when even the first derivative (the rate of growth) had been positive. ‘Plain bad’ means that the first derivative has also turned negative.

It is important to be clear about what this does and does not mean. It does NOT mean that the global economy is about to collapse again, as it did late last year, or even necessarily suffer a ‘double dip’. The pessimistic camp still expects that to happen, but the current signs of weakness provide no direct support for this view. What these signs of renewed weakness do indicate is that the optimistic scenario, of a sustained and rapid recovery – labeled the ‘V’ scenario in which a sharp decline is followed directly by a sharp rebound – is not being realised. Every setback, whether it relates to orders for durable goods, or new unemployment claims, or bank lending or whatever, is another nail in the coffin of the ‘V’ scenario and brings nearer the ‘U’ scenario in which the economy bumps along the bottom for quite a while, before gradually improving.

Most people living in the real world never had any illusion that things were getting much better very quickly, so the data confirming this state of affairs cannot shock them. However, people living in la-la-land – which includes almost all the mainstream financial institutions and those of their clients who chose to float off with them – have convinced themselves that the future is going to be like the pre-crash past, with share prices marching endlessly higher and house prices resuming their supposedly inevitable and endless rise in value. This mindset had been translated during the quarter just ended into a massive rally in global stock markets, predicated entirely on continuing, rapid and sustainable recovery in growth, profits and all the rest. If, as was always likely and is now being confirmed, this mindset was delusionary, the ‘correction’ needed to bring the equity markets back to the real world is likely to be sharp and painful.