- 27 January 2014
- By.. Mr Shailesh Dhuri

How QE infinity can possibly be reconciled with impending deflation?

As we have been pointing out in our previous posts, the global economy, especially the developed world, stands at the brink of deflation right now, in spite of relentless printing of paper money by central banks. We are aware that many policymakers do not foresee an onset of deflation. However, they also did not foresee the credit crisis of 2007 or the Euro crisis of 2011.

How do we possibly reconcile our deflation argument with infinite QE? Standard textbook explanation about the fall in velocity of money due to inability of banks to lever up fails to offer a sufficient and full explanation. First, banking leverage ratios across the world are not low currently by long-term historical standards, if we are ready to ignore the la la period of 2004-2008. Secondly, corporates are sitting on huge pile of cash. By some estimates, corporates in USA have about $1 trillion in cash. Clearly, at least the large corporates are not hindered by the lack of credit – they do not need credit. What is lacking is the animal spirit - or is it that corporates have found a way to grow by investing only a small fraction of their free cash flows? Maybe a strange mathematical formula might offer a cues to the current situation.

More than 101 years ago, in February 1913, Ramanujan, a poor Indian savant mathematician wrote in one of his many letters to Hardy, a renowned English mathematician in Cambridge “… that the sum of an infinite number of terms of the series:- 1+2+3+…..= -1/12 under my theory. If I tell you this, you will at once point out to me that the lunatic asylum is my goal.” 1

We, mere mortals, may ask how can well respected mathematicians claim the sum of infinite series of positive numbers be less than zero? The answer lies in the contrasting concepts of

A. What you should expect to be the ultimate answer if you were in the process of counting and have not yet given up on counting

B. What you should actually get as an answer the moment you stop counting at any large number and see what answer you have got

What Ramanujan rightly claimed is that in case of “A” the value of the infinite series is negative. However, as every high school student knows, in case of “B”, the moment you look at your actual answer, when you stop counting at some point, the actual answer will never be -1/12.

Strange mathematical results, which seem to have no relation to perceived reality have tendencies to find appropriate real world applications centuries later. The above formula for the sum of infinite natural numbers is used by physicists in areas as exotic as string theory. The imaginary number i, encountered by mathematicians while solving cubic equations found application centuries later in the field of electromagnetic waves. Complex numbers and analysis find wide application in quantum mechanics. The strange and rather non-intuitive non-Euclidian geometry discovered in mid 19th century later found real application in Einstein’s theory of relativity.

Maybe, similar to the strange Ramanujan's formula, something unexpected but real is happening in our current economic milieu. As long as central banks keep printing money and do not stop that action, the expected outcome of their action is deflation. One may reason this by saying that when central banks have so many emergency measures at work, no sane corporate executive will dare to think that the global economy is a safe place to invest, and hence will not invest.

On the contrary, when global central banks actually stop printing money and withdraw the emergency measures, we would have so much of high-powered money around that it could lead to sudden hyperinflation as companies begin their investment spree.

As an investor, how one should protect oneself in this scenario is an interesting question raised by the above analysis. We leave it to you to ponder on the same.

^{1} It should be noted that Euler, 1707-1783 had found this strange result before Ramanujan. However, the Indian Savant was self-taught and hence was unaware of the work of most mathematicians.