On Life, Statistics and Some Spectacularly Crazy Mathematicians

This blog is about random, independent and probably highly insignificant, non normal non-stationary statistical meanderings. The last I calculated it, the probability that anyone could finish reading such random stuff was about 0.00034.

So, there I was. In the midst of that terrific traffic chaos in Pune. 6:00 p.m. People, tired from the day’s work in office, wanting to get home. Mothers, with two little ones on scooty peps. School kids chattering dime to dozen on their bicycles, barely noticing the smog and laughing delightedly in a way that only a “school-is-over” event can bring on. In the rickshaw next to my car was an old man looking agitatedly at his watch and urging the rickshaw wallah to hurry. Hope nothing’s wrong, I thought. Hawkers selling roses and kiddie toys looking shrewd and snappy about the traffic jam; an extra 4 minutes at the signal means brisk business. The signal turned green. And the traffic moved.

In different moods and colors, to different destinations from different start points, with a sense of happiness and with irritation, the traffic moved as one. One rhythm, one direction, one sense of purpose. Radio Mirchi squawked “Traffic moving slowly and normally through Karve Road”…Eh? What was that? Normally?

Why is traffic normal, when there’s nothing normal about the individuals who are its components? A gentle tap on the window and I saw those twinkling eyes giving me my answer. Oh my God, are you really George Polya? Yes, he nodded at me gently. And then said the sentence that absolutely put to rest any doubt I could ever have about his identity. “I thought I am not good enough for Physics and too good for Philosophy. Mathematics is somewhere in between.” As Polya settled down in my car, his usual spry animated self, the answers dawned on my mind. The Central Limit.

I mean, look at all around you. You find those large number of random, independent variables, each with their own distribution, each going through the motions of love, happiness, stresses and tensions. People. Random variables. And yet, the summation of the populace, life in general, moving normally. Wow, I breathed softly, hats off! Polya, you crazy genius, in which fit of madness did you coin the words “Central Limit Theorem” to explain the most fundamental theorem in probability statistics. Its not just probability statistics; time and again I connect to the Central Limit and the Law of Large Numbers as theorems that hold the explanation to the process of life itself.

As life passes by, as the days go by, we find that we all tend to an average way of life, some average thoughts, some average standard of living. Sure, each person defines his own average differently. But the fact is that as the days collect into our kitty, we start living the Law of Large numbers. On a particular day, life may treat us rather well or unkindly; but the average life of the average person is on an average…average! How “mean”, you may well say, but there you are! Such is life; defined by the Law of Large Numbers.

I like to think of life as a time series; mostly non-stationary. It rejects almost all attempts to stationarize it. Should you manage to, it mostly turns out to be an ARMA process, part Auto-Regressive (anthropologists love to call this genes), part made up of a Moving Averages of past errors (and the psychologists call this environmental adaptation). Predicting the future (how rum is it that the master of forecasting should be named Box; this is one guy who is definitely out-of-box!) requires an artistic, atheoretical and unique approach and mostly is riddled with crazy levels of failure. And yet, most of us, wizards to muggles, want to study and understand the mad art and science of forecasting. They call it divination, and we, astrology. “Mars is bright tonight.” We try to fit patterns to the lines on the forehead and assess the statistical probability of combinations of stars creating situations of a particular type for us. By the way, did you know that the Ordinary Least Squares as a method of minimizing errors was suggested by Gauss in his work on movement of celestial objects? There you go. All statisticians have been enamored by it. The movement of the stars. Their effect on our lives.

Gauss. The other genius. He is always around in my life too. The Gaussian wrackspurt, if you will….

The other day in college, end-of-the-session babble broke out in the classroom as I wound up the discussion. And suddenly a student asked me a question. Such was the babble that I couldn’t really hear him. And merely guessing what he was saying, tried to give a rational answer to his question. His look told me that I had inferred wrong. A gentle tap on the door .“Inference. It always goes wrong when there’s way too much noise around you”. I swung around to see him walking into my class. The babble was still on; but my mind had turned into a silent zone. There was total silence. Till he decided to talk. Gauss. The Greatest Mathematician since Antiquity.

“To hear the question and give the answer: That’s estimation, my dear. But, to interpret the question correctly. Ah, that is the art and science of inference. If the model errors are too vocal, exhibiting auto-correlation or heteroscedasticity noise, the inference on the estimates goes wrong.”

How did you know, my mind was asking. How does the solution come to you…Does it come in a flash of lightning, or is it a slow, prolonged process.. “I have had my results for a long time: but I do not yet know how I am to arrive at them.”

A good poem and a rainy day. Can’t get better than that. A poem titled “Yevgeny Onegin”by Pushkin. Hmmm, on the continuation of life even as death takes us over individually. And what’s this? Markov’s commentary on Onegin? Andrei Markov. Really? I mean, could this be THE A. Markov? As in, the Markov chains guy? What in the world does HE have to do with Pushkin now? Quite a lot, as the story goes.

We go back in time to meet Pushkin and Markov. In the tsarist Russia of late 1890s. At that time, statistics had developed to a point where probabilities of sequences of events were being estimated as the product of the two events happening independently. So, if a day can be sunny or rainy, the P(Day is sunny) = 0.5 and P(Day is sunny when earlier day was sunny) = 0.5*0.5 = 0.25. But, events are usually dependent, aren’t they? So, if today is sunny, doesn’t it impact the probability of tomorrow being sunny? Isn’t it true that probabilistic chains necessarily need an intertemporal dimension? The probability of an event today HAS to depend on the event occurring in the most recent past, a little lesser into more distant past and so on. And therein lies the genesis of Markov chains.

Markov was a man possessed in proving the interdependence of chains of events in a temporal sequence. His choice of a sequence to prove interdependence? The poem “Onegin”by Pushkin. Oh, this is sublime!

He chose the first 20,000 letters in the poem arranging them without punctuation or breaks, counting 8,638 vowels and 11,362 consonants in the process. There were 1104 vowel-vowel pairs, wherein a vowel follows another. Now, if occurrence of a vowel in the sequence is independent of what occurs earlier, then, the P(vowel-vowel pair occuring) = (8638/20000) * (8638/20000) = 0.19. That implies that in 20,000 letters, such combinations should have occurred 3731 times, nearly thrice the 1104 number of times that they occurred!

Wow, wow and more wow! This necessarily means that independence of vowels stands rejected! Thus, letters in a word are NOT independent you see; there is an overwhelming tendency for vowels to alternate with consonants in a language! The same logic has hence been used in applications as diverse as understanding motions of gas particles to creating the Google algorithm.

Onegin may be a poem par excellence; but it will go down in the annals of history as the literary masterpiece that served as a workhorse for a uber creative mathematician. How befitting that Onegin should talk about continuity; because if there is one theme that Markov explored, it was one of continuity and interdependence…A gentle tap on my shoulder…I need to go. It’s Markov.

Analysis of the rate cut: What has changed in the past one month?

Wow! Early morning surprise by the RBI Governor: A rate cut of 25 bps on repo, pushing it from 8% to 7.75%. The other key rates and availability of liquidity under other windows such as repo have been kept constant. While I have been rooting for a rate cut for some time now, I must confess that I had thought that the Governor may choose to unveil the same only post-budget.

So, what has changed since December, except that India is now “used to” zero WPI inflation? I think that a big angle is that there is more certainty now, than in December, that the globe will remain a low interest rate place in 2015. So, a reduction in the Indian rates will not pose a threat of us being the only country out of synch with the others, causing pressure on the exchange rates. Here are a few factors that could have finally persuaded the inflation warrior to give a smallish rate cut, if only on repo:

• The world is confirmedly on a “soft” platform now. Multilateral agencies including the World Bank were looking at a global GDP growth rate of about 3.2%- 3.4% for 2015 and that has since December been revised downwards to 3%. It is, as usual, fruitful to remember that the 3% growth rate has long been a psychological benchmark for gauging “global recessionary” trends. In a soft growth world, there are lesser chances of interest rate hikes by any of the major trade partners of India and hence an interest rate reduction would not really put our monetary stance out of synch with any other banks’ stance.
• In particular, it is important to look at what Ms. Yellen is thinking if you want to analyze how Dr. Rajan works. In the past 3 months, the US data has been increasingly upbeat. The growth rate has firmed up nicely to about 2.5%, a long cry from the negative growth rates witnessed during the sub-prime. At the same time, the unemployment rate hit a 6-year low of 5.8% and in the month of December, the Fed was quoting that it could go further down to a level of about 5.3% by September 2015. In fact, the UK magazine “The Economist” made a remark tongue-in-cheek that the US seemed to be on a “rude” growth spree, growing at a time when the world was looking forlorn. Based on the growth and labor numbers, the Fed was increasingly hinting at a rate hike that could start in February or March 2015. What was not expected then was the oil could actually fall to $40 in January 2015. Now this fall in oil has had two consequences on the US interest rate prospects. First, of course, it has reduced the inflation levels in the US significantly, cooling the prospects of an immediate rate hike. What is now largely being said by analysts is that Ms. Yellen may now choose to spend the next 6 months “preparing” the markets for higher costs of borrowing. Second, a large chunk of those shale investments that will be hit by the reduction in crude are concentrated in the US. And hence, even as inflation falls, there is a hint that the investments in oil and gas in the US could also take a hit in 2015, thereby supporting the fact that those rate hikes in the US will be postponed some more.
• In the meanwhile, the East is faltering. China is on a deliberate slowdown mode and is grappling with its internal issues of banking, investments and growth. Japan, which has been frustrated with its deflationary history, is now facing issues as the price indices move predictably downwards with the crude oil softening. The Eurozone too is on the verge of a recession and the falling oil prices mean that the interest rates will stay low.
• Lets talk about Russia, where the interest rates have been….raised. Now, there is big trouble brewing there. Firstly, there was the issue wherein Crimea, which was a political part of Ukraine was separated and attached to Russia in March 2014 by Putin, a move which the EU has not taken to nicely. This caused the EU and the US to raise sanctions against Russia, which hurts their trade and investment prospects significantly. Secondly, Russia seems to be plagued by the notorious “Dutch disease.” Dutch disease describes a phenomenon wherein a country starts exploiting a natural resource sharply (in the Russian case, oil, which became its “lead” sector) and emerges as a chief seller of that commodity in the international markets. As the oil prices in the world increased from 2010 to early 2014, the Rouble too maintained its levels nicely, making it cheap for Russia to import the “non-oil” or the “lagging” sector commodities. So long as the oil prices were high, Russia had the FOREX to finance imports of the non-oil commodities. It also implies that in an appreciating Rouble phase, Russia would be privy to “cheaper” borrowings from abroad, which would help further the investments in the oil sector. Now with the falling oil prices and the sanctions, the export revenue of the economy stands massively reduced. This would put a pressure on FOREX reserves and/ or the exchange rate, and as we have seen, both the variables have been under significant pressure. The depreciation has meant that the cost of the repayment of the debt and interest has increased manifold. At the same time, the sanctions imply that the lenders are not really in a mood to roll-over any of those fast-maturing debts. Even if Russia increased her interest rates overnight, from 10.5% to 16%, this kind of an interest rate hike is not reflective of any regular monetary policy stance and does not fool anyone at all. In fact, such interest rate hikes are normally subjected to Catch 22 processes- the fact that the rates have been hiked tells everyone loud and clear that there is trouble; capital outflows post-hikes are normally notoriously higher than they were before. Thus, I do not think any Central Banker would be currently worried about being out-of-synch with the already-out-of-synch Russia.
• And then, there are the domestic factors. The Modi statement that the Government will not interfere with the workings of the banking sector has brought a hitherto unseen warmth in the Central Bank-Central Government relationship. Economically speaking, the fact is that not only the CPI and the WPI, but also the core inflation has shown significant slackening in December. Core inflation, since it removes the effect of food and fuel, is largely indicative of demand conditions in the manufacturing sector. Thus, softness in demand in manufacturing, low crude prices, lower than expected prices of foodgrains, especially cereals, and most interestingly, a reiteration of the commitment by the Modi Sarkar to stick to fiscal discipline, all suggest that price pressures in the immediate 6 months would not be daunting.
•  A final, and slightly technical point. The reduction of 25 bps in the repo does not really change the dynamics between the call money market rates and the LAF corridor since the call rates have been roughly at 7.50%- 7.60% levels in the past quarter, even when the repo was at 8%. Thus, the repo volumes need not really see a huge jump immediately even if the repo stands slashed to 7.75%.

Nice move, Governor. A signal, that we are looking at a softer interest rate regime in the next 6 months, without really affecting the real dynamics in the market.

Putin, Politics and Philosophy :)

The opening scene is Kremlin, where a worried (but outwardly unrelenting) Vladimir Putin is thoughtfully buttering his early morning toast, hoping that the rouble will sort itself out on its own.

Obama (This does not have to be THE B Obama…its just that Putin’s best friend’s name is also Obama) : Vlady, its just a bad case of Murphy’s Law. Its just that the sanctions had to happen just when the Saudi buggers decided to keep the oil prices low. Effectively, that’s what we are. Russia falling butter side down.

Vlady: I just hate this thought stream because its too…karma, if you know what I mean? There is an equal chance of the toast falling butter side up, 50%, Murphy be damned.

Obama (Eating his eggs sunny side up): But Vlady, there’s no butter side up for us. The Sunni side up in the Middle East has made it a real tough egg…err…I mean, look at all the numbers; everything is against you. The inflation is hitting 9% and FOREX reserves are down to $400 billion, about $100 billion of debt maturing this year and sanctions on rollovers, hardly any exports, and the rouble..

(Just then the TV screens show that the rouble has hit a new low of 90 to a dollar and Vlady drops the toast)

Obama: OMG, that’s butter side down! I told you, Vlady, its butter side down.

Vlady: Oh heck. Don’t get so excited Oby. I just buttered the wrong side!

Enters Sigmund and looks with total fond approval at Putin and at his unabashed Freudian reasoning capacities. That’s the way the Freudians work: They reason in such a way that you can’t possibly disprove their reasoning.

Sigmund: Lie on the couch Vlady and tell me, what is it that worries you. Where id was, the ego shall be. But id is so small damn it, how did you fill its place such a super sized ego.

Vlady: Crimea has always been an integral part of Russia in the hearts and minds of people!

Sigmund: Oh, this is wonderful! Tell me Vlady, tell me, why do you think that Crimea belongs to the Russians?

Vlady: Because…it has always belonged to the Russians!

Sigmund: This is delicious. Yes, yes, I begin to see. The post hoc ergo propter hoc fallacy complex.

Vlady: Talk Russian, will you?

Sigmund: After this, therefore because of this.

Vlady: After this session, Oby, I swear I will therefore because of this man, kick you real hard.

Oby (disturbed): Guys, focus..don’t let your personal issues get Russia down. The principle of parsimony. Occam’s razor. Keep it simple folks..Vlady, you were saying…

Vlady: Everything is for the best in this best of all possible worlds. So, Crimea belongs to Russia!

Sigmund (impressed): I never thought I’ll see the day when politicians confound me with Leibniz. But my dear man, illusions commend themselves to us because they save us pain and allow us to enjoy pleasure instead. We must therefore accept it without complaint when they sometimes collide with a bit of reality against which they are dashed to pieces.

Vlady: What the hell was that? Illusion? 90% of Crimeans favor secession. The referendum was absolutely in accordance with international law…ask Oby, I told his namesake as much on phone the other day but he wouldn’t listen to me. If he got the Nobel Peace Prize, I will get the Noble Piece Prize…because Crimea..belongs…to…Russia

Obama : Now, now, Vlady, don’t get all worked up. We’ve got’em anyways…and the sanctions too, by the way. Ok, ok, don’t look all fiery…what’s some sanctions anyways? But remember why I got Sigmund here…ask him about the lady. The German.

Vlady: Hmmm…I can’t understand her. She is such a quiet fighter, she is rather like me, but very different.

Sigmund: Ach so mein lieber mann…go on…tell me…who is this lady who entices you so..

Vlady: Entices, my foot. She is one hell of a problem, Angela. She has got the entire Eurozone convinced that sanctions against Russia are justified. Just a few days ago, the Polish Tusk…

Sigmund: Ah, my child…now I start seeing the pattern. When you visited the zoo in your childhood, you were threatened by the elephant.

Vlady (yelling): Oh, heaven help me! I am talking about THE Tusk guys! The Polish PM…can you believe that he had the guts to levy sanctions on me, the mighty Putin. Poland? Poland? Who is Poland? Nobody. Its not Tusk, its the Angelephant behind it. Otherwise would Poland have the guts to talk to RUSSIA? Me vs. Angela is guns vs. butter. And this moppet doesn’t blink at the sound of guns.

Sigmund: The great question that has never been answered, and which I have not yet been able to answer, despite my thirty years of research into the feminine soul, is ‘What does a woman want?

Vlady: Then get the hell out of here. I want a solution to the Euro stand off. And I don’t have thirty years…oh god, that’s already one day spent on psychoanalysis out of the two years in which I have claimed Russia regains her original avataar.

Obama: Vlady, India on line.

Vlady: Yes, let me chat up. By Jove, its good to hear a friendly voice. Earlier, of course, when I called in March to tell’em that now Crimea is ours because it was always ours, I was met by friendly silence. Now of course, there’s lot of noise. Yes, put him on…Krem cho?

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This blog is dedicated to the MBA Finance batch 2014-16 for having encouraged my ramblings on philosophy and Russia with unabashed enthusiasm. The book “Plato and the Platypus walk into a bar” has changed me forever and this blog takes off majorly on the anecdotes in the book. I am indebted to you, Pranav, always, for having given me this delicious read.