A handful of tricks!

Thought to share this wonderful post by Terry Tao, on problem solving strategies for the Real Analysis course. 

Many A Few Good Men

“Tis strange—but true; for truth is always strange,

Stranger than fiction: if it could be told,

How much would novels gain by the exchange!

How differently the world would men behold!”

So said Lord Byron. Fiction, is less strange than truth, because fiction has to adhere to the realm of possibilities, where truth doesn't have to abide by these restrictions. While pursuit of truth is a relentless goal, the appetite for fiction is perhaps stronger than the truth - at least in the world of finance. And nothing illustrates it better than the recent hullabaloo over the appointment of the Reserve Bank of India Governor and the reaction of markets. 

Ever since Rajan excused himself from an extension about a fortnight back, the markets have been ripe with speculation for the next probable governor. Immediately after Rajan's announcement, a list of credible probables was formed which included, among others, Urijit Patel, Arundhati Bhattacharya, Subir Gokarn and Rakesh Mohan.

Media quickly pounced on the list and one name stood out: Arundhati Bhattacharya. In Arundhati, they saw someone who could potentially become the first woman to break the glass ceiling at the Reserve Bank. In the age of women empowerment that made a pretty picture, without a doubt. The rumour had enough romanticism in it to last for about a couple of days, and so it did. 

But soon enough, the romance met its fate and the rumor ran out of the steam. The markets, which thrive on speculation, realised that they weren’t looking for a cornered contest. They were instead itching for a fight, a legitimate, pacy duel. After the dust started to settle down, the markets reasoned that perhaps, Arundhati was only a career commercial banker who lacked a background in economics. Urijit, on the other hand was labelled as Rajan’s best lieutenant and therefore, unlikely to find favor with government. Ultimately, as the analysts echoed in unison, the fight might just boil down to Rakesh Mohan and Subir Gokarn.

So, that was the duel, albeit sketched in a hurry. However, the cast of the duel was a little unequal right from its inception. Rakesh Mohan, as several pointed out, was as a little too seasoned and vocal for the job. Alas! that basically left Gokarn as the only contender for the position.  

But then again, one contender didn’t make for a good contest, did it? A lazy rumor reluctantly brought back Urijit’s name back in the contest, but by then, the markets had firmly made up their mind on his unlikely candidature. The winds were hunting for someone new. It was then that the name of Kaushik Basu, another eminent economist, was meekly floated. The markets listened poignantly. Kaushik had all the credentials to match Rajan. But hasn’t he been too leftist, and isn’t he a congressi?  The markets debated. Soon enough, Kaushik Basu was swiftly dismissed. Although he had all the right credentials, he failed to clear, apparently the most important, political allegiance test. 

A lull followed. 

The search for governor, at least for the markets, was turning out to be tiresome. A good rest during the weekend, brought back some clarity of thought. Creative energies were replenished. And the hunger for rumors restored. By now, the markets knew what they wanted. They wanted someone with good credentials and also close to the government. 

With the Monday, came the big “leak”: Arvind Panagariya emerged as a leading top contender out of nowhere! Arre, who is Panagriya, is he desi, is he dove,? The markets wondered. Immediately, Panagariya was frantically searched. Results revealed a self-proclaimed dovish, pro-growth economist and a favorite among Jaitely & Modi. Finally! Someone who ticks all the boxes (except the subramanian-swamy box). Immediately, the traders reacted. Bonds rallied in anticipation of a dovish governor. The volatility was far more than witnessed during the Brexit or closer to home, the Rajan’s exit.

In the world of finance, a credible rumor had (once again) beaten the facts. 

While the decision for the governor is still yet to be out (and can be out any minute - again, a rumor!) and it is anyone's guess on who that could be, one thing remains undeniable: when it comes to markets, truth may be more strange, but fiction is perhaps more strong (and perhaps, more persistent).   

Update: The last two days were spent in anticipation of announcement, however, nothing happened. Just when the markets were becoming to show signs of weariness another name has cropped up as a top contender: Shaktikanta Das. A neutral bureaucrat who has worked extensively and thought to be in sync with the government. The market however has not shown much of a reaction so far, because Das is at best thought to be only a feeble dove. Be that as it may, even Shaktikanta Das doesn't clear the Subramanian Swamy's check.

Update2: The latest to make a comeback in the list is Arundhati Bhattacharya, who is now being seen as the "best bet", when its only been about a week that the media was labelling her as "not a good choice". While all this is floating around, the market is just quietly waiting for the announcement -the sort of quiet before the storm. If its Arundhati Bhattacharya, there will be another rally in bonds, but only due to the additional dovish surprise. Somebody else than Arundhati or Panagariya may actually lead to a tumble because the market is sitting on a heavily internalised dovish expectation.

Update3: It is Friday morning and the announcement hasn't been made yet. The monsoon session of the Parliament starts on Monday. It is reasonable to assume that it would be convenient for the government to clear the air on governor before the parliament resumes. Few more hours to go before the sun sets on Friday. It has been a good build-up for climax. Will it be a wild card surprise? Tick Tock, Tick Tock, the clock pushes by...

Update4: Never has a wait been such a thriller. The latest top contenders are Urijit and Arvind Subramanian, the current chief economic advisor to the government. Arvind Subramanian is believed to be dovish inclined, if not as vocal a champion for rate-cuts as Panagariya. Notably, Rajan was also the chief economic advisor before he was appointed as the governor and like him, has a videshi green card. Tough choices, really!

Update5: It was speculated that the appointment would be announced before Monday, when the Parliament session begins. However, that didn't happen, which only leads to believe that the appointment will likely be announced in the Parliament first. In a related development, Kaushik Basu, one of the earlier contenders for the job, will be ending his term at the World Bank on July 31. Paul Romer, a very accomplished economist, has already been unofficially confirmed as his successor. This leaves Basu with a very smooth transition in the event that he is appointed as the Governor, although his age might be an adverse factor, as he already running 64+.

Update6: After about keeping the markets guessing for more than a month now, the government announced Urijit Patel as the governor. 

Which color will be the "Brexit Swan"

For a long time, the mankind believed that swans were only white in color because all the known swans in the world were white. And then one day, a black swan was spotted. That single bird, destroyed the belief which was held for centuries. Ever since then, the phrase “Black Swan” has come to denote an event which is rare and also extremely heavy in its impact. 

Taleb, a former trader and a mathematician has developed a Black Swan Theory which states a Black Swan as an event which has “rarity, extreme 'impact', and retrospective predictability”. History is flushed with such events, which according to Taleb have significantly altered the course of history, and decidedly so, changed the human life.

An event belonging to the same family which will unfold tomorrow is the verdict on “Brexit”. In very simple terms, the entire UK population is going to vote on whether UK should exit or remain as a member of the European Union.

Economics arguments aside, the recent polls suggest an evenly divided picture in the UK voters.

The financial markets around the world, however, seem to be heavily factoring in that Britain will vote to remain in the EU, for instance, as captured in the way Pound has picked up against dollar recently.

In such pro-remain sentiment, the exit verdict will probably be nothing short of a “Black Swan” event. A surprise which will send ripples through the financial markets. However, if history is any indicator, traders who have taken extreme contrarian positions, are likely to make a windfall gain.

After-all, who in the financial world hasn’t heard of George Soros, the man who while betting on sterling’s devaluation made $1 billion in one single day in the year 1992.

In my opinion, the poll vote estimates embed an upward bias for the "Bremain".  First, because the sample set is not adequately representative of the local Brits population. Second, such referendums are more about sentiment than reason. Despite the whole reasoning of economics, there is nothing new that we know today in terms of the consequences of Brexit which we didn't know an year back. The genesis of this movement lies in deep nationalistic sentiment - and not in economic projections. In the race to the ballot, sentiment almost always trumps the reason.

Exit or Remain, the verdict will be out in 24 hours and the swan will reveal its colour. White or Black, which one are you betting on?! My bet is that the exit swan will be the one that surfaces on Thames, tomorrow. 

A Banking Bankruptcy

Economics is like meteorology- everyone has a view on the weather, but few understand the science behind it.

What this unfairly does is that it gives a (birth)right to everyone on critiquing the policies or the subject in general often without actually understanding the various mechanisms that underlie or even an appreciation of the complexities that are embedded.

But Economics is not alone in this distinction.

A close cousin to it, is the Banking industry.

At the very least, Banking forms an important part of our activities throughout the life cycle. Spanning right from the education loan to the retirement savings, banking has a whole gamut of products and services which can significantly alter the quality of life.

But the amount of ignorance on the business of a bank is appalling - even amongst the people who work in a bank.

One may argue, that we don't really need to understand the business of a bank to use an ATM just as we don't have to understand the principles of combustion to drive a car. The analogy seems almost right but its misleading because of one vital thing: stakes. A dent on a car will at best upset you for a week. But a dent in the banking system can just erase a decade of one's productive life.

Perhaps, banking is like the monsoon: many want it badly, but few want to get wet!!

In Leaps and Bounds!

Sometimes news can make your head spin.

Just this week, Japan’s GDP numbers were announced and they report that the GDP has expanded by an annualized 1.9% and about 0.5% on a quarter-on-quarter basis.

Previous to these announcements, Japan was struggling to avert a recession, which is not surprising considering how it has been struggling to barely keep itself afloat for the last decade.

So you will think that a positive growth should really be a good news for Japan, right? Wrong. Instead of rejoicing in the growth numbers the economists seem worried. Well, we are all too familiar with their quibbles and quarrels but this time around the reason for their worry has got nothing to do with economics! 

Rather a queer phenomenon seems to have inflated these growth numbers: leap-year effect.

What could be this leap year effect? Well, as the name suggests, it has got to do with an extra day in February. A Jan-Mar quarter in 2016 will have to be adjusted for this one day before we compare it with a Jan-Mar quarter of 2015. But how much can just one extra day of spending, (not of earning, mind you) really change the growth numbers? 

A lot apparently, as the Japanese economists seem to point out and this is where the story starts to get interesting.

According to some estimates:

“The effect of the extra day from the leap year may have magnified first-quarter growth by about 0.9 percentage points on an annualized basis and by 0.3 percentage points on a q-o-q basis” Reuters

“Excluding the impact of leap year, which added an extra day to February, GDP probably expanded around 0.2 percent [on a q-o-q basis, instead of the reported 0.5%]” Reuters

Economists are infamous with their craft, but a 0.3% error on a 0.5% estimate is just too much trickery for even the economists!  So, what is really going on in here?

To understand the intricacies, let’s just brush up our concepts on GDP calculations. A typical year is divided into four quarters. While a calendar year starts with Jan-Mar quarter, a fiscal year starts with the Apr-Jun quarter. A quarter-on-quarter growth rate is measured as the GDP growth in the current quarter over the preceding quarter. For example, a q-o-q growth rate for Q4 2015-16 (fiscal year), would be the growth that happened in the months of Jan-March 2016 over that happened in Oct-Dec 2015. 

From this q-o-q growth rate, an annualized growth rate is derived. This annualized growth rate is a hypothetical number which extrapolates the q-o-q growth rate over the next three quarters to arrive at an annual figure, with the assumption that the next three quarters will behave exactly same as the current quarter.

With these definitions under the belt, let’s proceed to frame our problem here. Consider an economy where within a quarter, each day is exactly identical in terms of economic activities. People wake up, work, produce, consume, save and sleep in exactly the same amount and fashion each day of that quarter. Once every day in a quarter is identical, we can calculate "per day GDP" by simply dividing the GDP in a quarter with the total days in a quarter. We can then postulate that this per day GDP is what would have been counted for 29th Feb, and then simply deduct this from the quarterly numbers to get the leap-year adjusted number for GDP in the Jan-Mar quarter.

But for a moment think about this: what really changes on 29^th Feb? If you are a regular employee, do you get paid more? Do you pay an extra rental for the apartment? Do you pay extra on the monthly travel pass, membership cards? No, not really. But then do you pay for an extra day of gas, electricity bills? Do you buy groceries for that extra day? Yes!

So arguably, there are some portions of GDP which are insulated from the extra day effect, and some which will get increased. A per-day GDP estimate has both these portions embedded. In order to disentangle the portion which really gets affected by an extra day, we follow a rough fraction, say, 25%. Empirically, this number will be different, but for our immediate purpose this is a start.

So now our job is almost done. All that we have to do is to calculate a per-day GDP number and 25% of this is what we will deduct from the Jan-Mar GDP levels to adjust for the leap-year effect. Here are the sample calculations based on the actual numbers for Japan.

#	Item	Value	Comments
a	GDP in Oct-Dec 2015	4.4515	Japan's GDP in trillion $
b	Q-o-Q Growth Rate	0.50%	Official Figures
c	GDP in Jan-Mar 2016	4.4737	a*(1+b)
d	Annualized Growth Rate	2.02%	(1+b)^4-1
e	GDP per day in Oct-Dec	0.0484	a/(31 Oct+ 30 Nov+31 Dec)
f	GDP Increment on Leap Day	0.0121	25% of e
g	GDP in Jan-Mar without Leap Day	4.4616	c-e
h	Modified Q-o-Q growth rate	0.23%	(h/a)-1
i	Modified Annualized Growth Rate	0.92%	(1+h)^4
j	Difference in q-o-q growth	0.27%	b-h
k	Difference in annualized growth	1.10%	d-i

Well, the numbers do turn out to be similar to what Japanese have been suggesting: the difference in GDP growth rate on a q-o-q basis is around 0.27% and a difference of 1.1% on an annualized basis! Voila! Who would have thought that an innocuous day could make such a difference! 

For a country like Japan, where the q-o-q growth numbers are <0.5%, this makes a huge difference. What about India? Well, the leap year effect will definitely be there, but will it matter enough? Well that depends on how much portion of GDP really gets affected by an extra day. For our above calculations that portion was 25%. However, this will vary, country by country - and this number is really the crucial number here. The higher it is, the higher will be the leap year adjustment. 

All that said and done, the basic dilemma remains: why should we work when we don't get paid extra! Well, unsurprisingly, we are not alone in this thought. In-fact there is a Petition to make leap day a holiday!