Belling the Fat Tailed Cat

Though a useful statistical tool to simplify things and arrive at broad 'ballpark' conclusions, the normal curve, I believe, has been mistakenly used in contexts where it needs to be 'tempered' or adjusted, or where it should not be used at all. The normal distribution curve is called the bell curve because it looks like a bell (please refer to figure 1).

The 'Gaussian Probability Function' is based on the 'Normal distribution' (which presumes that the mean of a distribution is also its median and its mode)---which in plain English means that the number of values less than the mean of a given set of values (let's say test scores) is exactly equal to the number of values greater than the mean and the highest number of values flock around the mean. It is a tenet of the central limit theorem that any large distribution of variables (e.g. number of children per family, or CAT Test scores) tends to cluster around the mean value.

Applying the curve

To standardize and use the the Normal Distribution in different contexts (heights, stock market returns, test scores, IQ scores, number of stars in a constellation) it is applied to a probability density distribution ( a graph showing the frequency or probability of different values occuring). In this, we ascribe the value of zero a 50% probability, i.e. we now can have a 50% probabilty of values more than this and less than this respectively. Then values are ascribed to different points on the curve, based on the formula z=(x-m)/σ where x is the actual value, m is the mean and σ is the standard deviation. Each value on this normal distribution curve signifies a corresponding percentage.

Using this simple mathematical tool, given the mean (average) , standard deviation and the value of the variable, we can calculate the approximate frequency of its occurence. E.g. if the mean test score is 50, the standard deviation (SD) is 20, and the test score of a student is 80, z=(80-50)/20 = 1.5. Using a normal distribution table or the =NORMDIST function on an Excel, this corresponds to a frequency of 90% cumulative---which means that about 10% of students would get more than this score, and about 90% would have got less.

The assumptions, and the pitfalls

What people often forget while applying this beautiful piece of mathematics is that the real world, unfortunately, does not always have the simple purity of the bell curve. Moreover, the bell curve makes some very simplifying assumptions, which would not always hold true in real life. For example, it is presumed that 68% of the values of a distribution would occur within +/- 1 SD of the mean (please refer to figure 1) and 99.9% of values would occur within 3 SDs of the mean. Which means that we don't expect too many 'outliers', or statistical events at the far end of the curve on either side. The presence of outliers or extreme values, leads to 'fat tails', or in statistical terms, kurtosis values of greater than 3. If the Standard normal bell curve is used ot model these events, it can lead to 'model error' (figure 2 shows a 'fat tailed' curve).

Belling the Cat with the fat tail

When the standard normal curve is simplistically used in risk management, to forecast market returns and accordingly predict capital requirements (i.e. how much own capital do I need to tide over a worst case scenario, also called 'Value-at-Risk), it can lead to disaster, as risk managers have found out as a result of the recent financial crisis. The problem is not with the concept of Value-at-Risk (VaR), but with applying the bell curve to all markets and situations. Using data from bullish markets, mean and SD values were computed. These values were then juxtaposed into the normal bell curve, further aggravating the error factor in the model. The result: many banks were undercapitalized, vis-a-vis possible (but as per their models, improbable) trading losses. Lehman Brothers is a case in the point, which went under, with just USD 6 billion in losses, though it had overall assets of...

Moreover, the bell curve is a probability distribution of independent events (e.g. test scores, where there is no cheating). Real life may create correlated events (e.g. market sentiments across asset classes are often correlated; similarly cheating in an exam can cause one bright pupil to cause the marks of numerous pupils arounf him to get good marks).

Another area where the bell curve is often purportedly applied is employee performance. This application presumes that 70% of the employees will form a category, around the average (roughly +/- 1 SD if one is to apply the normal curve) and that the top 20% of the employees will perform beyond this. It imputes these values to populations of employees. However, what should be understood that in a given 'universe' of employees, there can be plenty of exceptions. Hence, more often than not, this becomes an arbitary, relative ranking---in which case, it is a method loosely based on the bell curve (or the central limit theorem, to be more precise), but by no means is it an application of the curve itself.

Falling out of the Curve

Nassim Nicholas Taleb in his book "The Black Swan" has also written about the pitfalls of using the normal curve to predict market returns, where the actual markets may have 'fatter tails' or more returns that may be considered 'extreme' . Chris Anderson, in his book "The Long Tail" wrote about how internet marketing companies create demand for 'out of the ordinary' products---e.g. retro music. Ian Bremmer and Preston Keat have recently come up with a book called "Fat Tail - The Power of Political Knowledge for Strategic Investing" which refers to the frequency of political instability affecting investment envornments and our tendency to think that they are rare events, whyen actually they may not be that rare.

So though the bell curve is a useful tool, it must be carefully 'stress tested' to verify if the variable being 'fitted' to the curve indeed matches it. The variable must also be tested for 'trending' or external correlations which may affect it, before proper models can be drawn up. Otherwise, it may actually be better to simply chart out historical data and draw inferences on that basis, presuming everething else remains the same (as with most other things, the Romans had a pithy latin phrase for this too--- ceteris paribus).

The Issues and non-issues in this election

In these 'General' elections, unfortunately, both the 'national' parties in India have not highlighted the real issues that blight milions of people in India. One party (the BJP) has been parroting the 'terrorism threat' ad nauseam and has propped up a doddering octagenerian as India;s 'Iron Man' (लौहपुरूष ). Now, with young Mr. Varun Gandhi ( rising star of the saffron brigade and of 'यह गाँधी नहीं, आंधी है' fame) making vitriolic and unabashed communal statements, they find themselves with a lot of dust in their mouths. With push coming to shove, the communal and sectarian fangs of the BJP have been bared.

The Congress is stuck to its 'One family rule'. It would be laughable---if the joke wasn't on us, the Indian people--- that India's largest, oldest and most secular party, the 'crucible of the idea of India', cannot find or groom leaders outside the 'Nehru-Gandhi' familyin the world's largest parliamentary democracy. This fact stands testament to our feudal psyche (which has been Pakistan's undoing too). Mr Rahul Gandhi is young, earnest and fairly charismatic. But he has not said, let alone done, anything of note as yet that would mark him out as a candidate for high office, other than the fact that he was born to Sonia and Rajiv Gandhi. Moreover, the BJP and the Congress have of late been locked in an unseemly personality battle between Mr. Advani and Dr. Manmohan Singh.

The regional parties have not been able to build a credible third front, primarily because of the very poor quality of people that most of them throw up. While many of them have a relatively high representation from marginalised or 'non-elite' groups, and in that sense are a toast to India's thriving democracy, it takes a very high level of competence to run a country as large and complex as India, and I am not very confident of how well uneducated local rabble rousers would be able to do the job. In any case, most of them stand on thin foundations of local caste, communal and linguistic equations.

I think the biggest tragedy with India's polity is the fact that we are unable to generate the right kind of leaders. The reason is that in the last two post independence generations, the educated, the most competent people in India have somehow looked upon politics as something obnoxious and unfashionable. They have concentrated on studying hard to crack competition, land 'respectable jobs' (the Civil Services or in the private sector) and then retire quietly to do their gardening and reading. When I told my wife that I aspired to join politics some day, she recoiled at the idea--- "How will I say that I am married to a politician?" she asked in horror. It was almost as if I was planning a career in drug peddling. This has been the bane; the apathy of the educated middle class. My own example is a case in the point - I could not even find time to register myself for voting in Mumbai. I am still registered in Kolkata.

The Real Issues

Politicians have been raking up issues relating to language and religion that have assailed the multi-ethnic fabric of India and sometimes, torn it to shreds to create a constituency for themselves. They have polarised people and distracted them from the real issues---like hunger, poverty, education, healthcare and infrastructure - roads, power and storage facilities for agricultural products. While the BJP is giving disproportionate importance to the issue of security (it is an issue, but I think Naxalism is a greater threat); people like Mr. Narendra Modi, Mr. Raj Thackeray and Mr. Varun Gandhi have been perniciously trying to divide the populace to create constituencies for themselves. And in feudal UP, Ms. Mayawati has been playing her old caste card and using the government as a personal fiefdom and a source of illegal patronage for her cronies (all as per local tradition). The alternative---a Mulayam Singh---is even worse; not only is he corrupt, he is also avowedly anti-development.

The Return of the Jedi

It is heartening to see a resurgence of interest among the educated middle class in political affairs. Groups like AGNI and Jaago Re (launched by Tata Tea) in Mumbai and Janaagraha in Bangalore have been creating awareness and have launched voter registration dirves and 'know your candidate' campaigns. People like Capt. Gopinath, Meera Sanyal and Mallika Sarabhai have jumped into the fray. If not anything else, they keep a Syed Shahabuddin or a Varun Gandhi out of Parliament. However, the Prime Minister (Dr. Manmohan Singh's) contention that independent candidates like Ms Sanyal tend to divide up the vote and do not really make a difference is partly right. It makes sense to join a party. Just making it to Parliament is not very effective in the curent reality, where government formation and even voting in Parliament tends to be driven by party lines. It should be the same Mantra that drives the private sector: optimum utilisation of scarce resources.
*********************************************************************************

The Glacier Moves

I think I had read in the Economist once that "The Indian Government was like a glacier---you know it is moving, but you can never see it move". However, perhaps partly because this is election year, and given the seriousness of the issues, the governemnt has moved quickly and fairly effectively on a number of issues.


6th Pay Commission Anomalies
The Ministerial committee has made some welcome recommendations on the anomalies in relation to members of the Armed forces, vis-a-vis their civilian counterparts: Lt. Cols and equivalents have been moved to PB 4; the pensions of other ranks (Jawans) have also been rationalised; and it has been announced that the Armed Forces will have a separate pay commission from now onwards. Whether this will be of any use or not, is left to be seen. I would rather have more representation from the Armed Forces in the existing Pay Commission so that such anomalies do not creep up in the future. However, the government made no commitment on pay parity between the Armed Forces and their civilian counterparts for all grades between Lt and Brigadier and placement of Lieutenant Generals in Higher Administrative Grade Plus pay scales. The Armed Forces must remain under civilian control in a democracy, but they should definitely be paid the same at the same level of government. Few bureaucrats have to face bullets in another day at the office.

Economic Stimulus - "We are all Keynesians now"
As would be expected from a Prime Minister who was the chief architect of India's economic liberalisation in the early 1990s, and a Finance Minister who has presented a budget widely touted by the press as the 'Dream Budget', the government has taken both preventive and curative action to stave off, or at least reduce the effect of recessionary pressures looming over the economy. As Richard Nixon once said, "We are all Keynesians" now. Lord Keynes showed that in a pessimistic economic environment, where there is a 'crisis of confidence', monetary policies are less effective, as banks are less inclined to lend (there is enhanced risk aversion) and consumption-led demand falls as businesses fail, creating a self-reinforcing cycle of depression. The way out seems to be for governments to spend on creation of infrastructure and other real goods, thereby creating value and at the same time, providing a stimulus to domestic demand in by job creation.

A Difficult Time

This has been a difficult time. The USA, India's largest trading partner, is officially in recession and is seeing the largest number of job losses since 1945. Effectively, we are witnessing the biggest slowdown in the US economy since the Great Depression of 1929-33. The Credit markets have seized up and the great giants of Wall Street---the venerable big 4 investment banks, have either gone belly up (Lehman Brothers) , or sold out (Merrill Lynch, Bear Stearns) or copped out to become plain vanilla commercial banks (Morgan Stanley and Goldman Sachs), protected by the FDIC and the Fed. For the first time since WWII, Euroe and America are slowing down at the same time. India, with 35% of its economy dependent on external trade, can obviously not remain immune to this meltdown. There was contraction in our manufacturing growth for the first time since 1983---in October 2008.

The government and RBI have fired on all directions---both monetary and fiscal to prevent this crisis from getting worse. The RBI has coinsiderably loosened its monetary strings, with phased reductions in the cash reserve ratio---the CRR--- (from 9% in September 2008) to 5 % in January 2009. The repo rate at hich the RBI lends to banks, has been reduced to 5.5%, reducing the cost of funds, and the reverse repo rate which the RBI pays for deposits, has been reduced to 4%, again creating incentives for low interest loans by reducing the rate of risk free investments. It has been estimated each percentage cut in CRR releases about Rs. 40,000 Crore in the system. However, as the good ol' Lord (Keynes) had predicted, this is not necessarily leading to banks going out into the streets with sacks of money , asking people to borrow. A lot of banks have been parking the extra funds in government securities driving down the yield of the 10-year government bond to an all-time low of 4.86% . Yields and bond prices have an inverse relationship. So demand for these instruments was obviously quite manic.

To salvage this situation, the government has come out with strong fiscal measures in order to inject liquidity into the system and create jobs and demand. The corruption-ridden National Rural Employment Guarantee Scheme, which aims to provide 100 days of employment to BPL (below poverty level) families is, forever whatever it is worth, already on. Moreover, the government also announced a slightly cavalier Rs. 70,000 crore farm loan waiver scheme at the time of the last budget in 2008. However, on top of these measures, the government also unvelied two stimulus packages in December 2008 and January 2009. In December 2008, the government unveiled a package of measures worth about Rs. 30700 crore including across the board excise duty reductions and increased spending on infrastructure (Rs. 20,000 crore). In Jan 2009, a further suite of measures was announced: rates on external commercial borrowings (ECB) were decontrolled, Non-banking finance companies (NBFCs) were allowed access to ECBs for infrastructure projects and government controlled IIFCL was allowed to raise Rs. 30,000 crore in tax free bonds for infrastructure spending.

The glacier, finally, has moved. Now let's hope we get to see the fresh water flow in the form of additional liquidity and demand in the economy.