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Fat tails have a tale to tell

Between 1998-2013, out of a total of 3,785 days, movement in the CNX 500 was outside 3 sigma on 60 occasions, that is 1.59% of the total. By normal distribution, less than 0.03% observations should fall outside the 3 sigma

In the world of investments, returns are measured by the first moment of prices (mean) and the risks are measured by the second moment (standard deviation or sigma). Most of the classical theories of finance are based on the assumption that the returns are normally distributed. In the probability theory, the normal distribution is a bell shaped curve of probability values for various natural events—hence the word ‘normal’. This distribution assumes that the tails or the ends are flatter and extreme events are rare. For example, this means that the probability of returns moving more than three standard deviations beyond the mean is 0.03%, or virtually nil. But what is ‘normal’ in markets?

In the Indian context, taking daily CNX 500 data from 1 January 1998 to 28 February 2013 (more than 15 years), 99.73% of the daily returns should ideally fall within -4.97% and 5.09%. Or less than 0.03% observations should fall outside the 3 sigma.

Out of a total of 3,785 daily observations during the period of analysis, 60 times the returns were outside 3 sigma in the case of CNX 500, that is 1.59% of the total observations. Clearly much more than we bargain for. The rule book says that if we are looking at daily events, a 5 sigma event would occur once in 4,776 years. A 6 sigma event would occur once in 1.388 million years and after that, the numbers are, let's just say too big to bother.

On 17 May 2004, the financial market experienced a more than 7 standard deviation fall, when markets crashed due to political uncertainty. Markets fell more than 5 to 6 standard deviations many times in 2007 and 2008, owing to global melt down. Similarly, the market posted a more than 9 standard deviation gain, once again due to the political scenario in the country at that time.

In reality, we have experienced 5, 6, 7 or even more than that, sigma events more frequently than what the normal distribution suggests and we dare to accept.

This is true globally, not just in India. For instance, Goldman Sachs, Citigroup, UBS, Merrill Lynch, all experienced large (as large as 25) sigma events on multiple days in 2007 and 2008. There was the South East Asian crisis, the 11 September 2001 attacks on the World Trade Centre, the Euro crisis, all in the past two decades.

It is not just that these events occur more frequently, these events have greater impact, as well. The impact is, in fact, higher due to the surprise element attached to them. It hits one at the place where it hurts the most and makes it very difficult to recover.

Our observations suggest that the distribution is more leptokurtic in nature, with fatter tails. This means that more observations are concentrated around the mean and tails are fatter, or have greater number of observations than suggested by the normal distribution.

So what we must do is first, acknowledge the limitation of our knowledge that we cannot explain everything and second, we must believe that such events occur more frequently than we had thought. This must call for better risk management systems. Perhaps these events indicate that we must prepare for more incorrigible things that will happen.

What this also points to is that the assumption of normal distribution does not hold. Hence, financial mathematicians must look at distributions with fatter tails for building their theories and models.

Additionally, Daniel Kahneman’s prospect theory says that humans are more likely to act to avoid loss than to achieve a gain, articulated very well in his book “Thinking fast and slow”. If we accept this to be true, then it becomes all the more important for the theorists and professional money managers to rethink the way they build models or the appropriateness of the models which they use.

As for the investors, it would be wise to question their financial advisor on the soundness of their advice during a large sigma event!

(Nupur Pavan Bang is a senior researcher at the Centre for Investment, Indian School of Business, Hyderabad. Khemchand H Sakaldeepi is a researcher at the Centre for Investment, Indian School of Business, Hyderabad.)

### User

Naïve brokers: Espirito Santo too gets “seduced and dumped” by hopes raised by the FM. Put GDP growth at 6.6% as the best-case for FY14

ESS has come out up with its monthly report and realised that its expectations were too high and needs toning down. But it still remains optimistic and expects the economy to recover and RBI to slash interest rates

The latest brokerage to get “seduced and dumped” is Espirito Santo Securities (ESS). Like BNP Paribas, it had kept its expectations rather high and was let down by P Chidambaram’s budget. ESS said, in its latest “Blackbook” titled Waiting for Dawn: “FII flows and market movements since August 2012 show that (high expectations). And the budget, with media hype around a ‘dream budget’ in the run up, was expected to provide the next leg up to reforms, but the FM disappointed." Despite the disappointment, ESS is optimistic that the Reserve Bank of India (RBI) would do its bit to stimulate the economy by cutting interest rates by as much as 50 basis percentage points (bps) within the next two months. ESS said, “On balance we’re slightly more bullish on rate cuts than consensus, and expect the RBI to cut the repo rate by another 50 bps by its May 2013 policy meeting, with a likely 25 bps cut in the March policy meeting." This is a big expectation indeed, given that inflation risks continue to persist.

Earlier we had written how other brokers like BNP Paribas fell for FM’s hardsell and were left high and dry. Check here for more information. Of course, it finally dawned to ESS that there was no basis for such hopes. In the report, it cautioned investors of the finance minister's so called ‘tricks’. It was stated: “And investors should be careful of expecting too many more reform rabbits up Chidambaram’s sleeve to offset disappointment in the actual fundamentals.” Oh well, the reality is dawning on analysts.

ESS expects populist measures to take the centre-stage as the election nears. This is something it should have thought of much before the budget and before the finance minister sold the idea of ‘reforms’ and India being the premier investment destination. The report said, “as elections draw closer in H2 pro-growth and pro-investment reforms are likely to take a back seat, and the shift will be towards more inclusive and populist measures.”

Given that the finance minister has all but dashed ESS’s hopes for a ‘reform’ budget, the brokerage has moderated India's GDP forecast to 6.6%. The report said: “Overall our analysis still suggests a recovery, just a slow and difficult one, with 6.6% GDP growth for 2014 probably a best case scenario now”.

It is also optimistic on inflation and expects 'core' inflation to “tread below 4.5%”, even though the government is going into full blown expenditure mode. It is hard to see how inflation go down can given how much headwinds is there in the economy, especially one reliant on imports and breaks in domestic competition and distribution.

With the markets in a ‘correction’ mode post-budget, ESS thinks there is value in select stocks and it has come up with a “silver bullet” list of stocks to buy and sell. They are ING Vysya Bank, Wipro, Gujarat Pipavav, Cipla, Jindal Steel & Power and Motherson Sumi. ESS has put a sell on L&T and Marico.

Apart from the “silver bullet” list, it has also come up with conviction ideas, a list of stocks which are primed to do well, according to its sales desk and analyst. One of its picks caught our eye—Dewan Housing Finance (DHFL). This is one of the companies which had been in the news for all the wrong reasons. According to the report, DHFL was accused of rigging of its share price at the time of the QIP offer. However, SEBI had reportedly investigated the company and given it a clean chit. This isn't surprising given how ineffectual SEBI has been in apprehending and punishing corporate wrong-doers.

The reason ESS has given this company a buy based on ‘facts’ is that its valuation is really low (according to the report, the stock is trading at 1x FY14 estimated price/book ratio).

Other “conviction ideas” includes Oriental Bank of Commerce and Shriram Transport Finance.

Another section of ESS report caught our attention was the IPO snapshot. A lot of investors are interested in raking in big bucks by investing in the primary market. But not all companies do well either because their pricing is totally out of whack with reality and works against investors. We noticed that in the ESS list, all the companies that were listed last year have given negative returns so far. Moreover, out of the 34 companies that were listed since 2010, according to the report, as many as 22 companies have given negative returns. Poor post-IPO returns shows how greedy the promoters have been egged on by investment bankers.

### User

February car sales growth tumble to 12-year low; even UVs take the hit

During February, while weakness persisted across most segments, it was more prominent in MHCV, tractor, passenger car, and two-wheeler segments. The UV segment, which had so far remained insulated from the slowdown, also witnessed initial signs of weakness

Automobile sales during February 2013 continued to suffer from extreme weakness, with utility vehicles (UVs) and sports utility vehicles (SUVs), the only segment that was growing, too taking a hit. During the month auto sales remained weak across most segments, led by continued weakness in domestic demand on account of high interest rates, inflation and slowdown in economic activity. High base effect due to pre-budget buying in February 2012 also impacted the growth.

“The decline in car sales in February was the biggest since December 2000, when sales declined by 39.86%. The market continues to be extremely difficult as high fuel prices, interest rates and overall macro economic factors are adding to low consumer sentiments,” Sugato Sen, deputy director general of Society of Indian Automobile Manufacturers (SIAM) told reporters in New Delhi.

According to the data released by the SIAM, during February, overall sales fell by 5.45% to 14.51 lakh units from 15.34 lakh units same month last year. Domestic passenger car sales fell 25.71% to 1.58 lakh units compared with 2.13 lakh units same month of 2012 taking the total passenger vehicle sales 16.67% down.

The automobile sector has witnessed a shift in demand in almost all the segment of vehicles. In the passenger vehicles segment, the gradual shift towards UVs against cars is evident as they are powered by cheaper fuel and have space to accommodate more people. UVs’ contribution in the total sales of passenger vehicles has increased to 20% from 14% last year.

While weakness persisted across most segments, it was more prominent in the medium and heavy commercial vehicle (MHCV), tractor, passenger car, and two-wheeler segments. The UV segment, which had so far remained insulated from the slowdown, also witnessed initial signs of weakness.

Maruti Suzuki India’s UV sales declined 2% mom (month-on-month). While passenger vehicle sales for Mahindra & Mahindra (M&M) grew 14% during February, Tata Motors’ domestic UV sales and car sales tumbled 57% and 73% to 2,844 units and 7,769 units, respectively, compared with a year-ago period.

Post Union Budget, both M&M and Tata Motors have increased prices of their SUVs in line with the increase in excise duty, which may impact sales for the only segment that was witnessing growth in automobile industry.

During the month, total sales of commercial vehicles declined by 11.1% to 68,388 units from 76,891 units in the year-ago period. In February, M&HCVs sales tumbled 34.72% due to hike in diesel prices and slow down in industrial activities.

Total two-wheeler sales in February 2013 slipped by 2.77% to 11.12 lakh units from 11.43 lakh units in the same period last year. Motorcycle sales during the month fell 4.48% to 8.00 lakh units from 8.37 lakh a year ago period, SIAM said.

In this segment, there is gradual rise (2.55%) in the sales of scooters over motorcycles. Scooters contribute around 21% in the total sales of two-wheelers, an increase of 3 percentage points from last year. Honda is a leader in scooters which is impacting sales of Hero MotoCorp and TVS Motors.

“Going ahead, we expect the demand environment to remain weak in fourth quarter of FY13 as a slowdown in economic growth coupled with higher interest rates and fuel expenses continue to dampen consumer sentiments,” said one brokerage in a research note.

4 years ago

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