Quriosity (October Issue) by Quantinuum (Analytics Committee)

CONTENTS 3

How Sensex Works

10 Cool and Famous Numbers

Movie Review: A Beautiful Mind

Quant Guru: Meghnad Saha

Quant News Review

Quant Fun

A Quantipedeâ&#x20AC;&#x2122;s Travels

Editor’s Note October 2015

Infinite Greetings! Team Quantinuum feels elated to present to you “Quriosity” the committee newsletter- which will keep you abreast with the World of Quants and Analytics. Sensex is regarded as the pulse of the domestic stock market. Aditi Mehta brings to you an article on How Sensex Works. Numbers are the basis of every quant application in this world. Saket Dhodapkar introduces you to 10 numbers that are very famous with his articles 10 – Cool and Famous Numbers. Lubna Usmani brings to you the movie review of this month for the movie – A Beautiful Mind. The issue pays tribute to Meghnad Saha, an Indian astrophysicist , credited for thr development of The Saha Equation in our “Quant Guru” section by Lubna Usmani. Saket Dhodapkar's News review section gives a gist of the effects the RBI rate cut will have. Dr. Nilakantan brings out various pieces of interesting quant information in this issue's “A Quantipede's Travels”. Rack your brains with the easy and difficult levels of SuDoku!! Happy Numbering !!! The Editorial Team.

COVER STORY October 2015

How Sensex Works History The premier Bombay Stock Exchange that pioneered the stock broking activity in India, 128 years of experience seems to be a proud milestone. A lot has changed since 1875 when 318 persons became members of what today is called The Stock Exchange, Mumbai by paying a princely amount of Re.1. Since then, the country's capital markets have passed through both good and bad periods. The journey in the 20th century has not been an easy one. Till the decade of eighties, there was no scale to measure the ups and downs in the Indian stock market. The Stock Exchange, Mumbai in 1986 came out with a stock index that subsequently became the barometer of the Indian stock market. What is Sensex comprised of? First compiled in 1986, Sensex comprises of Top 30 Stock traded in The Bombay Stock Exchange(BSE) comprising all major sectors such as IT, Cement, Oil and Natural Gas, Bank, Automobile, etc. Itâ&#x20AC;&#x2122;s a cumulative index. Remember it is just 30 stock indexes. Those 30 stocks are dynamic in nature and keeps on changing. SENSEX = SENSitive + index The base year of the Sensex is 1978-79 and the base value is 100.The index is widely reported in both domestic and international markets. The Sensex is the oldest stock market index in the country. It provides the time series data over a fairly long period of time. The Sensex is calculated using the 'free float market capitalisation' method. According to this method, the level of index at any point of time reflects the free-float market value of 30 component stocks relative to a base period.

Initially, the index was calculated based on the 'full market capitalisation' method. However, this was shifted to the free-float method with effect from September 1, 2003. Globally, the free-float market capitalisation method of index construction is regarded as an industry best practice. All major index providers like S&P, Dow Jones, MSCI, STOXX, and FTSE use the free-float method. The market capitalisation of a company is determined by multiplying the price of its stock by the number of shares issued by the company. This market capitalisation is further multiplied by the freefloat factor to determine the free-float market capitalisation. Market Capitalisation = Stock Price X Number of Shares X Free Float Factor The calculation of the Sensex involves dividing the free-float market capitalisation of 30 companies in the index by a number called the index divisor. The divisor keeps the index comparable over time and is the adjustment point for all index adjustments arising out of corporate actions, replacement of scrips etc. Sensex = Free-float market capitalisation of 30 companies รท Index Divisor During market hours, prices of the index scrips, at which latest trades are executed, are used by the trading system to calculate the Sensex every 15 seconds and disseminate in real time. The closing figure is computed taking the weighted average of all the trades on the Sensex constituents in the last 15 minutes of the trading session. If a Sensex constituent has not traded in the last 15 minutes, the last traded price is taken for computation of the index closure. If a Sensex constituent has not traded at all in a day, then its last day's closing price is taken for computation of the index closure. When a company, included in the compilation of the index, issues right shares, the free-float market capitalisation of that company is increased by the number of additional shares issued based on the theoretical (ex-right) price. An offsetting or proportionate adjustment is then made to the base market capitalisation. When a company, included in the compilation of the index, issues bonus shares, the market capitalisation of that company does not undergo any change. Therefore, there is no change in the base market capitalisation, only the 'number of shares' in the formula is updated. During market hours, prices of the index scrips, at which trades are executed, are automatically used by the trading computer to calculate the Sensex every 15 seconds and continuously updated on all trading workstations connected to the BSE trading computer in real time.In order to maintain continuity with the past, the base year average needs to be updated. The base year value adjustment ensures that replacement of stocks in the index, additional issue of capital and other corporate announcements like rights issue etc do not destroy the historical value of the index. The adjustments for corporate actions in the index should not per se affect the index values.

ADITI MEHTA PGDM FS(2015-17)

Sub-Article October 2015

10 Cool and Famous Numbers Below are the 10 most famous numbers, not in any particular order, you should be aware of: 1. Pi (22/7) One of the single most important numbers in history, its applications include its uses in world-wide statistics, predicting weather patterns, and in other applications that require massive computational power. The most recognized mathematical constant in the world, it is interesting to note that the Ď&#x20AC; (piwas) is the 16th letter in both the Greek and English alphabet. 2. 666(Number of the beast) Besides being interpreted as the number of the beast in the Bible, it has several other significant meanings to history buffs and conspiracy theorists alike, one of which was the duration of the Assyrian empire before it was conquered by Babylon. There are many references to this number in songs and movies. 3. Golden Ratio(1.6180339887) Also known as the Golden Mean or the Golden Section, this is an expression that describes universally perfect proportions in sciences such as architecture and anatomy. Approximately '1.6180339887', two quantities are considered to be in perfect golden ratio if the ratio of those two quantities and the larger one is the same as the ratio between the larger and smaller ones. 4. 911 An emergency telephone number in the North American Numbering Plan (NANP) it was established in 1968 and provides access to police, ambulance, and fire services. In Canada alone, 12 million calls were made to 911. It can also refer to the September 11, 2001 or 911 terrorist attacks. 5. 10 If you have spent a lot of time on the internet, you will surely notice a great number of top 10 posts. It seems that there is a list of top 10 for everything from losing weight to issues relating to history. Moreover, a good number of counting systems are base 10 so it's hard to escape the importance this number plays in our everyday lives. Also most of the times you see many lists on the internet depicting the top â&#x20AC;&#x153;10" items in particular category. In sports

like football and cricket this number enjoys a unique meaning implying the number 10 is considered to be the playmaker of the team. 6. Zero “0” Zero is known for being the number that enabled the denominational number system and became the basis for modern mathematics.The concept of zero as a number and not merely a symbol or an empty space for separation is attributed to India. In 498 AD, Indian mathematician and astronomer Aryabhata stated in his Aryabhatiya that "sthānāt sthānaṁ daśaguṇaṁ syāt" i.e., "from place to place each is ten times the preceding," which is the origin of the modern decimal-based place value notation. Also known as a 'neutral' element, it can be added to any number but will not change the value of the sum; and is known to be an 'absorbing' element in multiplication as everything that you multiply to it will still result in zero. 7. 13 Considered a bad omen due to the popularity of Friday the 13th, 13 black cats, or 1313 Mockingbird Lane; there is still an air of mystery surrounding this number. Even in modern times, you can easily note that there is no 13th floor in some high-rise buildings, while airplane flight numbers have been reassigned to avoid association with the number 13. It also has a religious significance for Christians when Jesus declared in the Last Supper that one of the 13 disciples will betray Him. 8. Number “3” Most of the races which take place end up awarding “three” prizes. Whenever we are comparing among multiple entities we generally narrow it down to the top 3 things. Most of the movie franchises come in trilogies (Batman, Godfather and Lord of the rings etc.). Pythagoras put forth his theorem describing triplets of numbers which would form a right angled triangle. These set of numbers were called Pythagorean triplets. 9. Number I i.e. “√-1” One of the coolest numbers on this list is actually imaginary. Today, “i” is used in signal processing, control theory, electromagnetism, fluid dynamics, quantum mechanics, cartography, and vibration analysis. The figure j is often substituted in these fields, which is used to represent the electric field current. The imaginary number also appears in several formulas, including the Euler Identity. 10. Euler's number “e” (2.718) Like pi, the Euler is an irrational, non-repeating and non-terminating number, which denotes the natural limit for many processes and applications in nature, science and mathematics, especially in economics. Named after Leonhard Euler, it was actually discovered by his student Bernoulli who went to a loan shark to borrow MONEY. Then while deciding on the rate of compound of interest that would be applied he came up with the approx. number that we now know as e, which functioned as a limiting factor.

References:- List25.com , sprott.physics.wisc.edu .

SAKET DHODAPKAR PGDM B(2015-17)

MOVIE REVIEW October 2015

A Beautiful Mind Directed by Ron Howard; written by Akiva Goldsman, based on the book by Sylvia Nasar, A BEAUTIFUL MIND , is a biography of the mathematician John Forbes Nash Jr. The author quotes one of his colleagues: ''All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to vicissitudes.'' Mr. Nash, whose life is a case study in the difficulty -- and also the wonder -- of living in both, now inhabits a third: the treacle palace of middlebrow Hollywood moviemaking, in which ambiguity is dissolved in reassuring platitudes and freshly harvested tears. Early on, the mathematician recalls a second grade teacher's evaluation of him as having been given two helpings of brain but only one helping of heart. So Nash goes through most of his life ashamed of his inability to relate to people with ease or grace. Mr. Nash, an inordinately gifted, deeply awkward man, possesses one of the most extraordinary mathematical intellects of his generation. By his early 30's, when mental illness overwhelmed his creative powers, he had done important work in a number of fields, including game theory, quantum mechanics and number theory. The movies have a way of pushing mental illness into corners. It is grotesque, sensational, cute, funny, willful, tragic or perverse. Here it is simply a disease, which renders life almost but not quite impossible for Nash and his wife, before he becomes one of the lucky ones to pull out of the downward spiral. After three decades of struggle with schizophrenia, he was granted what seemed like a miraculous remission. In 1994 he was awarded the Nobel Memorial Prize in economic science for work he had done as a graduate student at Princeton in the late 1940's. Nash struggles for years to keep his equilibrium despite his illness. Finally, he returns to Princeton where Hansen (Josh Lucas), his old rival from years ago, first allows him to use the library and eventually gives him a teaching position. Of course, by the time he received the Nobel Prize, he realized the truth of Helen Keller's observation: "The best and most beautiful things in the world cannot be seen or even touched; they must be felt in the heart." John and his wife, Alicia Nash were killed in a collision on the New Jersey Turnpikenear Monroe Township, New Jersey. LUBNA USMANI MMS A(2015-2017)

QUANT GURU October 2015

Meghnad Saha Meghnad Saha was an Indian astrophysicist best known for his development of the Saha equation, used to describe chemical and physical conditions in stars. Birth: th Meghnad Saha was born on 6 October, 1893 in Shaoratoli village near Dhaka, British India. He was born to Jagannath Saha and Bhubaneshwari Devi. He was their fifth child. Jagannath was a shopkeeper. Given their economic and social means, his parents had neither the means nor the inclination to educate their children beyond primary education. Education and Early Life: Saha joined the village primary school at the age of seven and demonstrated an unusual aptitude for learning from the very beginning. After completing his primary education, his family did not have the means to provide for his further education. A local doctor, Ananta Kumar Das, sponsored him by providing him free boarding and lodging in his house provided Saha washed his own plates and attend minor household works. Saha completed his middle school by topping the list of successful candidates in the entire district of Dhaka. As a result he secured a scholarship of Rs.4 per month. In 1905, Saha came to Dhaka, where he joined the Collegiate School, a government school. His elder brother sent him a monthly allowance of Rs.5. So Saha had Rs.11 to manage his food, lodging and other expenses. There were widespread political disturbances in Bengal in 1905. In this year Lord Curzon, the then Viceroy of British India, had decided to partition Bengal.

Saha, like many others, was affected by this political upheaval. He, along with some other students, were rusticated from the Collegiate School, because of their participation in the demonstration against the visit of the Bengal Governor, Sir Bamfylde Fuller, to the school. Besides being rusticated, Saha was deprived of his scholarship.

Fortunately a private school, named Kishori Lal Jubilee School, accepted Saha with a free studentship and a stipend. In 1909 Saha passed the Entrance Examination from Kishori Lal Jubilee School standing first amongst all the candidates from erstwhile East Bengal. After passing the Intermediate Examination of the Calcutta University in 1911 from the Dhaka College, Dhaka, Saha joined the Presidency College at Kolkata.

Saha passed his BSc Examination with Honours in Mathematics in 1913 and MSc (Applied Mathematics) Examination in 1915. Saha stood second in order of merit in both the examinations. Career: Saha was appointed lecturer in the Department of Applied Mathematics in 1916 in the University College of Science. He got himself transferred to the Physics Department. Raman joined as Palit Professor of Physics. After joining the physics department, Saha started giving lectures to the post-graduate classes on topics like hydrostatics, the figure of the Earth, spectroscopy and thermodynamics. For teaching physics to the postgraduate classes, Saha had to learn it himself first, as he studied physics only in the undergraduate classes. It was a great challenge indeed. Besides teaching Saha also started doing research. Saha had only one research facility at Presidency college, no guide for supervising his research work and no money to publish his research. By the end of 1917, he had written a long essay on `Selective Radiation Pressure' elaborating on theory of the role of radiation pressure acting on the atom selectively and compensating the action of gravity on solar atoms. He got a short note published in the Astrophysical Journal, Vol. 50,220 (1919) and submitted a duplicate of the original article on `selective radiation pressure and problem of solar atmosphere' ( Journal of the Department of Science, Calcutta University, 1919). He got a short note published in the Astrophysical Journal, Vol. 50,220 (1919) and submitted a duplicate of the original article on `selective radiation pressure and problem of solar atmosphere' ( Journal of the Department of Science, Calcutta University, 1919). Initially Saha worked on diverse topics as reflected from the titles of his published research papers as indicated below:· ·

“On the Limit of Interference in the Fabry-Perot Interferometer” ( Physical Review, 1917), ·

“On A New Theorem in Elasticity” ( Journal of the Asiatic Society, Bengal, 1918), “On the Dynamics of the Electron” ( Phil. Mag. 1918)

· ·

“On the Pressure of Light” ( Journal of the Asiatic Society, Bengal, 1928) “On the Influence of Finite Volume of Molecules on the Equation of State” ( Phil. Mag , 1918). This paper was jointly written with S.N. Bose.

· ·

“On Maxwell's Stresses” ( Philosophical Magazine, 1917), this paper was based on his studies of the electromagnetic theory of radiation;

“On the Mechanical and Electro-dynamical Properties of the Electron” ( Physical Review, 1919); “On the Radiation Pressure and the Quantum Theory” ( Astrophysical Journal, 1919);

Based on his above work Saha submitted his thesis for the degree of Doctor of Science of the Calcutta University in 1918. He was awarded the degree in 1919. The same year he was awarded the Premchand Roychand Scholarship for his dissertation on the 'Harvard Classification of Stellar Spectra'. He published four papers on his astrophysical research in the first six months of 1920 in the Philosophical Magazine viz. “Ionisation of the Solar Chromosphere” (March 04, 1920), “On the Harvard Classification of Stars” (May 1920), “On Elements in the Sun” (22 May 1920) and “On the Problems of Temperature-Radiation of Gases” (25 May 1920). In these papers Saha formulated his Theory of Thermal Ionisation.His thesis on the 'Origin of Lines in Stellar Spectra' won him the Griffith Prize of the Calcutta University in 1920. Saha, jointly with S.N. Bose prepared an English translation of Einstein's papers on theory of relativity and got it published in a book form. A Xerox copy of the Saha-Bose translation is now in the Einstein Achieves at Princeton”.

The Premchand Roychand Scholarship of the Calcutta University awarded in 1919 enabled Saha to spend about two years in Europe. In November 1921, Saha returned to India and joined the University of Calcutta as Khaira Professor of Physics. But Saha did not stay long in Kolkata. He moved to Allahabad in 1923 as Head of the Department of Physics. Meghnad Saha's best-known work concerned the thermal ionisation of elements, and it led him to formulate what is known as the Saha equation. This equation is one of the basic tools for interpretation of the spectra of stars in astrophysics. By studying the spectra of various stars, one can find their temperature and from that, using Saha's equation, determine the ionisation state of the various elements making up the star. He became a Fellow of Royal Society in 1927. Saha also invented an instrument to measure the weight and pressure of solar rays. He founded the journal Science and Culture and was the editor until his death. He was the leading spirit in organizing several scientific societies, such as the National Academy of Science (1930), the Indian Physical Society(1934), Indian Institute of Science (1935) and the Indian Association for the Cultivation of Science (1944). A lasting memorial to him is the Saha Institute of Nuclear Physics, founded in 1943 in Kolkata. Saha was also one of the prominient among the works on halley's comet. Saha was the chief architect of river planning in India and prepared the original plan for the Damodar Valley Project. Saha was an advocate of the peaceful use of nuclear energy. He had initiated the first Parliament debate on this subject on 10th May 1954. Saha was against the establishment of the Atomic Energy Commission. He was of the view that the researches on nuclear energy could be undertaken in the university sector. In fact he wanted the 'Indian Atomic Energy Act' to be scrapped altogether. Saha wanted that the Government should first build up necessary infrastructure and trained manpower before it undertook such a programme. Saha's work relating to reform of Indian calendar was very significant. Saha was the Chairman of the Calendar Reform Committee appointed by the Government of India in 1952 under the aegis of the Council of Scientific and Industrial Research. It was Saha's effort, which led to the formation of the Committee. The task before the Committee was to prepare an accurate calendar based on scientific study, which could be adopted uniformly throughout India. In 1952 Saha was elected Member of the Parliament as an independent candidate from the NorthWest Calcutta constituency. Death: Saha died suddenly due to a massive heart attack on his way to the office of the Planning Commission on 16 February 1956.

LUBNA USMANI MMS A(2015-17)

QUANT NEWS REVIEW October 2015

RBI Rate Cut The Reserve Bank of India (RBI) cut its policy interest rate to a 4-1/2 year low of 6.75 percent on th 29 September, in a bigger-than-expected move that, with inflation running at record lows, could help turn around an economy that has been slowing down. he RBI cut its growth forecast for the fiscal year to 7.4 percent from 7.6 percent previously, well below the government's target of 8 to 8.5 percent, but still faster than China. The central bank said it expects inflation to rise from August's record low of 3.66 percent to 5.8 percent in January, just below its 6 percent target. Some of the implications of this move by the RBI are as follows: 1. Mortgage: Lower interest rates would directly impact all type of mortgages like housing loan, car loan, and personal loans, among others. Lower interest rate is expected to push demand in these segments, which will have a cascading impact on the entire economy. Here the assumption is that the mortgage has been taken on a floating rate basis. For fixed interest rate mortgages there is unlikely to be any change. 2. Savings: One of the first rates that banks generally cut when the central bank announces a rate cut is in deposit rates. Banks do not want to take the risk of raising high-cost funds at a time when the borrowing rates are falling. Saving rates, be it a savings bank account or fixed deposit will go down from investors. Money markets which are the first to react will see their interest rates fall. 3. Economy: In the recent interaction between the government and corporate India it was pointed out that there are two main reasons why corporate India is not investing in the economy. First was the ease of doing business and second were high interest rates. Setting up capacity during a high interest era impacts the cost of the project and viability of the project. Now with lower interest rates the ball is in the government's court to announce policy changes in order to prompt corporate to invest. 4. Currency: Interest rate parity is the reason behind balancing of currency rates. Lower interest rates will not attract capital which is looking for higher yields, which would mean that the currency would weaken. If the Federal Reserve opts to increase interest rate the differential between India and the US will reduce further, resulting in further flight of capital. 5. Equity Markets: Equity markets are expected to gain on multiple reasons. First the positive impact on consumption on account of lower interest rates would mean better top line growth. Lower interest outgo would also mean high profit and thus better valuations. Further, lower interest rates means that money will move from lower yielding debt instruments to the equity market. SAKET DHODAPKAR PGDM B (2015-17)

QUANT FUN October 2015

LUBNA USMANI MMS A (2015-17)

A Quantipede’s Travels October 2015

What does a Quantipede do when (s)he is not travelling. (S)he travels the web. In this issue, we highlight ( in < 60 words) a few things of interest to us as quants. 1. D-Wave’s Quantum Computer A quantum computer uses qubits, which can be both a 0 and a 1 at the same time, and promises to vastly outperform regular binary bits for certain problems, like searching a database. But putting that theory into practice has proved tricky. D-Wave, claims that its quantum computer works 15 times faster than regular PCs . 2. China’s telescope on the moon During the first 18 months of the telescope’s operation, it has observed for 2000 hours and monitored 40 stars. Apollo 16 astronauts had used a manually operated UV telescope to take pictures of Earth, stars and the Large Magellanic Cloud. But the Chinese telescope is the first to be operated, remotely from Earth, in the hostile environment. 3. The first farmers on the Earth Till now, we thought that agriculture flourished in the Middle East and spread elsewhere. It is time to rethink how modern civilization took root as it is found recently that agriculture was independently invented at least 11 times in four continents. Archaeologists have found signs of curated forests, “proto-farming” on nearly every continent, transforming ideas of the dawn of agriculture. 4. Salary survey of predictive analytics professionals Recent salary survey of predictive analytics professionals (PAPs) Burtch Works says PAPs earn median annual salaries between $76,000 and $235,000 (without bonuses), depending on, not surprisingly, their experience, industry, job responsibilities and location. The survey, conducted over 12 months ending in April 2015, is based on responses from 1,757 PAPs working for > 800 different companies across the United States. 5. Customer data has monetary value but many organisations ignore it Many organizations do not manage customer data as a corporate asset, and the monetary value of that data is often ignored, according to Gartner, Inc. Although some organizations have begun to invest in big data technologies in relation to their customers, with a view to direct or indirect monetization, many organizations lack business models to monetize their customer data. Any Takers? In the last issue, I had raised a project idea and asked any takers? I am still waiting. For those who missed it, it is given below: Mumbai High Court has suggested to Railways that they should have standing compartments in suburban trains. We need to study quantitatively how this will reduce congestion and improve comfort. We need to understand new configurations, available areas, congestion measures and improvements. We will also report on what happens elsewhere. Any takers for this project? Prof.(Dr.) N.S.Nilakantan, Ph.D. Associate Professor - Quantitative methods Faculty Mentor - Quantinuum

QUANT CONNECT October 2015

Quantinuum, the Quant forum of KJ Somaiya Institute of Management Studies and Research aims to empower students and professionals alike to organize and understand numbers and, in turn, to make good and rational decisions as future managers. The newsletter published monthly consists of a gamut of articles for readers ranging from beginners to advanced learners so as to further enrich the young minds understand the contributions made to the field of mathematics along with a couple of brain- racking sections of Sudoku to tickle the gray cells. For any further queries and feedback, please contact the following addressKJ Somaiya Institute of Management Studies and Research, Vidya Nagar, VidyaVihar, Ghatkopar East, Mumbai -400077

Mentor Prof. N.S.Nilakantan (9820680741) â&#x20AC;&#x201C; email â&#x20AC;&#x201C; nilakantan@somaiya.edu

Team Leaders

Sai Dinesh Gurijala (+91 8008512986) Vaibhav Varadkar (+91 9594990215)

Editorial Team

Designing Team

Purva Shaktia (+91 7738343494) Saket Dhodapkar (+91 8886234445) Lubna Usmani (+91 7208732994) Aditi Mehta (+91 9757099599)

Sunakshi Bansal (+91 9978837728) Anshul Chauhan (+91 9582676050) Jatin Pande (+91 9503283563)