quantinuum september 11

7/31/2019 Quantinuum September 11

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September 2011 Volume 2: Issue 3

Quantinuum Newsletter


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Hi All,

All of us are learning data analysis and data modelling techniques during our

studies. Its high time we also understood how to use the techniques. Perhaps,the following articles will help you understand the issues and identify opportuni-ties in the area of data handling.

Mastering the art of collecting and analyzing massive amounts of data is nowmission-critical for companies hoping to gain and hold competitive advantage.Are you ready for the era of big data? defines this new territory and posesfive questions that every executive should consider when building a data strat-egy.

In a companion piece, Competing through data: Three experts offer their game

plans (which includes mult imedia features), a leading academic expert, an en-trepreneur, and a winning college basketball coach home in on how to use datato gain an edge.

The above articles are available in the recent issue of McKinsey Quarterly, whichcan be accessed athttps://www.mckinseyquarterly.com

The September issue is in your hands in which we have tried to cover the usualtopics. As all of you are aware, space limitation restricts us from elaborating onany of the topics. We do expect readers to follow up the leads and read and un-

derstand more.We also expect readers to comment and point out errors and omissions by writ-ing in.

Happy reading.

RegardsProf N.S.Nilakantan

TEAM QUANTINUUM

From the Facultys Desk...FROM THE FACULTYSDESK;

2

MAIN STO RY :

GOLDEN RATIO

ABIN ABRAHIM

3-4

QUANCEPT O F THE

MONT H: -

UTILIZATION FACTOR

6

QUANTITAIVE ANALYSIS

OF HEDGE FUNDS:

BRIJI KOMBAN

7-9

QUANT GURU OF THE

MONTH: PAUL PIERRE

LEVY

HARSHIT A SHRIVASTAV

10

QUAN T N EW S DIGEST 5

Quantinuum NewsletterS E P T E M B E R 1 1 V O L U M E 2 : I S S U E 3

QUANT S IN A LIGHTER

VEIN:

MANISHA AGARW AL

12

E-TAMBOLA:

QUANTINUUM EVENT OF

THE MONT H

GUN JAN JADO N

11

QUAN T Q UERIES OF TH E

MONTH

EDITORIAL TEAM

13


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What connects Mathematics, Advertising, Leonardo Da Vinci, the Great Pyramid and the Stock Market? The

wide range enlisted should keep one wondering for long. Learning is all about understanding patterns. The con-nection is the golden ratio.

In mathematics and design two quantit ies are in thegolden ratio if the ratio of the sum of the quantities to thelarger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrationalmathematical constant, approximately 1.6180339, it is also known as the divine proportion, golden mean, orgolden section. It is denoted by , or phi. Almost everything has dimensional properties that adhere to this ra-tio; it seems to be a fundamental function for the building blocks of nature, hence may be the divine proportionname-tag.

The Fibonacci Series

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, The ratio of each successive pair of numbers in the series approximates phi (1.618. . .), as 5 divided by 3 is1.666..., and 8 divided by 5 is 1.60.Going further the ratio of successive pairs converge to the golden ratio.Phi appears in:

The proportions of the human bodyPlantsDNAThe solar systemArt and architectureMusicPopulation growth

The stock marketLogo and Product design

Few of its application which are directly relevant to us b-school students:

Advert ising: Phi is recognized for its ability to give a sense of aesthetic appeal in balance and harmony of de-sign. Product logos represent an image that must make a posit ive and memorable impact on the conscious andsubconscious minds of consumers, so it is no surprise to find phi proport ions in many logos of major companies.Pepsi, Toyota, Nissan,the list goes on. An extension of the golden ratio, the golden rectangle is used for this pur-pose. In the diagram, a/b=(a+b)/a=

Q U A N T I N U U M N E W S L E T T E R

MAIN STORY : The Golden Ratio

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Now notice the same applied in the design of the Toyota logo.

Fascinating isnt it?It has also been used in product form design.

Stock Market Analysis and forex analysis: The golden ratio, or phi, appears frequently enough in the timing ofhighs and lows and price resistance points used in technical analysis of the markets. This helps in identifying keyturning points. When used in technical analysis, the golden ratio is typically translated into percentages: 38.2%, 50%, 61.8% and 100%which are obtained by dividing subsequent numbers in the Fibonacci series.

The movements in forex rate can be predicted with this ratio in a similar pattern.

Business learns a lot from history. The perennial debate on whether business is a science or an art has been go-ing on for long. But the marvels that art has produced have many lessons to be learnt from.Architecture and Art: The Great Pyramid of Giza built around 2560 BC is one of the earliest examples of the useof the golden ratio. The length of each side of the base is 756 feet, and the height is 481 feet. So, we can findthat the ratio of the vase to height is around 1.6. There are many more examples which can be given. Da Vinciused the ratio in painting his Last Supper, Vetruvian Man and the Mona Lisa.

Now as somebody once said, wouldnt the world have been a zero if there wasnt mathematics?

ABIN ABRAHIM

PGDM-B

2011-2013


P A G E 4


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Mathematicians ruling the market:

Mathematics which had previously played a role in risk management is now extending its influence to makemoney. A recent study has shown that Investment decisions are no longer being made by financiers, but increas-ingly by PhD mathematicians. Firms are now employing academic statisticians to track patterns or trends in trad-ing behaviour and create formulae to predict future market movements. These formulae are then fed into pow-erful computers that buy and sell automatically according to triggers generated by the algorithms. Computersmonitor market movements as well as trading trends in a process called high-frequency trading, in which stockscan be held for just a matter of seconds. These programs are immensely powerful, constantly monitoring trad-ing patterns and news flows and are capable of changing strategies within fractions of a second.

BBC News, 25 September 2011 Compiled by Manisha Agarwal

U.S., U.K. Regulators to Weigh High-Frequency Registration

Top market regulators of the U.S. and the U.K. this week will discuss the idea of formally registering high-speedelectronic trading firms, the chairman of the U.S. Commodity Futures Trading Commission said Tuesday.

So-called high-frequency tradinga method of rapidly buying and selling securitieshas come under scrut iny inrecent years as slower-moving investors have raised concerns around being outpaced, and financial marketshave increasingly come to rely on the liquidity offered by such firms.

The May 2010 "flash crash" saw several of the largest high-speed electronic traders pull out of the market, citingproblematic data coming from exchanges. Critics said their exit left fewer buyers to curb a wave of selling thatbriefly drove down the Dow Jones Industrial Average by about 1,000 points.

However, some like the CFTC's Mr. Chilton have raised concerns that regulators' reach isn't far enough to coverfirms that wield trading algorithms with the potential to disrupt markets if they aren't used properly

The WallStreet Journal, Oct 11, 2011 Compiled by Prof N.S. Nilakantan

Novel math theory - Success of certain cancer therapies can be predicted:

A research highlighted the emerging promise of applying mathematical and computational concepts to the study

of complex biological systems. With some simple measurements, it was found that one can determine when acancer is addicted to a part icular cancer gene and will respond to therapy targeting that gene. The phenomenonis called oncogene addiction, in which a cancer is dependent on the activity of one cancer-causing gene. How-ever, because individual cancers reflect the interplay of hundreds or thousands of mutations within each cell, it'svery difficult to tell which, or how many, tumours fall into that category. An equation was used to predict thekinetics of tumour cell elimination in cancer patients. The key point is that there's a certain rate of regressionwhere you're never going to get rid of your cancer completely, but at another rate you will.

ScienceDaily, October 6, 2011 Compiled by Manisha Agarwal


QUANT NEWS DIGEST

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While analyzing Queueing applications, we discuss a most important question.Try to answer the question given below:

If you have an average arrival rate of 20 customers per hour and your service t ime is 3 minutes per per-son on an average, what is the utilization factor and what will be the length of the queue?

While many will calculate the utilization factor correctly as 1, which is the arrival rate by the servicerate, the calculation of the length of the queue is not always correctly done. Many are bound to say

that the length of the queue is zero, which is wrong. Here, we bring in the concept of average and un-derstand it in the context of an associated variance. Since we are dealing with a mean and a variance( i.e. deviation from the mean), the lower arrival rate at some point of t ime will lead to idle time of theserver but the higher arrival rate will lead to overload and need not be matched with a higher servicerate. Hence the utilization factor of 1 is not found workable in the long run and will lead to an infinitequeue length. For the system to be stable, the utilization factor is required to be less than1. The formu-las derived for various measures of the system also indicate this premise.

Prof. N.S.Nilakantan


QUANCEPT OF THE MONTH: UTILIZATION FACTOR

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Hedge Funds:

An aggressively managed portfolio of investments that uses advanced investment strategies such as lever-aged, long, short and derivative posit ions in both domestic and international markets with the goal of generat-ing high returns.

Legally, hedge funds are most often set up as private investment partnerships that are open to a limited num-ber of investors and require a very large initial minimum investment. Investments in hedge funds are illiquid asthey often require investors keep their money in the fund for at least one year.

Some investment strategies include Global macro, directional, event-driven, relative value (economics), and

many others. Hedge funds are generally unsupervised by national regulatory agencies and, on occasion, havebeen accused of destabilizing various financial markets

Analysis:

Since hedge funds are complex and show asymmetric expected returns, the critical metrics mentioned here aregood to start with to rigorously analyze hedge fund performance.

Performance Returns: Just like mutual funds, hedge funds must be evaluated for absolute as well as relative

return performance. However, since each hedge fund is unique, one must understand the various types of re-turns to identify them. Absolute returns give an idea as to where to categorize the fund as compared to more

traditional types of investments. Hedge funds with low and stable returns will prove to be better substitutes for

fixed income than for emerging market equities. Relative returns help determine a fund's attractiveness as com-

pared to other investments on the basis of other hedge funds, mutual funds, etc. The investor must determine

the performance over several time periods and the returns should be considered relative to the risk inherent in

each investment. The best thing that an investor could do would be to define a list of peers including a cross

section of traditional mutual funds, equity or fixed-income indexes and other similar hedge funds. A good fund

performs in the top quart iles for each period.

Risk: Outsized returns can be generated only by taking risks, so although a fund may exhibit excellent returns,an investor should incorporate risk into the analysis to determine the risk-adjusted performance of the fund.

P A G E 7

QUANTITAIVE ANALYSIS OF HEDGE FUNDS


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The factors used to measure risk are as follows:

Standard Deviation- This is easy to calculate and the concept of a normal distribution of returns is also simple.However, this is also the reason why the inherent risks in hedge funds cant be described. Most hedge funds donot have symmetrical returns, and the standard-deviation can also fail to show the higher than expected chanceof a large loss.

Value At Risk(VAR) -Value at risk is based on a combination of mean and standard deviation. Unlike standarddeviation, it does not describe risk in terms of volati lity, but rather as the highest amount that is likely to be lostwith a 5% probability. In a normal distribution, it is represented by the leftmost 5% of probable results.

Skewness- Skewness is a measure of the asymmetry of returns. Figure 1 shows graphs with the same meansand standard deviations. The left one is positively skewed. Although this indicates a higher probability of a resultthat is less than the mean, it also indicates the probability, although low, of an extremely posit ive result, indi-

cated by the long tail on the right side.

0 skewness indicates a normal distribution. A posit ive skewness would be like the distribution on the left, whilea negative skewness would be like the one on the right. The risk of a negatively skewed distribution is the prob-ability of a very negative result.

Kurtosis It measures the level of f latness of a distribution. In Figure 2, the distribution on the left representsnegative kurtosis, which means there is a lower probability of results around the mean, and lower probability ofextreme values. On the other hand, a positive kurtosis represents a higher probability of results near the mean,but also a higher probability of extreme values.

Sharpe Ratio: It indicates the amount of additional return obtained for each level of risk taken. A ratio below 1can be judged based on the asset class or investment strategy used. Sharpe rations prove to be more useful dur-ing periods of low interest since the parameters used to calculate it are the mean, standard deviation, and therisk free rate.


P A G E 8


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Benchmark Ratios. There are several measures that can be applied to measure performance relative to a bench-mark; 3 common measures are beta, correlation, and alpha.

Beta- Beta or systematic risk is the measure of a fund's returns relative to the returns on an index. A mar-

ket or index being compared is assigned a beta value of 1. The value of beta determines how much eq-uity exposure a fund has and this allows an investor to determine if and/or how large an allocation to afund is warranted.

Correlation:It measures any relative changes in returns. However, unlike beta, which assumes that the mar-ket drives the performance of a fund to some extent, correlation measures how related the returns oftwo funds are. It is measured on a scale of -1 to +1, where -1 stands for a perfect negative correlation, 0for no apparent correlation, and +1 for a perfect posit ive correlation. The lower the correlation thatfunds have to each other, the more likely the portfolio is to be well diversified.

Alpha- It considers the difference in returns relative to the amount of risk taken. In other words, if the re-turns are 25% better than the benchmark, but the risk taken was 40% greater than the benchmark, al-

pha would actually be negative. Since this is what most hedge fund managers claim to add to returns, itis important to understand how to analyze it. Alpha is calculated using the CAPM model:

Expected Return = Risk Free Rate + Beta*(Expected Return of the Market Risk Free Rate)

To calculate whether a hedge fund manager added alpha or not, one could just substitute the beta value of thehedge fund in the above equation, which would give an expected return on the hedge fund's performance. If theactual returns exceed the expected return, the hedge fund manager has added alpha based on the risk taken. If

the actual return is lower than the expected return, then he/she hasnt added alpha. We, as investors, wouldwant hedge fund managers that add alpha to returns with the risk they take and not generate returns simply bytaking additional risk.

Briji Komban

PGDM-B

2011-2013


P A G E 9


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P A G E 1 0


QUANT GURU of the MONTH

Paul Pierre Levy was a Jewish French mathematician who was active especially in prob-ability theory, introducing martingales and Levy flights. Levy processes, Levy measures,Levys constant, the Levy distribution, the Levy skew alpha-stable distribution, the Levyarea, the Levy arcsine law, and the fractal Levy C curve are also named after him.

Levy was born in Paris, the son of Lucien Levy,an Examiner at the cole Polytechnique. Levyalso attended the cole Polytechnique andpublished his first paper in 1905 at the age of19, while still an undergraduate. His teacherand advisor was Jacques Hadamard.

It was Hadamard who was the major influencein determining the topics on which Lvy wouldundertake research. Finishing his studies at thecole des Mines in 1910 he began research infunctional analysis. His thesis on this topic wasexamined by mile Picard, Poincare and Hadamard in 1911 and he received his Docteur sSciences in 1912.

Lvy became professor cole des Mines in Paris in 1913, then professor of analysis at thecole Polytechnique in Paris in 1920 where he remained until he retired in 1959. DuringWorld War I Lvy served in the artillery and was involved in using his mathematical skillsin solving problems concerning defence against attacks from the air.

In 1919 Lvy was asked to give three lectures at the cole Polytechnique on calculus ofprobabilities and the role of Gaussian law in the theory of errors.

Not only did Lvy contribute to probability and functional analysis but he also worked onpartial differential equations and series. In 1926 he extended Laplace transforms tobroader function classes. He undertook a large-scale work on generalised differentialequations in functional derivatives. He also studied geometry.

HARSHITA SRIVASTAV

PGDM-A

2011-2013

15 September 1886 15 December 1971

QUANT GURUof the MONTHP A G E 1 0

14 is

thesmallest

even

number

n with no

solutionsto (m)

= n

Q U A N T T R I V I A


11/14

Gunjan JadonPGDM-B2011-2013


E-Tambola, an annual game which is a mix of acumen and luck or chance. It was conducted by Quantinuum

committee on 21st and 22nd of September. The event was like a housie game where tickets were sold to the par-ticipants where they need to strike out the numbers on the tickets. Though it is an interesting game butQuantinuum added logic into it by putting questions for every number on the tickets. Total number of ticketssold for the event was 250 which included participation from various specializations. The game was conducted intwo phases. The first phase was an online quiz on 21st where the participants were sent online questions on theirmail id and their answers in form of numbers were required to be struck out from the tickets. Here we foundtwo winners for the category Early 5 & Top 10. Next phase was conducted on 22nd,in which the participants wereasked to come with their tickets for the main event. The questions were given on the spot and the participantswere required to solve and strike off the answers which matched with the numbers on their tickets. The eventitself was a good mix of logic, knowledge and Luck.

Following were the winners in various categories:-Garima Sekhri -Early 5Shivani Bathla -First lineBriji Komban -Middle lineAnkur Arora -Bottom lineAnkur Arora -Top 10Shivani Bathla -Full housie-1stPradyumna Swain -Full Housie-2ndAnkur Arora -Full Housie-3rdKaran Thakur -Full Housie-4th (Combined)Dhwani Shah -Full Housie-4th (Combined)

The event also leads to the launch of quantinuum website which has been prepared by the quantinuum mem-bers. The website recorded 250 hits on the first day of its launch. This website will be act as a platform for shar-ing views related to the Quants and its application in everyday life. The website will feature SIMSR alumni andalso updates on various events. The website was launched by Prof. Nilakantan along with the students of thecommittee.Link for the website:

http://quantinuum.weebly.com/

P A G E 1 1

Event of the month: E-TAMBOLA


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An interesting fact about primesMathematicians of XVIIIth century proved that numbers 31; 331; 3331; 33331; 333331; 3333331; 33333331 areprimes. It was a big temptation to think that all numbers of such kind are primes. But the next number is not aprime.333333331 = 17 * 19607843

- 1

An elegant proof that

It is obvious that 1 = (2 -1).

= * (2-1)

= (1 + 2 + 22 + ... + 2n) * (2 -1)= (2 + 22 + 23 ... + 2n+1) - (1 + 2 + 22 + ... + 2n)

= 2n+1 - 1.

Manisha Agarwal

PGDM-FS2011-2013


P A G E 1 2

FUN FACTS: Quants in a lighter vein


13/14


Q U A N T T R I V I A

The FiveMostImportantNumbers in

Mathematics in OneEquation

e^ i* p i + 1 = 0

Answers and name of solvers will be published in the next

issue. Mail your answers to [email protected]

Solutions to Last Months QUANT QUERY

What no. is two places away from itself plus 3,three places away from itself doubled, twoplaces away from itself minus 2, two placesaway from itself plus 4, two places away fromitself minus 1 and two places away from itselfplus 6.Ans 5 (Fourth row, third number)

Solutions to Last Months SUDOKU

No correct entry was received for the above questions.

P A G E 1 3

25 13 10 1 17

8 24 11 12 4

19 6 21 7 5

9 15 5 18 3

14 20 22 16 2

QUANT QUERY OF THE MONTH


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Quantinuum@SIMSRQuantinuum, the Quant's forum of KJ Somaiya Institute of Management Studies and Research is formed

with two objectives. Firstly to remove the common myth from the students mind that mathematics is diffi-

cult. Secondly to give students an exposure on how to make decisions in real life business problems using

quantitative techniques. This helps to bridge the gap between theory and the practical application.

For any further queries and feedback, please contact the following address

KJ Somaiya Institute of Management Studies and ResearchVidya Nagar, Vidya ViharGhatkopar EastMumbai -400077

Mentors

Prof. N.S.Nilakantan (9820680741) email [email protected]

Prof. Anjali Chopra ( 9820495195) - email [email protected]

Leaders

Gaurav Agarwal (7738543891)Dhaval Trivedi (9224422442)Pramit Pratim Ghosh (7738543880)Tarun Sethi (9820388158 )

Editorial Team

Vaibhav Goel (9769456493)Satyadev Kalra (8291687568)

Harshita Shrivastav(9769552083)Manisha Agarwal(9372166242)

For more details: http://quantinuum.weebly.com/

Like our newsletter? Want to contribute and see your name being

published?

Feel free to contribute articles, concepts, trivia, facts and news about the

wonderful world of numbers and mail them [email protected]

http://simsrquantinuum.blogspot.com/

quantinuum september 11

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