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Q U R I O S I T Y - V O L - 8, E D I T I O N - 6
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Welcome to the latest issue of Quriosity, the monthly magazine of Quantinuum! Many current data analysis techniques are beyond the reach of most people. Obscure maths and daunting algorithms have created a chasm for problem solvers and decision makers. Quriosity is trying to bridge these gaps by giving appropriate inputs to our students and readers who are the future managers. The objective of Quriosity is to publish up-to-date articles on data analytics, alongside relevant and insightful news. This way the magazine aspires to be vibrant, engaging and accessible, and at the same time integrative. Needless to say, any articles that you wish to submit, either individually or collaboratively, are much appreciated and will make a substantial contribution to the development and success of the magazine.
Thank you and Happy Reading! Editorial Team Quantinuum
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by Aditya Sharma
by V V S Anudeep by Chaitanya Agarwal
by Rupal Doshi
by Priyakshi Mondal, Dropad Saxena, Sachin Bagi and Sonika Aheja by Sai Tejashyam Dontaraju and Devarshee Ranjan Bora by Kapil Gupta
by Akshay Nagpal and Tejal Jadhav
by Samoshri Mitra
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In the world of quantitative trading, it is believed that with the help of mathematical models and number crunching algorithms, trading opportunities can be identified and exploited. While a financial economist might be interested in the structural aspect of stock prices, a financial mathematician looks at the approaches based on stochastic calculus while evaluating stock prices. There are two broad branches in finance that require these advanced quantitative techniques: Derivatives Pricing, and Risk & Portfolio Management. The main difference between the two lies in the probabilities they use. Derivative pricing is based on the risk neutral probability (or arbitrage-pricing probability), whereas the risk & portfolio management works on the actual (or actuarial) probability. The rate of return, in case of arbitrage-pricing, is expected to be risk free, whereas, actuarial probability is all about minimizing an inevitable risk.
A derivative is a contract, between two or more parties, which derives its value from the fluctuations in underlying assets. In a derivative market rather than trading stocks directly we trade Futures and Options contracts which derive their value from different stocks, commodities or indices. Futures is a good example of derivatives which gives the buyer a right to buy a certain underlying asset, in future, at a price decided today. For example, I expected that Gold prices will reach 35000 after a couple of months, whereas it is at a rate of 30000 today and contracted a future on the same. If it actually reaches at 35000, the seller will have to sell it to me at today’s price i.e. 30000. There are various other derivatives such as forwards, swaps and mortgage backed securities. These derivatives have a potential that can make or break economies. In the 2008 crisis, it was mortgage backed securities and a particular type of swap that caused the trouble. In the rest of the article various mathematical techniques for derivative pricing have been presented, based on the chronology of their inception. In 1900, Louis Bachelier gave the theory of Brownian Motion in finance which states that predicting future stock prices is no different than the prices following a random walk. Let the ratio of today’s stock price and yesterday’s stock price be called as ‘X’. Bachelier observed that the values of logarithms of all these Xs of a time series follow Brownian motion, in which short term changes have a finite variance and causes the longer term changes to follow a Gaussian distribution. A simulation technique such as Monte4
Q U R I O S I T Y - V O L - 8, E D I T I O N - 6
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Carlo method can be utilized to obtain result from this random sampling, using predefined libraries in MATLAB.
In 1973, Black-Scholes model, which gives a theoretical estimate of the price of European-style options over time, extended Brownian motion theory. The Black Scholes model assumes log-normal distribution of stock prices and requires six input variables: strike price of an option, current stock price, time to expiration, risk-free rate, dividend yield and volatility. Over the next few decades, this model was found to be having certain shortcomings and the same was proposed to be rectified through modifications by various researchers. To further improve the accuracy of forecasts, Stochastic Volatility methods were incorporated. The Black Scholes model assumed that the volatility of the underlying security was constant, while stochastic volatility models categorized the price of the underlying security as a random variable allowing the prices to vary. In 1979, Binomial options pricing model was developed, which uses an iterative procedure. Under this assumption, it is able to provide a mathematical valuation of an option at each point in the timeframe specified. Due to its simple and iterative structure, the binomial option pricing model presents certain unique advantages. For example, since it provides a stream of valuations for a derivative for each node in a span of time, it is useful for valuing derivatives such as American options. It is also much simpler than other pricing models such as the Black-Scholes model. There are various other models in the industry, such as SLV, SABR, Levi models, etc. These models generally are a result of slight variations in basic partial differential equation of Black-Scholes model. Each model is suitable for some particular derivatives and can be tailored to suit the purpose. The problems in the world of derivative pricing are low dimensional in nature, and the calibration of parameters is the main challenge.
Source:-http://www.investopedia.com/ask/answers/060315/how-price-derivative-determined.asp Options, Futures and Other Derivatives by John C. Hull
By Aditya Sharma PGDM-FS (2017-19)
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The terms ‘performance rating’ and ‘Bell curve’ would ring a bell in many who have worked in large corporates. Normal probability distribution (bell curve) has been a successful tool in the annual employee performance rating in many organizations for quite some time. In many natural processes the random variation conforms to normal distribution function, for example people's heights, examination grades, snowflake sizes, and so on. The probability distributions are descriptions of the chances of occurrence of random phenomenon. Probability distributions are generally divided into two classes. Discrete probability distribution is one in which the set of possible outcomes are discrete, such as a card drawn from a deck. On the other hand, a continuous probability distribution is applicable to those scenarios where the set of possible outcomes can take values in a continuous range like, temperature on a given day. In continuous distributions probability for any one given value cannot be determined because the distribution is continuous, but we can determine the probability for a given interval of values. The probability for an interval is equal to the area under the density curve. The normal distribution is a commonly encountered continuous probability distribution. Properties of Normal distribution
Although there is a debate on using bell curve for assessing the human performance, it is widely accepted that normal distribution accurately describes the product quality and thus normal distribution is unarguably a great tool used in the operations segment of a business. The following case gives a better understanding of the usage. 100 components rolled out of a production line are sent for hardness testing and the results obtained were as follows;
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The distribution thus obtained is a normal distribution. The inference that can be drawn from this case is that if a component is picked up randomly from this product lot, the probability that its hardness value shall lie in between 211 and 213 will be around 49%. So, this concept is used by various manufacturing firms to decide the batch size for quality inspections. It would be appropriate if the usage of normal distribution in finance segment is mentioned here. Any investment has two aspects: risk and return. Investors look for the lowest possible risk and for highest possible return. The normal distribution quantifies these two aspects by the mean for returns and standard deviation for risk.
Standard Deviation: Standard deviation indicates the amount by which the values deviate on average from the mean. The higher the standard deviation, the riskier the investment is, as it leads to more uncertainty.
Normal distribution finds application in the field of marketing as well. One of the probability distributions that fits the consumer behavior of a product is normal distribution. The implication for marketers is understanding the segments of the bell curve, and using these segments to advantage as they orchestrate their marketing efforts. The quick message is that you can’t market to everyone – as you move across the curve from one end to the other needs of the consumer change dramatically. It is always better to market to a specific segment of the group, as opposed to the group as a whole. So, let us hope that the next time you hear the word ‘Bell curve’, it will ring an alarm on more than performance rating.
Sources: The Myth of the Bell Curve: Look for The Hyper-Performers in forbes.com magazine by josh bersin http://michaelmcmahon.com/marketing-to-the-bell-curve/
By V V S Anudeep PGDM (2017-19)
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Sherlock Holmes was one of the most celebrated and successful data analysts of all time. Holmes was basically a fictional character created by British author Sir Arthur Conan Doyle and he was portrayed as a consulting detective. He is known for his proficient observation, knowledge in forensic science and mindful application of his logical reasoning skills. Holmes is of the opinion that if a person knows how to use the data there is no need for manipulation and let the data speak on behalf of the person. Holmes was a master in converting raw data into variable insights. He combined the ‘science of deductions’ along with the facts and comes up with a solution with the problem. In this case, his decisions were based on the data collected which further resulted into greater accuracy and minimal duplication. Sherlock Holmes said that “It is a capital mistake to theorize before one has the facts, one begins to twist facts to suit theories, rather than theories to suit facts”. Deductions usually goes against the natural tendency of our minds to seek comfort and hence look for shortcuts. Observations were also used as a key indicator for analyzing the data. Through the stories of Sherlock Holmes one gets to know about the insights of Sherlock Holmes. He can decipher how the light enters in Watson’s based on how his beard is shaved and he also discovered the previous financial position of a man whom he had never seen before just by looking to the hat he was using. Holmes believed that the person should grasp whatever comes to his way and should not indulge in selective knowledge grasping as one never knows what piece of information is required at what piece of time. He developed a study about ashes from 140 types of cigarettes, smoking pipes and cigars which turned to be essential for solving some cases. So with technical skills, experience also has a great role to play in solving problems. In many situations, Holmes, after hearing the facts and extracting the data, plunges into his own universe and gets away from his faithful friend Watson to build his reasoning. In the environment, a person faces similar situations but Holmes preached to not minimize trivial situations and looking carefully into them might result in distinguished results than expected. So, this reference to that a data should not be ignored as every time the situations are not mere repetitions but can be unique. So, in that scenario, it becomes very difficult for an analyst to locate the actual source and its application. Holmes took into account the minutest details and tried to combine all the data and come up with a conclusion which can bear fruits. Sherlock Holmes said, “My name is Sherlock Holmes. It is my business to know what other people do not know”. It can therefore be concluded that data analysis plays a vital role in making decisions and a person should learn the various analytical tools and should constantly apply them to base their decisions upon. Source:- http://motiv8agency.com/blog/data-analytics-marketing-strategies-and-sherlock-holmes/
By Chaitanya Agarwal PGDM RM (2017-2019)
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Allama Mashriqi also known as Inayatullah Khan, born in Amritsar on 25 August 1888, was an Islamic scholar and founder of the Khaksar movement. Mashriqi had a passion for mathematics from his childhood. He completed his Master's degree in mathematics from the University of the Punjab at the age of 19 and broke all previous records. In October 1907 he went to Britain and matriculated at Christ's College, Cambridge, to read for the mathematics tripos. He was awarded a college foundation scholarship in May 1908. In June 1909 he was awarded first class honours in Mathematics Part I, being placed joint 27th out of 31 on the list of wranglers. For the next two years, he read for the oriental languages tripos in parallel to the natural sciences tripos, gaining first class honours in the former and third class in the latter. He was Fellow Geographical Society (Paris), Fellow Society of Arts (Paris), and Fellow of the Royal Society of Arts (F.R.S.A). Being a renowned Mathematician he became President of the Mathematical Society, Member of the Delhi University Board. He was awarded the Gold Medal by the World Society of Islam. While he was in England, he was contacted by the Maharaja of Alver for State Premiership. With least interest in this position or meeting the Maharaja, he declined the offer. After completing his education in England, he traveled around Europe and returned to India in 1912. Mashriqi was a noted intellectual who became a college Principal at the age of 25, and then became an Undersecretary at the age of 29, in the Education Department of the Government of India. He subsequently resigned the Government service and founded the Khaksar movement in 1930, aiming to advance the condition of the masses irrespective of any faith, sect or religion. He was imprisoned several times as the leader of the Khaksar movement. Through his philosophical writings, he asserted that the Science of Religions was essentially the Science of collective evolution of mankind. Allama Mashriqi was a sage in his own right but remained a controversial personality. He died of cancer in Lahore in August 1963. Source: https://en.wikipedia.org/wiki/Inayatullah_Khan_Mashriqi http://www.wisdomblow.com/?p=2421 By Rupal Doshi PGDM FS (2016-18)
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Quantinuum Summer Internship Competition, abbreviated QSIC, is an annual hunt for the best Quantitative method oriented summer project, held by Quantinuum at SIMSR. Held on 5th August this year, it provided a platform for all quant lovers to come together as second year students shared their project experience and gain exciting prizes. Students, currently in their second year MBA, who have done their summer internship with the use of Quantitative methods like Statistical Inference, Operations Research/ Management science applications and econometric methods, Excel based techniques had been invited to register and share their internship experience, if shortlisted. The first stage involved registration and submission of an abstract (not exceeding 500 words) including details of the quantitative techniques used by them. The applications received were reviewed and shortlisted by SIMSR faculty Prof. N.S. Nilakantan. This review and evaluation resulted in six participants bring shortlisted for the final presentation round, to be held on 5th August. The judges for the final round were SIMSR faculties Prof. N.S. Nilakantan and Prof. Sanjiwani Kumar, both of who come with a rich experience in O.R, Statistics, Excel Solver, SPSS, SAS, R and Minitab to name a few. SIMSR alumni, Shruti Kalghatgi, working with Hypercity as merchandise manager in domain chain stock analysis and Vatsal Mehta, ex Co Convener of Quantinuum, currently working as a financial analyst at Value Add Research Analytics were amongst the guests. The companies that the students had interned for during the internship ranged from BookMyShow and Performix.Convonix to Larsen&Toubro and Excel Industries. The tools and techniques used by the finalists in their projects included ARIMA and R Studio, Pareto, A/B Testing etc., engaged the audience. Applications of quantitative techniques and tools were observed in domains that ranged from insurance to country risk assessment and risk profiling. Intriguing questions – on quantitative teasers and general business knowledge in between successive presentations by the anchors and an opportunity to win exciting prizes on getting the answers right kept the audience hooked. After the presentations drew to a close, co-partner for QSIC, Mr. Prem Vellaiyan, owner of Steamy Mugs shared valuable inputs with the audience on how to follow one’s dream with passion.The judges declared the results after careful evaluation and consideration. Saumya Shrivastava (PGDM Comm), Saurabh Butala (MMS) and Ninad Puranik ( PGDM IB) bagged the first, second and third prizes respectively. Prizes/Cash rewards have been given to the winner and runner-up and certificates have been issued to all the shortlisted candidates. By Priyakshi Mondal and Dropad Saxena PGDM (2017-2019) and PG FS(2017-2019)
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Seat Occupancy Prediction for Cinemas under BookMyShow over for Saturday -Saumya Shrivastava Brief about the project and the presentation of the winner of QSIC indicating the tools and techniques followed by her. Objective: To predict the occupancy of each cinema under BookMyShow over the weekend (Friday, Saturday, Sunday) and use the predicted value of occupancy to predict penetration of BookMyShow over the weekend. Tools and Techniques used:
ARIMA- Auto Regressive Integrated Moving Average It is a model for forecasting a time series which can be made to be “stationary” by differencing (if necessary), perhaps in conjunction with nonlinear transformations such as logging or deflating (if necessary).
Auto Regressive(AR) terms known as p represents the number of past values on which the data depends Moving Average(MA) terms known as q represents the error of the model as a combination of previous error terms et Integrated(I) means the d term is the number of non-seasonal differences needed for stationary data Alteryx Data preparation was the first stage of the project which required creation of workflows and this was done by Alteryx.
R Studio 21 ARIMA models were created for different cities and clusters. These models were validated by using R Macro which was created in order to connect Alteryx with RStudio and split the files into a combination of CinemaId and Show dates using in-sample and out-sample validation of the data. By Sonika Aneja and Sachin Bagi PG FS(2017-2019) and PGDM (2017-2019)
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High Net worth Individuals (HNIs) have several investment options in the market. Some of them are purely debt instruments with a fixed coupon associated with them, some purely equity with capital appreciation being the motive of investment. However, there are several hybrid investments, which provide the features of both debt and equity, allowing exposure to equity and debt portions. One of such products is a structured product, called Market Linked Debenture (MLD). MLDs have off late grown exponentially as low-risk HNI investments. This project studies the outstanding issuances of MLDs in India, their issuer and rating trends since FY2013, their classification and pay-off analysis based on Market performance. The biggest question for any investor before investing into a particular instrument is how the instrument performs in various market conditions. Pay-off analysis covers how the returns of these MLDs vary with market performance, how the strategy varies with market and how far the Issuers have been successful in predicting the market performance from such strategies. An analysis of returns of MLDs compared to those of direct index investments has also been done, to strengthen the reason why MLDs should be preferred to direct market investments. By Sai Tejashyam Dontaraju MMS (2016-18)
The project was to establish a reporting structure and automate these reports in order efficiently track the implementation of the Location Strategy plan. The reports collated the data from various stakeholders/ sources and provided a consolidated view. The consolidation helped in the visibility of the various moving elements and flagged the areas which needed immediate attention. The automation of the whole process made the reports more user friendly and garnered more consumption as compared to previous reports. Four reports were created based on the needs of the stakeholders. The outputs of the reports were used to create online reports using Qlikview. Additional features were added to make the visualizations and the report more user friendly. I learned Qliksense and Qlikview as well as VBA automation. Along with my learnings I managed to save 0.5 FTE (4 hours). The Location Strategy plan was understood and the various stakeholders/touchpoints were identified. The consolidated report was created by understanding the business needs of all the stakeholders. Automation helped in easier consumption and removed any manual interruptions.
By Devarshee Ranjan Bora PGDM FS (2016-18)
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As Curiosity inches closer towards ascending Vera Rubin Ridge (VRR), the science team is continuing to be diligent in both characterizing the local surroundings while also looking ahead and imaging the ridge upon approach. The team selected several targets near the rover to analyze using its remote sensing instruments, while also allowing time for the rover to drive approximately 15 meters ahead and get into position for this weekend's long imaging campaign of VRR. After the planned ~15 meter drive to take place in the early Martian afternoon, Curiosity will perform some quick imaging of her surroundings and VRR using the Navcam cameras before sending these data up to the Mars Reconnaissance Orbiter and then back to Earth for tomorrow's science planning activities. Following this data transfer, Curiosity will complete her Navcam imaging (including a survey for nearby dust devils) and will use Mastcam to look for nearby rocks. ChemCam will also perform an automated chemistry analysis of a target of interest in the surrounding landscape using its AEGIS capabilities. Lastly, the Mars Descent Imager (MARDI) will continue its faithful tradition of imaging the terrain just below the rover's belly.
Mars Orbiter Mission (MOM), the maiden interplanetary mission of ISRO, launched on November 5, 2013 by PSLV-C25 got inserted into Martian orbit on September 24, 2014 in its first attempt. MOM completes 1000 Earth days in its orbit, well beyond its designed mission life of six months. 1000 Earth days corresponds to 973.24 Mars Sols (Martian Solar day) and MOM completed 388 orbits. MOM is credited with many laurels like cost-effectiveness, short period of realization, economical mass-budget, miniaturization of five heterogeneous science payloads etc. Satellite is in good health and continues to work as expected. Scientific analysis of the data received from the Mars Orbiter spacecraft is in progress. ISRO has also launched MOM Announcement of Opportunity (AO) programs for researchers in the country to use MOM data for R&D. The success of Mars Orbiter Mission has motivated India’s student and research community in a big way. Thirty-two proposals were supported under this AO. A Planetary data analysis workshop was also conducted to strengthen the MOM-AO scientist's research interest. Source: https://www.jpl.nasa.gov/news/ https://www.thebetterindia.com/105606/isro-mangalyaan-mom-celebrates-1000-earth-days-orbit/
By Kapil Gupta PGDM (2017-19)
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Wipro’s Industry Focused Big Data Analytics-as-a-Service Platform Now Available on Microsoft Azure Wipro announced the availability of Data Discovery Platform which is a big data analytics-as-a-service solution on Microsoft Azure. The solution would accelerate insight-driven decision making through prebuilt applications for these specific industries. With its industry specific apps, DDP covers the entire spectrum from data to information to insights. It not only empowers customers with relevant insights but allows businesses to gain valuable insights and bridge the gap between insights and information. It leverages techniques such as visual sciences and storytelling with data.
Facebook, YouTube Turn to Machine Learning to Control Content on their Platform While Facebook is fighting a tough battle against fake news, YouTube is aggressively trying to cut down the offensive and extremist content on its platform. And maybe machine learning is the solution to the problem. In a bid to bring it down, the social media giant will be using “updated machine learning” to detect potential hoaxes and send them to third-party fact checkers. Applied machine learning researchers and engineers develop machine learning algorithms that rank feeds, ads and search results, and create new text understanding algorithms that keep spam and misleading content at bay. New computer vision algorithms can “read” images and videos to the blind and display over 2 billion translated stories every day, speech recognition systems automatically caption the videos that play in your news feed, and we create new magical visual experiences such as turning panorama photos into fully interactive 360 photos. Source: http://analyticsindiamag.com/
By Akshay Nagpal & Tejal Jadhav PGDM (2017-19)
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Sudoku
Degree of Freedom
You have only 7 hats. Yet you want to wear a different hat every day of the week. On the first day, you can wear any of the 7 hats. On the second day, you can choose from the 6 remaining hats, on day 3 you can choose from 5 hats, and so on. When day 6 rolls around, you still have a choice between 2 hats that you haven’t worn yet that week. But after you choose your hat for day 6, you have no choice for the hat that you wear on Day 7. You must wear the one remaining hat. You had 7-1 = 6 days of “hat” freedom—in which the hat you wore could vary! That’s kind of the idea behind degrees of freedom in statistics. Degrees of freedom are often broadly defined as the number of "observations" (pieces of information) in the data that are free to vary when estimating statistical parameters
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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 address: KJ Somaiya Institute of Management Studies and Research, Vidya Nagar, VidyaVihar, Ghatkopar East, Mumbai 400077 or drop us a mail @ newsletter.quantinuum@gmail.com Mentor:
Prof. N.S.Nilakantan (+919820680741) Email – nilakantan@somaiya.edu
Team Leaders:
Vaibhav M (+917708521382) Maheshwaran Kumar (+919566173411) Rishita Shah (+919867290018)
Editorial Team:
Rupal Doshi (+919831427640) Amod Kulkarni (+919833701015) Aditya Gupta (+919621655806) Chaitanya Agarwal (+917009638623) Aditya Sharma (+918302525599) VVS Anudeep (+919441201685) Kapil Gupta (+917727936906) Samoshri Mitra (+918697440265)
Designing Team:
Shreyas Kulkarni (+918600106378) Ashish Mohadik (+919819741018)