The document summarizes a session on applied statistics using the R programming language. It provides an overview of using R to import and analyze sample data, including performing descriptive statistics, plotting histograms, and calculating measures of skewness and kurtosis. Examples are also given of using R to model portfolio returns and analyze the implications for the efficient frontier.
This document summarizes a session on financial econometric models. It discusses time series analysis principles including auto regressive processes, moving average processes, and ARMA models. The session aims to remind participants of key concepts from the previous session and conclude by reviewing time series analysis steps of identifying trends and seasonality, fitting appropriate models, and forecasting.
This document appears to be notes from a class on applied statistics and quantitative finance. It covers several topics:
- Reminders about the capital asset pricing model and thinking algorithmically
- Summarizing an interim exam and minimizing residuals when estimating parameters
- Discussing the binomial and normal distributions for estimations from sample data
- Explaining autoregressive models and components of time series like trends and seasonality
- Discussing portfolio optimization and the efficient frontier
This document summarizes a session on financial econometric models and R. Key points covered include downloading and using the open source R software, uploading data and calling variables, summarizing distributions with functions like mean and standard deviation, and visualizing data through histograms. Basic linear regression was demonstrated using the lm function. Coin tossing experiments were also conducted to explore binomial distributions.
This document summarizes a session on econometric modeling. It discusses autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), and autoregressive integrated moving average (ARIMA) time series models. It also introduces the concepts of heteroscedasticity, autoregressive conditional heteroscedasticity (ARCH), and generalized ARCH (GARCH) models to account for non-constant variance in time series data. Examples are provided to illustrate identifying and fitting AR, MA, ARMA and ARIMA models.
This document provides an overview of topics covered in the ESGF 4IFM Q1 2012 session on applied statistics. The session included reminders of the previous session, an introduction to multiple regression, and estimations. Games were used to reinforce statistical concepts. Topics covered included multiple regression, ordinary least squares, properties of stationary time series, autocorrelation, and confidence intervals. Estimation techniques like the binomial distribution, normal approximation, and Student's t-distribution were also discussed.
The document provides an overview of the topics to be covered in a quarterly statistics session, including descriptive statistics, the normal distribution, and applications of statistics in quantitative finance. Key points from the session include calculating descriptive statistics like the mean, standard deviation, skewness and kurtosis of a dataset; understanding that the normal distribution is widely used in quantitative models; and using R and Excel to analyze financial data and visualize distributions.
The document summarizes a session on financial econometric models. It will introduce models, their objectives of describing, modeling and forecasting data behavior. It will cover ordinary least squares regression, estimating intercepts and slopes to minimize residuals. It will also discuss calculating variances, covariances, correlation coefficients and assessing the quality of regressions. Examples using Excel functions like intercept, slope, var.p, covariance.p and stdev.p will be covered.
This document summarizes a session on financial econometric models. It discusses time series analysis principles including auto regressive processes, moving average processes, and ARMA models. The session aims to remind participants of key concepts from the previous session and conclude by reviewing time series analysis steps of identifying trends and seasonality, fitting appropriate models, and forecasting.
This document appears to be notes from a class on applied statistics and quantitative finance. It covers several topics:
- Reminders about the capital asset pricing model and thinking algorithmically
- Summarizing an interim exam and minimizing residuals when estimating parameters
- Discussing the binomial and normal distributions for estimations from sample data
- Explaining autoregressive models and components of time series like trends and seasonality
- Discussing portfolio optimization and the efficient frontier
This document summarizes a session on financial econometric models and R. Key points covered include downloading and using the open source R software, uploading data and calling variables, summarizing distributions with functions like mean and standard deviation, and visualizing data through histograms. Basic linear regression was demonstrated using the lm function. Coin tossing experiments were also conducted to explore binomial distributions.
This document summarizes a session on econometric modeling. It discusses autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), and autoregressive integrated moving average (ARIMA) time series models. It also introduces the concepts of heteroscedasticity, autoregressive conditional heteroscedasticity (ARCH), and generalized ARCH (GARCH) models to account for non-constant variance in time series data. Examples are provided to illustrate identifying and fitting AR, MA, ARMA and ARIMA models.
This document provides an overview of topics covered in the ESGF 4IFM Q1 2012 session on applied statistics. The session included reminders of the previous session, an introduction to multiple regression, and estimations. Games were used to reinforce statistical concepts. Topics covered included multiple regression, ordinary least squares, properties of stationary time series, autocorrelation, and confidence intervals. Estimation techniques like the binomial distribution, normal approximation, and Student's t-distribution were also discussed.
The document provides an overview of the topics to be covered in a quarterly statistics session, including descriptive statistics, the normal distribution, and applications of statistics in quantitative finance. Key points from the session include calculating descriptive statistics like the mean, standard deviation, skewness and kurtosis of a dataset; understanding that the normal distribution is widely used in quantitative models; and using R and Excel to analyze financial data and visualize distributions.
The document summarizes a session on financial econometric models. It will introduce models, their objectives of describing, modeling and forecasting data behavior. It will cover ordinary least squares regression, estimating intercepts and slopes to minimize residuals. It will also discuss calculating variances, covariances, correlation coefficients and assessing the quality of regressions. Examples using Excel functions like intercept, slope, var.p, covariance.p and stdev.p will be covered.
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
Economic Risk Factor Update: June 2024 [SlideShare]Commonwealth
May’s reports showed signs of continued economic growth, said Sam Millette, director, fixed income, in his latest Economic Risk Factor Update.
For more market updates, subscribe to The Independent Market Observer at https://blog.commonwealth.com/independent-market-observer.
STREETONOMICS: Exploring the Uncharted Territories of Informal Markets throug...sameer shah
Delve into the world of STREETONOMICS, where a team of 7 enthusiasts embarks on a journey to understand unorganized markets. By engaging with a coffee street vendor and crafting questionnaires, this project uncovers valuable insights into consumer behavior and market dynamics in informal settings."
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Lecture slide titled Fraud Risk Mitigation, Webinar Lecture Delivered at the Society for West African Internal Audit Practitioners (SWAIAP) on Wednesday, November 8, 2023.
How Does CRISIL Evaluate Lenders in India for Credit RatingsShaheen Kumar
CRISIL evaluates lenders in India by analyzing financial performance, loan portfolio quality, risk management practices, capital adequacy, market position, and adherence to regulatory requirements. This comprehensive assessment ensures a thorough evaluation of creditworthiness and financial strength. Each criterion is meticulously examined to provide credible and reliable ratings.
Vicinity Jobs’ data includes more than three million 2023 OJPs and thousands of skills. Most skills appear in less than 0.02% of job postings, so most postings rely on a small subset of commonly used terms, like teamwork.
Laura Adkins-Hackett, Economist, LMIC, and Sukriti Trehan, Data Scientist, LMIC, presented their research exploring trends in the skills listed in OJPs to develop a deeper understanding of in-demand skills. This research project uses pointwise mutual information and other methods to extract more information about common skills from the relationships between skills, occupations and regions.
[4:55 p.m.] Bryan Oates
OJPs are becoming a critical resource for policy-makers and researchers who study the labour market. LMIC continues to work with Vicinity Jobs’ data on OJPs, which can be explored in our Canadian Job Trends Dashboard. Valuable insights have been gained through our analysis of OJP data, including LMIC research lead
Suzanne Spiteri’s recent report on improving the quality and accessibility of job postings to reduce employment barriers for neurodivergent people.
Decoding job postings: Improving accessibility for neurodivergent job seekers
Improving the quality and accessibility of job postings is one way to reduce employment barriers for neurodivergent people.
2. Elemental Economics - Mineral demand.pdfNeal Brewster
After this second you should be able to: Explain the main determinants of demand for any mineral product, and their relative importance; recognise and explain how demand for any product is likely to change with economic activity; recognise and explain the roles of technology and relative prices in influencing demand; be able to explain the differences between the rates of growth of demand for different products.
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
Economic Risk Factor Update: June 2024 [SlideShare]Commonwealth
May’s reports showed signs of continued economic growth, said Sam Millette, director, fixed income, in his latest Economic Risk Factor Update.
For more market updates, subscribe to The Independent Market Observer at https://blog.commonwealth.com/independent-market-observer.
STREETONOMICS: Exploring the Uncharted Territories of Informal Markets throug...sameer shah
Delve into the world of STREETONOMICS, where a team of 7 enthusiasts embarks on a journey to understand unorganized markets. By engaging with a coffee street vendor and crafting questionnaires, this project uncovers valuable insights into consumer behavior and market dynamics in informal settings."
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Lecture slide titled Fraud Risk Mitigation, Webinar Lecture Delivered at the Society for West African Internal Audit Practitioners (SWAIAP) on Wednesday, November 8, 2023.
How Does CRISIL Evaluate Lenders in India for Credit RatingsShaheen Kumar
CRISIL evaluates lenders in India by analyzing financial performance, loan portfolio quality, risk management practices, capital adequacy, market position, and adherence to regulatory requirements. This comprehensive assessment ensures a thorough evaluation of creditworthiness and financial strength. Each criterion is meticulously examined to provide credible and reliable ratings.
Vicinity Jobs’ data includes more than three million 2023 OJPs and thousands of skills. Most skills appear in less than 0.02% of job postings, so most postings rely on a small subset of commonly used terms, like teamwork.
Laura Adkins-Hackett, Economist, LMIC, and Sukriti Trehan, Data Scientist, LMIC, presented their research exploring trends in the skills listed in OJPs to develop a deeper understanding of in-demand skills. This research project uses pointwise mutual information and other methods to extract more information about common skills from the relationships between skills, occupations and regions.
[4:55 p.m.] Bryan Oates
OJPs are becoming a critical resource for policy-makers and researchers who study the labour market. LMIC continues to work with Vicinity Jobs’ data on OJPs, which can be explored in our Canadian Job Trends Dashboard. Valuable insights have been gained through our analysis of OJP data, including LMIC research lead
Suzanne Spiteri’s recent report on improving the quality and accessibility of job postings to reduce employment barriers for neurodivergent people.
Decoding job postings: Improving accessibility for neurodivergent job seekers
Improving the quality and accessibility of job postings is one way to reduce employment barriers for neurodivergent people.
2. Elemental Economics - Mineral demand.pdfNeal Brewster
After this second you should be able to: Explain the main determinants of demand for any mineral product, and their relative importance; recognise and explain how demand for any product is likely to change with economic activity; recognise and explain the roles of technology and relative prices in influencing demand; be able to explain the differences between the rates of growth of demand for different products.
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
Creative operations teams expect increased AI use in 2024. Currently, over half of tasks are not AI-enabled, but this is expected to decrease in the coming year. ChatGPT is the most popular AI tool currently. Business leaders are more actively exploring AI benefits than individual contributors. Most respondents do not believe AI will impact workforce size in 2024. However, some inhibitions still exist around AI accuracy and lack of understanding. Creatives primarily want to use AI to save time on mundane tasks and boost productivity.
Organizational culture includes values, norms, systems, symbols, language, assumptions, beliefs, and habits that influence employee behaviors and how people interpret those behaviors. It is important because culture can help or hinder a company's success. Some key aspects of Netflix's culture that help it achieve results include hiring smartly so every position has stars, focusing on attitude over just aptitude, and having a strict policy against peacocks, whiners, and jerks.
PEPSICO Presentation to CAGNY Conference Feb 2024Neil Kimberley
PepsiCo provided a safe harbor statement noting that any forward-looking statements are based on currently available information and are subject to risks and uncertainties. It also provided information on non-GAAP measures and directing readers to its website for disclosure and reconciliation. The document then discussed PepsiCo's business overview, including that it is a global beverage and convenient food company with iconic brands, $91 billion in net revenue in 2023, and nearly $14 billion in core operating profit. It operates through a divisional structure with a focus on local consumers.
Content Methodology: A Best Practices Report (Webinar)contently
This document provides an overview of content methodology best practices. It defines content methodology as establishing objectives, KPIs, and a culture of continuous learning and iteration. An effective methodology focuses on connecting with audiences, creating optimal content, and optimizing processes. It also discusses why a methodology is needed due to the competitive landscape, proliferation of channels, and opportunities for improvement. Components of an effective methodology include defining objectives and KPIs, audience analysis, identifying opportunities, and evaluating resources. The document concludes with recommendations around creating a content plan, testing and optimizing content over 90 days.
How to Prepare For a Successful Job Search for 2024Albert Qian
The document provides guidance on preparing a job search for 2024. It discusses the state of the job market, focusing on growth in AI and healthcare but also continued layoffs. It recommends figuring out what you want to do by researching interests and skills, then conducting informational interviews. The job search should involve building a personal brand on LinkedIn, actively applying to jobs, tailoring resumes and interviews, maintaining job hunting as a habit, and continuing self-improvement. Once hired, the document advises setting new goals and keeping skills and networking active in case of future opportunities.
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
The document provides career advice for getting into the tech field, including:
- Doing projects and internships in college to build a portfolio.
- Learning about different roles and technologies through industry research.
- Contributing to open source projects to build experience and network.
- Developing a personal brand through a website and social media presence.
- Networking through events, communities, and finding a mentor.
- Practicing interviews through mock interviews and whiteboarding coding questions.
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A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
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Time Management & Productivity - Best PracticesVit Horky
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The six step guide to practical project managementMindGenius
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2. ESGF 4IFM Q1 2012
Summary of the session (est. 4.5h)
• R Steps by Steps
• Reminders of last session
• The Value at Risk
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• OLS & Exploration
2
3. R Step by Step
Downloadable for free (open source)
ESGF 4IFM Q1 2012
http://www.r-project.org/
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3
4. Main screen
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4
10. summary(DATA) Shows a quick summary of the distribution of all variables
SPX SPXr AMEXr AMEX
Min. : 86.43 Min. :-0.0666344 Min. : 97.6 Min. :-0.0883287
1st Qu.: 95.70 1st Qu.:-0.0069082 1st Qu.:104.7 1st Qu.:-0.0094580
Median :100.79 Median : 0.0010016 Median :108.8 Median : 0.0013007
ESGF 4IFM Q1 2012
Mean : 99.67 Mean : 0.0001249 Mean :109.4 Mean : 0.0005891
3rd Qu.:103.75 3rd Qu.: 0.0075235 3rd Qu.:114.1 3rd Qu.: 0.0102923
Max. :107.21 Max. : 0.0474068 Max. :123.5 Max. : 0.0710967
summary(DATA$SPX) Shows a quick summary of the distribution of one variable
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Min. 1st Qu. Median Mean 3rd Qu. Max.
86.43 95.70 100.80 99.67 103.80 107.20
min(DATA)
Careful using the following instructions max(DATA)
> min(DATA)
[1] -0.08832874
This will consider DATA as one variable > max(DATA)
[1] 123.4793
> sd(DATA)
SPX SPXr AMEXr AMEX
4.92763551 0.01468776 6.03035318 0.01915489 10
Mean & SD > mean(DATA)
SPX SPXr AMEXr AMEX
9.967046e+01 1.249283e-04 1.093951e+02 5.890780e-04
11. Easy to show histogram
ESGF 4IFM Q1 2012
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hist(DATA$SPXr, breaks=25, main="Distribution of SPXr", ylab="Freq", 11
xlab="SPXr", col="blue")
12. Obvious Excess Kurtosis
ESGF 4IFM Q1 2012
Obvious Asymmetry
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Functions doesn’t exists directly in R…
However some VNP (Very Nice Programmer) built and shared add-in
Package Moments 12
13. Menu: Packages / Install Package(s)
ESGF 4IFM Q1 2012
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• Choose whatever mirror (server) you want
• Usually France (Toulouse) is very good as it’s a
University Server with all the packages available
13
14. ESGF 4IFM Q1 2012
Once installed, you can load them with the
following instructions:
require(moments)
library(moments)
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New functions can now be used!
14
15. > require(moments)
> library(moments)
> skewness(DATA)
SPX SPXr AMEXr AMEX
-0.6358029 -0.4178701 0.1876994 -0.2453693
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> kurtosis(DATA)
SPX SPXr AMEXr AMEX
2.411177 5.671254 2.078366 5.770583
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Btw, you can store any result in a variable
> Kur<-kurtosis(DATA$SPXr)
> Kur
[1] 5.671254
15
16. Lost?
Call the help! help(kurtosis)
ESGF 4IFM Q1 2012
Reminds you the package
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Syntax
Arguments definition
16
17. Let’s store a few values
SPMean<-mean(DATA$SPXr)
SPSD<-sd(DATA$SPXr) Package Stats
Build a sequence, the x axis
ESGF 4IFM Q1 2012
x<-seq(from=SPMean-4*SPSD,to=SPMean+4*SPSD,length=500)
Build a normal density on these x
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Y1<-dnorm(x,mean=SPMean,sd=SPSD) Package Stats
Display the histogram
hist(DATA$SPXr, breaks=25,main="S&P Returns / Normal Package graphics
Distribution",xlab="Returns",ylab="Occurences", col="blue")
Display on top of it the normal density
lines(x,y1,type="l",lwd=3,col="red") Package graphics 17
19. Let’s build a spread Spd<-DATA$SPXr-DATA$AMEX
What is the mean?
ESGF 4IFM Q1 2012
Mean is linear ������ ������������ + ������������ = ������������ ������ + ������������(������)
������ ������ − ������ = ������ ������ − ������(������)
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Let’s verify
> mean(DATA$SPXr)-mean(DATA$AMEX)-mean(Spd)
[1] 0
19
20. What is the standard deviation?
Is standard deviation linear?
NO!
ESGF 4IFM Q1 2012
VAR ������������ + ������������ = ������2 ������������������ ������ + ������2 ������ ������ + 2������������������������������(������, ������)
> (var(DATA$SPXr)+var(DATA$AMEX)-2*cov(DATA$SPXr,DATA$AMEX))^0.5
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[1] 0.01019212
> sd(Spd)
[1] 0.01019212
Let’s show the implication in a proper manner
Let’s create a portfolio containing half of each stocks 20
25. LM stands for Linear Models
> lm(DATA$AMEX~DATA$SPXr)
ESGF 4IFM Q1 2012
Call:
lm(formula = DATA$AMEX ~ DATA$SPXr)
Coefficients:
(Intercept) DATA$SPXr
0.0004505 1.1096287
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������ = 1.1096������ + 0.04%
Will be used later for linear regression and hedging
25
26. Do you remember what is the most platykurtic distribution in the nature?
Toss Head = Success = 1 / Tail = Failure = 0
ESGF 4IFM Q1 2012
100 toss… Else memory issue…
> require(moments)
Loading required package: moments
> library(moments)
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> toss<-rbinom(100,1,0.5)
> mean(toss)
[1] 0.52
> kurtosis(toss)
[1] 1.006410
> kurtosis(toss)-3
[1] -1.993590
> hist(toss, breaks=10,main="Tossing a
coin 100 times",xlab="Result of the
trial",ylab="Occurence")
> sum(toss)
[1] 52
26
Let’s test the fairness
27. Density of a binomial distribution
������ + 1 ! ℎ
������ ������ ������ = ℎ, ������ = ������ = ������ (1 − ������)������
ℎ! ������!
ESGF 4IFM Q1 2012
Let’s plot this density with
ℎ = 52
������ = 48
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������ = 100
N<-100
h<-52
t<-48
r<-seq(0,1,length=500)
y<-
(factorial(N+1)/(factorial(h)*factori
al(t)))*r^h*(1-r)^t
plot(r,y,type="l",col="red",main="Pro
bability density to have 52 head out
100 flips")
27
28. If the probability between 45% and 55% is significant we’ll accept the fairness
ESGF 4IFM Q1 2012
vinzjeannin@hotmail.com
28
What do you think?
29. What is the problem with this coin?
Obvious fake! Assuming the probability of head is 0.7
Toss it! Head = Success = 1 / Tail = Failure = 0
ESGF 4IFM Q1 2012
100 toss
> require(moments)
Loading required package: moments
> library(moments)
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> toss<-rbinom(100,1,0.7)
> mean(toss)
[1] 0.72
> kurtosis(toss)
[1] 1.960317
> kurtosis(toss)-3
[1] -1.039683
> hist(toss, breaks=10,main="Tossing a
coin 100 times",xlab="Result of the
trial",ylab="Occurence")
> sum(toss)
[1] 72
29
Let’s test the fairness (assuming you don’t know it’s a trick)
30. If the probability between 45% and 55% is significant we’ll accept the fairness
N<-100
h<-72
t<-28
r<-seq(0.2,0.8,length=500)
y<-(factorial(N+1)/(factorial(h)*factorial(t)))*r^h*(1-r)^t
ESGF 4IFM Q1 2012
plot(r,y,type="l",col="red",main="Probability density or r given 72
head out 100 flips")
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Trick coin!
30
31. Reminders of last session
ESGF 4IFM Q1 2012
Normal Standard Distribution
Snapshot, 4 moments:
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Mean 0
SD 1
Skewness 0
Kurtosis 3
31
38. The Value at Risk
Estimate with a specific confidence interval (usually 95% or 99%) the worth loss
possible. In other words, the point is to identify a particular point on the left of
ESGF 4IFM Q1 2012
the distribution
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3 Methods
• Historical
• Parametrical
• Monte-Carlo
38
For now, we’ll focus on VaR on one linear asset… FCOJ is back!
39. Historical VaR
• No assumption about the distribution
• Easy to implement and calculate
ESGF 4IFM Q1 2012
• Sensitive to the length of the history
• Sensitive to very extreme values
Let’s get back to our FCOJ time series, last price is $150 cents
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If we work on returns, we’ve seen the use of the PERCENTILE
Excel function
• 1% Percentile is -5.22%, 99% Historical Daily VaR is -$7.83 cents
• 5% Percentile is -3.34%, 95% Historical Daily VaR is -$5.00 cents
39
Works as well on weekly, monthly, quarterly series
40. Historical VaR
ESGF 4IFM Q1 2012
Can be worked as well with prices variations
instead of returns but it’s going to be price
sensitive! So careful to the bias.
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• 1% Percentile in term of price movement is -$8.11 cents
• 5% Percentile in term of price movement is -$4.14 cents
40
41. Parametric VaR
• Easy to implement and calculate
• Assumes a particular shape of the distribution
ESGF 4IFM Q1 2012
• Not really sensitive to fat tails
FCOJ Mean Return: 0.1364%
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FCOJ SD: 2.1664%
We already know:
������ ������ ≤ −1.645 ∗ ������ + ������ = 0.05
������ ������ ≤ −2.326 ∗ ������ + ������ = 0.01
Then:
������ ������ ≤ −3.43% = 0.05 VaR 95% (-$5.15 cents) 41
������ ������ ≤ −4.90% = 0.01 VaR 99% (-$7.35 cents)
42. Parametric VaR
Very often you assume anyway a 0 mean, therefore:
ESGF 4IFM Q1 2012
������ ������ ≤ −3.57% = 0.05 VaR 95% (-$5.36 cents)
������ ������ ≤ −5.04% = 0.01 VaR 99% (-$8.10 cents)
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Lower values than the historical VaR
Problem with leptokurtic distributions, impact of fat tails isn’t
strong on the method
42
43. Monte Carlo VaR
ESGF 4IFM Q1 2012
• Most efficient method when asset aren’t linear
• Tough to implement
• Assumes a particular shape of the distribution
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Based on an assumption of a price process (for example GBM)
Great number of random simulations on the price process to build a
distribution and outline the VaR
43
44. Monte Carlo VaR
Let’s simulate 10,000 GBM, 252 steps and store the final result
ESGF 4IFM Q1 2012
library(sde)
require(sde)
FCOJ<-
read.csv(file="C:/Users/Vinz/Desktop/FCOJStats.csv",head=FALSE,sep=",")
Drift<-mean(FCOJ$V1)
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Volat<-sd(FCOJ$V1)
nbsim<-252
Spot<-150
Final<-rep(1,10000)
for(i in 1:100000){
Matr<-GBM(x=Spot,r=Drift, sigma=Volat,N=nbsim)
Final[i]<-Matr[nbsim+1]}
quantile(Final, 0.05)
quantile(Final, 0.01)
Don’t be fooled by the 252, we’re still making a daily simulation: what 44
to change in the code to make it yearly?
45. Monte Carlo VaR
> quantile(Final, 0.05)
5%
ESGF 4IFM Q1 2012
144.93
> quantile(Final, 0.01)
1%
142.7941
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• 95% Daily VaR is -$5.07 cents
• 99% Daily VaR is -$7.21 cents
Let’s take off the drift
45
46. Monte Carlo VaR
> quantile(Final, 0.05)
5%
ESGF 4IFM Q1 2012
144.7583
> quantile(Final, 0.01)
1%
142.6412
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• 95% Daily VaR is -$5.35 cents
• 99% Daily VaR is -$7.36 cents
46
47. Which is the best?
Comparison
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47
48. Going forward on the VaR
ESGF 4IFM Q1 2012
All method give different but coherent values
Easy? Yes but…
• We’ve involved one asset only
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• We’ve involved a linear asset
What about an option?
What about 2 assets?
48
49. Going forward on the VaR
Portfolio scale: what to look at to calculate the VaR?
ESGF 4IFM Q1 2012
Big question, is the VaR additive?
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NO!
Keywords for the future: covariance, correlation, diversification
49
50. Going forward on the VaR
Options: what to look at to calculate the VaR?
ESGF 4IFM Q1 2012
4 risk factors:
• Underlying price
• Interest rate
• Volatility
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• Time
4 answers:
• Delta/Gamma approximation knowing the distribution of the underlying
• Rho approximation knowing the distribution of the underlying rate
• Vega approximation knowing the distribution of implied volatility
• Theta (time decay)
Yes but,… Does the underling price/rate/volatility vary independently? 50
Might be a bit more complicated than expected…
51. OLS & Exploration
OLS: Ordinary Least Square
ESGF 5IFM Q1 2012
Linear regression model
Minimize the sum of the square vertical distances
between the observations and the linear
approximation
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������ = ������ ������ = ������������ + ������
Residual ε
51
52. Two parameters to estimate:
• Intercept α
• Slope β
ESGF 5IFM Q1 2012
Minimising residuals
������ ������
������ = ������������ 2 = ������������ − ������������������ + ������ 2
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������=1 ������=1
When E is minimal?
When partial derivatives i.r.w. a and b are 0
52
54. ������������
Leads easily to the intercept
������������
������ ������
������ ∗ ������������ + ������������ = ������������
������=1 ������=1
ESGF 5IFM Q1 2012
������������������ + ������������ = ������������
������������ + ������ = ������
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������ = ������ − ������������
The regression line is going through (������ , ������)
The distance of this point to the line is 0 indeed
54
57. ������ Covariance
������=1(������������ − ������ )(������������ − ������)
������ = ������ 2
������=1(������������ − ������ ) Variance
ESGF 5IFM Q1 2012
������������������������������
������ =
������2������
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������ = ������ − ������������
You can use Excel function INTERCEPT and SLOPE
57
58. Calculate the Variances and Covariance of X{1,2,3,3,1,2} and Y{2,3,1,1,3,2}
ESGF 5IFM Q1 2012
vinzjeannin@hotmail.com
58
You can use Excel function VAR.P, COVARIANCE.P and STDEV.P
59. Let’s asses the quality of the regression
Let’s calculate the correlation coefficient (aka Pearson Product-Moment
Correlation Coefficient – PPMCC):
ESGF 5IFM Q1 2012
������������������������������
������ = Value between -1 and 1
������������ ������������
������ = 1
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Perfect dependence
������ ~0 No dependence
Give an idea of the dispersion of the scatterplot
59
You can use Excel function CORREL
61. What is good quality?
ESGF 5IFM Q1 2012
Slightly discretionary…
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If
3
������ ≥ = 0.8666 …
2
It’s largely admitted as the threshold for acceptable / poor
61
62. The regression itself introduces a bias
Let’s introduce the coefficient of determination R-Squared
ESGF 5IFM Q1 2012
Total Dispersion = Dispersion Regression + Dispersion Residual
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2 2 2
������������ − ������ = ������������ − ������������ + ������������ − ������
Dispersion Regression
������2 =
Total Dispersion
In other words the part of the total dispersion explained by the regression 62
You can use Excel function RSQ
63. In a simple linear regression with intercept ������2 = ������ 2
ESGF 5IFM Q1 2012
Is a good correlation coefficient and a good coefficient of
determination enough to accept the regression?
vinzjeannin@hotmail.com
Not necessarily!
Residuals need to have no effect, in other word to be a white noise!
63
65. Don’t get fooled by numbers!
ESGF 5IFM Q1 2012
For every dataset of the Quarter
������ = 9
������ = 7.5
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������ = 3 + 0.5������
������ = 0.82
������2 = 0.67
Can you say at this stage which regression is the best?
65
Certainly not those on the right you need a LINEAR dependence
66. ESGF 5IFM Q1 2012
Is any linear regression useless?
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Think what you could do to the series
Polynomial transformation, log transformation,…
66
Else, non linear regressions, but it’s another story
67. First application on financial market
S&P / AmEx in 2011
ESGF 5IFM Q1 2012
vinzjeannin@hotmail.com
67
68. ������������������������������������������,������&������
������ = = 0.8501
������������������������������ ������������&������
������2 = ������ 2 = 0.7227
ESGF 5IFM Q1 2012
Oups :-o
Is Excel wrong?
vinzjeannin@hotmail.com
R-Squared has different calculation methods
Let’s accept the following regression then as the quality seems pretty good
������������������������������ = 0.06% + 1.1046 ∗ ������������&������
68
69. How to use this?
ESGF 5IFM Q1 2012
• Forecasting? Not really…
Both are random variables
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• Hedging? Yes but basis risk
Yes but careful to the residuals…
In theory, what is the daily result of the hedge? ������
Let’s have a try!
69
70. Hedging $1.0M of AmEx Stocks with $1.1046M of S&P
ESGF 5IFM Q1 2012
vinzjeannin@hotmail.com
It would have been too easy… Great differences… Why?
Sensitivity to the size of the sample
70
Heteroscedasticity Basis Risk
71. The purpose was to see if the market as effect an effect on a particular stock
The dependence is obvious but residuals too volatile for any stable application
ESGF 5IFM Q1 2012
But attention!
We are looking for causation, not correlation!
Causation implies correlation
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Reciprocity is not true!
DON’T BE FOOLED BY PRETTY NUMBERS
71
Let prove this…
72. ESGF 5IFM Q1 2012
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Perfect linear dependence
Excellent R-Squared
72
Residuals are a white noise
What’s the problem then?
73. ESGF 5IFM Q1 2012
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Do you really think fresh lemon reduces car fatalities?
73