O documento discute como a entropia pode ser usada para medir a diversificação de uma carteira de investimentos e prever o risco em situações de estresse. O autor desenvolveu modelos usando entropia que tiveram melhor desempenho do que modelos anteriores na Ventor Investimentos para medir o risco de carteiras longas, curtas e long-short.
O PRESENTE TRABALHO ABORDA DE MANEIRA CLARA AS TIPOLOGIAS E DEFINIÇÕES DE RISCOS, O PERFIL DO INVESTIDOR INDIVIDUAL LEVANDO EM CONSIDERAÇÃO OS RISCO INCORRIDOS.
IA e o Futuro do Trabalho (Flavio Abdenur / SLQ)Flavio Abdenur
Slides de palestra sobre inteligência artificial e o mercado de trabalho. Economia, tecnologia e psicologia bem costurados, longe das bobajadas que geralmente dominam os discursos sobre o assunte.
O PRESENTE TRABALHO ABORDA DE MANEIRA CLARA AS TIPOLOGIAS E DEFINIÇÕES DE RISCOS, O PERFIL DO INVESTIDOR INDIVIDUAL LEVANDO EM CONSIDERAÇÃO OS RISCO INCORRIDOS.
IA e o Futuro do Trabalho (Flavio Abdenur / SLQ)Flavio Abdenur
Slides de palestra sobre inteligência artificial e o mercado de trabalho. Economia, tecnologia e psicologia bem costurados, longe das bobajadas que geralmente dominam os discursos sobre o assunte.
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
This article is all about what AI trends will emerge in the field of creative operations in 2024. All the marketers and brand builders should be aware of these trends for their further use and save themselves some time!
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.
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.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
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
This article is all about what AI trends will emerge in the field of creative operations in 2024. All the marketers and brand builders should be aware of these trends for their further use and save themselves some time!
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.
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.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
Palestra - Entropia e Risco Financeiro
1. Entropia e Risco 1
Entropia e Gestão de Risco
Flavio Abdenur
FA Análise de Risco
(flavio.abdenur@gmail.com)
(palestra no IME/UERJ – 16/09/2015)
2. Entropia e Risco 2
Introdução
Bacharel em economia pela PUC (2000), doutor em matemática
pura pelo IMPA (2002)
Matemático acadêmico entre 2002 e 2011: postdoc no IMPA,
depois professor na PUC-Rio
Analista de risco entre 2011 e 2013: Ventor Investimentos
3. Entropia e Risco 3
Introdução
1)Fundo multimercado “macro”
1)PL na época: aprox. R$1.500.000.000
5. Entropia e Risco 5
Introdução
Ativos negociados pela Ventor:
1)Moeda: dólar vs real, euro vs dólar, euro vs real, e opções
2)Juros: títulos públicos, DI futuro, e opções
3)Ações: índice futuro, acões long, ações short
6. Entropia e Risco 6
Medida de Risco I: VaR
I. Value at Risk (VaR): supõe que a distribuição de retornos do
ativo em questão é log-normal e estipula a priori um intervalo de
confiança: 1%, 5%, etc.
8. Entropia e Risco 8
Medida de Risco I: VaR
O VaR:
é calculado separadamente para cada classe de ativos (i.e.,
moedas, juros, ações)
é matematicamente elegante: dado por uma fórmula fechada
9. Entropia e Risco 9
Medida de Risco I: VaR
O VaR:
leva em consideração correlações recentes entre os ativos na
carteira
usa a volatilidade (i.e., o desvio-padrão) dos retornos recentes
10. Entropia e Risco 10
Medida de Risco I: VaR
Exemplo: dada uma carteira de R$200 milhões em ações (e seus
derivativos), um VaR de um dia de 5% de R$10 milhões indica
que há uma chance em vinte da carteira perder R$10 milhões ou
mais naquele dia.
11. Entropia e Risco 11
Medida de Risco I: VaR
Um defeito grave: o VaR subestima o risco quando a volatilidade
recente é muito baixa.
Algumas grandes crises financeiras foram antecedidas por
períodos de calmaria.
Quem usa exclusivamente o VaR para limitar a sua exposição ao
risco cedo ou tarde se estrepa.
12. Entropia e Risco 12
Medida de Risco I: VaR
Duas sugestões:
“The Black Swan” (N. Taleb) “When Genius Failed” (R. Lowenstein)
13. Entropia e Risco 13
Medida de Risco II: Stress Test
II. Stress Test: simula um grande movimento da classe de ativo na
direção contrária à posição que o fundo assumiu naquela classe.
14. Entropia e Risco 14
Medida de Risco II: Stress Test
II. Stress Test: simula um grande movimento da classe de ativo na
direção contrária à posição que o fundo assumiu naquela classe.
Obs: aqui grande significa uma variação percentual substancial,
geralmente definida no olhômetro a partir de um histórico de
muitos anos.
15. Entropia e Risco 15
Medida de Risco II: Stress Test
Exemplo: se o stress de ações é de 8% e a carteira de ações está
comprada em R$150 milhões, entao o cenário de estresse é uma
queda de 8% em todas as ações e a perda hipotética é de
R$12milhões = 8%× R$150milhões
16. Entropia e Risco 16
Medida de Risco II: Stress Test
O Stress Test:
ignora correlações e volatilidade recentes
é artesanal: feito sob medida pra cada fundo, e sem fórmula
fechada
é mais realista do que o VaR sob situações extremas
17. Entropia e Risco 17
Limites de Risco
A partir de agora focamos no Stress Test
Considere um fundo com PL de R$1 bilhão cuja perda máxima
tolerada (considerando a soma das três classes) é de 5% do PL num
dia.
18. Entropia e Risco 18
Limites de Risco
No máximo do consumo de risco, a perda projetada pela soma
dos Stress Tests de moeda, juros, e ações é portanto de R$50
milhões
Se stress de ações é de 8%, o teto para a porção da carteira que
pode ser comprada (ou vendida) em ações é então de
R$625milhões =
5%
8%
× R$1000milhões
19. Entropia e Risco 19
Diversificação e Entropia
Em situações de estresse carteiras diversificadas são ceterius
paribus mais seguras do que carteiras concentradas.
Então um bom Stress Test precisa levar em consideração o grau
de diversificação da carteira.
20. Entropia e Risco 20
Diversificação e Entropia
Como medir a diversificação de uma carteira distribuída em ações
de um conjunto (finito) de empresas distintas?
Não basta contar o número de empresas; o peso relativo de cada
empresa na carteira também tem que entrar na conta.
21. Entropia e Risco 21
Diversificação e Entropia
Seja I = [0 , 1] o intervalo unitário, representando uma carteira de
digamos R$100 milhões.
Seja Ρ uma partição de I em subintervalos P1, ..., PN, onde Pj
corresponde à participação percentual da ação j na carteira I.
22. Entropia e Risco 22
Diversificação e Entropia
Então a entropia (de Shannon) da partição Ρ = {P1, ..., PN} de I é
dada por
onde c(Pj) é o comprimento do intervalo Pj.
Ent(Ρ) ≡ c(P1)× ln(c(P1))+...+ c(PN )× ln(c(PN ))
23. Entropia e Risco 23
Diversificação e Entropia
A função Ent leva o espaço de todas as partições (finitas) de P no
conjunto R+
de reais não-negativos.
A partição trivial tem entropia zero; já a partição Ρ de I em N
subintervalos de comprimento 1/N tem entropia ln(N).
24. Entropia e Risco 24
Diversificação e Entropia
Pelo teorema abaixo a entropia mede de maneira “natural” o
quanto a partição P estilhaça a carteira I:
Teorema (Shannon): se F é uma função do espaço de partições
finitas de I em R+
que satisfaz um certo conjunto de axiomas
“naturais” – incluindo continuidade, máximo nas partições
uniformes, e monotonicidade – então existe uma constante positiva
c tal que F=c×Ent.
25. Entropia e Risco 25
Diversificação e Entropia
Resultados da teoria da informação indicavam a priori que a
entropia seria uma boa medida de diversificação
Faltava testar empiricamente o desempenho de Ent como
“previsor” de risco em situações de estresse.
26. Entropia e Risco 26
Diversificação e Entropia
Geramos aleatoriamente cerca de 10.000 carteiras hipotéticas.
Testamos essas carteiras hipotéticas contra cerca de 8 anos de
dados históricos.
Resultado: o modelo gerado via entropia tem um fit bem melhor
do que o modelo recursivo antes usado na Ventor.
27. Entropia e Risco 27
Diversificação e Entropia
No novo modelo o stress da carteira deixou de ser definido como
uma porcentagem fixa e se tornou uma função (polinomial e
decrescente) da entropia da carteira.
O stress test via entropia é empiricamente mais confiável e
computacionalmente muito mais barato do que o modelo anterior.
28. Entropia e Risco 28
Diversificação e Entropia
A Ventor também vende ações a descoberto – i.e., shorteia ações.
Estendemos o modelo via entropia para carteiras long-short –
carteiras que incluem simultaneamente ações compradas e ações
vendidas.
29. Entropia e Risco 29
Diversificação e Entropia
No modelo long-short o estresse percentual da carteira depende
de duas variáveis: a entropia da carteira long e a entropia da
carteira short.
Testamos 10.000 carteiras long-short geradas aleatoriamente
contra cerca de 8 anos de dados históricos.
30. Entropia e Risco 30
Diversificação e Entropia
Estes 10.000 pontos geraram uma nuvem que admite um bom fit
polinomial (de duas variáveis).
O formato da superfície polinomial lembrava um pássaro em vôo,
então a apelidamos de gaivota.