Introduces and explains the use of multiple linear regression, a multivariate correlational statistical technique. For more info, see the lecture page at http://goo.gl/CeBsv. See also the slides for the MLR II lecture http://www.slideshare.net/jtneill/multiple-linear-regression-ii
A walk-through of the mathematics of covariance, the covariance matrix, and use cases when combined with k-means clustering. Focus on how to actually use the math, and shows how the equations turn into simple JavaScript code.
Introduces and explains the use of multiple linear regression, a multivariate correlational statistical technique. For more info, see the lecture page at http://goo.gl/CeBsv. See also the slides for the MLR II lecture http://www.slideshare.net/jtneill/multiple-linear-regression-ii
A walk-through of the mathematics of covariance, the covariance matrix, and use cases when combined with k-means clustering. Focus on how to actually use the math, and shows how the equations turn into simple JavaScript code.
Correlation & Regression Analysis using SPSSParag Shah
Concept of Correlation, Simple Linear Regression & Multiple Linear Regression and its analysis using SPSS. How it check the validity of assumptions in Regression
Overview and about R, R Studio Installation, Fundamentals of R Programming: Data Structures and Data Types, Operators, Control Statements, Loop Statements, Functions,
Descriptive Analysis using R: Maximum, Minimum, Range, Mean, Median and Mode, Variance, Standard Deviation, Quantiles, IQR, Summary
Discrete Mathematics - Sets. ... He had defined a set as a collection of definite and distinguishable objects selected by the means of certain rules or description. Set theory forms the basis of several other fields of study like counting theory, relations, graph theory and finite state machines.
Definition- Problems for construction. Construction of price, quantity, value and cost of living index numbers, ideal index, tests and uses of index numbers.
Correlation & Regression Analysis using SPSSParag Shah
Concept of Correlation, Simple Linear Regression & Multiple Linear Regression and its analysis using SPSS. How it check the validity of assumptions in Regression
Overview and about R, R Studio Installation, Fundamentals of R Programming: Data Structures and Data Types, Operators, Control Statements, Loop Statements, Functions,
Descriptive Analysis using R: Maximum, Minimum, Range, Mean, Median and Mode, Variance, Standard Deviation, Quantiles, IQR, Summary
Discrete Mathematics - Sets. ... He had defined a set as a collection of definite and distinguishable objects selected by the means of certain rules or description. Set theory forms the basis of several other fields of study like counting theory, relations, graph theory and finite state machines.
Definition- Problems for construction. Construction of price, quantity, value and cost of living index numbers, ideal index, tests and uses of index numbers.
Empowering Innovation Portfolio Decision-Making through SimulationSopheon
New product development is a complex, high-risk endeavor for any organization. In order to execute a game-changing innovation program, leaders must be willing to engage the unknowns around future markets and the technologies that will serve them.
This webinar discusses how simulation and specialized business processes can provide a risk-free proving ground to challenge and compare innovation strategies, thereby empowering analysts and executives to confidently make difficult investment decisions.
To view this webinar, go to http://budurl.com/zgs5
Introduction à la gestion du risque de change.: définition du risque, régimes de changes, crises de change, définition et mise en pratique des solutions de couverture
Introduction à la gestion des risques en finance : définition du risque, typologie des risques, principales mesures du risque, définition de la couverture et instruments de couverture
During the 1980s, the liberalization of financial markets was supported by an intellectual framework provided by academic studies focused on the efficient market hypothesis. From the 1990s and more over the 2000s, the succession of financial crises motivated a growing questioning on this theoretical framework unable to explain bubbles and crashes. Today, let's review the theories dealing with the behavior of financial markets.
Analyse de la performance financière avec RJérémy Morvan
Introduction à l'analyse de la performance financière des actifs cotés. Après un rappel de la définition de la performance en finance, l'intervention est centrée sur l'analyse statistique sous le langage de programmation R.
Available in English as soon as possible!
Présentation de l'investissement socialement responsable
1. Définition de la responsabilité sociale de l'entreprise
2. Définition de l'investissement socialement responsable
3. Performance(s) de l'investissement socialement responsable
Monetary policy: monetary orthodoxy or quantitative easing?Jérémy Morvan
What is monetary policy?
Presentation of conventional monetary policy and quantitative easing. The presentation also includes a (brief) history of the monetary policies of some major central banks: European Central Bank, Fed Reserve System, Bank of England and, Bank of Japan.
Introduction à la politique monétaire
Présentation de la politique monétaire conventionnelle et de l'assouplissement quantitatif (quantitative easing).
La présentation reprend également un historique des politiques monétaires de certaines des principales banques centrales : Banque Centrale Européenne, Fed Reserve System, Bank of England, Bank of Japan.
Un siècle d'évolution des marchés financiers (1914 2015)Jérémy Morvan
Introduction à l'histoire des marchés financiers (1914-2015)
La présentation insiste sur l'importance des éléments qui constituent le risque systématique : contexte géopolitique, innovation, croissance, pétrole, réglementation
Partie II - Strategie et gouvernance universitairesJérémy Morvan
Introduction à la stratégie et à la gouvernance universitaire
- Connaitre les fondamentaux du diagnostic stratégique
- Définir un plan stratégique
- Connaitre les modalités d’application du plan stratégique
Partie I - L'université et sa gouvernanceJérémy Morvan
Introduction au système universitaire français
- positionner l'université dans son environnement institutionnel
- Connaître les grands agrégats de gestion des universités
- Connaître la composition et le fonctionnement des conseils de l'université
Partie III - Gestion opérationnelle universitaireJérémy Morvan
Introduction à la gestion opérationnelle d'une composante universitaire
- Connaître les principaux acteurs de la gestion financière de l’établissement
- Comprendre les droits et obligations des ordonnateurs
- Comprendre la construction et l’exécution budgétaire
- Connaître les catégories de personnels
- Comprendre les enjeux de la gestion de la masse salariale
La direction d'une composante universitaire en FranceJérémy Morvan
Introduction à la direction d'une composante universitaire en France.
Le support présente les principaux éléments juridiques, organisationnels et financiers rencontrés lors d'un mandat de direction d'une composante.
Le support peut faire l'objet d'améliorations en s'élargissant à certaines structures (ESPE par exemple), à certains outils (Cocktail) ou selon l'évolution de la législation.
how can i use my minded pi coins I need some funds.DOT TECH
If you are interested in selling your pi coins, i have a verified pi merchant, who buys pi coins and resell them to exchanges looking forward to hold till mainnet launch.
Because the core team has announced that pi network will not be doing any pre-sale. The only way exchanges like huobi, bitmart and hotbit can get pi is by buying from miners.
Now a merchant stands in between these exchanges and the miners. As a link to make transactions smooth. Because right now in the enclosed mainnet you can't sell pi coins your self. You need the help of a merchant,
i will leave the telegram contact of my personal pi merchant below. 👇 I and my friends has traded more than 3000pi coins with him successfully.
@Pi_vendor_247
Exploring Abhay Bhutada’s Views After Poonawalla Fincorp’s Collaboration With...beulahfernandes8
The financial landscape in India has witnessed a significant development with the recent collaboration between Poonawalla Fincorp and IndusInd Bank.
The launch of the co-branded credit card, the IndusInd Bank Poonawalla Fincorp eLITE RuPay Platinum Credit Card, marks a major milestone for both entities.
This strategic move aims to redefine and elevate the banking experience for customers.
how to swap pi coins to foreign currency withdrawable.DOT TECH
As of my last update, Pi is still in the testing phase and is not tradable on any exchanges.
However, Pi Network has announced plans to launch its Testnet and Mainnet in the future, which may include listing Pi on exchanges.
The current method for selling pi coins involves exchanging them with a pi vendor who purchases pi coins for investment reasons.
If you want to sell your pi coins, reach out to a pi vendor and sell them to anyone looking to sell pi coins from any country around the globe.
Below is the contact information for my personal pi vendor.
Telegram: @Pi_vendor_247
How to get verified on Coinbase Account?_.docxBuy bitget
t's important to note that buying verified Coinbase accounts is not recommended and may violate Coinbase's terms of service. Instead of searching to "buy verified Coinbase accounts," follow the proper steps to verify your own account to ensure compliance and security.
how to sell pi coins at high rate quickly.DOT TECH
Where can I sell my pi coins at a high rate.
Pi is not launched yet on any exchange. But one can easily sell his or her pi coins to investors who want to hold pi till mainnet launch.
This means crypto whales want to hold pi. And you can get a good rate for selling pi to them. I will leave the telegram contact of my personal pi vendor below.
A vendor is someone who buys from a miner and resell it to a holder or crypto whale.
Here is the telegram contact of my vendor:
@Pi_vendor_247
how to sell pi coins in South Korea profitably.DOT TECH
Yes. You can sell your pi network coins in South Korea or any other country, by finding a verified pi merchant
What is a verified pi merchant?
Since pi network is not launched yet on any exchange, the only way you can sell pi coins is by selling to a verified pi merchant, and this is because pi network is not launched yet on any exchange and no pre-sale or ico offerings Is done on pi.
Since there is no pre-sale, the only way exchanges can get pi is by buying from miners. So a pi merchant facilitates these transactions by acting as a bridge for both transactions.
How can i find a pi vendor/merchant?
Well for those who haven't traded with a pi merchant or who don't already have one. I will leave the telegram id of my personal pi merchant who i trade pi with.
Tele gram: @Pi_vendor_247
#pi #sell #nigeria #pinetwork #picoins #sellpi #Nigerian #tradepi #pinetworkcoins #sellmypi
What website can I sell pi coins securely.DOT TECH
Currently there are no website or exchange that allow buying or selling of pi coins..
But you can still easily sell pi coins, by reselling it to exchanges/crypto whales interested in holding thousands of pi coins before the mainnet launch.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and resell to these crypto whales and holders of pi..
This is because pi network is not doing any pre-sale. The only way exchanges can get pi is by buying from miners and pi merchants stands in between the miners and the exchanges.
How can I sell my pi coins?
Selling pi coins is really easy, but first you need to migrate to mainnet wallet before you can do that. I will leave the telegram contact of my personal pi merchant to trade with.
Tele-gram.
@Pi_vendor_247
The Evolution of Non-Banking Financial Companies (NBFCs) in India: Challenges...beulahfernandes8
Role in Financial System
NBFCs are critical in bridging the financial inclusion gap.
They provide specialized financial services that cater to segments often neglected by traditional banks.
Economic Impact
NBFCs contribute significantly to India's GDP.
They support sectors like micro, small, and medium enterprises (MSMEs), housing finance, and personal loans.
USDA Loans in California: A Comprehensive Overview.pptxmarketing367770
USDA Loans in California: A Comprehensive Overview
If you're dreaming of owning a home in California's rural or suburban areas, a USDA loan might be the perfect solution. The U.S. Department of Agriculture (USDA) offers these loans to help low-to-moderate-income individuals and families achieve homeownership.
Key Features of USDA Loans:
Zero Down Payment: USDA loans require no down payment, making homeownership more accessible.
Competitive Interest Rates: These loans often come with lower interest rates compared to conventional loans.
Flexible Credit Requirements: USDA loans have more lenient credit score requirements, helping those with less-than-perfect credit.
Guaranteed Loan Program: The USDA guarantees a portion of the loan, reducing risk for lenders and expanding borrowing options.
Eligibility Criteria:
Location: The property must be located in a USDA-designated rural or suburban area. Many areas in California qualify.
Income Limits: Applicants must meet income guidelines, which vary by region and household size.
Primary Residence: The home must be used as the borrower's primary residence.
Application Process:
Find a USDA-Approved Lender: Not all lenders offer USDA loans, so it's essential to choose one approved by the USDA.
Pre-Qualification: Determine your eligibility and the amount you can borrow.
Property Search: Look for properties in eligible rural or suburban areas.
Loan Application: Submit your application, including financial and personal information.
Processing and Approval: The lender and USDA will review your application. If approved, you can proceed to closing.
USDA loans are an excellent option for those looking to buy a home in California's rural and suburban areas. With no down payment and flexible requirements, these loans make homeownership more attainable for many families. Explore your eligibility today and take the first step toward owning your dream home.
when will pi network coin be available on crypto exchange.DOT TECH
There is no set date for when Pi coins will enter the market.
However, the developers are working hard to get them released as soon as possible.
Once they are available, users will be able to exchange other cryptocurrencies for Pi coins on designated exchanges.
But for now the only way to sell your pi coins is through verified pi vendor.
Here is the telegram contact of my personal pi vendor
@Pi_vendor_247
Currently pi network is not tradable on binance or any other exchange because we are still in the enclosed mainnet.
Right now the only way to sell pi coins is by trading with a verified merchant.
What is a pi merchant?
A pi merchant is someone verified by pi network team and allowed to barter pi coins for goods and services.
Since pi network is not doing any pre-sale The only way exchanges like binance/huobi or crypto whales can get pi is by buying from miners. And a merchant stands in between the exchanges and the miners.
I will leave the telegram contact of my personal pi merchant. I and my friends has traded more than 6000pi coins successfully
Tele-gram
@Pi_vendor_247
how can I sell pi coins after successfully completing KYCDOT TECH
Pi coins is not launched yet in any exchange 💱 this means it's not swappable, the current pi displaying on coin market cap is the iou version of pi. And you can learn all about that on my previous post.
RIGHT NOW THE ONLY WAY you can sell pi coins is through verified pi merchants. A pi merchant is someone who buys pi coins and resell them to exchanges and crypto whales. Looking forward to hold massive quantities of pi coins before the mainnet launch.
This is because pi network is not doing any pre-sale or ico offerings, the only way to get my coins is from buying from miners. So a merchant facilitates the transactions between the miners and these exchanges holding pi.
I and my friends has sold more than 6000 pi coins successfully with this method. I will be happy to share the contact of my personal pi merchant. The one i trade with, if you have your own merchant you can trade with them. For those who are new.
Message: @Pi_vendor_247 on telegram.
I wouldn't advise you selling all percentage of the pi coins. Leave at least a before so its a win win during open mainnet. Have a nice day pioneers ♥️
#kyc #mainnet #picoins #pi #sellpi #piwallet
#pinetwork
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
So if you are interested in selling your pi network coins at a high rate tho. Or you can't wait till the mainnet launch in 2026. You can easily trade your pi coins with a merchant.
A merchant is someone who buys pi coins from miners and resell them to Investors looking forward to hold massive quantities till mainnet launch.
I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
The secret way to sell pi coins effortlessly.DOT TECH
Well as we all know pi isn't launched yet. But you can still sell your pi coins effortlessly because some whales in China are interested in holding massive pi coins. And they are willing to pay good money for it. If you are interested in selling I will leave a contact for you. Just telegram this number below. I sold about 3000 pi coins to him and he paid me immediately.
Telegram: @Pi_vendor_247
Introduction to Indian Financial System ()Avanish Goel
The financial system of a country is an important tool for economic development of the country, as it helps in creation of wealth by linking savings with investments.
It facilitates the flow of funds form the households (savers) to business firms (investors) to aid in wealth creation and development of both the parties
what is the future of Pi Network currency.DOT TECH
The future of the Pi cryptocurrency is uncertain, and its success will depend on several factors. Pi is a relatively new cryptocurrency that aims to be user-friendly and accessible to a wide audience. Here are a few key considerations for its future:
Message: @Pi_vendor_247 on telegram if u want to sell PI COINS.
1. Mainnet Launch: As of my last knowledge update in January 2022, Pi was still in the testnet phase. Its success will depend on a successful transition to a mainnet, where actual transactions can take place.
2. User Adoption: Pi's success will be closely tied to user adoption. The more users who join the network and actively participate, the stronger the ecosystem can become.
3. Utility and Use Cases: For a cryptocurrency to thrive, it must offer utility and practical use cases. The Pi team has talked about various applications, including peer-to-peer transactions, smart contracts, and more. The development and implementation of these features will be essential.
4. Regulatory Environment: The regulatory environment for cryptocurrencies is evolving globally. How Pi navigates and complies with regulations in various jurisdictions will significantly impact its future.
5. Technology Development: The Pi network must continue to develop and improve its technology, security, and scalability to compete with established cryptocurrencies.
6. Community Engagement: The Pi community plays a critical role in its future. Engaged users can help build trust and grow the network.
7. Monetization and Sustainability: The Pi team's monetization strategy, such as fees, partnerships, or other revenue sources, will affect its long-term sustainability.
It's essential to approach Pi or any new cryptocurrency with caution and conduct due diligence. Cryptocurrency investments involve risks, and potential rewards can be uncertain. The success and future of Pi will depend on the collective efforts of its team, community, and the broader cryptocurrency market dynamics. It's advisable to stay updated on Pi's development and follow any updates from the official Pi Network website or announcements from the team.
Financial Assets: Debit vs Equity Securities.pptxWrito-Finance
financial assets represent claim for future benefit or cash. Financial assets are formed by establishing contracts between participants. These financial assets are used for collection of huge amounts of money for business purposes.
Two major Types: Debt Securities and Equity Securities.
Debt Securities are Also known as fixed-income securities or instruments. The type of assets is formed by establishing contracts between investor and issuer of the asset.
• The first type of Debit securities is BONDS. Bonds are issued by corporations and government (both local and national government).
• The second important type of Debit security is NOTES. Apart from similarities associated with notes and bonds, notes have shorter term maturity.
• The 3rd important type of Debit security is TRESURY BILLS. These securities have short-term ranging from three months, six months, and one year. Issuer of such securities are governments.
• Above discussed debit securities are mostly issued by governments and corporations. CERTIFICATE OF DEPOSITS CDs are issued by Banks and Financial Institutions. Risk factor associated with CDs gets reduced when issued by reputable institutions or Banks.
Following are the risk attached with debt securities: Credit risk, interest rate risk and currency risk
There are no fixed maturity dates in such securities, and asset’s value is determined by company’s performance. There are two major types of equity securities: common stock and preferred stock.
Common Stock: These are simple equity securities and bear no complexities which the preferred stock bears. Holders of such securities or instrument have the voting rights when it comes to select the company’s board of director or the business decisions to be made.
Preferred Stock: Preferred stocks are sometime referred to as hybrid securities, because it contains elements of both debit security and equity security. Preferred stock confers ownership rights to security holder that is why it is equity instrument
<a href="https://www.writofinance.com/equity-securities-features-types-risk/" >Equity securities </a> as a whole is used for capital funding for companies. Companies have multiple expenses to cover. Potential growth of company is required in competitive market. So, these securities are used for capital generation, and then uses it for company’s growth.
Concluding remarks
Both are employed in business. Businesses are often established through debit securities, then what is the need for equity securities. Companies have to cover multiple expenses and expansion of business. They can also use equity instruments for repayment of debits. So, there are multiple uses for securities. As an investor, you need tools for analysis. Investment decisions are made by carefully analyzing the market. For better analysis of the stock market, investors often employ financial analysis of companies.
3. Introduction
• Financial performance assessment is an important issue
• An economic issue
• Financialization of the economy has led financial markets to drive
economic coordination
• A methodological issue
• How assessing portfolio performance?
• A theoretical issue
• How do financial markets work?
3
4. Introduction
• This course is an introduction to financial performance
analysis by using the programming language R
• What is performance in finance?
• What are the expected results according to modern portfolio
theory?
• What are the measures of performance?
4
7. Performance in finance
• Historical
• Performance analysis is one of the basic issues that built the
modern portfolio theory
• Bachelier (1900) highlights that the rise and the fall of prices are
equiprobable at any time
• Prices fluctuate randomly
• Cowles (1933, 1944) highlights that investment advices from financial
analysts do not allow to outperform the market
• It is impossible to predict future prices
7
8. Performance in finance
• Efficient market hypothesis
• Definition
8
[…] the ideal is a market in which prices provide accurate signal for ressource
allocation: that is, a market in which firms can make production-Investment decisions,
and investors can choose among the securities that represent ownership of firms’
activities under the assumption that security prices at any time "fully reflect" all
available information. A market in which prices always "fully reflect" available
information is called "efficient". (Fama E., 1970)
[the market efficiency hypothesis is] the simple statement that security prices fully
reflect allavailable information. A precondition for this strong version of the hypothesis
is that information and tranding costs, the costs of getting prices to reflect information,
are always 0 (Grossman and Stiglitz (1980). A weaker and enconomically more
sensible version of the efficiency hypothesis says that prices reflect information to the
point where the marginal benefits of acting on information (the profits to be made) do
not exceed the marginal costs (Jensen (1978). (Fama E., 1991)
9. Performance in finance
• Efficient market hypothesis
• Definition
• The definition of efficient markets varies according to the informational
set considered (Fama, 1970)
9
Present information
(semi-strong form
efficiency)
Past information
(weak-form
efficiency)
All information sets,
including private
information (strong-
form efficiency)
10. Performance in finance
• Efficient market hypothesis
• Consequences
• Price is an unbiased estimate of the intrinsic value of a security
• There is no better financial analyst than the market
• Future variations are independent of past variations
• Random walk theory
• Investors cannot forecast prices successully
• The theory assumes that managers do not add value (a) to the portfolio
10
11. Performance in finance
• Efficient frontier (Markowitz, 1952)
• The efficient frontier is the set of optimal portfolios that offers the
highest expected return for a given level of risk or the lowest risk for
a defined level of expected return
• Two stochastic dominance decision rules
• An efficient portfolio optimizes the risk/reward ratio
• A diversified portfolio should have at least 50 investments (see Euro
Stoxx 50)
11
At a given level of return,
investors choose the less
risky asset
At a given level of risk,
investors choose the asset
with highest returns
12. Performance in finance
• Efficient frontier (Markowitz, 1952)
• Well-diversified portfolios tend to have similar return (given account
the risk) and rare extreme returns
12
Asset 1
Asset 2
Rf
0,00%
2,00%
4,00%
6,00%
8,00%
10,00%
12,00%
14,00%
0,00% 5,00% 10,00% 15,00% 20,00% 25,00%
Return (Ri)
Volatility (si)
Portfolio of two risky assets Portfolio with one risky asset and the risk free asset
13. Performance in finance
• Expected results
• Financial performance integrates return and risk
• There are several measures of return (max, mean…) and risk (min, s,
VaR…)
• Returns are random
• The most common representation of randomness is the Gaussian
distribution
• A skilled manager shows a similar performance to the market given
the risk
• Outperformance is impossible
• Underperformance is possible
13
A great number of causes Causes are independant
Each cause has
a small effect
14. Performance in finance
• Critics
• Behavioral Finance
• Many behavioral biases impact investment decisions
• Market anomalies
• Calendar anomalies
• "January effect" is an abnormal increase in stock prices in January
• "Weekend effect": stock returns on Monday are often significantly lower
• Other anomalies
• Small firms tend to outperfom
• There is a negative relation between PER and returns and between market to
book ratio and returns
• The Gaussian distribution imperfectly represents return ditribution
• … by underestimating risk
14
16. Data analysis
• Definition
• Statistical procedure to determine the main characteristics of a
dataset
• We use the programming language
16
#install packages (collections of functions which allow more
statistical techniques, and graphical devices)
install.packages("quantmode")
install.packages("fBasics")
install.packages("moments")
install.packages("PerformanceAnalytics")
install.packages("normtest")
install.packages("tseries")
install.packages("roll")
install.packages("xts")
Data are available in the data.csv file with
- Pi are daily closing prices of the stock i
- Pm are daily closing prices of the market index m
- RFR are daily closing rates of a 10-year constant maturity fictitious sovereign bond
17. • Calculation of daily returns
• Logarithmic returns are a better measure
17
#read data
data<-read.csv2(file= file.choose(),header = TRUE,sep = ";",dec = ",")
#Compute daily returns
library(quantmode)
data$Ri<-Delt(x1 = data$Pi,x2 = NULL,k = 1,type = "log")
data$Rm<-Delt(x1 = data$Pm,x2 = NULL,k = 1,type = "log")
data$Rf<-log(1+data$RFR/250)
#Clean up data object
#suppress 1st row
data<-data[-1,]
#suppress colums 2,3,4 (we only keep colums 1, 5 to 7)
data<-data[,c(1,5:7)]
1,
,
, ln
ti
ti
ti
R
R
R
Data analysis
If the package “quantmode” doesn’t
work (it happens !), we can compute
daily returns as follows data$Ri[2:774]<-log(data$Pi[2:774]/data$Pi[1:773])
data$Ri[2:774]<-diff(log(data$Pi))
18. • Descriptive statistics
• Main measures
18
Ri Rm Rf
nobs 773.000000 773.000000 774.000000
NAs 0.000000 0.000000 0.000000
Minimum -0.035737 -0.032272 0.000093
Maximum 0.035524 0.025047 0.000156
I. Quartile -0.004088 -0.004349 0.000114
3. Quartile 0.005653 0.005855 0.000142
Mean 0.000491 0.000529 0.000127
Median 0.000639 0.000844 0.000130
Sum 0.379467 0.409023 0.097973
SE Mean 0.000298 0.000299 0.000001
LCL Mean -0.000094 -0.000057 0.000125
UCL Mean 0.001075 0.001115 0.000128
Variance 0.000069 0.000069 0.000000
Stdev 0.008278 0.008300 0.000017
Skewness -0.369131 -0.391430 -0.352644
Kurtosis I.794045 I.091768 -1.073065
n
t
itii RR
n 1
2
,
2
1
1
s
n
t
tiii R
n
RRE
1
,
1
library(fBasics)
basicStats(data[,2:4])
3
i
ii
i
RR
ESk
s
4
i
ii
i
RR
EK
s
Data analysis
19. • Descriptive statistics
• Main measures
19
Measures Definition
Mean
In finance, mean is a performance measure
The average is calculated on daily data. It must be annualized (n = 252 days)
Variance
In finance, the variance is a risk measure
The variance is calculated on daily data. It must be annualized
The variance is expressed in the square of the unit of measure ("%²"). The
standard deviation is the square root of the variance.
yMean.Ri<-mean(data$Ri)*252
yMean.Rm<-mean(data$Rm)*252
ySD.Ri<-sd(data$Ri)*sqrt(252)
ySD.Rm<-sd(data$Rm)*sqrt(252)
Data analysis
20. • Descriptive statistics
• Main measures
20
Measures Definition
Skewness
(Sk)
Skewness is a measure of asymmetry of the probability distribution
• If > 0, the most part of the distribution is concentrated on the left of the figure (the right tail
is longer)
• If < 0, the most part of the distribution is concentrated on the right of the figure (the left tail
is longer)
Kurtosis
(K)
Kurtosis is a measure of of the probability distribution (1 < K < ∞)
• If > 3, leptokurtic distribution (the data are heavy-tailed: extreme returns are more frequent
than predicted by the gaussian distribution)
• If < 3, platykurtic distribution (the data are light-tailed: extreme returns are less frequent
than predicted by the gaussian distribution)
Data analysis
21. Data analysis
• Descriptive statistics
• Main measures
• Some measures of kurtosis
• Kurtosis is sometimes calculated in excess of 3
21
[1] 1.794045
attr(,"method")
[1] "excess“
[1] 4.794045
[1] 1.806473
[1] 4.806473
library(moments)
kurtosis(data$Ri)
mean(((data$Ri-mean(data$Ri))/sd(data$Ri))^4)
library(PerformanceAnalytics)
kurtosis(data$Ri, na.rm = FALSE, method = "excess")
kurtosis(data$Ri, na.rm = FALSE, method = "moment")
Most explicit
command!
22. Data analysis
• Descriptive statistics
• Main measures
• Some measures of skewness
22
library(moments)
skewness(data$Ri)
mean(((data$Ri-mean(data$Ri))/sd(data$Ri))^3)
library(PerformanceAnalytics)
skewness(data$Ri, na.rm = FALSE)
Delt.1.log
-0.3698488
[1] -0.3691314
[1] -0.3698488
There are sometimes
(small) differences in
the results
24. Normality tests
• Histogram of returns
• For financial theory, markets evolve randomly
• A common representation of randomness is the Gaussian distribution
• The Gaussian distribution has a causal structure that defines a relatively
stable world
• ... consistent with the EMH (and perfect competition)
• Extreme returns are rare
• Returns around mean are the most frequent
24
Brownian motion Stochastic process Random walk
25. Normality tests
• Histogram of returns
• Definition
• Graphic that represents the distribution of numerical data
• It is a graphical way to compare empirical and theoretical distributions
25
hist(data$Ri,main = "Histograms of Ri and Rm", breaks = 100, freq =
FALSE, xlab = "Ri", xlim = c(min(data$Ri,data$Rm),
max(data$Ri,data$Rm)), col = "green",axes = F)
axis(1, pos = 0, cex.axis = 0.8)
axis(2,pos = 0,cex.axis = 0.8,las = 2)
hist(data$Rm,breaks = 50, freq = FALSE, xlim =
c(min(data$Ri,data$Rm), max(data$Ri,data$Rm)), col = "red",,axes =
F,add = TRUE)
curve(dnorm(x, mean(data$Ri), sd(data$Ri)), xlim = c(min(data$Ri),
max(data$Ri)), lwd = 2,col = "grey", add = TRUE)
curve(dnorm(x, mean(data$Rm), sd(data$Rm)), xlim = c(min(data$Rm),
max(data$Rm)), lwd = 2,col = "red", add = TRUE)
legend("topleft",c("Histogram of Ri","Histogram of Rm"),lty =
c(1,1),col = c("green","red"),bty = "n")
26. Normality tests
• Histogram of returns
26
Sharper
distribution
Less returns
than expected
on both sides
"fat" tails
27. Normality tests
• Histogram of returns
• The Gaussian distribution poorly approximates the return
distribution
• It underestimates the probability of extreme returns
27
(min(data$Ri)-mean(data$Ri))/sd(data$Ri)
pnorm(q = (min(data$Ri)-mean(data$Ri))/sd(data$Ri),mean = 0,sd =
1, lower.tail = TRUE, log.p = FALSE)
format(x = pnorm(q = -4.376432,mean = 0,sd = 1, lower.tail =
TRUE,log.p = FALSE),scientific = FALSE, digits = 10)
format(x = 1/(pnorm(q = -4.376432, mean = 0, sd = 1,TRUE,
FALSE)*nrow(data$Ri)), scientific = FALSE, digits = 10)
[1] -4.376432
[1] 6.03189e-06
[1] "0.000006031890184"
[1] "214.4702608"
the worst return occurred 1 time
out of 773 or 214 times too
often…
28. • Normality test of distributions
• Jarque-Bera non-parametric test (1980) (for n >> 0)
• H0: Sk = 0 and K = 3 (the data follows a Gaussian distribution)
• H1: Sk ≠ 0 or K ≠ 3 (the data do not follow a Gaussian distribution)
28
Jarque-Bera test for normality
data: data$Ri
JB = 122.73, p-value < 2.2e-16
Title:
Jarque - Bera Normalality Test
Test Results:
STATISTIC:
X-squared: 122.7298
P VALUE:
Asymptotic p Value: < 2.2e-16
Jarque Bera Test
data: data$Ri
X-squared = 122.73, df = 2, p-value < 2.2e-16
22
3
4
1
6
ii
i
i KSk
n
JB
Normality tests
library(normtest)
jb.norm.test(data$Ri)
library(fBasics)
jarqueberaTest(data$Ri)
library(tseries)
jarque.bera.test(data$Ri)
29. Normality tests
• Normality test of distributions
• Non-parametric test of Kolgomorov-Smirnov
• H0: D = D0 (the data follow the Gaussian distribution)
• H1: D ≠ D0 (the data do not follow the Gaussian distribution)
29
Title: One-sample Kolmogorov-Smirnov test
Test Results:
STATISTIC:
D: 0.4878
P VALUE:
Alternative Two-Sided: < 2.2e-16
Alternative Less: < 2.2e-16
Alternative Greater: < 2.2e-16
library(fBasics)
ksnormTest(data$Ri)
At a = 10%, criticial value = 1,223/√n
At a = 5%, criticial value = 1,358/ √n
At a = 1%, criticial value = 1,629/ √n
If oberved value D > criticial value, H0 is rejected
31. • Definition
• Combination of statistical hypothesis tests
• Parametric tests assume that sample data follow a probability
distribution based on a given set of parameters
• Two risks of error
• The type I error rate is the probability of rejecting the null hypothesis
given that it is true
• The type I error is the p-value (or significance level) a = 1%, 5% or 10%
• The type II error occurs when the null hypothesis is false, but is not
rejected
• The rate of the type II error (b is linked to the power of the test (1− b)
31
Mean-variance analysis
32. F-test of equality of
variances
Student t-test
Parameter
Null hypothesis
(H0)
Alternative
hypothesis (H1)
• Definition
• Combination of two statistical hypothesis tests on variance and
mean
32
21 mm
21 mm
22
1 2
ss
22
1 2
ss
1
1
2
2
22
1
2
11
1;1 21
n
Sn
n
Sn
F nn
2
11
21
21
2
22
2
11
2121
221
nn
nn
SnSn
mmXX
T nn
When n1 = n2, 2
2
2
1
1;1 21
S
S
F nn
Mean-variance analysis
33. • Parametric tests
• Decision rule
• F-test of equality of variances
• Student t-test
33
0
H0 is valid H0 is rejected
1 Critical value
at 10%
Critical value
at 5%
Critical value
at 1%
The value is more and more frequently calculated
• If p value < 1%, H0 is rejected at 1% (***)
• If p value < 5%, H0 is rejected at 5% (**)
• If p value < 10%, H0 is rejected at 10% (*)
Mean-variance analysis
H0 is valid H0 is rejected
Critical value
at 10%
Critical value
at 5%
Critical value
at 1%
34. • Parametric tests
• F-test of equality of variances
• Is the variance of Ri different from the variance of Rm?
34
F test to compare two variances
data: data$Ri and data$Rm
F = 0.99478, num df = 772, denom df = 772, p-value = 0.9421
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.8637999 1.1456325
sample estimates:
ratio of variances
0.994785
var.test(x = data$Ri,y = data$Rm)
The test
doesn’t follow
the convention
2
2
2
1 ss
Mean-variance analysis
ifelse(var(data$Ri) > var(data$Rm), var(data$Ri) / var(data$Rm),
var(data$Rm) / var(data$Ri))
35. • Parametric tests
• Student t-test
• Is the mean of Ri different from the mean of Rm?
35
Paired t-test
data: data$Ri and data$Rm
t = -0.13619, df = 772, p-value = 0.8917
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.0005893457 0.0005128742
sample estimates:
mean of the differences
-3.823577e-05
t.test(x = data$Ri,y = data$Rm,paired = TRUE)
Mean-variance analysis
37. • Critics
• Volatility is not stable over time
• Calculation of 20 day rolling volatility
37
#Computing 20 day rolling Std dev
library(roll)
data$SD_Ri<-roll_sd(data$Ri,width = 20)*sqrt(252)
data$SD_Rm<-roll_sd(data$Rm,width = 20)*sqrt(252)
#Converting date data to date format
date<-as.Date(data$Date,format = "%d/%m/%Y")
data<-cbind(date,data[,-1])
library(xts)
data<-xts(data[,2:6],order.by = data[,1])
#Drawing plot
windows()
plot(data$SD_Ri[23:773], xlab = "Date", ylab = "Annualized Std
Dev",type = "l", col = "green")
lines(data$SD_Rm,col = "red")
legend("topleft",c("Std dev of Ri","Std dev of Rm"),lty =
c(1,1),col = c("green","red"),bty = "n")
title(main = "20 day rolling std dev of Ri and Rm")
Mean-variance analysis
39. Mean-variance analysis
• Critics
• Volatility is not stable over time
data<-read.csv2(file.choose(),header=T,sep=";",dec=",")
data$Ri[2:774]<-diff(log(data$Pi))
data<-data[-1,]
library(roll)
data$Ri<-as.matrix(data$Ri)
data$SD_Ri<-roll_sd(data$Ri,width = 20)*sqrt(252)
windows()
par(mfrow=c(2,1))
plot(data[,2],type="h",col="grey",xlab="Date",ylab="Price
(€)",ylim=c(round(min(data[,2])-5),round(max(data[,2])+5)),axes=F)
axis(1,pos=40)
axis(2,pos=0)
title(main="Price of i")
plot(data[,6],type="h",col="grey",xlab="Date",ylab="20 day rolling
volatility (%)",ylim=c(0,0.35),axes=F)
axis(1,pos=0)
axis(2,pos=0)
title(main="20 day rolling volatility of i")
42. Conclusion
• Statistics is “the science of collecting, analyzing,
presenting, and interpreting data”
• Descriptive statistics summarize the population data
• The histogram and the normality test make it possible to evaluate
the adequacy between a variable and the statistical law of
reference
• The expectation variance analysis allows a comparison of the
variables
42
43. Conclusion
• Financial modelling seeks to improve the mathematical
representation of the behavior of securities
• Monofactorial models are the precursors
• Market model (Sharpe, 1963)
• Capital Asset Pricing Model (Lintner, 1965)
• Multifactor models try to integrate more variables
• Market timing (Treynor-Mazuy, 1966)
• Arbitrage pricing theory (Ross, 1976)
• Fama-French three factor model (1993)
• Carhart four factor model (1997)
43
44. References
Finance
• Bachelier L. (1900), Théorie de la spéculation, Annales scientifiques de l’ENS, (17)3, 21-86
• Carthart M. (1997), “On persistence of Mutual Fund Performance”, Journal of Finance, (52), 57-82
• Cowles A. (1933), “Can Stock Market Forecasters Forecast?”, Econometrica, (1)3, 309-324
• Cowles A. (1944), “Stock Market Forecasting”, Econometrica, (12)3-4, 206-214
• Fama E. (1970), “Efficient Capital Markets: A review of Theory and Empirical Work”, Journal of Finance,
(25)2, 383-417
• Fama E. (1991), “Efficient Capital Markets”, Journal of Finance, (46)5, 1575-1617
• Fama E., K. French (1993), “Common Risk Factors in the Returns on Stocks and Bonds”, Journal of
Financial Economics, (33), 3-56.
• Lintner J. (1965), “The valuation of risk assets and the selection of risky investments in stock portfolios and
capital budgets”, Review of Economics and Statistics, 47(1), 13–37
• Markowitz H. (1952), “Portfolio Selection”, Journal of Finance, (7)1, 77-91
• Ross S. (1976), "The Arbitrage Theory of Capital Asset Pricing". Journal of Economic Theory, (13)3, 341-
360
• Sharpe W. (1963), “A Simplified Model for Portfolio Analysis”, Management Science, (9)2, 277-293
• Treynor, J., Mazuy, K. (1966), “Can Mutual Funds Outguess the Market?” Harvard Business Review, (44),
131-136
Statistics
• Jarque C., Bera A. (1980). “Efficient tests for normality, homoscedasticity and serial independence of
regression residuals”, Economics Letters. (6) 3, 255–259
44