Statistics For Management 3 October

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STATISTICS & ECONOMICS

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STATISTICS & ECONOMICSDr. T.K. Jain.

AFTERSCHO☺OLCentre for social entrepreneurship

Bikaner M: [email protected]

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Find rank correlation between the following?


Solution

1. Find the difference in the two ranks2. Square the differences3. Use the following formula to solve it : • 1 – { 6∑d^2 / (n(n^2 -1))}• 1 – { 6 * 36 / (8 *63)}• =1 - .4285 = .572 answer.


Solution …

rank of x 7 6 2 4 5 3 1 8

rank of y 5 4 6 3 8 2 1 7

difference 2 2 -4 1 -3 1 0 1

diff. sq 4 4 16 1 9 1 0 1 36


Question on regression…

• Following data relate to the heights of 10 pairs of fathers and sons:

• (175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175) (169, 170), (170, 173)

• The regression equation of height of son on that of father is given by


Solution …

• ∑ Y = Na + b ∑X• ∑XY = A ∑X + B ∑X^2• 1721 = 10 A + B 1714• 295012 = 1714A + 293860 B• Y = A + BX• 172.1 = A + .405 (171.4) • A = 172.1 – 69.417 • A = 102.68


solutionX y dx dy dxdy dx^2 dy^2 XY X ^2 Y^2

175 173 3.6 0.9 3.24 12.96 0.81 30275 30625 29929

172 172 0.6 -0.1 -0.06 0.36 0.01 29584 29584 29584

167 171 -4.4 -1.1 4.84 19.36 1.21 28557 27889 29241

168 171 -3.4 -1.1 3.74 11.56 1.21 28728 28224 29241

172 173 0.6 0.9 0.54 0.36 0.81 29756 29584 29929

171 170 -0.4 -2.1 0.84 0.16 4.41 29070 29241 28900

174 173 2.6 0.9 2.34 6.76 0.81 30102 30276 29929

176 175 4.6 2.9 13.34 21.16 8.41 30800 30976 30625

169 170 -2.4 -2.1 5.04 5.76 4.41 28730 28561 28900

170 173 -1.4 0.9 -1.26 1.96 0.81 29410 28900 29929

1714 1721 32.6 80.4 22.9 295012 293860 296207

171.4 172.1 0 0 3.26 8.04 2.29 29501.2 557095 562485

0.405473


Regression • The two lines of regression are given by• 8x + 10y = 25 and 16x + 5y = 12 respectively.• If the variance of x is 25, what is the standard

deviation of y? • Soluton • 25 and 12 are constant. • 10 Y = -8X & 5 Y = -16X; Variance of X is 25, so

10 Y = -8 *sqrt(25) or Y = - 40/10• Y = 4, or 16. The variance of Y = (16 *4 ) = 64

thus standard deviation is 8. answer.


The correlation coefficient between the number of railway accidents

and the number of babies born per year was found to be 0.75.

comment It is important to know how to interpret statistics. There can

be many types of fallacies. Correlation does not tell us about the cause and effect relation between two variables. It only tells us about relation between two variables. The relation can be positive or negative. Correlation only tells us that the data are moving together or not. It would be wrong to draw any cause –effect inference merely from this relationship.


A correlation co-efficient r=0.8 between X and V implies a

relationship twice as close as r = 0.4.

comment.

• Correlation tells us that there is relationship between two variables, but we cannot exactly quantify and say that the relation is twice between the two variables.


A credit sale of Rs. 1,000 to Santhanam has been wrongly passed through the Purchases

Book.

• Santham Ac. Dr. 2000• To Purchase 1000 (credit)• To Sales 1000 (credit)


Microeconomics and macroeconomics convey the same

meaning. --- comment…

• No they are different. • Macroeconomics deals with global issues.

They relate to the whole world

• Microeconomics relate to decision making at individual level – at firm level. They affect each other – but not same.


Return to scale describes the change in output in response to an equi-proportionate change in

one input.

• Yes, but it relates to small period. • For long term, we generally use the word

returns to scale.


WTO facilitate international trade among nations.

• Yes – WTO encourages free international trade. It has been trying to reduce treaties and promote international agreements.


An increase in cash reserve ratio for banks can increase their capacity of credit creation.

No, if CRR is increased, the banks have to keep more cash with them and therefore they cannot give that much of money as loans. Thus increase in CRR and SLR will reduce the capacity of banks in credit creation. Answer.



NORMAL DISTRIBUTION …

1/10 2/10 4/10 2/10 1/10 Values of a variable,

say test scores60 70 80 90

In this example 10 people took a test. The height of each bar is the relative frequency or percentage of those in that range of scores.What % of people had test scores between 70 and 80? 40%What % of people had scores less than 70? 30%If you add up all the fractions what do you get? 1


The Normal Distributions - Basic idea

The normal distribution is a tool we use to try to convey the same information as we get from a relative frequency histogram.

The normal distribution has been used a lot in statistics and we will use it later, so we will look at some details about it.

But, first let’s look at circles - yes I mean circles!


circles and density

Imagine you are at the intersection by Dairy Queen. Now imagine a large circle is placed on the earth such that the center of the circle is at the intersection plus enough houses have been included so 1,000,000 people live in the circle.

New York City has a similar intersection and circle, except the circle is smaller (WHY?).


circles and density The New York circle is shorter because

you travel a shorter distance from the center to get an equal density of people in New York.

The smaller circle in a sense has a smaller standard deviation(actually it has a smaller radius) - the distance is less spread out.

One thing similar about the two circles is that you can divide them both up into quarters. Let’s do this on the next screen with two circles


circles and density

Aa

25% of the area is in A on the large circle and 25% of the area of the small circle is in part a.How can they both be 25%?It is 25 % of its own total.There are as many different normal distributions as there are circles. BUT, normal distributions are dividedup, not into quarters, but in another way.


The Normal Distributions - normal dist. and density

Normal distributions can roughly be drawn by modifying a circle.

flip this partout to left flip this part

out to rightlike this


The Normal Distributions - normal dist. and density

Let’s label parts of the normal distributions.

numberline forthe variable-like test score

This is the center of thedistribution. It really is the mean value.

This point is where thebottom part of the circle flipped.Let’s call it the inflection point.There is one on the other side as well.

This point on the number line is directly below the inflection point. It turns out that the point on the number line is one standard deviation away from the center.


On the previous screen we see a graph of a normal distribution. Let’s consider an example to highlight some points.

Say a company has developed a new tire for cars. In testing the tire it has been determined that the mean tire mileage is 36,500 miles and the standard deviation is 5000 miles.

Along the horizontal axis we measure tire mileage. The normal distribution rises above the axis. Note the highest point of the curve occurs above the mean - in our tire example we would be at 36,500.

On the curve we have two inflection points, and these occur 1 standard deviation away from the mean. So, mileages 31,500 and 41,500 are 1 standard deviation for the mean and the inflection points occur above them.


The Normal Distributions - notation

In general, now, we will talk about a variable having a normal distribution. We will say variable X is normally distributed with mean mu and standard deviation sigma.

More simply, we say X is N(mu,sigma).

Don’t let the N(---) part fool you, it means N(mean value listed first, then standard deviation value listed).


The Normal Distributions - example with graphical thinking

Say we have a variable X is N(3, 1)

X is measuredon the line

3

3 is the mean

2 4Use the dots asyour guide todraw the normaldist.

Why is this dot,and the one across, above #’s2 and 4?


The Normal Distributions - another example with graphical thinking

Say we have a variable X is N(3, 2)

X is measuredon the line

3

3 is the mean

2 4

Use the dots as your guide to draw the normal dist.

Why is this dot,and the one across, above #’s1 and 5?

1 5


The Normal Distributions - compare the two examples

here is what the two examples look like, one on top of the other

32 41 5

X is N(3, 1)

X is N(3, 2)


The Normal Distributions - compare the two examples

Note on the previous screen how the X is N(3, 2) had its inflection points wider than on the X is N(3, 1).

Remember how we labeled the quarters of the different circles A and a. We said there was 25% of the circle in both A and a, but based on its own total.

Normal dist.’s have a similar rule. 68% of the area under the curve is between the two inflection points. There is more.


The Normal Distributions - 68-95-99.7 rule

On any normal distribution the inflection points will be 1 standard deviation on either side of the mean. 68% of the area under the curve will be within this one standard dev.

By moving out 2 standard deviations on either side of the mean you have about 95% of the area under the curve.

By moving out 3 stand. dev.’s you have 99.7 % of the area under the curve.


The Normal Distributions - 68-95-99.7 rule

What is the meaning of the phrase, “1 standard dev. on either side of the mean?”

The answer is best seen by an example. X is (10, 2.5) means X is normal with mean 10 and standard deviation 2.5. Thus 7.5 is 1 stand. dev. on the low side of the mean and 12.5 is 1 stand. dev. on the high side of the mean. Thus being anywhere from 7.5 to 12.5 is within 1 standard deviation of the mean.


Note about normal distribution:

1. There are many normal distributions, each characterized by a mean value and a standard deviation.

2. The high point of the curve is above the mean and for a normal distribution the mean = median = mode.

3. Depending on the variable, the mean can be negative, zero, or positive.

4. The normal curve is symmetric. This means each side is a mirror image of itself.

5. Larger standard deviations result in a flatter, wider distribution.

6. Probabilities for the variable are found from areas under the curve - the 65, 95, 99.7 rule is an example of this.


miles 26,500 31,500 36,500 41,500 46,500

-2 -1 0 1 2 z

Remember the concept of a z score from earlier.

z = ( a value minus the mean)/standard deviation. So the value 26,500 has a z = (26,500 - 36,500)/5000 = -2. This means 26,500 is 2 standard deviations below the mean. You can check the other values.


The standard normal distribution

Remember how we said there are many different circles and many different normal distribution? Sure you do. The z value translates any normally distributed variable into what is called the standard normal variable. Technically the picture I have on the previous screen is misleading because the z’s are a different scale than the miles, but don’t worry.

In the book there is a table with z values and areas under the curve. Let’s see how to use the table. Here is one place where I want you to be extra careful when you calculate z. Round z to 2 decimal places. The z value is broken up into two parts a.b and .0c. when added we get a.bc. For example the number 2.13 is broken up into 2.1 and .03


Using the standard normal table

The z = 2.13 means we should go down the table to 2.1 and then over to .03. The number in the table is .9834. This means the probability of getting a value less than z = 2.13 is 98.34%.

In the tire example if we look at the mean value 36,500, we see the z = (36,500 - 36,500)/5000 = 0.00 and in the table we see the value .5000. Thus, there is a 50% chance the tire mileage will be less than 36,500.

So the table has the area under the curve to the left of the value of interest. We may want other z’s and other areas. What do we do?


Say we want the area to the right of a z that is greater than 0? The table has the area to the left. Whatever the z is,

go into the table and get the area and then take 1 minus the area in the table.

ab The z here would be negative.

Say we want area b. Area a is in the table and b is 1 minus area a.Area b would be found in

a similar way to what is above.


Back in the old days when I had to walk to school uphill both ways in three feet of snow, the standard normal table was all we had to calculate probabilities for a normal distribution. Now we have Microsoft Excel to make the calculations.

The NORMSDIST function assumes we have a z value and we want to find the area the the left of the z - the area to the left is the cumulative probability. The function has the form =NORMSDIST(z), where z is the value we have. z can be negative in Excel.

The NORMDIST function allows us to just work with the variable without getting the z and we can still have the cumulative probability. The function has the form =NORMDIST(value, mean, standard deviation, TRUE). This is an innovation of Excel over the old days.


Sometimes we may have an area and want to know the z. The function NORMSINV asks us to give an area to the left of a value and the function will give us the z value. The form of the function is =NORMSINV(cumulative probability).

The function NORMINV does the same, except not in z value form. It just give the value in the same form as the variable. The form of the function is =NORMINV(cumulative prob, mean, standard deviation)


What is bailout

• To save a company is called bailout .


Which company is buying Australian Airlines?

• Luftansa from Germany


What is bleak economy?

• Economy in recession.


Fastest supercomputer

• Tesla supercomputers from NVIDIA


NEW CM OF MAHARASTRA?

• Ashok Chavan


Who is India president of Rolls Royce?

• Anil Shrikhande


Best movie as per American National Review of Movies?

• Slumdog Millionaires.


Who is this ?

• Executive Vice president of Nokia – Robert Anderson


Who is this ?

• Ranjan Das – CEO of SAP India

http://economictimes.indiatimes.com/Interview/Ranjan_Das_CEO_SAP_India/articleshow/3786137.cms


What is bullish and bearish?

• Bullish = when the prices are moving up, it is called bullish

• Bearish: when the prices are falling down, it is called bearish.


Who is O J Simpson?

• American footballer, recently put to jail for 15 years.


Name the act under which Banks can takeover a company which is

not making payment

• Sarfaesi Act.


What is NPA?

• Non- performing Asset ( when a company is not making payment for 2 instalments then it is called NPA and legal action is taken or the case may be taken to BIFR (BOARD OF INDUSTRIAL AND FINANCIAL RECONSTRUCTION).


Define takeover?

• When a company takes over shares of another company , it is called takeover.

• As per SEBI (securities and Exchange board of India), when a company goes for takeover, it has to buy at least 20% shares by public call. The threshold limit is 10% (once you cross 10% limit, you may go for takeover).


What is NB FC?

• Non-banking finance company .• Example : (fullerton, India bulls, Anagram)

…


What is ECB & FCCB?

• ECB = External commercial borrowing• FCCB= foreign currency convertible bond


What is GDR?

• Global Depository receipt.


What is AMC?

• IT IS A COMPANY SET UP AS PER SEBI REGULATIONS AND OTHER GUIDELINES TO MANAGE THE ASSETS OF A MUTUAL FUND. AMC HAS TO BE APPROVED BY SEBI. IT MAKES AGREEMENT WITH TRUSTEES OF A MUTUAL FUND TO FORMULATE SCHEMES, RAISE MONEY AGAINST THEM AND TO INVEST THE FUNDS AND DISTRIBUTE INCOME.


WHAT IS BACK END LOAD?

• It denotes the charges levied by the mutual funds to calculate the price of a scrip of a mutual fund.

• For example, if back end load is 2% and NAV is Rs. 20 then the share price will be :

• 20 / (1.02) = 19.60 ans.


WHAT IS CDSC?

• Contingent Deferred Sales Charges• This is the charge that mutual funds can

charge as a part of BACK END LOAD. • As per SEBI guidelines, maximum back

end load or front end load can be 7%.


What are highest symbols of ICRA for debt, insurance and equity

grades?

• For debt : mfAAA and also M1• For insurance companies : iAAA• For equity: ER1A.


What are the highest rating symbols of CARE for long term and

short term debt?

• For long term : CARE AAA• For short term instruments : PR1


WHAT ARE THE HIGHTEST RATING SYMBOLS OF FITCH

INDIA FOR LONG TERM, SHORT TERM AND TERM DEPOSITS?

• LONG TERM: AAA (IND)• FOR SHORT TERM : F1• FOR TERM DEPOSITS : tAAA


What is CP?

• Commercial paper


What is ICD?

• Inter-corporate deposits.


What is CD?

• Certificate of deposits.


What is the minimum networth required of a CRA?

• CRA = CREDIT RATING AGENCY• As per SEBI (credit rating agencies)

regulations 1999, it should be minimum Rs. 5 Crores ( the promotors should have minimum networth of Rs. 100 crores).


What is a BENAMI transaction?

• All the transactions where the source of the transaction cannot be identified because there is no real name (fictitious names are there).

• It is banned by Benami Trasaction (prohibition) Act 1988.


When was depositories Act enacted?

• 1996


WHAT IS NSCCL?

• National Securities Clearing Corporation Ltd.


What is WDM?

• Wholesale Debt Market.


Mention any 3 points that you will consider while deciding about

pricing of a buy back of the shares?

• Past performance• Prices• Book value per share• Industry outlook• Networth of the company• Previous buy back.


When is buy back not permitted?

• When shares are not fully paid up. • When there is inadequate reserve. • When the company has defaulted in

payment of deposits (as per companies (acceptance of deposits ) reules 1975).


Can the company keep the shares with itself after buy back?

• No • Because the shares have to be physically

destroyed in 7 days of the buy back.


When should company inform SEBI about completion of buy back • Within 30 days of buy back. (file a return

with SEBI).


You want to takeover a company ,what steps will you

follow? 1. Study the financial condition of the

company to be taken over. 2. Appoint a merchant banker3. Give public offer (as per regulation 14). 4. Give a letter of offer to SEBI5. Despatch letter of offer to shareholders6. Open escrow account


What are the purpose for which you may get GDR / EURO ISSUE

• CAPITAL EXPENDITURE (setting up a new plant etc.)

• Repayment of external borrowing• Equity investments in joint ventures

(remember, investments in stock market and real estate sector cannot be permitted out of it).


What is STP relating to SEBI?

• STRAIGHT TRHOUGH PROCESSING – it enables end to end processing in the case of financial instruments.


Name any ERP?

• SAP R3


WHAT CRITERIA WILL YOU HAVE WHILE RATING A

COMPANY?

1. Industry risk2. Company’s market position3. Financial position of the company4. Financial leverage 5. Cash flow & funds flow6. Evaluation of management7. Operating efficiency.


What is ETF?

• Exchange traded funds.• They represent a basket of scrips which

are traded in a stock exchange. They are just like mutual funds. They represent a basket of scrips which are purchased / sold from stock markets.


What are the activities that a merchant banker may do?

• Managing public issues• Managing advisory services and

underwriting services• Private placement of shares• Stock broking• Dealerships regarding securities


Who cannot participate in ESOS?

• ESOS = employee stock option scheme• DIRECTORS AND PROMOTORS

CANNOT PARTICIPATE IN ESOS


What are 4Ps?

• Product• Price • Place• Promotion• In services industry, we take 3 more: • Physical evidence• People• Public relations.


What are 4 c?

• Cost• Convenience• Communication• Consumer’s needs.


What is margin trading?

• SEBI has put margin trading requirements. A client will have to deposit some amount as margin to the broker to meet the requirements as per the SEBI guidelines. Thus a client has to deposit some advance money at the time of transactions.


What is capital market

• The market where you may deal in money for a long period – where investors and borrowers deal in financial instruments, which have long maturity period or have long investment possibilities. Capital market instruments include shares, debentures, bonds, deep discount bonds, prefernece shares etc.


When did ETF start ?

• Exchange traded funds started in 1993. • (it was suggested by Leland Obrien, of

Rubernstein Associates)in 1980.


What are price bands?

• If the price of a scrip is 100, and if it goes upto certain limit (called price band), then trading will halt for half an hour.

• Currently price band is 8% +4% = 12%. • Now price bands are from 5% to 20%.

There is no price band in case of scrips in futures and options.


MCFS?

• Modified Carry Forward System


ALBM

• Automated Lending and Borrowing Mechanism.


Green Shoe Option…

• A tool to stabilise share price


What is sweat equity shares?

• The shares issued to employees (sec. 79 A ) of companies Act.

• These issues are issued only after at least 1 year of commencement of business.

• It should be passed by special resolution..


What is deep discount bond?

• Those bonds with are issued on very heavy discount. They are for long period. They don’t carry any interest. For example a bond of face value Rs. 100 issued for Rs. 25 for 50 years.


The first Indian company to issue DDB?

• IDBI issued it – at 2700 the DDB of Rs. 100000 for 25 years


What is networth?

• Equity + reserves


Mention any 3 points from the code of conduct of merchant banker?

1. Keep the interest of the investor protected

2. Ensure that investor is able to read prospectus and other documents before investing

3. Shall not give any advice regarding investment in any company.

4. Shall give best possible advice to clients5. Make adequate disclosures Etc.


Mention any 3 points that you will add in statutory public

announcement for buy back

1. Dates and details2. Inforation about company3. Details of escrow account4. Capital structure5. Time table6. Details of offer


Mention any 3 points of public offer being made for takeover of

the company• No. of shares to be acquired• Price • Dates• Detail of holding• Approval of banks et. • Other required information. ….


Mention 3 obligations of the directors regarding insider

trading….

1. Maintain confidentiality of all price sensitive information

2. Security of confidential files3. Conduct all security related dealings in

valid trading window4. Disclose information as per SEBI

requirements. ..etc.


Mention 3 money market instruments…

• Treasury bills• Intercorporate deposits• Bill discounting • Etc.


Mention 3 guidelines regarding 75% book building process….

• The book runner should maintain records • Details regarding who is the institutional

investor and who is the private investor should be maintained

• Separate accounts should be there for these

• The institutional investor will also forward its offers through book runner.


What is mandatory client code?

• In order to bring transparancy, every broker has been given a unique code.


What is DVP?

• DELIVERY VERSUS PAYMENT


What is minimum public offer?

• At least 10% of post issue capital subject to minimum of 20 lakhs shares of amount of 100 crores.


No delivery period…

• Earlier we used to have at least 7 days of no delivery period - now this has been abolished.



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Why such a programme?

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Who are our supporters?

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About AFTERSCHO☺OL PGPSE – the best programme for developing great

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relevance


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where?• Embrace change – and compete with yourself

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Statistics For Management 3 October