Decision Science Mod I Solution for Test 2012-13 (1)

7/28/2019 Decision Science Mod I Solution for Test 2012-13 (1)

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INSTITUTE FOR TECHNOLOGY & MANAGEMENT

PGDM (Jrs) Decision Sciences Max. Marks: 20

Term I (2012) Test IMax. Time: 75 Mins

SOLUTION OF THE QUESTIONS

NOTE :

i. This paper contains 4 question. All questions are compulsory.ii Calculators are permittediii Graph Papers will not be supplied. If required, draw Charts on answer sheet itself.iv. Marks against each question has been mentioned below that question

Q 1: Mutual Fund industry provides different modes of investment for the prospective investors.The different modes of investment in a mutual fund are by cash in any designated bank, by

cheque or demand draft in any collection center, by ATM payment, by direct ECS payment, by

Systematic Investment Plan (SIP). The SIP plans have been especially designed for those persons

who do not want to investment in lumpsum rather they want to investment systematically ie., on

monthly basis. The mutual fund companies claim that, if the investors use the SIP mode, they get

benefit by way of lowering of average cost.

Justify their claim with the help of the data given in the following table. The data pertains to the

NAV of a mutual fund on 10th of every month in a financial year.

Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar 80.52 81.49 71.87 72.64 81.74 87.49 93.75 97.30 104.98 111.39 122.2

1

127.84

(3 Marks)

Solution:

STEP 1 :

The claim of the mutual fund relates to the benefits accrued to the investor if they choosethe SIP route.To verify the same, we take a situation whereby an investor decides to invest Rs 100 /- permonth. The allotted number of units would be as follows:


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Month NAV No of units gained (assume Rs100 is deposited in SIP everymonth )

APRL 80.52

1.24

MAY 81.49 1.23

JUNE 71.87 1.39

JULY 72.64 1.38

AUG 81.74 1.22

SEPT 87.49 1.14

OCT 93.75 1.07

NOV 97.3 1.03

DEC 104.98 0.95

JAN 111.39 0.9

FEB 122.21 0.82

MARCH 127.84 0.78

Total units for 12 months in SIP = 13.15

STEP 2 :

Now, as an alternative of SIP route the investor may select to invest Rs 1200/- at any point oftime in the entire year.Since, when the investor (s) might enter is not known thus, average NAV would be idealparameter to decided how much units will be allotted.

80.52 + 81.49 + ...................................... + 127.84

Average NAV = ----------------------------------------------------------12

= 94.435

Thus, The investor would get = (1200 / 94.435) = 12.70715 units

STEP 3 :

Comparison and Interpretation: Since the average number of units allotted under the lumpsum

investment is lower than the total number of units allotted under the SIP mode.


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Thus, the claim of the Mutual Fund Company is appropriated and justified.

Disclaimer: The above calculations shown are indicative and based upon historic data. It may

get repeated in future or may not. There is no guarantee that this concept will always hold

true, however in the given circumstances it gets proved. Moreover, empirical evidences show

that SIP route is always better than lumpsum investments

Marking Scheme: Each STEP contains 1 marks

Q 2 (A): The coefficient of variation of wages of male and female workers is 55% and 70%

respectively, while their corresponding standard deviations are 220 and 154. Calculate the average

wage of a worker given the fact that 80% of them are male.

(2 Marks)

2A.

MALE FEMALE

CV= 55% CV= 70%

SD=220 SD=154

Assume there are 100 workers in the organization.

Nm = 80 (no. Of males) Nf = 100-80= 20 (No. Of females)

CV (M) = (SD/MEAN) *100 CV (F) = (SD/MEAN)*100

STEP 1 :

55 = ( 220 / mean ) x 100,

Thus, Mean of Males = 400

Similarly, Mean of Females = 220

STEP 2:

COMBINED MEAN =[ Nm * MEAN male + Nf * MEAN female ] / (N m + N f )

SUBSTITUTING we get combined mean as 364. so average wage of worker is 364.

Marking Scheme : Each step is worth 1 marks

Q 2 (B) : Which of the following statements is not true?

Standard deviation is unchanged ifa) a constant is added to all the observationsb) a constant is subtracted from all the observations

c) a constant is either added or subtracted from all observations

d) all the observations are multiplied by a constant.e) All the above

(1 Marks)


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2B. correct answer is d (All the observations are multiplied by a constant).

Q 2 (C) :Scatter diagram depicts:a) variations in x and y

b) joint variation in x and yc) variation in y for given values of x.

d) variation in x for given values of y.e) none of the above

(1 Marks)

2C. correct answer is b (Joint variation in x and y).

Q 2 (D) :For a distribution based on 200 observations partly reproduced below, mean is 1.46. Find

the missing frequencies:

No. of Accidents 0 1 2 3 4 5

Frequency 46 ? ? 25 10 5

(2 Marks)

Solution

No of accidents (x) Frequency (f) fixi

0 46 0

1 f2 f2

2 f3 2f3

3 25 75

4 10 40

5 5 25

Total N = 86 + f2 + f3 140 + f2 + 2f3

Given Total 200

Mean= fixi /N

Thus, we get two equations

1.46 = [140 + f2 + 2f3] / 200 ---------------- (I)Also given in the question is :

46 + f2 + f3 + 25 + 10 + 5 = 200 ------------------------- (II)86+ f2 +f3 = 200

F3= 200 86-F2 F3 = 114 F2 (II)Substitute II in I

1.46*200 = 140 + f2 + 2 ( 114 F2 )

Solving we get f2 = 76Substituting in II we get f3 = 38

Marking Scheme:

If any student is in a position to frame the equations -------- 1 MarksFinding of the Missing Values ------------ 1 Marks


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Q 3: Dr Jhamjham is running a security trading company. She provides Portfolio Management

Services (PMS) to the clients. One of the customers once asked her can you enlighten me on the

beta of a stock. In reply to this query, she said beta of a security is nothing but the slope of the line

of regression and it is calculated with the same formula. The customer was not in a position to

understand the calculation part of the beta and requested Dr Jhamjham to illustrate with an example.

In turn Dr Jhamjham asked Rimzhim to collect the information and make the customer understand

the concept of beta of a stock.Rimzhim has collected the data pertaining to ICICI banks equity shares as given in the table. After

having collected the data, she will first calculate the Rate of Return (ROR) for both the series ie.,

ROR for ICICI shares and NIFTY. She will be using the formula given below for calculating ROR:

Current value previous value

ROR = -----------------------------------------

Previous value

She will further assume that ROR of ICICIs shares will be Y series and that of CNX NIFTY as X

series.

Year Month

Average Closing price of ICICIs bank

shares

Average Closing value of S&P CNX

NIFTY

2009 Jan 140.5 1154.67Feb 149.9 1178.72

Mar 149.3 1084.64

Apr 133.75 1038

May 121.15 1122.32

Jun 137.95 1272.21

July 150.15 1337.86

Aug 159.15 1538.08

Sep 179.7 1610.21

Oct 204.5 1770.08

Nov 247 1837.98Dec 250.1 2139.93

Since Rimzhim is having multiple jobs at hand, she is not in a position to proceed further with the

calculations. Please help Rimzhim by providing her the value of correlation coefficient through

which she will be calculating the value of beta. In short, you are required to calculate the correlation

between the two ROR. Can we prove that there exists a relationship between the CNX NIFTY and

ICICI banks stocks using t-test. Also calculate Coefficient of determination.

Interpret the results.

(5 Marks)

X Y

S. no ICICI CNX NIFTY ICICICNX

NIFTY

ROR ROR

1 140.5 1154.67

2 149.9 1178.72 148.9 1177.72

3 149.3 1084.64 148.3 1083.64

4 133.75 1038 132.75 1037

5 121.15 1122.32 120.15 1121.32

6 137.95 1272.21 136.95 1271.21

7 150.15 1337.86 149.15 1336.868 159.15 1538.08 158.15 1537.08

9 179.7 1610.21 178.7 1609.21


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10 204.5 1770.08 203.5 1769.08

11 247 1837.98 246 1836.98

12 250.1 2139.93 249.1 2138.93

Correlatio

n (r)

0.932730

737Coeff. Of

Det86.99866

272

(r square)

t cal 7.76

t tab 2.262

Interpretation: The degree of linear relationship between the stock of ICICI bank and CNX NIFTY is

very good. In short, correlation is very good (0.93).

The strength of the relationship is also very good (87%). Thus, it can be said that, upto 87 % of the

variations in the ICICIs security is because of the variations in the stock market. In other words, if the

stock market rises then probably the ICICI banks stock will also rise and viceversa will also be true.

Proof of the existence of relationship can be achieved by testing the correlation coefficient by

using students t-test.

Ho: There exists no relationship between ICICI banks stock and the CNX NIFTY

H1: There exists a significant relationship between ICICI bank stock and the CNX NIFTY

Using the formula, t cal = 7.76

and from the t-table on the question paper we get, t tab = 2.262.

Interpretation: Since the calculated t is greater than the tabulated t at 9 d.f. and 5% level of

significance, we reject the Null Hypothesis. Accordingly, there exists a significant relationship between

the ICICI bank stock with CNX NIFTY.

We can further clearly mention that, whenever there will be rise in the value of the stock market, there

would be corresponding increase in the value of the stock of ICICI bank. Also, we know that the rising

value of the market price of any stock leads to the shareholders value creation. Thus, stock market

increase also affects the shareholders value creation.

Marking Scheme:

Only ROR values: 2 marks

ROR and Correlation Values: 2 + 1 = 3 marks

ROR + Correlation Values + Coefficient of Determination and / or t test: 2 + 1 + 1 = 4 marks

ROR + Correlation Values + Coefficient of Determination and / or t-test + Interpretation = 5

marks

Q 4: DIVERSIFICATION OF PORTFOLIO


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Diversification is done by creating a portfolio of securities. Portfolio simply means a group of assets

an investor owns. The assets can be stocks, bonds, commodities and so on. A portfolio can also

have securities from different industries/sectors. The inclusion of different assets in portfolio helps

the investor to reduce underlying risk. In the case of shares the diversification reduces the risk.

Many analysts opine that if a portfolio is created including 15 securities the investor can reduce the

risk to zero level. However studies reveal that although by increasing the number of securities in a

portfolio we can reduce the risk, we cannot bring it down to zero level. To explain this, furtherportfolio of securities were created representing different sectors listed in National stock exchange.

15 companies listed in NSE were selected randomly of various sectors and portfolios have been

created where number of securities are 1 , 2, 3, 5 , 7 and 10. Historic data of these securities from 15

June 2009 to 15 June 2012 were used for analysis of standard deviation, beta of stock for a period of

three years and correlation coefficients.

Refer the attached Sheets for getting the full data related to the various statistical results.

Study the data carefully and interpret them giving full definition and explanation of the

terms. Highlight your answer with usability of the statistical tools in this specific situation.

(6 Marks)

Solution:

This question needs pure analytical thinking. The answer will have to be evolved rather thanfollowing any pattern. Any set strategy may not work because for the first time the studentswill come across for the first time this type of question.While attempting this type of questions, student needs to take a view point that traceabilitycan be drawn to the theory for reaching to the analytics.Accordingly, first of all the student should trace linkages backwards. The following pointsillustrate it:

A 1) Descriptive Statistics def : Collection, representation and characterization of data. It canbe classified into broad categories Pictorial and Numerical methods.

This case is using both methods. Chart is showing the s.d. and no of stocks while you havetable for the same.

A 2) Numerical methods primarily are the measures of central tendency and measures ofdispersion.

Definitions are required to be produced for both the above as asked in the question.

A 3) The case also gives correlation coefficients between few stocks. For interpretation themstudent must define measures of association.

A 4) In the question, there is a statement which is asking the student to highlight the usabilityof the tools and techniques used. Here the concept of risk (mean return) and return (standarddeviation and variance) are to be mentioned.

B) Having completed the above points, interpretation of the data needs to be made. Though

the interpretation may differ from person to person but few generalized conclusions are givenbelow which are indicative in nature:


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B1) Risk of a portfolio is directly proportional to the number of stocks in it.

B2) The standard deviation of the portfolio is decreasing with the increasing number ofstocks in the portfolio. It means that, increasing number of stocks in the portfolio leadsto declining in levels of portfolio risk.

B3) The correlation between most of the stocks are very low which, indicates thatinclusion of these stocks in the portfolio will reduce the portfolio risk.

B4) If the correlation between the stocks are low, it produces good results for theportfolio.

Marking Scheme:

A1 to A4 contains 3 marksB (ie, B1 to B3) contains 3 marks

Best of Luck

Appendix A: Tabulated t values at 2.5 % and 5% level of significance

d. f. 1 2 3 4 5 6 7 8 9 10 11 12 >400

Values(

2.5%)

6.31 2.29 2.35 2.13 2.02 1.94 1.9 1.86 1.83 1.81 1.8 1.79

Values

(5%)

12.70 4.30 3.18 2.77 2.57 2.45 2.365 2.31 2.262 2.228 2.20 2.18 1.966

Documents

Decision Science Mod I Solution for Test 2012-13 (1)