SAPM

Analysis of risk & return of 2companies under 2 Portfolios (minimum variance portfolio)

Presented By:Raju Avhad

(01)Arpita Chakraborty

(06)Sonali Daine

(11)Digamber Jangam

(22)Nishank Gonsalves

(16)

Investment analysis

• Portfolio Management

• Portfolio Selection

• Security Analysis

– Assessing the Risk

– Assessing the Return

Portfolio management

Investment objectives & Constraints

Investment objectives & Constraints

Choice of Asset MixChoice of Asset Mix

Portfolio StrategyPortfolio Strategy

Selection of SecuritiesSelection of Securities

Portfolio EvaluationPortfolio Evaluation

Portfolio RevisionPortfolio Revision

Portfolio ExecutionPortfolio Execution

Portfolio selection

• Portfolio Theory- Harry Markowitz (1950)

• Diversification of a Risk

• Portfolio Risk

• Optimal Portfolio

Security Analysis

• Return

– Reward for undertaking investment

– Measurement of a historical return

– Components of a Return:• Periodic Return• Capital Gain/Loss

Cont…

Total Return= Dividend+ (P1- P0) P0 Where, P1= Ending Price of the

Investment P0= Beginning price

Rate of Return= Total Return * 100

Risk

• Possibility that the actual outcome of an investment will differ from its expected outcome

• Types of a Risk:-– Business Risk– Interest Rate Risk– Market Risk

Cont…

• It is associated with variability in the return

• Methods to measure variability of a return:-

– Range of Return– Variance– Standard Deviation

Measuring historical risk

• Measures of a risk are variance or standard deviation

n

• Variance= Σ (Ri – R ) / n-1

i=1 • Standard Deviation = ( Variance)

1/2

2_

Cont…

• Where, Ri = return from stock in period

( i= 1, 2, …….., n) R = arithmetic return n = number of periods

_

covariance

• Changing pattern of securities

• Positive Covariance

• Negative Covariance

• Minimum Variance Portfolio

• State Bank of India(SBI).

• Larsen & Toubro(L & T)

• Hero Honda

• Tata Consultancy Services (TCS)

Selection of Securities in 2 Portfolios

Portfolio 1 Portfolio 2

Introduction of companies

• Largest state-owned banking and financial services company in India

• Founded: 1st July 1955

• Chairman- O. P. Bhatt

• Banking Services

Cont…

• Revenue: $ 28.212 billion

• Profit : $ 2.4732 billion

• Total Assets: $ 323.04 billion

• Total Equity: $ 18.519 billion

Financial Condition of SBI

Mar ' 10 Mar ' 09 Mar ' 08 Mar ' 07 Mar ' 06

Profit before tax 13,926.10 14,180.64 10,438.90 7,625.08 6,837.36

Net cashflow-operating activity

-1,804.99 29,479.73 -856.87 -1,776.07 6,039.14

Net cash used in investing activity

-1,761.52 -1,651.93 -2,798.01 -284.56 -1,134.18

Net cash used in fin. activity

-3,359.67 5,097.38 19,371.12 9,494.11 461.98

Net inc/dec in cash and equivlnt

-6,926.18 32,925.18 15,497.65 7,433.49 5,366.94

Cash and equivalnt begin of year

1,03,110.02 71,478.62 51,968.69 44,535.20 39,322.10

Cash and equivalnt end of year

96,183.84 1,04,403.80 67,466.34 51,968.69 44,689.04

Cash flow

Dividend HistoryDividend History

Quarterly Trends Annual Trends

Graphs to Study

Stock Prices at BSE

Larsen & toubro

• Multinational Conglomerate Company

• Founded : Mumbai (1938)

• Engineering & IT Services

• Products: Power Generation, Cement Plants, Ships

Cont…


• Operating Income: $ 1.59 billion

• Net Income: $ 1.18 billion

Financial Condition of L&T

Cash flow





5,482.75 1,478.57 1,945.24 2,130.45 1,369.25


-6,071.73 -3,308.53 -5,241.89 -1,588.17 -1,326.30

Netcash used in fin. activity

1,245.56 1,640.79 3,166.68 -31.05 -287.77


656.58 -189.17 -129.97 511.23 -244.82


775.29 964.46 1,094.43 583.20 828.02


1,431.87 775.29 964.46 1,094.43 583.20

Graphs to Study

Stock Prices at BSE

Hero Honda

• Joint venture between hero group of India & honda of Japan

• Automotive Industry

• Founded: 19th January 1984

• Chairman: Brijmohan Lal Munjal

Cont…

• Products: Motorcycles, Scooters


• Second largest two-wheeler manufacturer in the world

Financial Condition of Hero Honda


Graphs to Study

Stock Prices at BSE

Tata consultancy services

• Largest provider of Information Technology & business process outsourcing services in India

• Industry: IT Services

• Founded : 1968

• Chairman: Ratan Tata

http://upload.wikimedia.org/wikipedia/en/5/59/TCS_Logo.svg

Cont…

• Services: Outsourcing, Software Products


• Operating Income: $ 1.8 billion

• Profit: $ 1.58 billion

• Total Assets: $ 6.112 billion

Financial Condition of TCS

Cash flow





6,264.74 4,874.12 3,827.91 3,551.26 2,344.42


-4,556.64 -3,162.22 -2,404.90 -2,076.42 -1,464.97

Netcash used in fin. activity

-1,969.65 -1,588.25 -1,424.77 -1,075.35 -882.30


-261.55 123.65 -29.62 385.97 -5.10


554.83 417.00 557.14 171.17 176.27


293.28 540.65 527.52 557.14 171.17

Quaterly Trends Annual Trends

Graphs to Study

Stock Prices at BSE

Table For Calculation of Return

Year Closing Date

Dividend Rate of Return(%)

Date Closing Date

Dividend Rate of Return (%)

Aug-2005 917 0 - Aug-2005 1332.95 17.50 -

Aug-2006 930 14 2.94 Aug-2006 2401.05 22 81.78

Aug-2007 1599.50 14 73.77 Aug-2007 2582.75 11 8.03

Aug-2008 1403.60 21.50 -10.90 Aug-2008 2589.85 15 0.86

Aug-2009 1743.05 29 26.25 Aug-2009 1567.60 10.50 -39.07

Aug-2010 2764.85 20 59.77 Aug-2010 1812.45 12.50 16.42

State Bank Of India Larsen and Toubro

Risk, Variance and Standard Deviation

Year(1)

Return(Ri)(2)

Deviation(Ri-Ravg)(3)

Square of Deviation(4)

Return(Rj)(5)

Deviation(Ri-Ravg)(6)

Square of Deviation(7)

(Ri-Riavg)*(Rj-Rjavg)(3)*(6)

2006 2.94 -27.37 749.12 81.78 68.17 4647.15 -1865.81

2007 73.49 43.18 1864.51 8.03 -5.58 31.14 -240.94

2008 -10.90 -41.21 1698.26 0.86 -12.75 162.56 525.43

2009 26.25 -4.06 16.49 -39.07 -52.68 2775.18 213.88

2010 59.77 29.46 867.89 16.42 2.81 7.8961 82.78

State Bank Of India Larsen and Toubro

For SBI

• Expected Return- Ri = 30.31

= 5196.25/4 =1299.07

= 36.04

_

Time Series of Yearly Rates of Return For SBI

For L&T


= 7623.92/4 = 1905.98

= 43.65

_

Time Series of Yearly Rates of Return For L&T

Interpretation

• Standard deviation of L & T is more than SBI but return is less

• Risk factor is more in case of L & T

– Risk Lover- L & T– Risk Averse- SBI

Covariance and Correlation

• Covariance between SBI & L&T =• Σ (Ri – R ) (Rj – R ) /5

=-1284.66/5= -256.93

»Correlation = Covariance/i*j

= -256.93/ (36.04*43.66) = -0.16

_ _

InterpretationsParticulars SBI Securities L&T Securities

Expected Returns 30.31 13.61

Standard Deviation(Risk) 36.04 43.66

Correlation -0.16

Covariance -256.93

• The Return of SBI shares are more than that of L&T.

• The Risk associated with SBI is lesser than that of L&T.

• The negative correlation between 2 securities indicates

that the returns for the two stocks does not move

together in a linear manner.

Time Patterns of Returns for 2 assets with Negative Correlation

Table For Calculation of Return

Year Closing Date

Dividend Rate of Return(%)

Date Closing Date

Dividend Rate of Return (%)

Aug-2005 646.70 20 - Aug-2005 1405.85 8 -

Aug-2006 720.30 20 14.47 Aug-2006 996.05 3 -28.58

Aug-2007 648.60 17 -7.59 Aug-2007 1065 3 7.22

Aug-2008 825.05 17 29.53 Aug-2008 812.45 3 -23.43

Aug-2009 1511.35 19 85.49 Aug-2009 527 2 -34.89

Aug-2010 1791.80 80 23.85 Aug-2010 843.85 2 60.50

Hero Honda Tata Consultancy Services

Risk, Variance and Standard Deviation

Year Return(Ri)

Deviation(Ri-Ravg)

Square of Deviation

Return(Rj)

Deviation(Ri-Ravg)

Square of Deviation

(Ri-Riavg)*(Rj-Rjavg)

2006 14.47 -14.74 217.26 -28.58 -32.43 1051.06 477.87

2007 -7.59 -36.8 1354.24 7.22 11.06 122.32 -407.01

2008 29.83 0.62 0.3844 -23.43 -19.59 383.77 -12.15

2009 85.49 56.28 3167.44 -34.89 -31.05 964.10 -1747.49

2010 23.85 -5.36 28.73 60.50 64.34 4139.64 -344.89

Hero Honda Tata Consultancy Services

For Hero Honda


= 4768.05/4 =1192.01

= 34.53

_

Time Series of Yearly Rates of Return For Hero Honda

For TCS

• Expected Return- Ri = -3.84

= 6660.89/4 = 1665.22

= 40.81

_

Time Series of Yearly Rates of Return For TCS

Covariance and Correlation

• Covariance between Hero Honda & TCS =• Σ (Ri – R ) (Rj – R ) /5

= -2033.64/5= -406.74

»Correlation = Covariance/i*j

= -406.74 / 34.53*40.81 = -0.29

_ _

InterpretationsParticulars Hero Honda Securities TCS Securities

Expected Returns 29.21 -3.84

Standard Deviation(Risk) 34.53 40.81

Correlation -0.29

Covariance -406.73

• The Return of Hero Honda shares are more than that of TCS.

• The Risk associated with Hero Honda is lesser than that of

TCS.

• The negative correlation between 2 securities indicates

that the returns for the two stocks does not move together in a

linear manner.

Time Patterns of Returns for 2 Assets with Negative Correlation

Minimum Variance Portfolio• Weights of the Individual Assets in the Portfolio:-• W = - Cov + - 2Cov

= (43.66) – (-256.93) =0.58 (36.04)+(43.66)-2*(-256.93)

• W = - Cov + - 2Cov

= (36.04) – (-256.93) =0.42 (36.04)+(43.66)-2*(-256.93)

SBI SL

SLS L

L

SL

SLL

S

S

2

2 2

2

22

2

2 2

2

2 2L&T

Return and Risk of Portfolio

• Return On Portfolio E(R ) = W * E(R ) + W * E(R )

= 0.42 * 13.61 + 0.58 * 30.31 = 23.296 = 23.30

• Risk of Portfolio = ( * W + * W + 2* * * Corr * W * W )

= [(36.04) * (0.58) + (43.66) * (0.42) +2*36.04*43.66*(-0.16)*0.58*0.42]

= (650.538) = 25.51

p S S L L

p S S S SL L L LSL2222 1/2

1/2

1/2

2 2 2 2

Minimum Variance Portfolio• Weights of the Individual Assets in the Portfolio:-• W = - Cov + - 2Cov

= (40.81) – (-406.73) =0.56 (34.53)+(40.81)-2*(-406.73)

• W = - Cov + - 2Cov

= (34.53) – (- 406.73) =0.44 (34.53)+(40.81)-2*(-406.73)

Hero Honda

HT

HTH T

T

HT

HTT

H

H

2

2 2

2

22

2

2 2

2

2 2TCS

Return and Risk of Portfolio

• Return On Portfolio E(R ) = W * E(R ) + W * E(R )

= 0.56 * 29.21 + 0.44 * (-3.84) = 14.67

• Risk of Portfolio = ( * W + * W + 2* * * Corr * W * W )

= [(34.53) * (0.56) + (40.81) * (0.44) +2*34.53*40.81*(-0.29)*0.56*0.44]

= (494.96) = 22.25

p H H T T

p H H H HT T T THT2222 1/2

1/2

2 2 2 2

1/2

Conclusion

• The return on Portfolio 1 is more than that of Portfolio 2.

• The risk associated with Portfolio 1 is more than that of Portfolio 2.

SAPM

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