Construction of Portfolio

8/2/2019 Construction of Portfolio

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CONSTRUCTION OF

OPTIMAL PORTFOLIO

Submitted by:-Pankaj Rathor

Nitin Agrawal

Malav Pariekh

Devendra Rajput


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Flow of presentation

Portfolio

Investment & factor affecting investment

Portfolio management theory Utility score

Optimal Risky Portfolios

Sharp ratio

Risk & Return of various Risky assets


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Portfolio

portfolio refers to any collection of financial

assets such as stocks, bonds and cash.

Portfolios may be held by individual investors

and/or managed by financial professionals,

hedge funds, banks and other financial

institutions.


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Investment

An investment is an exposure of cash that has

the objective of producing cash inflows in the

future.

In finance, investment means buying

securities or other monetary or paper

(financial) assets in the money markets or

capital markets.


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factor affecting investment

Risk

Return

Liquidity Taxation

Inflation

Term Timing


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Portfolio management theory

maximize portfolio expected return for a givenamount of portfolio risk

Harry Markowitz introduced PMT in a 1952

article and a 1959 book Portfolio theory also assumes that investors

are risk averse, meaning that; Given a choice

between two assets with equal rates of return,most investors will select the asset with thelower level of risk.


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Utility Score

Utility Score = Expected Return 0.005A2

Utility Score Shows that:-

Return for Risk taker

Return for Risk Aversion

Harry Markowitz introduced in 1960

If utility score for particular security is less

than risk free rate than money should not be

invested in that security


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Optimal Risky Portfolios

OP is the one which give maximum return for

a given level of risk or minimum risk for a

given level of return

Portfolios of Two Risky Assets

Portfolio of two risky assets and one risk-free

asset


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Sharp Ratio

The Sharpe ratio is a measure of the excess

return (or risk premium) per unit of deviation

in an investment asset

The higher the Sharpe ratio number the better

In 1966, William Forsyth Sharpe developed

what is now known as the Sharpe ratio


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Risk & Return of various assets

Gold

Nifty

Crude FIPP

T-Bill


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Year Observation Return % xi-x xi-x^2

1999 278.98

2000 279.11 0.046598 -13.7721 189.6705

2001 271.04 -2.89133 -16.71 279.2249

2002 309.73 14.27465 0.455954 0.207895

2003 363.38 17.32154 3.502847 12.26994

2004 409.72 12.75249 -1.0662 1.136784

2005 444.74 8.547301 -5.27139 27.78756

2006 603.46 35.68827 21.86958 478.2784

2007 695.39 15.23382 1.415127 2.002584

2008 871.96 25.39151 11.57282 133.9301

2009972.35 11.51314 -2.30555 5.315554

2010 1109.72 14.12763 0.308938 0.095442

Total = 152.0056 112.992

x = 13.81869

Risk=

10.62977

Gold


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Year Observation Return % xi-x xi-x^2

2000 - -31.89 -62.8227 3946.695

2001 - -5.44 -36.3727 1322.975

2002 - 19.36 -11.5727 133.928

2003 - 107.27 76.33727 5827.379

2004 - 27.15 -3.78273 14.30903

2005 - 47.61 16.67727 278.1314

2006 - 49.36 18.42727 339.5644

2007 - 54.9 23.96727 574.4302

2008 - -47.71 -78.6427 6184.679

2009 - 73.1 42.16727 1778.079

2010 - 46.55 15.61727 243.8992

Total = 340.26 2064.407

x = 30.93273

Risk = 45.43574

FIPP


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1999 992.45

2000 1654.8 66.73888 43.954 1931.954

2001 1351.4 -18.3345 -41.1194 1690.807

2002 1142.05 -15.4913 -38.2762 1465.069

2003 1063.4 -6.88674 -29.6716 880.4051

2004 1800.3 69.2966 46.51171 2163.339

2005 2103.25 16.82775 -5.95713 35.48742

2006 3074.7 46.18804 23.40316 547.7079

2007 3745.3 21.81026 -0.97462 0.949893

2008 5223.5 39.46813 16.68325 278.3309

2009 2763.65 -47.092 -69.8769 4882.777

2010 4922.3 78.10866 55.32378 3060.72

Total = 250.6337 1693.755

x = 22.78488

Risk = 41.15525

Nifty


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Year Observation in $ Return % xi-x xi-x^2

1999 16.55

2000 27.4 65.55891 47.62022 2267.685

2001 23 -16.0584 -33.9971 1155.802

2002 22.81 -0.82609 -18.7648 352.1171

2003 27.69 21.39413 3.455428 11.93998

2004 37.41 35.10293 17.16423 294.6107

2005 49.81 33.14622 15.20752 231.2687

2006 58.3 17.04477 -0.89393 0.799105

2007 64.2 10.12007 -7.81863 61.13095

2008 91.48 42.49221 24.55351 602.8751

2009 53.48 -41.5391 -59.4778 3537.6122010 70 30.89005 12.95136 167.7376

Total = 197.3257 868.3579

x = 17.9387

Risk = 29.46791

Crude


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Year Observation in $ Return % xi-x xi-x^2

1999 0 10.61952000 0 9.553 2.999873 8.999236

2001 0 8.932 2.378873 5.659035

2002 0 6.372 -0.18113 0.032807

2003 0 5.719 -0.83413 0.695768

2004 0 4.384 -2.16913 4.7051132005 0 5.619 -0.93413 0.872594

2006 0 6.769 0.215873 0.046601

2007 0 7.652 1.098873 1.207521

2008 0 7.5128 0.959673 0.920972

2009 0 4.6042 -1.94893 3.798318

2010 0 4.9674 -1.58573 2.514531

Total = 72.0844 2.94525

x = 6.553127

Risk = 1.716173

T-Bills


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UTILITY SCORE FOR SINGLE INVESTMENT

Us= E(r)-0.005*A*stdev^2s Rf = 6.55%

Risk Aversion (A) is assumed to be moderate i.e. 3.

Asset R(s) V(s) U(s) result

GOLD 13.82 112.997 12.12505 invest

FTPP30.93 2064.794 -0.04191 no

CRUDE 17.94 868.48 4.9128 no

NIFTY 22.79 1694.146 -2.62219 no


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Portfolio R(p) R(f) stdev(p)

Slope of

portfolio

(p)

GOLD & NIFTY 14.726 6.55 10.31 0.793016

GOLD & FTPP 16.164 6.55 10.48 0.917366

GOLD & CRUDE 14.726 6.55 8.69 0.940852

NIFTY & FTPP 25.966 6.55 20.34 0.954572

CRUDE & FTPP 23.475 6.55 3.79 4.465699

CRUDE & NIFTY 20.229 6.55 27.28 0.50143

Sharpe Ratio


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Conclusion

Analysing the single security investment with thehelp of Utility Score model we can say that onlyGOLD gives positive return over prevailing riskfree rates of 10 years. Thus if we want to invest in

a single security we should invest in GOLD ratherthan any other securities.

From the derived correlations of portfolio we canconclude that portfolio of NIFTY-CRUDE is most

effectively correlated. While portfolios likeCRUDE-FIPP & NIFTY-FIPP is negatively correlatedthus we should not go for these portfolios.


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Conclusion

Reward to variability of portfolio CRUDE FIPP

is highest thus we should go for these

portfolio as it is the optimum portfolio. The

slope of these portfolio derived is highest onCapital allocation line.


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THANK YOU

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Construction of Portfolio