PORTFOLIO ANALYSIS:

Asmik Akhverdyan

Ruzanna Ayvazyan

Davit Matevosyan Mariam Petrosyan

Marina Sedrakyan 1

Dow jones IT and Banking componentsDow jones IT and Banking components

Prof. Grigoryan

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Risk represents uncertainty of a return and the potential for financial loss.

Measures of risk:

•Range

•Mean absolute deviation

•Variance (standard deviation)

•Coefficient of variation

Return on an investment is the financial outcome for the investor.

An investment’s distribution of returns follows a normal distribution

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Assets with higher return are always riskier

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• Diversifiable Risk versus Market Risk /Systematic and Unsystematic Risks/

• Market Risk: Beta Risk• Other Risks

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Beginning with one stock and adding randomly selected stocks to portfolio

• Diversifiable risk decreases as stocks added, because they would not be perfectly correlated with the existing portfolio.

• Expected return of the portfolio would remain relatively constant.

• Eventually the diversification benefits of adding more stocks dissipates (after about 10 stocks)

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Stand-alone risk = Market risk + Diversifiable risk

• Market risk – portion of a stock’s stand-alone risk that cannot be eliminated through diversification. Measured by beta.

• Diversifiable risk – portion of a stock’s stand-alone risk that can be eliminated through proper diversification.

# Stocks in Portfolio10 20 30 40 2,000+

Diversifiable Risk

Market Risk

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Stand-Alone Risk, p

p (%)35

Diversification effects of a stock portfolio

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Other Risks

• Different currency denominations • Political risk• Economic and legal ramifications• Role of governments• Language and cultural differences

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• Why do investors prefer portfolios?

• What is a feasible portfolio?

• What is an optimal portfolio?

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• Second oldest stock index

• Price-weighted average

• Includes 30 components

• The components are selected by the WSJ

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Regression Statistics for IT

Multiple R 0,79184

R Square 0,627011

Adjusted R Square 0,623991

Standard Error 0,004165

Observations 251

Regression Statistics for Banking

Multiple R 0,392918115

R Square 0,154384645

Adjusted R Square 0,147565166

Standard Error 0,00616765

Observations 251

Regression Statistics for HP

Multiple R 0,288077233

R Square 0,082988492

Adjusted R Square 0,075563298

Standard Error 0,006530247

Observations 251

DJ=0,0027-0,003*i-0,001WRDJ=-0,566+0,129*i +0,665*WR

DJ=-0,3287+0,085*i+0,161*HR

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  Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 0,0027154 0,0019136 1,419025013 0,1571473 -0,0010535 0,0064845

i -0,0031343 0,0004778 -6,55884033 3,13175E-10 -0,004076 -0,002193

WR -0,0010849 0,0012583 0,862237592 0,03893898 -0,0035632 0,0139335

  Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept -0,5658546 0,130166769 -4,3471511 2,02E-05 -0,822233 -0,30948

i 0,1290238 0,08489222 1,51985399 0,129827 -0,038182 0,296229

WR 0,6648816 0,032822503 2,25688175 2,03E-54 0,600234 0,729529

  Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept -0,3287197 0,203257181 -1,61726 0,107099 -0,7290581 0,071618637

i 0,0847991 0,018788707 4,513298 9,88E-06 0,0047792 0,0121805

HR 0,161222659 0,133158229 1,21076 0,022714 -0,0101048 0,0423497

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Root Mean Squared Error 0.4

Theil Inequality Coefficient 0.32

2m

imi

- co-variation of stock and market

- coefficient of dispersion of market return

> 1, stock is more risky < 1, less sensitive to market changes

= 1, the same risk level as the market

im

2m

Measure of the risk contribution of an individual

security to a well-diversified portfolio.

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Markowitz’s Portfolio theory

Sharp, Treynor…

R=Rf + β*(RM-Rf)RM= Rf + Risk premium

R is the expected return on security,

Rf is the risk free rate

β is beta of the security25

WR=0.009*RP

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R-Squared 62.3%

Coefficient β 0.009

P-value (Sig. t) 0.0000 < 0.05

P-value

Weighted banking=0.004*RP

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R-Squared 14.9%

Coefficient β 0.004

P-value (Sig. t) 0.0000 < 0.05

P-value

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29P-values for all the regressions were < 0.05 which means H0 is rejected and Ha is accepted.

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Sharp Ratio Treynor Ratio

IT Banking

Sharp 0.58 0.21

Treynor 51 43

𝑇𝑟𝑒𝑦𝑛𝑜𝑟 𝑖𝑛𝑑𝑒𝑥= (𝑅𝑃 − 𝑅)𝛽 𝑆ℎ𝑎𝑟𝑝 𝑖𝑛𝑑𝑒𝑥= (𝑅𝑃− 𝑅)𝑠𝑡.𝑑𝑒𝑣

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