Risk/return ratio of an investment portfolio

Made by Maria Lavrova

13 June 2013

The aim of the ThesisThe aim of the Thesis is to consider the technique of the investment portfolio formation

and the creation of optimal portfolios for the different kind of investors depending on

their risk tolerance as well as their requirements to the received returns.

The set goals are:

•To investigate the process of portfolio creation by inquiring the basic theoretical

background

•To explore the techniques of portfolio crafting and choose methods for practical use

•To define the investment policy and structure of the portfolio

•To assess the risk and return of the created portfolios using different kind of techniques

•To suggest which kind of investor the created portfolios are more suitable for.

Methodology

• Modern Portfolio Theory of Harry Markowitz

• Capital Assets Pricing Model of William Sharpe

• Value at Risk Theory of J.P. Morgan

• Backtesting

• Stresstesting

• Wealth stages of Charles Jones

• Royal Bank`s formula for investing

Place for potential investments- India

• Over the longer-term India is likely to be one of the fastest growing large economies with at least 7% annual GDP growth

• India’s working-age population will increase by 240 million over the next 20 years, which will significantly increase consumption and lead to India’s consumer markets boom.

• Government investment in the country’s infrastructure is soaring.

• India has heavy investments in education, health and agriculture to give a new deal to rural India.

• Corporate earnings in India are growing at 35% annual rate, especially among the manufacturing biggies and telecommunication companies.

• The Indian stock-market has generated investment returns of over 15% per annum for the last 10 years and experts predict this rate to increase in the next decade.

Results- Expected returns and risks of the stocks

E(R)

ExpReturn StandDevE(R)/

Return/Risk

OIL 0,42% 15,51% 2,7%

INDIAN EXT 2,87% 27,42% 10,4%

G&C 3,01% 18,58% 16,2%

CEMENTS 1,99% 28,91% 6,9%

ABBOTT 2,17% 8,28% 26,2%

BINANI 0,95% 22,36% 4,3%

INFOSYS 0,78% 9,19% 8,5%

SATYAM -1,41% 16,63% -8,5%

MPHASIS 1,29% 13,66% 9,5%

TATA 0,67% 11,10% 6,1%

MEAN 1,27% 17,2%  

Optimal Portfolios

Objective MaxE(R) Min σ MaxE(R) Min σ

Constraining variable at σ≤ E(R)≥ at σ≤ E(R)≥Value of constrain 8,28% 3,01% 17,16% 1,27%

WeightsOIL 0,00% 0,00% 0,00% 0,00%INDIAN EXT 12,88% 0,00% 11,01% 5,75%G&C 26,90% 100,00% 88,99% 4,67%

CEMENTS 0,00% 0,00% 0,00% 2,67%ABBOTT 60,22% 0,00% 0,00% 50,07%BINANI 0,00% 0,00% 0,00% 0,00%INFOSYS 0,00% 0,00% 0,00% 28,70%SATYAM 0,00% 0,00% 0,00% 0,74%

MPHASIS 0,00% 0,00% 0,00% 0,00%TATA 0,00% 0,00% 0,00% 7,39%ΣW= 100% 100% 100% 100%μ(p)= 2,49% 3,01% 2,99% 1,71%σ(p)= 8,28% 18,58% 17,16% 6,55%μ/σ(p)= 0,3 0,16 0,17 0,26D

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Results of CAPM – return on equity

Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4r(equity) 0.15% 0.25% 0.18% 0.27%

Risk assessment- VaR of the portfolios

Portfolio

VAR

(95%)

VAR

(99%)

1 11,36% 17,31%

2 28,04% 41,40%

3 25,69% 38,03%

4 9,23% 13,94%

PortfolioVAR

(95%)

VAR

(99%)

1 8,39% 14,74%

2 23,81% 34,49%

3 21,18% 30,74%

4 8,87% 13,81%

Variance-Covariance method Historical Simulation method

Risk assessment- VaR of the portfolios

Portfolio VAR(95%) VAR(99%)

1 1,61% 2,26%

2 4,01% 5,30%

3 3,68% 4,87%

4 1,34% 1,80%

Monte-Carlo Simulation

Risk assessment- VaR of the portfolios (Backtesting)

VARCOV

JAN 08 - DEC 12 DEC 04 - NOV 09

Portfolio VAR(95%) VAR(99%) VAR(95%) VAR(99%)

1 11,36% 17,31% 13,41% 19,79%

2 28,04% 41,40% 29,53% 43,44%

3 25,69% 38,03% 26,11% 38,53%

4 9,23% 13,94% 12,25% 17,90%

Variance-covariance method

Results- the least risky portfolio

• Relying on the results, the best risk/return opportunities are presented by the first and the fourth portfolios. First portfolio offers higher standard deviation, at the same time it offers higher average return. Fourth portfolio is least risky with lower return. Markowitz risk/return tradeoff is confirmed there.

• Those portfolios suit more to risk-averse investors or for those individuals who, according to Charles Jones (2010), view their wealth in spending phase.

• According to Royal Bank`s formula of investing, such portfolios are more preferable for those who are not far from the retirement and do not like to take much risk.

Results- the most risky portfolio

• The most risky is the second portfolio. For investors it is not recommended to construct such portfolios like the second portfolio, because the investor`s risk tolerance level should be very high there.

• The third portfolio may be suitable for the young investors who are in the accumulation stage and can afford to take large risks.

• Investors should remember: the higher the return, the higher the risk.

• An investment may result in accumulation of investor`s wealth or dissipation of his resources.

Thank you for your attention!