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Assumptions of Portfolio Theory

• Investors are rational. • Investors are basically risk averse. • Investors wants to maximize the returns from his/her investments for a given level of risk. • Investor portfolio includes all of his/her assets and liabilities. • The relationship between the returns of assets in the portfolio is important since the returns from these investments interact with each other.

Risk Aversion

• Portfolio Theory assumes investors are basically risk averse. • Risk aversion means an investor, given a choice between two assets with equal rates of return, will select the asset with the lower level of risk. • Does not imply everybody is risk averse. • Most investors ...view middle of the document...

• For a given level of risk, investors prefer higher returns to lower returns. Similarly, for a given level of expected return, investors prefer less risk to more risk.

Efficient Asset or Portfolio

• Under the assumptions of Markowitz Portfolio Theory, a single asset or portfolio of assets is considered to be efficient if no other asset or portfolio of assets offers higher expected return with the same (or lower) risk, or lower risk with the same (or higher) expected return.

Alternative Measures of Risk

• Variance or standard deviation of expected returns. • Range of returns. • Returns below expectations or semivariance.

Standard Deviation

• A statistical measure of the dispersion of returns around the expected value where a larger variance or standard deviation indicates greater dispersion. • The more disperse the expected returns, the greater the uncertainty of future returns.

Standard Deviation

-3

-2

-1

μ

+1 +2 +3

Approximately 50% of all observations fall in the interval μ ± (2/3) σ Approximately 68% of all observations fall in the interval μ ± σ Approximately 95% of all observations fall in the interval μ ± 2 σ Approximately 99% of all observations fall in the interval μ ± 3 σ

Range of Returns

• Assumes that a larger range of expected returns, from the lowest to the highest return, means greater uncertainty and risk regarding future expected returns.

Expected Rate of Return of A Risky Individual Asset • Working Example:

Probability 0.25 0.25 0.25 0.25 Possible Rate of Expected Return (%) Return(%) 0.08 0.0200 0.10 0.0250 0.12 0.0300 0.14 0.0350 E( Ri ) = 0.1100

Expected Rate of Return For a Portfolio of Risky Assets

• Working Example:

Weight (Wi) (% of Portfolio) 0.20 0.30 0.30 0.20 Expected Security Return E ( Ri ) % 0.10 0.11 0.12 0.13 Expected Portfolio Return [Wi x E (Ri )] 0.0200 0.0330 0.0360 0.0260 E ( Ri ) = 0.1150

Variance of the Expected Rate of Return For An Individual Risky Asset • Working Example:

Possible Rate Of Return (Ri ) 0.08 0.10 0.12 0.14 Expected Ri -E(Ri) Return E (Ri ) 0.11 -0.03 0.11 -0.01 0.11 0.01 0.11 0.03 [Ri -E(Ri)]2 0.0009 0.0001 0.0001 0.0009

Pi

0.25 0.25 0.25 0.25

[Ri -E(Ri)]2Pi Variance 0.000225 0.000025 0.000025 0.000225 0.000500

Variance (σ2) = 0.000500 Standard Deviation (σ) = √ 0.000500 = 0.02236

Variance of the Expected Rate of Return For An Individual Risky Asset • Working Example – Neptune Corp.:

Demand for Company’s Products Strong Normal Weak Probability of this Demand Occurring (2) 0.30 0.40 0.30 Rate of Return if this Demand Occurs (3) 100% 15% -70% Expected Rate of Return (2)x(3) 30% 6% -21% 15%

Variance of the Expected Rate of Return For An Individual Risky Asset • Working Example – Saturn Corp.:

Demand for Company’s Products Strong Normal Weak Probability of this Demand Occurring (2) 0.30 0.40 0.30 Rate of Return if this Demand Occurs (3) 20% 15% 10% Expected Rate of Return (2)x(3) 6% 6% 3% 15%

Probability...

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