B.  Efficient Diversification

• Harry Markowitz - won Nobel Prize in Economics

1.  Diversification and risk

• Market risk - risk attributable to market wide risk sources (economic conditions)

- Also known as systematic risk and nondiversifiable  risk

- Can't eliminate this risk

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• Firm-specific risk - risk unique to the firm (R&D success, management, etc.)

- Also known as unique risk, nonsystematic risk, and diversifiable risk

- Diversification reduces this risk

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2.  Asset allocation with two risky assets

a.  Covariance and correlation

• Measures the association between two variables

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b.  Three rules of two-risky-assets portfolios

(1)  Rate of return on a portfolio is the weighted average of returns on the component securities, with the investment proportions as weight

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(2)   Expected rate of return on a portfolio is the weighted average of the expected returns on the component securities, with the investment proportions as weight

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(3)  Variance of the rate of return:

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c.  Risk-return trade-off

• Investment opportunity set - set of available risk-return combinations

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d.  Mean-variance criterion

• One portfolio preferred over another if it has a higher mean return and lower variance or standard deviation

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3.  Optimal risky portfolio with a risk-free asset

• Best combination of risky assets and safe assets to form a complete portfolio

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4.  Efficient diversification with many risky assets

a.  Efficient frontier of risky assets

• Efficient frontier - the set of portfolios that maximize expected returns at each level of portfolio risk

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b.  Choosing the optimal risky porfolio

• Choose capital allocation line with the highest Sharpe ratio

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c.  Preferred complete portfolio

• Investor chooses the appropriate mix of the optimal risky portfolio and the risk-free asset

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• Separation property - portfolio choice can be separated into two independent tasks:

(1) Determination of the optimal risky porfolio

(2)  Personal choice of the best mix of the risky portfolio and the risk-free asset

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5.  Single-index stock market

• Index model - relates stock returns to returns on both a broad market index and firm-specific factors

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a.  Diversification in a single-index security market

• Diversification can eliminate firm-specific risk

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b.  Security analysis with the index model

• Active portfolio - optimal combination of analyzed stocks

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6.  Risk of long-term investments

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