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Chapter 7
Portfolio Mean And Variance
®1999 South-Western College Publishing
1
Weight Asset 1
Portfolio
of
Assets
Weight Asset 2
Weight Asset 3
Weights Sum to 100%
®1999 South-Western College Publishing
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Measuring Portfolio Risk
• Variance
• Standard Deviation
• Degree of Dependency
– Positive
– Negative
• Lower risk
• Lower risk premium
®1999 South-Western College Publishing
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What Is The Risk Premium?
• Required to Compensate Investors for Risk
• Higher the Variance or Standard Deviation, the
Higher the Required Risk Premium
• Degree of Dependency Affects the Risk Premium
– The more negative the degree of dependency
– The lower the risk of the portfolio
– The lower the required risk premium
®1999 South-Western College Publishing
4
What Does A Risk-Averse
Investor Require?
• A Risk Premium
– Requires a risk premium that decreases as
the degree of dependency decreases
– The required risk premium is a function
of the asset’s variance and its dependency
with other assets
®1999 South-Western College Publishing
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Summary
• One Asset
– Variance is measurer of risk
– Higher the variance, the higher the required risk
premium
• More Than One Asset
– Risk is a function of both
• The asset’s variance
• The degree of dependency
– Portfolio’s variance (Key factor)
• Larger the variance
• Higher the risk premium
• Larger the risk premium on each asset
®1999 South-Western College Publishing
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Expected Rate Of Return On
The Portfolio E(R)
• Calculate All Possible Return on the
Portfolio, and Then Calculate its E(R)
• Use Equation 7.2
W1 • E(R1) + W2 • E(R2) = E(Rp)
• Both Methods Provide the Same Results
®1999 South-Western College Publishing
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Covariance
Expected value of the Product of
Deviations From the Mean
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Covariance
• Measures the Degree of Dependency of 2 Assets
– Positive
• Rates of return moves together
– Zero
• Rates of return have independent movements
– Negative
• Rates of return move in opposite directions
®1999 South-Western College Publishing
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Correlation Coefficient
• Correlation Coefficient of 2 Stocks
Cov(RA, RB)
A,B =
A B
• Strength of Dependency
– +1 perfectly positive
– 0 no correlation
– - 1 perfectly negative
• Correlations are Directly Comparable
no units or $
®1999 South-Western College Publishing
10
Portfolio Variance
• Direct Method (easy to calculate)
– Calculate rate of return
– Calculate variance
• Indirect Method (demonstrates relationship)
– Equation based on variance & covariance
– Sheds light on factors affecting risk
reduction
®1999 South-Western College Publishing
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Low Correlation
• Reduce Portfolio Fluctuation
• Achieved by Diversification
• Attractive to Risk-Averse Investors
®1999 South-Western College Publishing
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Set 1 Bonus Questions for Ch. 1
®1999 South-Western College Publishing
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