2. ®1999 South-Western College Publishing 1 Chapter 7 Portfolio Mean And Variance

3. ®1999 South-Western College Publishing 2 Portfolio of Assets Weight Asset 1 Weight Asset 2 Weight Asset 3 Weights Sum to 100%

4. ®1999 South-Western College Publishing 3 Measuring Portfolio Risk VarianceVariance Standard DeviationStandard Deviation Degree of DependencyDegree of Dependency –Positive –Negative Lower riskLower risk Lower risk premiumLower risk premium

5. ®1999 South-Western College Publishing 4 What Is The Risk Premium? Required to Compensate Investors for RiskRequired to Compensate Investors for Risk Higher the Variance or Standard Deviation, the Higher the Required Risk PremiumHigher the Variance or Standard Deviation, the Higher the Required Risk Premium Degree of Dependency Affects the Risk PremiumDegree 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

6. ®1999 South-Western College Publishing 5 What Does A Risk-Averse Investor Require? A Risk PremiumA 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

7. ®1999 South-Western College Publishing 6 Summary One AssetOne Asset –Variance is measurer of risk –Higher the variance, the higher the required risk premium More Than One AssetMore Than One Asset –Risk is a function of both The asset’s varianceThe asset’s variance The degree of dependencyThe degree of dependency –Portfolio’s variance (Key factor) Larger the varianceLarger the variance Higher the risk premiumHigher the risk premium Larger the risk premium on each assetLarger the risk premium on each asset

8. ®1999 South-Western College Publishing 7 Expected Rate Of Return On The Portfolio E(R) Calculate All Possible Return on the Portfolio, and Then Calculate its E(R)Calculate All Possible Return on the Portfolio, and Then Calculate its E(R) Use Equation 7.2Use Equation 7.2 W 1 E(R 1 ) + W 2 E(R 2 ) = E(R p ) Both Methods Provide the Same ResultsBoth Methods Provide the Same Results

9. ®1999 South-Western College Publishing 8 Covariance Expected value of the Product of Deviations From the Mean

10. ®1999 South-Western College Publishing 9 Covariance Measures the Degree of Dependency of 2 AssetsMeasures the Degree of Dependency of 2 Assets –Positive Rates of return moves togetherRates of return moves together –Zero Rates of return have independent movementsRates of return have independent movements –Negative Rates of return move in opposite directionsRates of return move in opposite directions

11. ®1999 South-Western College Publishing 10 Correlation Coefficient Correlation Coefficient of 2 StocksCorrelation Coefficient of 2 Stocks Cov(R A, R B ) Cov(R A, R B )  A,B =  A  B  A  B Strength of DependencyStrength of Dependency –+1 perfectly positive – 0 no correlation –- 1 perfectly negative Correlations are Directly ComparableCorrelations are Directly Comparable no units or $ no units or $

12. ®1999 South-Western College Publishing 11 Portfolio Variance Direct Method (easy to calculate)Direct Method (easy to calculate) –Calculate rate of return –Calculate variance Indirect Method (demonstrates relationship)Indirect Method (demonstrates relationship) –Equation based on variance & covariance –Sheds light on factors affecting risk reduction

13. ®1999 South-Western College Publishing 12 Low Correlation Reduce Portfolio FluctuationReduce Portfolio Fluctuation Achieved by DiversificationAchieved by Diversification Attractive to Risk-Averse InvestorsAttractive to Risk-Averse Investors

14. ®1999 South-Western College Publishing 13 Set 1 Bonus Questions for Ch. 1