1. Chapter 8 The Gain From Portfolio Diversification

2. Level of Risk
Determine
Optimal Portfolio
Expected Return

3. Investment Weights Affect the Portfolio’s Variance
Minimize Portfolio’s Risk
Determine the Investor’s Risk Exposure
1 Strategy of Weights Will Yield a Portfolio with No Risk

4. Weights For The 2 Asset Portfolio
WA + WB = 1
WB = 1 - WA
WA + (1 - WA) = 1 or 100%
only need to solve for one variable

5. Gains From Diversification
Lower Correlation
Smaller Portfolio Variance
Larger Gains From Diversification
For a Given Set of Weights

6. Minimize Portfolio’s Risk
Selecting Assets With Low Correlation
Balancing the Investment Weights
Degree of Correlation
Influences the portfolio’s level of risk
Lower the correlation, the larger the gain from diversification

7. How Many Stocks Are Required For Adequate Diversification?
The More Stocks, the Better
Increasing Transaction Costs
10-15 Stocks Sufficient
90% of Maximum Benefit with 12-18
Most Benefits Achieved with 10
Diminishing Benefits with Additional Stocks

8. “A Little Diversification Goes A Long Way”
As the Number of Assets Increases the Incremental Contribution to Variance Reduction Becomes Smaller and Smaller

9. Mutual Funds Diminishing Benefits of More Stocks are Still Positive
There is some gain
Low Cost of Data
Large Funds Have to Invest in Many Stocks
Avoid buying and selling affects
Regulation M
Own  5% of any company’s stock

10. MVP Minimum Variance Portfolio
Portfolio With the Smallest Variance From the Mean-Variance Frontier
Mean-Variance Frontier
Efficient frontier
Dominate portfolio
Inefficient frontier

11. What Is The Implication Of Diversification For Portfolio Management?
Not All Diversification Strategies are Desirable
Some Strategies are Inefficient
No Investor Would Select Portfolios From the Segment Below Point MVP
see next slide

12. E(R) •
Efficient Frontier
MVP
Inefficient Frontier
Standard Deviation

13. Two Assets With Different Correlations
The Higher the Correlation, the Smaller the Gain From Diversification
As Correlation Declines, Risk Reduction Increases
Implies larger risk reduction because of diversification

14. Complicated Portfolio Choices
More Than Two Assets to Choose From
Assets do not Have the Same Mean or Variance
Nonzero correlations prevail
Must Find the Mean-Variance Frontier
Identify the Efficient and Inefficient Sets

15. Unrelated Industries Significant Risk Reduction
Achieved by diversifying across different industries
Stocks From Same Industry
Highly positively correlated
Stocks From Different Industries
Negative correlation