1. WHY DIVERSIFY? CHAPTER FOURTEEN
© 2001 South-Western College Publishing 1

2. Use More Than One Basket for Your Eggs
Don’t put all your eggs in one basket.
Failure to diversify may violate the terms of
fiduciary trust.
Risk aversion seems to be an instinctive trait
in human beings. 4

3. Preliminary Steps in Forming a Portfolio
Identify a collection of eligible investments
known as the security universe.
Compute statistics for the chosen securities.
e.g. mean of return
variance / standard deviation of return
matrix of correlation coefficients 5

4. Preliminary Steps in Forming a Portfolio
Interpret the statistics.
1. Do the values seem reasonable?
2. Is any unusual price behavior expected to
recur?
3. Are any of the results unsustainable?
4. Low correlations: Fact or fantasy? 6

5. The Role of Uncorrelated Securities
The expected return of a portfolio is a weighted average of the component expected returns.
where xi = the proportion invested in security i

6. The Role of Uncorrelated Securities
The total risk of a portfolio comes from the variance of the components and from the relationships among the components.
two-security
portfolio risk
= riskA + riskB + interactive risk 6

7. The Role of Uncorrelated Securities
The point of diversification is to achieve a given level of expected return while bearing the least possible risk.
expected return
risk
better
performance
A portfolio dominates all others
if no other equally risky portfolio has a higher expected return, or if no portfolio with the same expected return has less risk.

8. The Efficient Frontier : Naive Diversification
Naive diversification is the random selection of portfolio components without conducting any serious security analysis.
As portfolio size increases,
total portfolio risk, on average, declines. After a certain point, however, the marginal reduction in risk from the addition of another security is modest.
total risk
nondiversifiable
risk
number of securities

9. The Efficient Frontier : Naive Diversification
The remaining risk, when no further diversification occurs, is pure market risk.
Market risk is also called systematic risk and is measured by beta.
A security with average market risk has a beta equal to 1.0. Riskier securities have a beta greater than one, and vice versa.

10. The Efficient Frontier : Optimum Diversification of Risky Assets
The efficient frontier contains portfolios that
are not dominated.
expected return
risk
(standard deviation of returns)
impossible
portfolios
dominated
efficient frontier

11. The Efficient Frontier : The Minimum Variance Portfolio
The right extreme of the efficient frontier is a single security; the left extreme is the minimum variance portfolio.
expected return
risk (standard deviation of returns)
single security
with the highest
minimum variance
portfolio

12. The Efficient Frontier : The Effect of a Risk-Free Rate
When a risk-free investment complements the set of risky securities, the shape of the efficient frontier changes markedly.
expected return
risk (standard deviation of returns)
dominated
portfolios
impossible M Rf C
efficient frontier:
Rf to M to C

13. The Efficient Frontier : The Effect of a Risk-Free Rate
In capital market theory, point M is called the market portfolio.
The straight portion of the line is tangent to the risky securities efficient frontier at point M and is called the capital market line.
Since buying a Treasury bill amounts to lending money to the U.S. Treasury, a portfolio partially invested in the risk-free rate is often called a lending portfolio.

14. The Efficient Frontier with Borrowing
Buying on margin involves financial leverage, thereby magnifying the risk and expected return characteristics of the portfolio. Such a portfolio is called a borrowing portfolio.
expected return
risk (standard deviation of returns)
dominated
portfolios
impossible M Rf C
efficient frontier:
the ray from Rf through M
lending
borrowing

15. The Efficient Frontier : Different Borrowing and Lending Rates
Most of us cannot borrow and lend at the same interest rate.
expected return
dominated
portfolios
impossible M RL N
efficient frontier : RL to M, the curve to N, then the ray from N
risk (standard deviation of returns) RB

16. The Efficient Frontier : The Single Index Model
A pair-wise comparison of the thousands of stocks in existence would be an unwieldy task. To get around this problem, the single index model compares all securities to a benchmark measure.
The single index model relates security returns to their betas, thereby measuring how each security varies with the overall market.

17. The Efficient Frontier : The Single Index Model
Beta is the statistic relating an individual security’s returns to those of the market index. 17

18. The Efficient Frontier : The Single Index Model
The relationship between beta and expected return is the essence of the capital asset pricing model (CAPM), which states that a security’s expected return is a linear function of its beta. 18

19. The Efficient Frontier : The Single Index Model
beta
E(Ri) - Rf
security market line + -

20. Use More Than One Basket for Your Eggs
Review
Use More Than One Basket for Your Eggs
The Axiom
The Concept of Risk Aversion Revisited
Preliminary Steps in Forming a Portfolio
The Reduced Security Universe
Security Statistics
Interpreting the Statistics
The Role of Uncorrelated Securities
The Variance of a Linear Combination
Diversification and Utility
The Concept of Dominance 18

21. The Efficient Frontier
Review
The Efficient Frontier
Optimum Diversification of Risky Assets
The Minimum Variance Portfolio
The Effect of a Risk-free Rate
The Efficient Frontier with Borrowing
Different Borrowing and Lending Rates
Naive Diversification
The Single Index Model 19