1. Portfolio Selection (chapter 8)

2. Building a Portfolio Diversification is key to risk management
Asset allocation most important single decision
Using Markowitz Principles
Step 1: Identify optimal risk-return combinations using the Markowitz analysis
Inputs: Expected returns, variances, covariances
Step 2: Choose the final portfolio based on your preferences for return relative to risk

3. Example: NOT on the EXAM
100% stocks
100% bonds

4. The Efficient Frontier
Efficient Frontier – represents the set of all mean/variance efficient (optimal) portfolios
Optimal portfolio has maximum return for a given level of risk or minimum risk for a given level of return
Portfolios on the efficient frontier dominate all other portfolios
No portfolio on the efficient frontier dominates another portfolio on the frontier

5. Efficient Portfolios
Efficient frontier or Efficient set (curved line from A to B)
Global minimum variance portfolio (represented by point A)
Portfolios on AB dominate those on AC x B A C y
Risk = 
E(R)

6. Selecting an Optimal Portfolio of Risky Assets
Portfolio weights are the output from Markowitz analysis
Assume investors are risk averse
Indifference curves (ICs) help select individual’s optimal portfolio
IC, description of preferences for risk and return
IC reflects portfolio combinations that are equally desirable
ICs match investor preferences with portfolio possibilities

7. The Optimal Portfolio • •
Investor 2 indifference/utility curves
Investor 1 indifference curves
Efficient Frontier • •
Goal is to achieve highest (most NW) attainable curve)

8. Selecting an Optimal Portfolio of Risky Assets
Markowitz portfolio selection model
Assumes investors use only risk and return to decide
Generates a set of equally “good” portfolios
Does not address the issues of borrowed money or risk-free assets
Cumbersome to apply

9. Selecting Optimal Asset Classes
Another way to use Markowitz model is with asset classes
Allocation of portfolio to asset types
Asset class rather than individual security is most important for investors
Can be used when investing internationally
Different asset classes offer various returns and levels of risk
Correlation coefficients may be quite low

10. Asset Allocation Includes two dimensions Asset classes include:
Diversifying between asset classes
Diversifying within asset classes
Asset classes include:
Equities – foreign and domestic
Bonds
Treasury Inflation-Protected Securities (TIPS)
Alternative assets – real estate, commodities, private equity, hedge funds, etc.

11. Asset Allocation Correlation among asset classes must be considered
Correlations change over time
For investors, allocation depends on
Time horizon
Risk tolerance
Diversified asset allocation does not guarantee against loss
8-11

12. Asset Allocation Index Mutual Funds and ETFs
Cover various asset classes: domestic and foreign stocks (all investment styles), alternative assets (e.g. real estate, commodities), bonds of all types
Life Cycle Analysis
Varies asset allocation based on investor age
Life-cycle funds (target-date funds) vary allocation as investor ages
No one “correct” approach to allocation

13. Systematic & Unsystematic Risk
Total = Systematic Unsystematic
Risk Risk Risk
p2 = Systematic Unsystematic
Variance Variance
The variance (risk) of a portfolio, or a single security, consists of both systematic risk and unsystematic risk

14. Systematic & Unsystematic Risk
Systematic risk is not diversifiable
Systematic risk - risk of an overall movement in the market
nondiversifiable  systematic  market
Unsystematic risk is diversifiable
Unsystematic risk - risk of an event that is unique to the asset or a small group of assets
diversifiable  unsystematic  unique

15. Portfolio Risk and Diversification
sp % 35 20
Total risk
Diversifiable (nonsystematic) risk
Nondiversifiable (systematic) risk
Number of securities in portfolio

16. Learning objectives
Know the concept of optimal risk-return combinations
Know the concepts of efficient frontier, global minimum variance, efficient set, indifference curves, and selecting optimal portfolio
International diversification
Important conclusions about Markowitz model
Asset Allocation decision and major asset classes
Asset allocation using stocks and bonds
Systematic and nonsystematic risk
End of chapter 8.1 to 8.7;