Portfolio Selection (chapter 8)

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

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

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

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)

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

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

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

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

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.

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

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

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

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

Portfolio Risk and Diversification sp % 35 20 Total risk Diversifiable (nonsystematic) risk Nondiversifiable (systematic) risk 10 20 30 40 ...... 100+ Number of securities in portfolio

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;