Portfolio Selection Chapter 8 Charles P. Jones, Investments: Analysis and Management, Twelfth Edition, John Wiley & Sons

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

Portfolio Theory Optimal diversification takes into account all available information Assumptions in portfolio theory A single investment period (one year) Liquid position (no transaction costs) Preferences based only on a portfolio’s expected return and risk

An Efficient Portfolio Smallest portfolio risk for a given level of expected return Or largest expected return for a given level of portfolio risk From the set of all possible portfolios Only locate and analyze the subset known as the efficient set

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 only variable that can change in Markowitz analysis Assume investors are risk averse Indifference curves help select from efficient set Description of preferences for risk and return Portfolio combinations which are equally desirable Match investor preferences with portfolio possibilities

Selecting an Optimal Portfolio of Risky Assets International diversification unlikely to offer as much risk reduction as it has in the past 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 assets to asset types Asset class rather than individual security decisions likely most important for investors Can be used when investing internationally Different asset classes offers 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 International equities Bonds Treasury Inflation-Indexed Securities (TIPS) Real estate Gold Commodities

Correlation among asset classes must be considered Correlations change over time For individual investors, allocation depends on Time horizon Risk tolerance Diversified asset allocation doesn’t necessarily provide benefits or guarantee against loss 8-10

Index Mutual Funds and ETFs Investors can buy funds covering various asset classes Domestic large-cap stocks, domestic small-cap stocks International stocks Bond funds Life Cycle Analysis Varies asset allocation based on age of investor Life-cycle funds (target-date funds) hold various asset classes and the allocation changes as investor ages No one “correct” approach to allocation 8-11

Impact of Diversification on Risk Total risk = systematic (nondiversifiable) risk + nonsystematic (diversifiable) risk Systematic risk is market risk and common to virtually all securities Nonsystematic risk is company-specific risk Total risk can go no lower than systematic risk Both risk components can vary over time Affects number of securities needed to diversify

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

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