Chapter_8_-_Portfolio_Selection

Chapter_8_-_Portfolio_Selection - Portfolio Portfolio...

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Unformatted text preview: Portfolio Portfolio Selection Chapter 8 Charles P. Jones, Investments: Analysis and Management, Tenth Edition, John Wiley & Sons 8-1 Portfolio Selection Diversification is key to optimal risk management Analysis required because of the infinite number of portfolios of risky assets How should investors select the best risky portfolio? How could riskless assets be used? 8-2 Building a Portfolio Step 1: Use the Markowitz portfolio selection model to identify optimal combinations combinations Estimate expected returns, risk, and each covariance between returns Step 2: Choose the final portfolio based on your preferences for return relative to risk 8-3 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 8-4 An Efficient Portfolio Smallest portfolio risk for a given level of expected return 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 as the efficient set Lowest risk for given level of return 8-5 Investment Opportunity Set for Bond and Stock Stock Funds Investment Opportunity Set for Stock and Bonds Bonds with Various Correlations Selecting an Optimal Portfolio of of Risky Assets Assume investors are risk averse Indifference curves help select from efficient efficient set Description of preferences for risk and return Portfolio combinations which are equally desirable Greater slope implies greater the risk aversion 8-8 Selecting an Optimal Portfolio of of Risky Assets Markowitz portfolio selection model Generates a frontier of efficient portfolios which are equally good Does not address the issue of riskless borrowing or lending Different investors will estimate the efficient frontier differently El Element of uncertainty in application 8-9 Two Asset Portfolio Return – Stock and and Bond r =w r +w r r = Portfolio Return w = Bond Weight r = Bond Return Weig h w = Stock Weig htt r = Stock Return p B p B B S S B S S In General, for an n-security portfolio portfolio: rp = Weighted average of the n securities securities σp2 = (Consider all pair-wise covariance measures) Numerical Example: Bond and Stock Returns Bond = 6% Stock = 10% Standard Standard Deviation Bond = 12% Stock = 25% Weights Bond = .5 Stock = .5 Correlation Correlation Coefficient (Bonds and Stock) = 0 Return and Risk for Example Return = 8% 8% .5(6) + .5 (10) Standard Deviation = 13.87% [(.5)2 (12)2 + (.5)2 (25)2 + … 2 (.5) (.5) (12) (25) (0)] ½ [192.25] ½ = 13.87 The Single Index Model Relates returns on each security to the returns on a common index, such as the the S&P 500 Stock Index Expressed R = α following e by the + β R + equation i i i M i Divides return into two components a unique part, αi unique a market-related part, βiRM 8-14 The Single Index Model b measures the sensitivity of a stock to stock market movements If securities are only related in their common response to the market Securities covary together only because of their common common relationship to the market index Security covariances depend only on market risk and can be written as: σ ij = 2 βi β j σ M 8-15 The Single Index Model (SIM) Single index model helps split a security’s total risk into Total risk = market risk + unique risk market 2 σi = 2 βi [σ M ] 2 + σ ei Multi-Index models as an alternative Between the full variance-covariance method of Markowitz and the single-index model 8-16 Selecting Optimal Asset Classes Another way to use Markowitz model is with asset classes Allocation of portfolio assets to broad asset categories Asset class rather than individual security decisions most important for investors Different asset classes offers various returns returns and levels of risk Correlation coefficients may be quite low 8-17 Asset Allocation Decision about the proportion of portfolio assets allocated to equity, fixed-income, and money market securities Widely used application of Modern Portfolio Theory Theory Because securities within asset classes tend to move together, asset allocation is an important investment decision Should consider international securities, real real estate, and U.S. Treasury TIPS and Treasury 8-18 Implications of Portfolio Selection Investors should focus on risk that cannot be managed by diversification Total risk =systematic (nondiversifiable) risk + nonsystematic (diversifiable) risk Systematic risk Variability in a security’s total returns directly associated with economy-wide events Common to virtually all securities Both risk components can vary over time Affects Affects number of securities needed to diversify 8-19 Portfolio Risk and Diversification σp % Portfolio risk 35 20 Market Risk 0 10 20 30 40 ...... Number of securities in portfolio 100+ ...
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