chapter 7 (slides) - 7-1OPTIMAL RISKY PORTFOLIOSCHAPTER...

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Unformatted text preview: 7-1OPTIMAL RISKY PORTFOLIOSCHAPTER 77-2Outline of the Chapter•Sources of risk and advantages of diversification•Forming a portfolio, P with two risky assets– Expected value and variance of the portfolio, P– Correlation between two risky assets– Finding optimum weights for the minimum-variance portfolio P– Defining portfolio opportunity sets•Forming optimal portfolio with two risky and a risk-free asset– Finding optimum weights of risky assets in Portfolio P (when there is a risk-free asset)– Finding the optimum weight invested in the risky portfolio P •The Markowitz portfolio selection model– How to construct an optimum portfolio with many risky securities and a risk-free asset7-3Diversification and Portfolio Risk• Sources of risk (uncertainty):– Market risk• Risk that comes from conditions in the general economy• Business cycle, inflation, interest rates, and exchange rates...• Systematic or nondiversifiable– Firm-specific risk• A company’s success in research and development and personnel changes...• Unique, diversifiable or nonsystematic7-4Diversification and Portfolio Risk (Continued)7-5Diversification and Portfolio Risk (Continued)•Panel A– All risk is firm-specific– A diversification (including additional securities in the portfolio) can reduce the risk (portfolio standard deviation) to low levels– All risk sources are independent and diversification reduces the exposure to any particular source of risk to a negligible level7-6Diversification and Portfolio Risk (Continued)•Panel B– Common sources of risk (market risk) affects all firms– Diversification can reduce the risk but can not eliminate risk , can not decrease the risk to negligible level• On average portfolio risk reduces with diversification, but the power of diversification is limited by the market risk7-7Portfolios of Two Risky Assets• Efficient diversification– Construct risky portfolios to provide the lowest possible risk for any given level of expected return• Portfolio of two risky assets– Asset allocation decision• Two mutual funds• D: a bond portfolio (long-term debt securities)E: a stock portfolio (equity securities)7-8Portfolios of Two Risky Assets (Continued)•wD: proportion invested in the bond fundwE=1- wD: proportion invested in the equity fundrP: rate of return on the portfoliorD: rate of return on the debt fundrE: rate of return on the equity fund•rP= wD* rD + wE*rEE(rP)= wD* E(rD) + wE*E(rE)The expected return on the portofolio is a weighted average of expected returns on the component securities with portfolio proportions as weights7-9Portfolios of Two Risky Assets (Continued)•σ2P=w2Dσ2D +w2Eσ2E+2wDwECov(rD,rE)whereσ2D: variance of the debt fundσ2E: variance of the equity fundCov(rD,rE): covariance of the returns on the debt and equity fundThe variance of the portfolio is nota weighted average of the individual asset variances7-10Portfolios of Two Risky Assets (Continued)•Variance of the portfolio is reduced if the...
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This note was uploaded on 04/03/2010 for the course FEAS 311.01 taught by Professor Attilaodabaşı during the Spring '10 term at Boğaziçi University.

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chapter 7 (slides) - 7-1OPTIMAL RISKY PORTFOLIOSCHAPTER...

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