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Unformatted text preview: 71OPTIMAL RISKY PORTFOLIOSCHAPTER 772Outline 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 minimumvariance portfolio P– Defining portfolio opportunity sets•Forming optimal portfolio with two risky and a riskfree asset– Finding optimum weights of risky assets in Portfolio P (when there is a riskfree 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 riskfree asset73Diversification 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– Firmspecific risk• A company’s success in research and development and personnel changes...• Unique, diversifiable or nonsystematic74Diversification and Portfolio Risk (Continued)75Diversification and Portfolio Risk (Continued)•Panel A– All risk is firmspecific– 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 level76Diversification 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 risk77Portfolios 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 (longterm debt securities)E: a stock portfolio (equity securities)78Portfolios 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 weights79Portfolios 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 variances710Portfolios of Two Risky Assets (Continued)•Variance of the portfolio is reduced if the...
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 Spring '10
 AttilaOdabaşı
 Variance, Portfolio Manager, risky assets

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