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Chapter 8 Diversification and Portfolio Management Diversification – Eliminating risk When diversification works Beta – Measure of Risk in a Portfolio Using Beta Company: A Portfolio of Projects Risk and Return in a Portfolio that is Not Well Diversified

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Diversification – Eliminating Risk Easy way to lower or eliminate risk Choose risk-free investment Get a lower return Task – eliminate some risk without giving up return Don’t put all your eggs in one basket Spread out your investment across many assets Calculate expected return and risk

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Diversification – Eliminating Risk Example, Mars Bars and Klingon Four states of economy Boom, Good, Normal, and Bust Each with probability of state Returns in each state for two assets Calculating Expected Return E(r) = probability of state x conditional return Mars Bars Inc. = 10% Klingon LTD = 10%

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Diversification – Eliminating Risk Calculate “risk” as the standard deviation of the conditional returns σ = [Σ (probability i x (return i – average )2 ] 1/2 Mars Bars Inc. σ = 12.02% Klingon LTD σ = 7.63% Combining Mars Bars and Klingon (50/50) Same return, 10% Lower risk, 0.82% Spreading investment lowers risk

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When Diversification Works Co-movement of stock returns Correlation Coefficient Covariance of two assets divided by their standard deviations (equation 8.2) Positive Correlation No benefit if perfectly positively correlated Example Peat and Repeat Companies Negative Correlation Eliminate all risk if perfectly negatively correlated Example Zig and Zag Companies

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Beta – Measure of Risk in a Portfolio Systematic Risk – risk you cannot avoid Unsystematic Risk – risk you can avoid Beta is measure of systematic risk Standard Deviation is measure of both systematic and unsystematic risk Diversification can eventually eliminate all unsystematic risk Only systematic risk counts, so use β

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Beta – Measure of Risk in a Portfolio Using Beta for finding the risk of a portfolio In a well diversified portfolio only systematic risk remains Systematic risk of portfolio is weighted betas Example 8.1 (Tom’s Portfolio) Peat’s β = 0.8, Repeat’s β = 1.2, Zig’s β = 0.6, Zag’s β = 1.4 Equally weighted portfolio (Tom’s Portfolio) Portfolio’s β = 1.0 1.0 = 0.25 x 0.8 + 0.25 x 1.2 + 0.25 x 0.6 + 0.25 x 1.4

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Using Beta Beta Facts Beta of zero means no risk (i.e. T-Bill) Beta of 1 means average risk (same as market risk) Beta < 1, risk lower than market Beta > 1, risk greater than market Expected Return and Beta use asset weights in portfolio for portfolio e(r) and β Expected Return = Σ w i x return i Beta = Σ w i x β i

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Using Beta Beta also determines expected return of individual asset Known, risk-free rate Estimate, expected return on market Each asset’s expected return function of its risk as measured by beta and the risk-reward tradeoff (slope of SML)

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Company: A Portfolio of Projects All companies are a portfolio of individual projects (or products and services) Concept of portfolio helps explain Viewing each project or product with different level of risk (project β) and contribution (expected return) Different project or product combinations can lower overall risk of the firm Projects plotting above the SML (buy) Projects plotting below the SML (sell)

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Risk and Return in a Portfolio that is Not Well Diversified George Jetson investing choice Only four assets in portfolio (equally weighted) Expected return = 9.35% Standard Deviation = 4.29% Weighted average standard deviations of four assets = 4.4% Little benefit from diversification Portfolio needs more assets for benefits of diversification

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Problems Problem 1 – Expected Returns Problem 2 – Variance and Standard Deviation Problem 3 – Portfolio Expected Return Problem 4 – Portfolio Variance and Standard Deviation Problem 9 – Benefits of Diversification Problem 11 – Beta of Portfolio Problem 12 – Expected Return of Portfolio

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