Chapter 8 Diversification and Portfolio Management

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Chapter 8Diversification 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
• Dont 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
• s S (probabilityi x (returni average)21/2
• Mars Bars Inc. s 12.02
• Klingon LTD s 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 ß

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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 (Toms Portfolio)
• Peats ß 0.8, Repeats ß 1.2, Zigs ß 0.6,
  Zags ß 1.4
• Equally weighted portfolio (Toms Portfolio)
• Portfolios ß 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 lt 1, risk lower than market
• Beta gt 1, risk greater than market
• Expected Return and Beta use asset weights in
  portfolio for portfolio e(r) and ß
• Expected Return S wi x returni
• Beta S wi x ßi

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Using Beta

• Beta also determines expected return of
  individual asset
• Known, risk-free rate
• Estimate, expected return on market
• Each assets 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 ß) 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