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CHAPTER FOURTEEN WHY DIVERSIFY? © 2001 South-Western College Publishing

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2 Outline Use More Than One Basket for Your Eggs The Axiom The Concept of Risk Aversion Revisited Preliminary Steps in Forming a Portfolio The Reduced Security Universe Security Statistics Interpreting the Statistics The Role of Uncorrelated Securities The Variance of a Linear Combination Diversification and Utility The Concept of Dominance

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3 Outline The Efficient Frontier Optimum Diversification of Risky Assets The Minimum Variance Portfolio The Effect of a Risk-free Rate The Efficient Frontier with Borrowing Different Borrowing and Lending Rates Naive Diversification The Single Index Model

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4 Use More Than One Basket for Your Eggs Failure to diversify may violate the terms of fiduciary trust. Risk aversion seems to be an instinctive trait in human beings. Don’t put all your eggs in one basket.

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5 Preliminary Steps in Forming a Portfolio Identify a collection of eligible investments known as the security universe. Compute statistics for the chosen securities. e.g. mean of return variance / standard deviation of return matrix of correlation coefficients

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6 Preliminary Steps in Forming a Portfolio Interpret the statistics. 1. Do the values seem reasonable? 2. Is any unusual price behavior expected to recur? 3. Are any of the results unsustainable? 4. Low correlations: Fact or fantasy?

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7 The Role of Uncorrelated Securities The expected return of a portfolio is a weighted average of the component expected returns. where x i = the proportion invested in security i

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The Role of Uncorrelated Securities two-security portfolio risk = risk A + risk B + interactive risk The total risk of a portfolio comes from the variance of the components and from the relationships among the components. 8

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9 The Role of Uncorrelated Securities expected return risk better performance A portfolio dominates all others if no other equally risky portfolio has a higher expected return, or if no portfolio with the same expected return has less risk. The point of diversification is to achieve a given level of expected return while bearing the least possible risk.

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10 The Efficient Frontier : Optimum Diversification of Risky Assets expected return risk (standard deviation of returns) impossible portfolios dominated portfolios efficient frontier The efficient frontier contains portfolios that are not dominated.

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11 The Efficient Frontier : The Minimum Variance Portfolio expected return risk (standard deviation of returns) single security with the highest expected return minimum variance portfolio The right extreme of the efficient frontier is a single security; the left extreme is the minimum variance portfolio.

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12 The Efficient Frontier : The Effect of a Risk-Free Rate expected return risk (standard deviation of returns) dominated portfolios impossible portfolios M RfRf C efficient frontier: R f to M to C When a risk-free investment complements the set of risky securities, the shape of the efficient frontier changes markedly.

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13 The Efficient Frontier : The Effect of a Risk-Free Rate In capital market theory, point M is called the market portfolio. The straight portion of the line is tangent to the risky securities efficient frontier at point M and is called the capital market line. Since buying a Treasury bill amounts to lending money to the U.S. Treasury, a portfolio partially invested in the risk-free rate is often called a lending portfolio.

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14 The Efficient Frontier with Borrowing expected return risk (standard deviation of returns) dominated portfolios impossible portfolios M RfRf C efficient frontier: the ray from R f through M lending borrowing Buying on margin involves financial leverage, thereby magnifying the risk and expected return characteristics of the portfolio. Such a portfolio is called a borrowing portfolio.

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15 The Efficient Frontier : Different Borrowing and Lending Rates expected return dominated portfolios impossible portfolios M RLRL N efficient frontier : R L to M, the curve to N, then the ray from N risk (standard deviation of returns) RBRB Most of us cannot borrow and lend at the same interest rate.

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16 The Efficient Frontier : Naive Diversification As portfolio size increases, total portfolio risk, on average, declines. After a certain point, however, the marginal reduction in risk from the addition of another security is modest. total risk nondiversifiable risk number of securities Naive diversification is the random selection of portfolio components without conducting any serious security analysis.

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17 The Efficient Frontier : Naive Diversification The remaining risk, when no further diversification occurs, is pure market risk. Market risk is also called systematic risk and is measured by beta. A security with average market risk has a beta equal to 1.0. Riskier securities have a beta greater than one, and vice versa.

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18 The Efficient Frontier : The Single Index Model A pair-wise comparison of the thousands of stocks in existence would be an unwieldy task. To get around this problem, the single index model compares all securities to a benchmark measure. The single index model relates security returns to their betas, thereby measuring how each security varies with the overall market.

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The Efficient Frontier : The Single Index Model Beta is the statistic relating an individual security’s returns to those of the market index. 19

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The Efficient Frontier : The Single Index Model The relationship between beta and expected return is the essence of the capital asset pricing model (CAPM), which states that a security’s expected return is a linear function of its beta. 20

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21 The Efficient Frontier : The Single Index Model beta E(R i ) - R f security market line + + - - 0

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22 Review Use More Than One Basket for Your Eggs The Axiom The Concept of Risk Aversion Revisited Preliminary Steps in Forming a Portfolio The Reduced Security Universe Security Statistics Interpreting the Statistics The Role of Uncorrelated Securities The Variance of a Linear Combination Diversification and Utility The Concept of Dominance

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23 Review The Efficient Frontier Optimum Diversification of Risky Assets The Minimum Variance Portfolio The Effect of a Risk-free Rate The Efficient Frontier with Borrowing Different Borrowing and Lending Rates Naive Diversification The Single Index Model

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