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CHAPTER SIXTEEN WHY DIVERSIFY? Practical Investment Management Robert A Strong 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 South-Western / Thomson Learning © 2004 16 - Outline The Efficient Frontier Optimum Diversification of Risky Assets The Minimum Variance Portfolio The Effect of a Riskfree Rate The Efficient Frontier with Borrowing Different Borrowing and Lending Rates Naive Diversification The Single Index Model South-Western / Thomson Learning © 2004 16 - Use More Than One Basket for Your Eggs Don’t put all your eggs in one basket Failure to diversify may violate the terms of a fiduciary trust Risk aversion seems to be an instinctive trait in human beings South-Western / Thomson Learning © 2004 16 - 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 South-Western / Thomson Learning © 2004 16 - Preliminary Steps in Forming a Portfolio Insert Figure 16-1 here South-Western / Thomson Learning © 2004 16 - Preliminary Steps in Forming a Portfolio Insert Figure 16-2 here South-Western / Thomson Learning © 2004 16 - Preliminary Steps in Forming a Portfolio Interpret the statistics Do the values seem reasonable? Is any unusual price behavior expected to recur? Are any of the results unsustainable? Low correlations: Fact or fantasy? South-Western / Thomson Learning © 2004 16 - The Role of Uncorrelated Securities The expected return of a portfolio is a weighted average of the component expected returns E ( R portfolio ) = ∑ x i E ( Ri ) n i =1 where xi = the proportion invested in security i South-Western / Thomson Learning © 2004 16 - The Role of Uncorrelated Securities Insert Table 16-5 here South-Western / Thomson Learning © 2004 16 - 10 The Efficient Frontier : The Effect of a Riskfree 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 riskfree rate is often called a lending portfolio South-Western / Thomson Learning © 2004 16 - 18 expected return The Efficient Frontier with 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 Efficient frontier: the ray from Rf through M impossible portfolios le ing d n Rf bo in w rro g M dominated portfolios risk (standard deviation of returns) South-Western / Thomson Learning © 2004 16 - 19 The Efficient Frontier : Different Borrowing and Lending Rates Most of us cannot borrow and lend at the same interest rate expected return Efficient frontier : RL to M, the curve to N, then the ray from N impossible portfolios N M RB RL dominated portfolios risk (standard deviation of returns) South-Western / Thomson Learning © 2004 16 - 20 The Efficient Frontier : Naive Diversification Naive diversification is the random selection of portfolio components without conducting any serious security analysis total risk Nondiversifiable risk 20 40 number of securities South-Western / Thomson Learning © 2004 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 16 - 21 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 South-Western / Thomson Learning © 2004 16 - 22 The Efficient Frontier : The Single Index Model A pairwise 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 South-Western / Thomson Learning © 2004 16 - 23 The Efficient Frontier : The Single Index Model Beta is the statistic relating an individual security’s returns to those of the market index ρ imσ i cov( Ri , Rm ) βi = = σm σ m2 where Rm = Ri = σi = σm = ρ im = the return on the market index the return on security i standard deviation of security i returns standard deviation of market returns correlation between security i returns and market returns South-Western / Thomson Learning © 2004 16 - 24 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 ( E(Ri ) − R f = β i E Rm − R f where R f Ri Rm βi South-Western / Thomson Learning © 2004 = = = = ) riskless interest rate return on security i return on the market beta of security i 16 - 25 The Efficient Frontier : The Single Index Model Insert Figure 16-11 here South-Western / Thomson Learning © 2004 16 - 26 The Efficient Frontier : The Single Index Model Insert Figure 16-12 here South-Western / Thomson Learning © 2004 16 - 27 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 South-Western / Thomson Learning © 2004 16 - 28 Review The Efficient Frontier Optimum Diversification of Risky Assets The Minimum Variance Portfolio The Effect of a Riskfree Rate The Efficient Frontier with Borrowing Different Borrowing and Lending Rates Naive Diversification The Single Index Model South-Western / Thomson Learning © 2004 16 - 29 Appendix: Arbitrage Pricing Theory Theory presumes that market return is determined by a number of distinct, unidentifiable macroeconomic factors Four factors that make the market move: The economy Fed policy Valuation Investor sentiment South-Western / Thomson Learning © 2004 16 - 30 Appendix: Arbitrage Pricing Theory South-Western / Thomson Learning © 2004 16 - 31 Appendix: Arbitrage Pricing Theory South-Western / Thomson Learning © 2004 16 - 32 ... Learning © 2004 16 - 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... Learning © 2004 16 - 16 The Efficient Frontier : The Effect of a Riskfree Rate When a riskfree investment complements the set of risky securities, the shape of the efficient frontier changes
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