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**Practical Investment Management**

CHAPTER SIXTEEN WHY DIVERSIFY? Practical Investment Management Robert A. Strong 1

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**Use More Than One Basket for Your Eggs**

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 2

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**The Efficient Frontier**

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 3

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**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. 4

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**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 5

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**Preliminary Steps in Forming a Portfolio**

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**Preliminary Steps in Forming a Portfolio**

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**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? 6

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**The Role of Uncorrelated Securities**

The expected return of a portfolio is a weighted average of the component expected returns. where xi = the proportion invested in security i

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**The Role of Uncorrelated Securities**

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**The Role of Uncorrelated Securities**

The total risk of a portfolio comes from the variance of the components and from the relationships among the components. two-security portfolio risk = riskA + riskB + interactive risk

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**The Role of Uncorrelated Securities**

Investors get added utility from greater return. They get disutility from greater risk. The point of diversification is to achieve a given level of expected return while bearing the least possible risk. expected return risk better performance

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**The Role of Uncorrelated Securities**

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.

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**The Efficient Frontier : Optimum Diversification of Risky Assets**

The efficient frontier contains portfolios that are not dominated. expected return risk (standard deviation of returns) impossible portfolios dominated Efficient frontier

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**The Efficient Frontier : The Minimum Variance Portfolio**

The right extreme of the efficient frontier is a single security; the left extreme is the minimum variance portfolio. expected return risk (standard deviation of returns) single security with the highest minimum variance portfolio

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**The Efficient Frontier : The Minimum Variance Portfolio**

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**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 markedly. expected return risk (standard deviation of returns) dominated portfolios impossible M Rf C Efficient frontier: Rf to M to C E D

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**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.

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**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. expected return risk (standard deviation of returns) dominated portfolios impossible M Rf Efficient frontier: the ray from Rf through M lending borrowing

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**The Efficient Frontier : Different Borrowing and Lending Rates**

Most of us cannot borrow and lend at the same interest rate. expected return dominated portfolios impossible M RL N Efficient frontier : RL to M, the curve to N, then the ray from N risk (standard deviation of returns) RB

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**The Efficient Frontier : Naive Diversification**

Naive diversification is the random selection of portfolio components without conducting any serious security analysis. 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 20 40

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**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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**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.

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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.

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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.

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**The Efficient Frontier : The Single Index Model**

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**The Efficient Frontier : The Single Index Model**

Insert Figure here.

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**Use More Than One Basket for Your Eggs**

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 18

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**The Efficient Frontier**

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 19

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**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 19

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**Appendix: Arbitrage Pricing Theory**

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**Appendix: Arbitrage Pricing Theory**

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