CHAPTER SIXTEEN WHY DIVERSIFY Practical Investment Management Robert

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

Outline w Use More Than One Basket for Your Eggs ú The Axiom ú The Concept of Risk Aversion Revisited w Preliminary Steps in Forming a Portfolio ú The Reduced Security Universe ú Security Statistics ú Interpreting the Statistics w The Role of Uncorrelated Securities ú The Variance of a Linear Combination ú Diversification and Utility ú The Concept of Dominance South-Western / Thomson Learning © 2004 16 - 2

Outline w The Efficient Frontier ú ú ú ú 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 - 3

Use More Than One Basket for Your Eggs u Don’t put all your eggs in one basket. u Failure to diversify may violate the terms of a fiduciary trust. u Risk aversion seems to be an instinctive trait in human beings. South-Western / Thomson Learning © 2004 16 - 4

Preliminary Steps in Forming a Portfolio w Identify a collection of eligible investments known as the security universe. w 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 - 5

Preliminary Steps in Forming a Portfolio Insert Figure 16 -1 here. South-Western / Thomson

Preliminary Steps in Forming a Portfolio Insert Figure 16 -2 here. South-Western / Thomson

Preliminary Steps in Forming a Portfolio w 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? South-Western / Thomson Learning © 2004 16 - 8

The Role of Uncorrelated Securities u The expected return of a portfolio is a weighted average of the component expected returns. where xi = the proportion invested in security i South-Western / Thomson Learning © 2004 16 - 9

The Role of Uncorrelated Securities Insert Table 16 -5 here. South-Western / Thomson Learning

The Role of Uncorrelated Securities u The total risk of a portfolio comes from the variance of the components and from the relationships among the components. two-security portfolio risk = risk. A + risk. B + interactive risk South-Western / Thomson Learning © 2004 16 - 11

The Role of Uncorrelated Securities Investors get added utility from greater return. They get disutility from greater risk. u The point of diversification is to achieve a given level of expected return while bearing the least possible risk. expected return u better performance risk South-Western / Thomson Learning © 2004 16 - 12

The Role of Uncorrelated Securities u 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. South-Western / Thomson Learning © 2004 16 - 13

The Efficient Frontier : Optimum Diversification of Risky Assets The efficient frontier contains portfolios that are not dominated. expected return u Efficient frontier impossible portfolios dominated portfolios risk (standard deviation of returns) South-Western / Thomson Learning © 2004 16 - 14

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 u single security with the highest expected return minimum variance portfolio risk (standard deviation of returns) South-Western / Thomson Learning © 2004 16 - 15

The Efficient Frontier : The Minimum Variance Portfolio Insert Figure 16 -6 here. South-Western

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 u Rf Efficient frontier: Rf to M to C impossible portfolios C E D M dominated portfolios risk (standard deviation of returns) South-Western / Thomson Learning © 2004 16 - 17

The Efficient Frontier : The Effect of a Riskfree Rate w In capital market theory, point M is called the market portfolio. w The straight portion of the line is tangent to the risky securities efficient frontier at point M and is called the capital market line. w 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 u 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 g din n le Rf ing w ro r bo 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 u 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 u 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 Nondiversifiable risk from the addition of 20 40 another security is modest. number of securities total risk u South-Western / Thomson Learning © 2004 16 - 21

The Efficient Frontier : Naive Diversification w The remaining risk, when no further diversification occurs, is pure market risk. w Market risk is also called systematic risk and is measured by beta. w 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 w 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. w 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 u Beta is the statistic relating

The Efficient Frontier : The Single Index Model u 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. South-Western / Thomson Learning © 2004 16 - 25

The Efficient Frontier : The Single Index Model Insert Figure 16 -11 here. South-Western

The Efficient Frontier : The Single Index Model Insert Figure 16 -12 here. South-Western

Review u Use More Than One Basket for Your Eggs The Axiom u The Concept of Risk Aversion Revisited u u Preliminary Steps in Forming a Portfolio The Reduced Security Universe u Security Statistics u Interpreting the Statistics u u The Role of Uncorrelated Securities The Variance of a Linear Combination u Diversification and Utility u The Concept of Dominance u South-Western / Thomson Learning © 2004 16 - 28

Review u The Efficient Frontier Optimum Diversification of Risky Assets u The Minimum Variance Portfolio u The Effect of a Riskfree Rate u The Efficient Frontier with Borrowing u Different Borrowing and Lending Rates u Naive Diversification u The Single Index Model u South-Western / Thomson Learning © 2004 16 - 29

Appendix: Arbitrage Pricing Theory presumes that market return is determined by a number of distinct, unidentifiable macroeconomic factors u u. Four factors that make the market move: u. The economy u. Fed policy u. Valuation u. Investor sentiment South-Western / Thomson Learning © 2004 16 - 30