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

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

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

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

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

Preliminary Steps in Forming a Portfolio Insert Figure 16-1 here.

Preliminary Steps in Forming a Portfolio Insert Figure 16-2 here.

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

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

The Role of Uncorrelated Securities Insert Table 16-5 here.

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

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

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.

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

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

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

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

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.

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

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

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

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.

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.

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

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.

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

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

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

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

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

Appendix: Arbitrage Pricing Theory 19

Appendix: Arbitrage Pricing Theory 19