CHAPTER FOURTEEN WHY DIVERSIFY 2001 SouthWestern College Publishing

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 fiduciary trust. u Risk aversion seems to be an instinctive trait in human beings. 2

Preliminary Steps in Forming a Portfolio u Identify a collection of eligible investments known as the security universe. u Compute statistics for the chosen securities. e. g. mean of return variance / standard deviation of return matrix of correlation coefficients 3

Preliminary Steps in Forming a Portfolio u 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? 4

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 5

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 6

The Role of Uncorrelated Securities u The point of diversification is to achieve a given level of expected return while bearing the least possible risk. 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. expected return u better performance risk 7

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 another security is modest. number of securities total risk u 8

The Efficient Frontier : Naive Diversification u The remaining risk, when no further diversification occurs, is pure market risk. u Market risk is also called systematic risk and is measured by beta. u A security with average market risk has a beta equal to 1. 0. Riskier securities have a beta greater than one, and vice versa. 9

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) 10

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) 11

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

The Efficient Frontier : The Effect of a Risk-Free Rate 1. In capital market theory, point M is called the market portfolio. 2. The straight portion of the line is tangent to the risky securities efficient frontier at point M and is called the capital market line. 3. 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. 13

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. Rf efficient frontier: the ray from Rf through M g impossible n i w portfolios orro b C g M n i d len dominated portfolios risk (standard deviation of returns) 14

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) 15

The Efficient Frontier : The Single Index Model 1. 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. 2. The single index model relates security returns to their betas, thereby measuring how each security varies with the overall market. 16

The Efficient Frontier : The Single Index Model u Beta is the statistic relating an individual security’s returns to those of the market index. 17

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. 18

The Efficient Frontier : The Single Index Model E(Ri) - Rf + t e k ar c e s ir ty u m e n li + 0 - beta 19

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 20

Review u The Efficient Frontier Optimum Diversification of Risky Assets u The Minimum Variance Portfolio u The Effect of a Risk-free Rate u The Efficient Frontier with Borrowing u Different Borrowing and Lending Rates u Naive Diversification u The Single Index Model u 21