Slides_Fundamentals of Investments - Chapter 17 doc

17 17 C h a p t e r Diversification & Asset AllocationDiversification & Asset Allocation second edition Fundamentals of Investments Valuation & Management Charles J. Corrado Bradford D.Jordan McGraw Hill / Irwin Slides by Yee-Tien (Ted) Fu © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 2 Don’t Put All Your Eggs in One Basket © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 3 Diversification and Asset Allocation Our goal in this chapter is to examine the role of diversification and asset allocation in investing. Goal  The role and impact of diversification were first formally explained in the early 1950s by Harry Markowitz.  Based on his work, we will look at how diversification works, and how we can be sure we have an efficiently diversified portfolio. © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 4 Expected Returns  Recall that risk premium = expected return – risk-free rate Expected return Average return on a risky asset expected in the future. This is calculated as the sum of the possible returns multiplied by their probabilities. [] ∑ ×= i ii p returnreturn expected © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 5 Expected Returns © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 6 Calculating the Variance  Variance is calculated as the sum of the squared deviations from the expected return multiplied by their probabilities. ( ) [ ] ∑ −×= i ii p 2 return expectedreturnvariance  The standard deviation is the square root of the variance. Standard deviation = σ = √variance. © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 7 Calculating the Variance © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 8 Portfolios  One convenient way of describing a portfolio is to list the percentages of the portfolio’s total value that are invested in each portfolio asset. We call these percentages the portfolio weights. Portfolios Group of assets such as stocks and bonds held by an investor. © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 9 Portfolios  The expected return on a portfolio is a linear combination of the expected returns on the assets in that portfolio. where E(R P ) = expected portfolio return w i = portfolio weight of portfolio asset i E(R i ) = expected return on portfolio asset i ( ) ( ) [ ] ∑ ×= i iiP REwRE © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 10 Portfolios  Note that portfolio variance is not generally a simple combination of the variances of the portfolio assets.  Moreover, it may be possible to construct a portfolio of risky assets with zero portfolio variance! where VAR(R P ) = variance of portfolio return p s = probability of state of economy s E(R s ) = expected portfolio return given state s () () ( ) { } [ ] ∑ −×= s PssP REREpRVAR 2 [...]... © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 16 Why Diversification Works McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 17 Why Diversification Works McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 18 Calculating Portfolio Risk For a portfolio of two assets, A and B, the variance of the return on the.. .17 - 11 Diversification and Portfolio Risk McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 12 The Principle of Diversification McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 13 Why Diversification Works Correlation The tendency of the returns on two assets to move together Imperfect... possible combinations of risk and return available from portfolios of these two assets A portfolio that offers the highest return for its level of risk is said to be an efficient portfolio The undesirable portfolios are said to be dominated or inefficient McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 23 More on Correlation & the Risk-Return Trade-Off McGraw Hill /... is not usually extended to large collections of individual assets because of the data requirements McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 26 Work the Web Perform a Markowitz-type analysis at: http://www.finportfolio.com McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 27 Chapter Review Expected Returns and Variances... McGraw-Hill Companies, Inc All rights reserved 17 - 20 Correlation and Diversification McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 21 Correlation and Diversification McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 22 Correlation and Diversification The various combinations of risk and return available all fall on a smooth... 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 28 Chapter Review Diversification and Portfolio Risk The Effect of Diversification: Another Lesson from Market History The Principle of Diversification Correlation and Diversification Why Diversification Works Calculating Portfolio Risk More on Correlation and the Risk-Return TradeOff McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies,... / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 24 Risk and Return with Multiple Assets McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 25 The Markowitz Efficient Frontier Markowitz efficient frontier The set of portfolios with the maximum return for a given standard deviation For the plot, the upper left-hand boundary is the Markowitz... portfolio weight of asset A wB = portfolio weight of asset B such that wA + wB = 1 McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 19 Correlation and Diversification Suppose that as a very conservative, riskaverse investor, you decide to invest all of your money in a bond mutual fund Is this decision a wise one? McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies,... Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 14 Why Diversification Works The correlation coefficient is denoted by Corr(RA, RB) or ρ It measures correlation and ranges from -1 (perfect negative correlation) to 0 (uncorrelated) to +1 (perfect positive correlation) McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 15 Why Diversification... Risk More on Correlation and the Risk-Return TradeOff McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 17 - 29 Chapter Review The Markowitz Efficient Frontier Risk and Return with Multiple Assets McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved . McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 16 Why Diversification Works © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 17 Why. Irwin Slides by Yee-Tien (Ted) Fu © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 17 - 2 Don’t Put All Your Eggs in One Basket © 2002 by The McGraw-Hill Companies,. / Irwin 17 - 3 Diversification and Asset Allocation Our goal in this chapter is to examine the role of diversification and asset allocation in investing. Goal  The role and impact of diversification