1 / 24

CHAPTER SEVEN

CHAPTER SEVEN. THE PORTFOLIO SELECTION PROBLEM. INTRODUCTION. THE BASIC PROBLEM: given uncertain outcomes, what risky securities should an investor own?. INTRODUCTION. THE BASIC PROBLEM: The Markowitz Approach assume an initial wealth a specific holding period (one period)

ranee
Download Presentation

CHAPTER SEVEN

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CHAPTERSEVEN THE PORTFOLIO SELECTION PROBLEM

  2. INTRODUCTION • THE BASIC PROBLEM: • given uncertain outcomes, what risky securities should an investor own?

  3. INTRODUCTION • THE BASIC PROBLEM: • The Markowitz Approach • assume an initial wealth • a specific holding period (one period) • a terminal wealth • diversify

  4. INTRODUCTION • Initial and Terminal Wealth • recall one period rate of return where rt = the one period rate of return wb = the beginning of period wealth we= the end of period wealth

  5. INITIAL AND TERMINAL WEALTH • DETERMINING THE PORTFOLIO RATE OF RETURN • similar to calculating the return on a security • FORMULA

  6. INITIAL AND TERMINAL WEALTH • DETERMINING THE PORTFOLIO RATE OF RETURN Formula: where w0 = the aggregate purchase price at time t=0 w1 = aggregate market value at time t=1

  7. INITIAL AND TERMINAL WEALTH • OR USING INITIAL AND TERMINAL WEALTH where w0 =the initial wealth w1 =the terminal wealth

  8. THE MARKOWITZ APPROACH • MARKOWITZ PORTFOLIO RETURN • portfolio return (rp) is a random variable

  9. THE MARKOWITZ APPROACH • MARKOWITZ PORTFOLIO RETURN • defined by the first and second moments of the distribution • expected return • standard deviation

  10. THE MARKOWITZ APPROACH • MARKOWITZ PORTFOLIO RETURN • First Assumption: • nonsatiation: investor always prefers a higher rate of portfolio return

  11. THE MARKOWITZ APPROACH • MARKOWITZ PORTFOLIO RETURN • Second Assumption • assume a risk-averse investor will choose a portfolio with a smaller standard deviation • in other words, these investors when given a fair bet (odds 50:50) will not take the bet

  12. THE MARKOWITZ APPROACH • MARKOWITZ PORTFOLIO RETURN • INVESTOR UTILITY • DEFINITION: is the relative satisfaction derived by the investor from the economic activity. • It depends upon individual tastes and preferences • It assumes rationality, i.e. people will seek to maximize their utility

  13. THE MARKOWITZ APPROACH • MARGINAL UTILITY • each investor has a unique utility-of-wealth function • incremental or marginal utility differs by individual investor

  14. THE MARKOWITZ APPROACH • MARGINAL UTILITY • Assumes • diminishing characteristic • nonsatiation • Concave utility-of-wealth function

  15. THE MARKOWITZ APPROACH UTILITY OF WEALTH FUNCTION Utility Utility of Wealth Wealth

  16. INDIFFERENCE CURVE ANALYSIS • INDIFFERENCE CURVE ANALYSIS • DEFINITION OF INDIFFERENCE CURVES: • a graphical representation of a set of various risk and expected return combinations that provide the same level of utility

  17. INDIFFERENCE CURVE ANALYSIS • INDIFFERENCE CURVE ANALYSIS • Features of Indifference Curves: • no intersection by another curve • “further northwest” is more desirable giving greater utility • investors possess infinite numbers of indifference curves • the slope of the curve is the marginal rate of substitution which represents the nonsatiation and risk averse Markowitz assumptions

  18. PORTFOLIO RETURN • CALCULATING PORTFOLIO RETURN • Expected returns • Markowitz Approach focuses on terminal wealth (W1), that is, the effect various portfolios have on W1 • measured by expected returns and standard deviation

  19. PORTFOLIO RETURN • CALCULATING PORTFOLIO RETURN • Expected returns: • Method One: rP = w1 - w0/ w0

  20. PORTFOLIO RETURN • Expected returns: • Method Two: where rP = the expected return of the portfolio Xi = the proportion of the portfolio’s initial value invested in security i ri = the expected return of security i N = the number of securities in the portfolio

  21. PORTFOLIO RISK • CALCULATING PORTFOLIO RISK • Portfolio Risk: • DEFINITION: a measure that estimates the extent to which the actual outcome is likely to diverge from the expected outcome

  22. PORTFOLIO RISK • CALCULATING PORTFOLIO RISK • Portfolio Risk: where sij= the covariance of returns between security i and security j

  23. PORTFOLIO RISK • CALCULATING PORTFOLIO RISK • Portfolio Risk: • COVARIANCE • DEFINITION: a measure of the relationship between two random variables • possible values: • positive: variables move together • zero: no relationship • negative: variables move in opposite directions

  24. PORTFOLIO RISK CORRELATION COEFFICIENT • rescales covariance to a range of +1 to -1 where

More Related