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Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
Portfolio Selection, Wealth Management And Market Risk
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Portfolio Selection, Wealth Management And Market Risk

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  • 1. 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 r t = the one period rate of return
        • w b = the beginning of period wealth
        • w e = 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 w 0 = the aggregate purchase price at time t=0
    • w 1 = aggregate market value at time t=1
  • 7. INITIAL AND TERMINAL WEALTH
    • OR USING INITIAL AND TERMINAL WEALTH
    • where
    • w 0 =the initial wealth
    • w 1 =the terminal wealth
  • 8. THE MARKOWITZ APPROACH
    • MARKOWITZ PORTFOLIO RETURN
      • portfolio return (r p ) 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
    Wealth Utility Utility of 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 (W 1 ), that is, the effect various portfolios have on W 1
        • measured by expected returns and standard deviation
  • 19. PORTFOLIO RETURN
    • CALCULATING PORTFOLIO RETURN
      • Expected returns:
        • Method One:
            • r P = w 1 - w 0 / w 0
  • 20. PORTFOLIO RETURN
      • Expected returns:
        • Method Two:
        • where r P = the expected return of the portfolio
        • X i = the proportion of the portfolio’s initial value invested in security i
        • r i = 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  ij = 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

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