Portfolio Theory

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					Vicentiu Covrig                       FIN352

            Portfolio Theory
                  (Jones chapter 7)

Vicentiu Covrig                                     FIN352

                  Investment Decisions
    nInvolve uncertainty
    nFocus on expected returns
        - Estimates of future returns needed to consider
          and manage risk
    nGoal is to reduce risk without affecting
        - Accomplished by building a portfolio
        - Diversification is key

Vicentiu Covrig                                    FIN352

           Dealing With Uncertainty
    nRisk that an expected return will not be
    nInvestors must think about return
     distributions, not just a single return
    nProbabilities weight outcomes
        - Should be assigned to each possible outcome to
          create a distribution
        - Can be discrete or continuous

Vicentiu Covrig                                             FIN352

        Calculating Expected Return
n Expected value
   - The single most likely outcome from a particular
     probability distribution
   - The weighted average of all possible return outcomes
   - Referred to as an ex ante or expected return

Vicentiu Covrig                                            FIN352

   Example: Given the following probability distribution,
      calculate the expected return of security XYZ.
  n Security XYZ's     Potential return      Probability
                              20%                   0.3
                              30%                   0.2
                              -40%                  0.1
                              50%                   0.1
                              10%                   0.3
  E(R) = Ripri = (20)(0.3) + (30)(0.2) + (- 40)(0.1) +
  (50)(0.1) + (10)(0.3) = 22 percent

Vicentiu Covrig                                        FIN352

                  Calculating Risk
    nVariance and standard deviation used to
     quantify and measure risk
        - Measures the spread in the probability
        - Variance of returns: σ² = (Ri - E(R))²pri
        - Standard deviation of returns:
                              σ =(σ²)1/2
        - Ex ante rather than ex post σ relevant

Vicentiu Covrig                                       FIN352

           Portfolio Expected Return
    nWeighted average of the individual security
     expected returns
        - Each portfolio asset has a weight, w, which
          represents the percent of the total portfolio

Vicentiu Covrig                                            FIN352

                      Portfolio Risk
n Portfolio risk not simply the sum of individual security risks
n Emphasis on the risk of the entire portfolio and not on risk of
  individual securities in the portfolio
n Measured by the variance or standard deviation of the portfolio’s
   - Portfolio risk is not a weighted average of the risk of the
      individual securities in the portfolio

Vicentiu Covrig                                    FIN352

         Risk Reduction in Portfolios
 nRandom diversification
     - Diversifying without looking at relevant investment
     - Marginal risk reduction gets smaller and smaller as
       more securities are added
 nCorrelation drives the diversification benefits
 nA large number of securities is not required for
  significant risk reduction
 nInternational diversification benefits
Vicentiu Covrig                                     FIN352
        Portfolio Risk and Diversification
 sp %
   35                   Portfolio risk

                   Market Risk
              10   20      30         40   ......   100+
            Number of securities in portfolio
Vicentiu Covrig                                             FIN352

               The benefits of diversification
   n Come from the correlation between asset returns

   n The smaller the correlation, the greater the risk reduction
     potential  greater the benefit of diversification

   n If r = +1.0, no risk reduction is possible

   § Adding extra securities with lower corr/cov with the existing
     ones decreases the total risk of the portfolio

Vicentiu Covrig                                     FIN352

          Markowitz Diversification
    nNon-random diversification
        - Active measurement and management of
          portfolio risk
        - Investigate relationships between portfolio
          securities before making a decision to invest
        - Takes advantage of expected return and risk for
          individual securities and how security returns
          move together

Vicentiu Covrig                                           FIN352

           Measuring Portfolio Risk
    nNeeded to calculate risk of a portfolio:
        - Weighted individual security risks
           uCalculated by a weighted variance using the
            proportion of funds in each security
           uFor security i: (wi × i)2
        - Weighted comovements between returns
           uReturn covariances are weighted using the
            proportion of funds in each security
           uFor securities i, j: 2wiwj × ij

Vicentiu Covrig                               FIN352
                  Portfolio Risk and Return
  n Expected Portfolio Return

  n Standard Deviation of Portfolio Returns

Vicentiu Covrig                                    FIN352

           Calculating Portfolio Risk
    nEncompasses three factors
        - Variance (risk) of each security
        - Covariance between each pair of securities
        - Portfolio weights for each security
    nGoal: select weights to determine the
     minimum variance combination for a given
     level of expected return

Vicentiu Covrig                           FIN352
            Example: NOT on the EXAM



Vicentiu Covrig                                                 FIN352
                   Learning objectives
 Know the concept of uncertainty
 Know how to calculate expected return (probabilities)
 Know how to calculate portfolio expected return (weights)
 Concept of risk, portfolio risk
 Firm and market specific risks; correlation; diversification
 Know the concepts of correlation and diversification
 NOT on the EXAM:
        - covariance section p. 176-177
        -calculations with standard deviations p. 178- 183

 End of chapter 7.1 to 7.5; 7.23; 7.26; problems 7.1, 7-2


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