Vicentiu Covrig                      FIN352
            Building a Portfolio
   Diversification is key to risk management
   Asset allocation most important single decision
   Using Markowitz Principles
     - Step 1:  Identify optimal risk-return combinations using the 
      Markowitz analysis 
       Inputs:  Expected returns, variances, covariances
     - Step 2:  Choose the final portfolio based on your 
      preferences for return relative to risk
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   Vicentiu Covrig                                                                                       FIN352
                          Example: NOT on the EXAM
               % in stocks         Risk       Return               Portfolo Risk and Return Combinations
                   0%             8.2%        7.0%
                   5%             7.0%        7.2%            n12.0%
                  10%             5.9%        7.4%            r11.0%
                                                              u
                                                              t
                  15%             4.8%        7.6%            e10.0%                                       100% 
                                                              R
                  20%             3.7%        7.8%             
                                                              o 9.0%                                       stocks
                                                              i
                                                              l
                  25%             2.6%        8.0%            o
                                                              f 8.0%
                                                              t
                  30%             1.4%        8.2%            r
                                                              o 7.0%
                  35%             0.4%        8.4%            P                                100% 
                                                                6.0%                           bonds
                  40%             0.9%        8.6%              5.0%
                  45%             2.0%        8.8%                 0.0%  2.0% 4.0%  6.0%  8.0% 10.0% 12.0% 14.0% 16.0%
                 50.00%          3.08%        9.00%
                  55%             4.2%        9.2%                       Portfolio Risk (standard deviation)
                  60%             5.3%        9.4%
                  65%             6.4%        9.6%
                  70%             7.6%        9.8%
                  75%             8.7%        10.0%
                  80%             9.8%        10.2%
                  85%             10.9%       10.4%
                  90%             12.1%       10.6%
                  95%             13.2%       10.8%
                  100%            14.3%       11.0%
                                                               3
  Vicentiu Covrig                                 FIN352
                The Efficient Frontier
     Efficient Frontier – represents the set of all 
       mean/variance efficient (optimal) portfolios
        - Optimal portfolio has maximum return for a 
         given level of risk or minimum risk for a given 
         level of return
        - Portfolios on the efficient frontier dominate all 
         other portfolios
        - No portfolio on the efficient frontier dominates 
         another portfolio on the frontier
                              4
  Vicentiu Covrig                                FIN352
                Efficient Portfolios
                                    Efficient frontier or 
                                      Efficient set 
                          B           (curved line from A 
                    x                 to B)
          E(R)                      Global minimum 
                A                     variance portfolio 
                   y   C              (represented by 
                  Risk =             point A)
                                    Portfolios on AB 
                                      dominate those on 
                                      AC
                              5
 Vicentiu Covrig                      FIN352
                Selecting an Optimal Portfolio 
                    of Risky Assets
    Portfolio weights are the output from Markowitz analysis
    Assume investors are risk averse
    Indifference curves (ICs) help select individual’s optimal 
     portfolio
     - IC, description of preferences for risk and return
     - IC reflects portfolio combinations that are equally desirable
     - ICs match investor preferences with portfolio possibilities
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