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					Asset Management
     Lecture 22
Review class
            Asset management process
• Planning with the client                                Risk aversion
   • Investor objectives, constraints and preferences
• Execution by the asset manager:
                                              Markovic model,
   • Asset allocation
                                            Single index model,
       • Risk and return, effects of diversification (views on inflation,
         growth, etc.)                Structural multifactor model
   • Security selection                   Black-litterman model
       • Market efficiency: can we beat the market? (private info)
   • Execution
                                               Portfolio evaluation,
       • How and when do you trade? (trading speed, trading costs)
                                            Performance attribution
• Evaluation:
   • What are the risk and the return of the portfolio?
   • Does the manager underperform or outperform?
          Risk Aversion and utility values
• Risk aversion
                                   1
• Utility value        U  E (r )  A 2
                                   2
• Calculate certainty equivalent rate
• Estimating risk aversion
    Markowitz portfolio selection model
                  n
      E (rp )   wi E (ri )
                 i 1
             n    n
      p   wi w j Cov (ri , rj )
       2

            i 1 j 1




• Sharpe Ratio
                     Single-Index Model

 E ( Ri )  i  i E ( RM )
     i2  i2 M   2 (ei )
                2



   Cov(ri , rj )  i  j M
                           2



                  i  j M i M  j M
                          2        2      2

Corr (ri , rj )                            Corr (ri , rM ) xCorr (rj , rM )
                    i j      i M  j M
              Optimal Risky Portfolio
             of the Single-Index Model

      n 1
a p   wi ai       an 1  aM  0
      i 1

      n 1
 p   wi  i       n 1   M  1
      i 1


             n 1
 (e p )   wi (ei )  (en 1 )   (eM )  0
  2                  2          2      2

             i 1
                  Optimal Risky Portfolio
                 of the Single-Index Model

• Maximize the Sharpe ratio
  • Expected return, SD, and Sharpe ratio:

                                    n 1              n 1
     E ( RP )   P  E ( RM )  P   wi i  E ( RM ) wi i
                                    i 1              i 1
                                                                       1
                                1  2  n 1       2
                                                   n 1 2 2          2
      P    P M   (eP )    M   wi  i    wi  (ei ) 
           
               2 2     2
                              
                                2

                                    i 1
                                                  i 1           
                                                                   
           E ( RP )
     SP 
            P
             Optimizing procedure
                                                 n                     n
                                                            (e A )   wi2 2 (ei )
     ai
                                           a A   wi ai
                               0
w  2                     w
 0                                                             2
 i
    (ei )       wi     n
                               i
                                                i 1                  i 1

                         wi0
                        i 1

                                   n                          0
       aA            A   wi  i              w* 
                                                            wA
      2 (e A )                i 1
                                                 A
                                                     1  (1   A ) wA
                                                                     0

wA 
 0
     E ( RM )
        M
         2
                                                 wM  1  w*
                                                  *
                                                           A



E ( R p )  ( wM  w*  A ) E ( RM )  w*  A
               *
                    A                   A



 P  ( w  w  A )   w  eA 
             *      *          2       2        *          2
             M      A                  M        A
               The Black-Litterman Model


•   Step 1: Estimate the covariance matrix from historical data
•   Step 2: Determine a baseline forecast
•   Step 3: Integrating the manager’s private views
•   Step 4: Developing revised (posterior) expectations
•   Step 5: Apply portfolio optimization
                      The Black-Litterman Model


• Step 3: Integrating the manager’s private views
   P  (1,1)
   R  ( RB , R S )
   PR'  Q  


• Step 4: Developing revised (posterior) expectations
   • BL Updating formulas
                               D E ( R )  CovE ( RB ), E ( RS )
                                2
       E ( RB | P)  E RB                 B

                                              D2




         E ( RS | P)  E RS  
                                     
                                   D CovE ( RB ), E ( RS )   E ( RS )
                                                                 2
                                                                            
                                                    D
                                                     2
• Structural multifactor model and factor choice

• Tracking portfolio

• Beta adjustment

• Alpha precision adjustment

• Style analysis
                              Tracking error
• Portfolios are often compared against a benchmark
• Tracking error       T  R RE        P        M

   RP  w* a A  [1  w* (1   A )]RM  w* eA
         A             A                  A


   TE  w* a A  w* (1   A ) RM  w* eA
         A        A                  A



• Benchmark Risk: SD of Tracking error

    Var (TE )  [ w* (1   A )]2  M  [ w*  (eA )]2
                   A
                                    2
                                           A


      (TE )  w* (1   A ) 2  M   2 (eA )
                A
                                 2
            Risk Adjusted Performance
Sharpe                         (rP  rf )
                                  P
Treynor                        (rP  rf )
                                  P
Jensen
                            P  rP   rf   P (rM  rf ) 
                                                           

Information ratio
                             p / (ep)
M2
                               M 2  rP*  rM
                Performance Attribution

• Calculate the return on the ‘Bogey’ and on the managed
  portfolio
• Explain the difference in return based on component weights or
  selection
• Summarize the performance differences into appropriate
  categories
          Formula for Attribution

                       Total contribution from asset
w pi rpi  wBi rBi    class i
( w pi  wBi ) rBi    Contribution from asset
                       allocation
w pi ( rpi  rBi )     Contribution from security
                       selection
         Formula for International Attribution

w pi ( rpi  Ei )  wBi ( rBi  Ei )     Total contribution
w pi rpi  wBi rBi  w pi Ei  wBi Ei 
( w pi  wBi ) rBi      Contribution from country allocation
w pi ( rpi  rBi )       Contribution from stock selection
( w pi  wBi ) Ei       Contribution from currency selection
• Foreign exchange rate risk

• Country risk

• Home bias

• Hedge funds, strategies, and performance evaluation

• Alpha transfer
• Behavioral finance: limits to arbitrage and investor
  irrationality

• Technical analysis

				
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posted:9/13/2011
language:English
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