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					Empirical Financial Economics


        5. Current Approaches to
       Performance Measurement



Stephen Brown NYU Stern School of
Business
UNSW PhD Seminar, June 19-21 2006
      Overview of lecture

Standard approaches
Theoretical foundation
Practical implementation
Relation to style analysis
Gaming performance metrics
   Performance measurement
             Leeson     Market    Short-term
             Investment (S&P 500) Government
             Managemen Benchmark Benchmark
             t
    Average .0065           .0050         .0036
     Return
        Std. .0106          .0359         .0015
   Deviation
        Beta .0640          1.0           .0
      Alpha .0025            .0            .0
               (1.92)
                                            at
Sharpe Style: Index Arbitrage, 100% in cash.0 close of
        Ratio .2484          .0318
       trading
                    1
                         1
 -1




            0
                     0
                              20
                                        30




                5
                          5
                                   25
                                             35
   .0
-0 0 %
   .5
      0%
 0.
    00
 0. %
    50
        %
  1.0
      0%
  1.5
      0
 2. %
    00
 2. %
    50
 3. %
    00
 3. %
    50
 4. %
    00
 4. %
    50
 5. %
                                                      monthly returns




    00
 5. %
    50
 6. %
    0
      0
                                                  Frequency distribution of




 6. %
    50
        %
      Universe Comparisons
40%                                   Brownian Management
35%                                   S&P 500
30%

25%

20%

15%

10%

5%


      One Quarter       1 Year     3 Years       5 Years

                    Periods ending Dec 31 2002
     Total Return comparison
Average Return
                 A

                 B
                 C
                 D
     Total Return comparison
Average Return
                 A                Manager A best
RS&P = 13.68%    S&P 500
                 B
                 C                Manager D worst
                 D




    rf = 1.08%   Treasury Bills
     Total Return comparison
Average Return
                 A

                 B
                 C
                 D
     Sharpe ratio comparison
Average Return
                             A

                     B
                         C
                 D




                                 Standard
                                 Deviation
     Sharpe ratio comparison
Average Return

RS&P = 13.68%                              A
                                          S&P 500
                                      B
                                          C
                            D




    rf = 1.08%   Treasury Bills


                                  σ           Standard
                                  ^ S&P = 20.0%
                                              Deviation
           Sharpe ratio comparison
  Average Return

    RS&P = 13.68%                                   A
                                                   S&P 500
                                               B
Sharpe ratio =                                     C   Manager C worst
                                     D                 Manager D best
    Average return – rf
    Standard Deviation



         rf = 1.08%       Treasury Bills


                                           σ           Standard
                                           ^ S&P = 20.0%
                                                       Deviation
     Sharpe ratio comparison
Average Return

RS&P = 13.68%                              A
                                          S&P 500
                                      B
                                          C
                            D




    rf = 1.08%   Treasury Bills


                                  σ           Standard
                                  ^ S&P = 20.0%
                                              Deviation
        Jensen’s Alpha comparison
  Average Return

    RS&P = 13.68%                                   A
                                                   S&P 500
                                               B      Manager B worst
Jensen’s alpha =                       C              Manager C best
                                       D
    Average return –
    {rf + β (RS&P - rf )}



          rf = 1.08%        Treasury Bills


                                             βS&P = 1.0 Beta
   Intertemporal equilibrium model

                          j             
Multiperiod problem: Et   U (ct  j ) 
                   Max
                          j 0           

First order conditions:

           U (ct )   j Et  (1  ri ,t  j )U (ct  j ) 
                                                           
Stochastic discount factor interpretation:
                                                             U (ct  j )
           1  Et  (1  ri ,t  j ) mt , j  ,
                                              mt , j   j

                                                             U (ct )
 mt , j “stochastic discount factor”, “pricing
    Value of Private Information

                               I1  I
Investor has access to information 0

Value of  I 0 is given byR1  R0 )mt ]
        I1              Et [(                where0
                                             R1  R
 and                                  I1
                  are returns on optimal I 0
 portfolios given and

 Et [( R1  R0 )mt ] (Chen  t ( mt rft ) 
Under CAPM  1t  rft & 1Knez1996)1

Jensen’s alpha measures value of private
 information
The geometry of mean variance

                           a  2bE  cE 2
       E                
                        2

                               ac  b 2



       a               1  1/ b 
                                  x  1/ b 1
       b               2  0 
                         a  1
                         2



              
                 a                  
                b
 Note: returns are in excess of the risk freer f
       Informed portfolio strategy

Excess return1  rf  R0  rf  
             R                     on informed
              
 strategy where is the return on an optimal
 orthogonal portfolio (MacKinlay 1995)

Sharpe ratio squared of informed strategy
 12  (0  rf )1 (0  rf )   1  02  2  02
Assumes well diversified portfolios
       Informed portfolio strategy

Excess return1  rf  R0  rf  
             R                     on informed
              
 strategy where is the return on an optimal
 orthogonal portfolio (MacKinlay 1995)

Sharpe ratio squared of informed strategy
 12  (0  rf )1 (0  rf )   1  02  2  02
Assumes well diversified portfolios

      Used in tests of mean variance efficiency of
      benchmark
             Practical issues

Sharpe ratio sensitive to
 diversification, but invariant to
 leverage
     Risk premium and standard deviation
      proportionate to fraction of investment
      financed by borrowing


Jensen’s alpha invariant to   
                    2  0
 diversification, but sensitive to
 leverage
     In   a complete market      implies
     Changes in Information Set

                      1t 
How do we measure alpha 1t  rft  1t ( mt  rft )
 when information set is not constant?
                  I1t

       Rolling   regression, use subperiods to estimate
       1  1  rf  1 (  m  rft )
       (no t subscript) – Sharpe (1992)

       Usemacroeconomic variable controls – Ferson
       and Schadt(1996)

       UseGSC procedure – Brown and Goetzmann
       (1997)
Style management is crucial …




                     Economist, July 16, 1995

But who determines styles?
 Characteristics-based Styles

       rjt   Jt   Jt I t   jt     jJ
 Traditional approach …

    Jt are changing characteristics (PER,
   Price/Book)
    It
   are returns to characteristics
                                Jt
   Style benchmarks are given by
             rjt   Jt   jt        jJ
      Returns-based Styles

       rjt   Jt   Jt I t   jt     jJ
 Sharpe (1992) approach …

    Jt are a dynamic portfolio strategy
   I t are benchmark portfolio returns
                                 Jt
   Style benchmarks are given by

             rjt   Jt   jt        jJ
      Returns-based Styles

       rjt   Jt   Jt I t   jt     jJ
 GSC (1997) approach …

    jT ,  Jt vary through time but are fixed for
                                                  J
   style                                   Jt
   Allocate funds to styles directly using
                                   Jt
   Style benchmarks are given by
             rjt   Jt   jt        jJ
  Eight style decomposition

 0
1 0%
80%
60%
40 %
20 %
 0%
       GSC1 GSC2 GSC3 GSC4 GSC5 GSC6      GSC7 GSC8
Ot her                   Pure Propert y
Pure Emerging Market     Pure Leveraged Currency
Global Macro             Non Direct ional/Relat ive Value
Event Driven             Non-US Equit y Hedge
US Equit y Hedge
   Five style decomposition
 0
1 0%
80%
60%
40 %
20 %
  0%
        GSC1       GSC2   GSC3       GSC4        GSC5
Ot her                    Pure Propert y
Pure Emerging Market      Pure Leveraged Currency
Global Macro              Non Direct ional/Relat ive Value
Event Driven              Non-US Equit y Hedge
US Equit y Hedge
       Style classifications

GSC1   Event driven international
GSC2   Property/Fixed Income
GSC3   US Equity focus
GSC4   Non-directional/relative value
GSC5   Event driven domestic
GSC6   International focus
GSC7   Emerging markets
GSC8   Global macro
        Regressing returns on
     classifications: Adjusted R2


                 GSC8              GSC5             TASS 1  7
Year N       classifications   classifications   classifications
1992 1 49        0.3827                71
                                   0.1 3             0.4441
1993 21 2        0.2224            0.1320               1
                                                     0.186
1994 288         0.1662            0.1040           0.0986
1995 405        0.0576            0.0548            0.0446
1996 524         0.1554           0.0769             0.1523
1997 61 6       0.3066             0.1886           0.2538
1998 668         0.281 3           0.201 9           0.1998
   Average      0.2246             0.1328            0.1874
     Variance explained by prior
    returns-based classifications

                 8 GSC          8 Principal    8 Benchmarks
Year N       Classifications   Components     (predetermined)
1992 198        0.3622           0.0572           0.1769
1993 276         0.1779           0.0351          0.1748
1994 348         0.1590           0.0761          0.0481
1995 455         0.061 1         0.0799           0.0862
1996 557         0.1543          0.0286           0.0691
1997 649        0.2969            0.021 1         0.0642
1998 687        0.2824           0.2862           0.2030
   Average       0.21 34         0.0835              1
                                                   0.175
      Variance explained by prior
            factor loadings

                 8 GSC          8 Principal    8 Benchmarks
Year N       Classifications   Components     (predetermined)
1992 198         0.2742           0.1607          0.2552
1993 276         0.21 70         0.0928           0.0932
1994 348         0.1760           0.1577          0.0700
1995 455        0.0670           0.0783           0.0829
1996 557         0.1444          0.0888           0.0349
1997 649         0.31 35         0.3069           0.0899
1998 687         0.2752          0.3744           0.3765
   Average      0.2096            0.1799          0.1432
 Percentage in cash (monthly)

 20
1 %

 0
1 0%

80%

60%

40 %

20 %

 0%
31      98
  -Dec-1 9   15-May-1991   26 -Sep-1992   8 -Feb-1994
Examples of riskless index
      arbitrage …
     Percentage in cash (daily)

20 0 %
  0
 1 0%
   0%
  0
-1 0 %
-20 0 %
-30 0 %
-40 0 %
-50 0 %
-6 0 0 %
  31       98
     -Dec-1 9   15-May-1991   26 -Sep-1992   8 -Feb-1994
“Informationless” investing
     Concave payout strategies
Zero net investment overlay strategy (Weisman
 2002)

  Uses only public information
  Designed to yield Sharpe ratio greater than benchmark
  Using strategies that are concave to benchmark
     Concave payout strategies
Zero net investment overlay strategy (Weisman
 2002)

  Uses only public information
  Designed to yield Sharpe ratio greater than benchmark
  Using strategies that are concave to benchmark

Why should we care?

  Sharpe ratio obviously inappropriate here
  But is metric of choice of hedge funds and derivatives
   traders
         We should care!

Delegated fund management
  Fund flow, compensation based on
   historical performance
  Limited incentive to monitor high
   Sharpe ratios
Behavioral issues
  Prospect theory: lock in gains, gamble
   on loss
  Are there incentives to control this
   behavior?
Sharpe Ratio of Benchmark

  0
 1 0%

  50 %

   0%

 -50 %                                    Benchmark

  0
-1 0 %

  50
-1 %

-20 0 %
     -50 %     0%        50 %       0
                                   1 0%
             Sharpe ratio = .631
     Maximum Sharpe Ratio

  0
 1 0%

  50 %
                                          Benchmark
   0%

 -50 %

-1 0 %
  0                                       Maximum
                                          Sharpe Rat io
                                          St rat egy
  50
-1 %

-20 0 %
     -50 %     0%        50 %       0
                                   1 0%
             Sharpe ratio = .748
 Concave trading strategies

  0
 1 0%

  50 %
                                Benchmark
   0%
                                Loss Averse
 -50 %                          Trading
                                (Median)
  0
-1 0 %                          Maximum
                                Sharpe Rat io
  50
-1 %                            St rat egy

-20 0 %
     -50 %   0%   50 %    0
                         1 0%
 Examples of concave payout
         strategies

Long-term asset mix guidelines
 Examples of concave payout
         strategies




Unhedged short volatility
  Writing out of the money calls and
   puts
 Examples of concave payout
         strategies




Loss averse trading
 a.k.a. “Doubling”
 Examples of concave payout
         strategies
Long-term asset mix guidelines


Unhedged short volatility
  Writing out of the money calls and
   puts

Loss averse trading
  a.k.a. “Doubling”
         Forensic Finance

Implications of concave payoff
 strategies

  Patterns of returns
            Forensic Finance

Implications of Informationless
 investing

  Patterns of returns
     are   returns concave to benchmark?
            Forensic Finance

Implications of concave payoff
 strategies

  Patterns of returns
     are   returns concave to benchmark?
  Patterns of security holdings
            Forensic Finance

Implications of concave payoff
 strategies

  Patterns of returns
     are   returns concave to benchmark?
  Patterns of security holdings
     dosecurity holdings produce concave
     payouts?
            Forensic Finance

Implications of concave payoff
 strategies

  Patterns of returns
     are   returns concave to benchmark?
  Patterns of security holdings
     dosecurity holdings produce concave
     payouts?
  Patterns of trading
            Forensic Finance

Implications of concave payoff
 strategies

  Patterns of returns
     are   returns concave to benchmark?
  Patterns of security holdings
     dosecurity holdings produce concave
     payouts?
  Patterns of trading
     does   pattern of trading lead to concave
            Conclusion

Value of information interpretation of
 standard performance measures

New procedures for style analysis

Return based performance measures
 only tell part of the story

				
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