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					    CIA Annual Meeting




LOOKING BACK…focused on the future
                                     1
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Long-Term Equity Returns
     •   Christian-Marc Panneton




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Agenda
     •   CSOP
     •   Sub-committee mandate
     •   Review Existing Models
     •   “Canadian” Models
     •   Historical Period




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
•    CSOP - Practice-Specific Standards for Insurers
     2340 Other Assumptions: Economic
     Non-fixed income assets: investment return

     .11 The actuary’s best estimate of investment return on a non-
          fixed income asset would not be more favourable than a
          benchmark based on historical performance of assets of
          its class and characteristics.




    LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Agenda
     •   CSOP
     •   Sub-committee mandate
     •   Review Existing Models
     •   “Canadian” Models
     •   Historical Period




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments

  •   Sub-committee Composition
       •   Christian-Marc Panneton (Chair)
       •   Bruno Benoit
       •   Brian Fortune
       •   Alexis Gerbeau
       •   Julie Perks
       •   Stephan Sabourin
       •   Brian Simpson



 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments

  •   Sub-Committee Mandate
       •   Is there a link between interest rates and equity returns?
  •   Does lower interest rates implies lower equity
      returns?
       •   Market equilibrium theory
              as the risk premium increase, utility of stocks increase, …
  •   Review of Literature
       •   Wilkie Model
       •   Hilbbert, Mowbray and Turnbull
       •   CAS and SOA Research
 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Agenda
     •   CSOP
     •   Sub-committee mandate
     •   Review Existing Models
     •   “Canadian” Models
     •   Historical Period




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments

 •   Wilkie Model
     •   Benchmark model in U.K.
     •   Postulates that inflation is the independent
         variable
     •   Cascade approach to model other variables




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Wilkie Model
                      Retail prices index


                       Equity share yield


       Equity share dividends           Consols yield


                Equity price index



 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
     •   First-order autoregressive model for inflation
                          ln 1  it   i  aln 1  it 1   i   i t
                                                     Pt 1 
     •   Return on equity                            P 
                                            yt  ln        
                                                     t 
                                                                                                     Dt
            •   Price established from the dividend yield                                    Pt 
                                                                                                    ye t 
            •   Dividend yield based on current inflation and an
                autoregressive process
  14%

                                                                 ln  ye t    ye ln 1  it   ln  ye   t
  12%                                    Dividend yield
  10%                                    Inflation
   8%
   6%
   4%
                                                                               t   yet 1   ye ye t 
   2%
   0%
  -2%
     1955       1965   1975    1985       1995            2005



 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
    •   Share dividends
         •   depend in part on the rate of inflation and in part on a
             lagged autoregressive term with a mixture of residuals
        D 
    ln  t   det   de ln 1  it   de   de ye ye t  1   de de de t  1   de de t 
       D 
        t 1 
                  t   de ln 1  it   1   de t 1

    •   No simple relation between equity returns and
        interest rate levels



 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Hilbbert, Mowbray and Turnbull, 2001
     •   Propose a different approach
     •   Equity return in excess of the nominal interest
         rate as a Markov regime switching model
                   yt   ln Pnom t  t , t   xt

                   where         xt ~ N E ,1 ,  E ,1 
                                                   2
                                                             if in regime 1
                                 xt ~ N E , 2 , E , 2 
                                                   2
                                                             if in regime 2




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Hilbbert, Mowbray and Turnbull, 2001
     •   Equity dividend yields
          •   log of the equity yield is assumed to follow an
              autoregressive process
                     ln d t   cd  d ln d t 1    d  d t 


                        where                  d   E ,1             if in regime 1
                                               d   E ,2             if in regime 2
     •   Estimated parameters for U.K.


 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   CAS and SOA Research
     •   Modeling of economic Series Coordinated with
         Interest Rate Scenarios, July 2004
          •   Kevin C. Ahlgrim
          •   Stephen P. D’Arcy
          •   Richard W. Gorvett
     •   Report available at
                   http://www.casact.org/research/econ/




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
    •   Modeling of economic Series Coordinated with
        Interest Rate Scenarios, July 2004
         •   Did a review of different models
         •   For equity return, used the same approach as in HMT
         •   US Large Stocks Parameters (1871-2002) monthly
             data
                 E ,1  0.8%         E ,1  3.9%      p1, 2  1.1%    1  84 %
                 E , 2   1 .1 %    E , 2  11 .3%   p2,1  5.9%     2  16 %




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Agenda
     •   CSOP
     •   Sub-committee mandate
     •   Review Existing Models
     •   “Canadian” Models
     •   Historical Period




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Canadian Market
     •   Data - StatCan
          •   TSX price index: V122620
          •   Price Earning Ratio: V122629
          •   Dividends: V122628
          •   3-Month T-Bill: V122541
          •   CPI: V735319




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Comparison of Models (Monthly)
     •   Log-Normal Model              yt     t

                yt  0.49 %  4.52 % t                log lik  984.4

               Expected annual return: 7.35%        std dev.: 16.92%


     •   Alternate Model 1             yt  rt     t
           yt  1.07 rt  1.07 %  4.51 % t          log lik  985.8
               If short-term rate at 3%: expected annual return: 11.47%
               If short-term rate at 9%: expected annual return: 4.57%


 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Comparison of Models (Monthly)
     •   Alternate Model 2                yt  rt     t
                yt  rt  0.06 %  4.55 % t             log lik  978.6
                 If short-term rate at 3%: expected annual return: 3.57%
                 If short-term rate at 9%: expected annual return: 9.94%

     •   Alternate Model 1 has the highest likelihood
          •   the lower the interest rate, the higher expected equity
              return



 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Comparison of Models (Monthly)
     •   Regime-Switching           yt        t

              Regime 1 (1.03%, 3.36%)                    log lik  1025.8
              Regime 2 (-1.71%, 7.21%)
              Expected annual return: 7.63%         std dev.: 17.76%


     •   HMT Model                  yt  rt        t

              Regime 1 (0.55%, 3.37%)                 log lik  1023.4
              Regime 2 (-2.51%, 7.15%)
              If short-term rate at 3%: expected annual return: 3.95%
              If short-term rate at 9%: expected annual return: 10.01%

 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Comparison of Models (Monthly)
     •   Alternate Model 3            yt  rt        t

                 Regime 1 (1.52%, 3.35%)                 log lik  1025.9
                 Regime 2 (-0.94%, 7.24%)
                 If short-term rate at 3%: expected annual return: 11.38%
                 If short-term rate at 9%: expected annual return: 4.49%

     •   Conclusion?
          •   No link between equity returns and short-term
              interest rate levels


 LOOKING BACK…focused on the future
       CIA Annual Meeting
       Session 5610 - CLIFR on Investments
           •   Conclusion
                 •    No clear relationship between equity returns
                      and short-term intererest rate for Canada
                       •    correlation: -0.07
30%                                       TSX Price return   25%

20%                                       3-month T-Bills
                                                             20%
10%
                                                             15%
 0%
                                                             10%
-10%
-20%                                                         5%

-30%                                                         0%
    1955       1965        1975   1985   1995        2005      -30%   -20%   -10%   0%      10%   20%

                                                                         TSX Price return

           LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Conclusion
     •   Alternate metrics
          •   correlation of price return with
                 short-term interest rate: – 0.07
                 variation in short-term interest rate: – 0.19
                 % variation in short-term interest rate: – 0.14
                 inflation: – 0.02
                 capitalisation rate: – 0.09




 LOOKING BACK…focused on the future
       CIA Annual Meeting
       Session 5610 - CLIFR on Investments

                  •    Weak relationship between equity returns and
                       short-term intererest rate change for Canada
                         •    correlation: -0.19
20%                                                         4%
                                                            3%
10%                                                         2%
 0%                                                         1%
                                                            0%
-10%                                                        -1%
-20%       TSX Price return                                 -2%
           3-month T-Bills Variation                        -3%
-30%                                                        -4%
    1955      1965           1975      1985   1995   2005      -30%   -20%   -10%   0%      10%   20%

                                                                         TSX Price return

           LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Comparison of Models (Monthly)
     •   Regime-Switching             yt        t

                Regime 1 (1.03%, 3.36%)                    log lik  1025.8
                Regime 2 (-1.71%, 7.21%)
                Expected annual return: 7.63%         std dev.: 17.76%

     •   Alternate Model 4 yt   rt  rt 1         t
                 1.67
                                                           log lik  1039.5
                Regime 1 (1.08%, 3.29%)
                Regime 2 (-2.05%, 7.09%)
                If short-term rate up 2%: expected annual return: 4.05%
                If short-term rate down 2%: expected annual return: 11.22%
 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Conclusion
     •   No direct link between interest rate levels and
         equity returns
     •   Possibly some indirect relationship
          •   As interest rate reach an historical low,
          •   lower probability to see interest rates decrease more.
          •   If higher equity returns when decreasing rates,
          •   then should observe lower equity returns




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Agenda
     •   CSOP
     •   Sub-committee mandate
     •   Review Existing Models
     •   “Canadian” Models
     •   Historical Period




 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
•    Which Historical Period?
     •   Example: TSX Total return index
          •    Last 25 years of historical data
          •    All available data
                  Canadian Markets: since January 1956
         14%
                   Last 25 years                                               Range
         13%       Since January 1956                        Last 25 years   9.1 - 13.8 %
         12%
                                                             Since Jan 56    9.0 - 10.8 %
         11%
         10%
                                                                  Complete history
         9%                                                     provides less random
         8%                                                         fluctuations!
           1989    1992     1995        1998   2001   2004


    LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Historical Period Selection
                      •     Statistical significance: standard error
                                                                                                                       
                                                                                                                       ˆ   standard error
                                                                                                          4.0%
     20%                                                                                                                               last 25 years
                                                                                                                                       since Jan 1956
     10%
                                                                                                          3.5%
      0%
     -10%                                                                                                 3.0%
     -20%
     -30%                                                                                                 2.5%
            févr-56
                          févr-62
                                    févr-68
                                              févr-74
                                                        févr-80
                                                                  févr-86
                                                                            févr-92
                                                                                      févr-98
                                                                                                févr-04

                                                                                                          2.0%
                                                                                                             1989-12   1994-12    1999-12       2004-12

                                                                                                          More stable and precise estimate by
                                                                                                           lengthening the historical dataset!

 LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
•   Goal is to find best estimate of future returns
     •   Which historical period?
              Using longest possible period
                  relationship with projection period
                  more stable: adding current experience has less impact
                  There was shocks in the past and there will be in the future
                  Cover both increasing and decreasing interest rate period
                            25%
                                                            3-month T-Bills
                            20%
                            15%
                            10%
                             5%
                             0%
                               1955   1965   1975   1985   1995       2005


    LOOKING BACK…focused on the future
CIA Annual Meeting
Session 5610 - CLIFR on Investments
 •   Returns for the Canadian Market
     •   TSX index from January 1956 - May 2005
     •   Capital appreciation (price return)
                                                           12
                                              9607 .3    592
          •   Geometric average:    6.07 %                    1
                                              525 .63 
          •   Continuous return:      5.89%         exp    6.07 %
                                      15.63%      exp   1  2  7.37 %
                                                              2

     •   Total return (include dividends reinvestment)      12
                                             22434 .39    592
          •   Geometric average:   9.57 %                      1
                                              246 .77 

          •   Continuous return:      9.14%        exp    9.57 %
                                      15.62%                        
                                                     exp   1  2  10 .92 %
                                                             2

 LOOKING BACK…focused on the future
    CIA Annual Meeting




LOOKING BACK…focused on the future
                                     33

				
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