1. LOOKING BACK…focused on the future
CIA Annual Meeting
LOOKING BACK…focused on the future

2. Long-Term Equity Returns
Christian-Marc Panneton

3. Agenda CSOP Sub-committee mandate Review Existing Models
“Canadian” Models
Historical Period
Maybe make clear the stochastic modeling is on non fixed income? Not Interest rate models.

4. 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.

5. Agenda CSOP Sub-committee mandate Review Existing Models
“Canadian” Models
Historical Period
Maybe make clear the stochastic modeling is on non fixed income? Not Interest rate models.

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

7. 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

8. Agenda CSOP Sub-committee mandate Review Existing Models
“Canadian” Models
Historical Period
Maybe make clear the stochastic modeling is on non fixed income? Not Interest rate models.

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

10. Equity share dividends
Wilkie Model
Retail prices index
Equity share yield
Equity share dividends
Consols yield
Equity price index

11. First-order autoregressive model for inflation
Return on equity
Price established from the dividend yield
Dividend yield based on current inflation and an autoregressive process

12. No simple relation between equity returns and interest rate levels
Share dividends
depend in part on the rate of inflation and in part on a lagged autoregressive term with a mixture of residuals
No simple relation between equity returns and interest rate levels

13. Hilbbert, Mowbray and Turnbull, 2001
Propose a different approach
Equity return in excess of the nominal interest rate as a Markov regime switching model
where
if in regime 1
if in regime 2

14. Hilbbert, Mowbray and Turnbull, 2001
Equity dividend yields
log of the equity yield is assumed to follow an autoregressive process
where
if in regime 1
if in regime 2
Estimated parameters for U.K.

15. 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

16. 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 ( ) monthly data

17. Agenda CSOP Sub-committee mandate Review Existing Models
“Canadian” Models
Historical Period
Maybe make clear the stochastic modeling is on non fixed income? Not Interest rate models.

18. Canadian Market Data - StatCan TSX price index: V122620
Price Earning Ratio: V122629
Dividends: V122628
3-Month T-Bill: V122541
CPI: V735319

19. Comparison of Models (Monthly)
Log-Normal Model
Expected annual return: 7.35% std dev.: 16.92%
Alternate Model 1
If short-term rate at 3%: expected annual return: 11.47%
If short-term rate at 9%: expected annual return: 4.57%

20. Comparison of Models (Monthly)
Alternate Model 2
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

21. Comparison of Models (Monthly)
Regime-Switching
Regime 1 (1.03%, 3.36%)
Regime 2 (-1.71%, 7.21%)
Expected annual return: 7.63% std dev.: 17.76%
HMT Model
Regime 1 (0.55%, 3.37%)
Regime 2 (-2.51%, 7.15%)
If short-term rate at 3%: expected annual return: %
If short-term rate at 9%: expected annual return: 10.01%

22. Comparison of Models (Monthly)
Alternate Model 3
Regime 1 (1.52%, 3.35%)
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: %
Conclusion?
No link between equity returns and short-term interest rate levels

23. Conclusion
No clear relationship between equity returns and short-term intererest rate for Canada
correlation: -0.07
TSX Price return

24. 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

25. Weak relationship between equity returns and short-term intererest rate change for Canada
correlation: -0.19
TSX Price return

26. Comparison of Models (Monthly)
Regime-Switching
Regime 1 (1.03%, 3.36%)
Regime 2 (-1.71%, 7.21%)
Expected annual return: 7.63% std dev.: 17.76%
Alternate Model 4
Regime 1 (1.08%, 3.29%)
Regime 2 (-2.05%, 7.09%)
If short-term rate up 2%: expected annual return: %
If short-term rate down 2%: expected annual return: 11.22%

27. 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

28. Agenda CSOP Sub-committee mandate Review Existing Models
“Canadian” Models
Historical Period
Maybe make clear the stochastic modeling is on non fixed income? Not Interest rate models.

29. Complete history provides less random fluctuations!
Which Historical Period?
Example: TSX Total return index
Last 25 years of historical data
All available data
Canadian Markets: since January 1956
Last 25 years
Since Jan 56
Range % %
Complete history provides less random fluctuations!

30. Historical Period Selection
Statistical significance: standard error
standard error
More stable and precise estimate by lengthening the historical dataset!

31. 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

32. Returns for the Canadian Market
TSX index from January May 2005
Capital appreciation (price return)
Geometric average:
Continuous return:
Total return (include dividends reinvestment)

33. LOOKING BACK…focused on the future
CIA Annual Meeting
LOOKING BACK…focused on the future