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Long-Term Equity Returns Christian-Marc Panneton

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.

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.

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.

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

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

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.

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

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

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

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

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

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.

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/

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

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.

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

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%

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

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: 3.95% If short-term rate at 9%: expected annual return: 10.01%

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: 4.49% Conclusion? No link between equity returns and short-term interest rate levels

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

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

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

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: 4.05% If short-term rate down 2%: expected annual return: 11.22%

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

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.

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 9.1 - 13.8 % 9.0 - 10.8 % Complete history provides less random fluctuations!

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

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

Returns for the Canadian Market TSX index from January 1956 - May 2005 Capital appreciation (price return) Geometric average: Continuous return: Total return (include dividends reinvestment)

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