1. Developing the Asset Liability for the CPP Investment Board Sterling Gunn VP, Portfolio and Risk Analysis CPP Investment Board Presented October 17, John Deutsch Institute, Queens University, Kingston, Ontario

2. 2 September 15 © 2007 copyright CPP Investment Board  Key Messages We are developing an asset liability model designed to maximize the CPPIB contribution to fund sustainability Our risk measure is explicitly linked to plan sustainability Our optimal portfolio strategy will account for the dynamics of asset returns and the net liabilities

3. 3 September 15 © 2007 copyright CPP Investment Board  Model the right Objective CPPIB Objective “To invest its assets with a view of achieving a maximum rate of return, without undue risk of loss, having regard to the factors that may affect the funding of the CPP”

4. 4 September 15 © 2007 copyright CPP Investment Board  Model the decision rights of key actors Key players make decisions critical to fund sustainability Chief actuary assesses fund sustainability based on estimates of the sustainable contribution rate CPPIB Plan Stewards committed to harvesting market returns CPPIB management recommends portfolio mix

5. 5 September 15 © 2007 copyright CPP Investment Board  Modeling uncertain liabilities and assets Developing a model that represent net liability cash flows and asset returns as stochastic processes Dynamics of net liability cash flows exogenous to ALM Changes in fund wealth driven by investment returns and net liabilities Investment returns are ‘controlled’ by portfolio allocation Objective function appropriate to CPP “minimize the probability of failing the Chief Actuary’s test of plan sustainability any time in the future” Posed as a stochastic dynamic control problem Find the portfolio strategy for dynamically adjusting asset allocation that minimizes the objective function

6. 6 September 15 © 2007 copyright CPP Investment Board  The optimal portfolio strategy minimizes the probability of failing the Chief Actuary’s test Change in wealth from T-1 to T is a function of asset allocation, a T-1, at time T-1 Wealth at time T is a stochastic variable which depends on asset allocation a T-1 made at time T-1 Riskier allocation increases expected return but also volatility For a given level of wealth at time T-1, find the optimal allocation at time T-1, a T-1, that minimizes the expected probability of failing test at time T-1 Result: Optimal asset allocation strategy dependent upon fund wealth and time t=T t=T-1 Algorithm works backward in time  w(a T-1 ) wealth

7. 7 September 15 © 2007 copyright CPP Investment Board  Model outcomes are relevant and objective An optimal portfolio strategy Maximizes our contribution to sustainability of CPP fund Dynamic allocation to a set of mutual funds –Sharpe Optimal growth portfolio (best return per unit of risk) –Minimum risk portfolio (safest portfolio) –A portfolio most ‘correlated’ with net liabilities used to modulate exposure to net liabilities Portfolio allocation depends upon fund wealth, time, net liabilities and other state variables Probability of failing the Chief Actuary’s test This risk measure is explicitly linked to fund objectives Indicator of fund sustainability

8. 8 September 15 © 2007 copyright CPP Investment Board  Stylized ALM Results Allocation between Sharp optimal portfolio (SOP) and minimum risk portfolio (MRP) Allocation to SOP declines as relative wealth increases Portfolio mix approaches fixed mix of SOP and MRP as wealth increases Fund is levered if allocation to SOP > 100% Probability of failing the Chief Actuary’s test declines as fund wealth increases

9. 9 September 15 © 2007 copyright CPP Investment Board  Summary We are developing an ALM that explicitly models the CPPIB contribution to CPP sustainability The optimal portfolio strategy maximizes our contribution to fund sustainability The probability of failing the Chief Actuary’s sustainability test is a natural and objective risk measure explicitly related to fund objectives

10. Developing the Asset Liability for the CPP Investment Board Sterling Gunn VP, Portfolio and Risk Analysis CPP Investment Board Email: sgunn@cppib.ca Phone: (416) 868-6673