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
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
July 17
© 2007 copyright CPP Investment Board
2
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”
July 17
© 2007 copyright CPP Investment Board
3
Model
the decision rights of key actors
Key players make decisions critical to fund
sustainability
•
•
•
July 17
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
© 2007 copyright CPP Investment Board
4
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
July 17
© 2007 copyright CPP Investment Board
5

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 aT-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,
aT-1, that minimizes the expected probability of failing test at time T-1
min ET 1  wT aT 1 
aT 1
• Result: Optimal asset allocation strategy dependent upon fund wealth and time
wealth
Algorithm works backward in time
t=T-1
July 17
t=T
© 2007 copyright CPP Investment Board
6

Model outcomes are relevant and
objective
July 17
•
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
© 2007 copyright CPP Investment Board
7
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%
Stylized allocation to Sharpe Optimal Portfolio
% allocation to SOGP
Stylized
fund wealth
• Probability of failing the Chief
Actuary’s test declines as fund
wealth increases
Stylized Probability of failing OCA test
Probability
1
0
fund wealth
July 17
© 2007 copyright CPP Investment Board
8
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
July 17
© 2007 copyright CPP Investment Board
9
Developing the Asset Liability
for the CPP Investment
Board
Sterling Gunn
VP, Portfolio and Risk Analysis
CPP Investment Board
Email: [email protected]
Phone: (416) 868-6673