The Future of Pension Plan Funding London School of Economics UBS Pensions Research Programme

1
The Future of Pension Plan FundingLondon School
of Economics UBS Pensions Research Programme

• Paper
• Optimal Portfolio Allocation for Pension Funds in
  the Presence of Background Risk
• by
• David McCarthy (Imperial College) and David Miles
  (Morgan Stanley)
• Discussant
• Francisco Gomes
• London Business School

2
Goal of the Paper

• This paper studies the optimal asset allocation
  for a defined benefit pension fund.
• The pension fund has a deterministic finite
  horizon
• Terminal date at which its assets are converted
  into annuities that are used to pay off its
  liabilities.
• The fund chooses an investment strategy in every
  period before the terminal date
• It can invest in equities and an
  optimally-chosen portfolio of short and
  long-term bonds.

3
Model Set-up

• Important The pension funds liabilities are
  known in advance.
• The fund is closed to new employees.
• There is no accrual of new pension liabilities.
• Important The fund only manages its initial
  funds, since it receives no additional income.
• There are no additional contributions from
  existing employees.

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Model Set-up (cont.)

• This set-up significantly simplifies the problem,
  since there are only two sources of uncertainty
• Asset returns.
• Shocks to survival probabilities.
• Concern Ignoring other sources of uncertainty
  significantly decreases the degree of background
  risk faced by the pension fund
• Potential large positive bias in the optimal
  equity allocation.

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Model Set-up (cont.)

• Future worker contributions are like riskless
  asset holdings. In that case you get the Merton
  problem with a riskless income stream
• The contributions act as an implicit bond
  holding, and thus ignoring them will biased the
  optimal equity investment downwards.
• So we have two important missing features that
  might affect the results (they are opposing
  biases but unlikely to cancel out each other).

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Model Set-up (cont.)

• Firms usually extract fund surpluses gradually,
  by taking contribution holidays this might
  also affect the optimal investment incentives of
  trustees.

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Objective Function

• The funds trustees are assumed to maximize
• CRRA power utility preferences.
• Defined over the funds final asset position
  (after potential adjustments for deficits or
  surplus).
• Is this the right objective function?
• Study observed trustee behaviour.
• Ask trustees.

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Treatment of Deficits and Surpluses

• If the funds assets (at the terminal date)
  exceed its liabilities then
• The sponsor will (potentially) collect a fraction
  (t) of the surplus.
• If the funds assets (at the terminal date) fail
  to meet its liabilities then
• The sponsor will cover any deficits with
  probability p.
• If the sponsor defaults (probability 1-p), the
  insurer will cover a fraction (s) of the deficit.
• Multiple cases are consider for t, p and s. Good!

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Non-convexity in the asset allocation decision

• The paper discusses in detail the non-convexities
  in the optimal allocation just before the
  terminal date.
• These are theoretically interesting but
  probability not very important in practice.
• They dont exist for tT-10 and probably in other
  periods as well the objective function is made
  concave by the probabilities.
• So this would likely disappear as well if we were
  to add uncertainty in the terminal period, the
  size of the contributions, the size of the
  liabilities, etc.

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Numerical Solution and Related OR Literature

• The non-convexities in the objective function
  make this a very hard problem to solve
• Computationally intensive.
• Suggestion look at the OR literature on
  asset-liability management
• Scenario optimization tools will probably be
  faster.
• This OR literature might have studied similar
  types of problems before.

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Summary

• Conclusion This is a very nice paper!
• The authors are tackling a very interesting and
  important problem in a realistic model.
• Main suggestion Think of ways to try to
  incorporate even more realism into the analysis
  (clever short-cuts or alternative solution
  techniques).