Pension Fund Death Spiral

In a very simplified model (Pensions Dynamics, PPT), professor of investment strategy, Alan White, concludes that defined benefit pension plans probably cannot succeed on the long term.

Death Spiral
White shows that every pension fund with a non risk-free asset approach, will eventually encounter a “Death Spiral” which will lead to the collapse of the fund. The only solutions are:

• Raising contribution rates
• Lowering promised pension benefits.

Assumptions
All conclusions are based on the next summarized main assumptions:

• Compensation growth: 2% per year
• Pension contribution: 15% of yearly compensation
• Yearly retirement income objective: 70% of his final salary
• Risk-free rate of interest is 3%;Risk premium on the risky assets: 3%
• Annual volatility of the risky assets: 15%
• Time horizon: 100-year
• Risky Assets investment part : 60% of the portfolio
• Corresponding final pay pension defined as 20 year annuity
• Required minimum average Pension Fund asset value in steady state
  - at 3% return: €/$ 47,200
  - at 6% return: €/$ 23,600

Frequency Distribution Outcome
One of the most striking outcomes of this study is the fact that as we look farther in to the future of the simulated pension fund, the amplitude of the frequency distribution of asset values appears to be dropping to zero. The chance that (average) asset values will be between $10,000 and $100,000 gets smaller and smaller.

The reason for this is that the probability of very high asset values and the probability of entering a collapsed state (the collapsed funds are not shown in the next figure) both increase as we expand out time horizon. As a result the probability that assets remain in the intermediate interval, is reduced.

Another interesting facts are:

• Asset values appear to become more sustainable as the part 'risky assets' increases
• Collapse rates for growing pension funds are, (almost) independently of the asset mix, negligible.
• Collapse rates for more mature (steady state) pension funds are substantial and increase to deadly percentages as the time horizon increases from 50 to 100 years.

Remarks
Although Whites model is perhaps oversimplified and can be easily criticized, it clearly shows the essential principles of running a pension fund.

In a commentary, Rob Bauer (ABP, University of Maastricht) argues White's conclusions. Nevertheless, interesting stuff, that stimulates actuarial insight.

Links
Interesting corresponding links:

• Longer Horizons Can Handle Riskier Holdings
• Stochastic Interest rate models (2008)
• The calculus of retirement income