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Goal-Driven Multi-Period Equilibrium for Retirement Glide Paths

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Summary

This report summary presents a method for setting equity allocations across a retirement investment horizon when the investor has a specified terminal wealth goal. It works backward from that goal, optimizing allocations while controlling risk. Two objective formulations are described: minimizing expected periodic contribution costs together with their volatility, or minimizing the initial outlay needed to reach the terminal goal at a chosen probability. A repeated, backward multi-period optimization uses Nash equilibrium so that later re-optimization does not undermine the original glide path.

The summary discusses sensitivity analysis and random simulations, reporting that greater risk aversion lowers equity weights and that equity return assumptions affect allocations more than volatility assumptions. A China-market target-date fund example uses six representative assets; the described path starts with relatively high equity exposure and declines toward retirement. Its reported historical backtest covers 2009–2017 and gives annualized return and Sharpe ratio, but the annualized volatility figure is missing. The source is a summary rather than the full report, and it cautions that mature-market assumptions may not transfer directly to local markets.

Key ideas

  • The allocation path is derived backward from a specified retirement wealth target under risk constraints.
  • Risk can be represented by the volatility of periodic costs or by the probability of missing the terminal goal.
  • A Nash equilibrium approach is used to keep allocations consistent when decisions are revisited over time.
  • The summary reports that greater risk aversion reduces equity weights, while higher expected equity returns increase them.
  • The China-market example is based on a historical backtest, and the source warns that market-specific conditions limit direct transfer of assumptions.

Tags

Multi-assetPortfolio constructionRisk managementBacktesting

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.