I want to spend a bit more time considering sustainable spending rates if we had foreknowledge of future investment returns. This analysis will help illustrate the impacts of two important matters:

- What happens to sustainable spending rates as the planning horizon extends further, and
- What happens to sustainable spending rates if we build in a constraint to preserve wealth and not allow portfolio depletion at the end of the planning horizon.

This analysis will consider inflation-adjusted investment returns, which will allow the sustainable spending rate to be defined as a percentage of the assets available at the initial date, with the spending amount adjusting for the realized inflation experience in subsequent years.

Exhibit 1 begins the analysis with planning horizons of ten to fifty years, real investment returns of 0%-6%, and an objective of depleting wealth by the end of the planning horizon. In looking at this exhibit, the sustainable spending rates for a 0% real return should be intuitive. With no returns, spending 10% of assets will deplete the portfolio in ten years, spending 5% per year will deplete the portfolio in twenty years, and so on. Without real investment growth, longer time horizons continue pushing the sustainable spending rate to lower levels.

As we move down the rows, we see that earning returns on the underlying portfolio naturally allows the spending rate to increase. For longer time horizons, spending rates continue to decline, but at a slower rate. In other words, long horizons allow for relatively more investment growth to better stabilize spending. For instance, with the investment growth associated with a 5% real return, the sustainable spending rate is 12.3% over ten years and 5.2% over fifty years.

To provide context, the assumptions of the traditional 4% rule can be found in this exhibit: it uses a spending horizon of thirty years and allows wealth to be depleted at the end of the horizon. With these circumstances, a 1% return supports a 3.8% spending rate, and a 2% return supports a 4.4% spending rate.

We can therefore understand that the real compounded return that led to the 4% rule fell somewhere between 1% and 2%. This aligns with what we found earlier using the PMT formula: the 4% spending rate matches a real investment return of 1.3%.

Exhibit 1Sustainable Spending Rates for Different Time Horizons and Investment Returns Objective: Deplete All Assets at End of Time Horizon | ||||||

Spending Horizon (in Years) | ||||||

10 | 20 | 30 | 40 | 50 | ||

Inflation-Adjusted Investment Return | 0% | 10.0% | 5.0% | 3.3% | 2.5% | 2.0% |

1% | 10.5% | 5.5% | 3.8% | 3.0% | 2.5% | |

2% | 10.9% | 6.0% | 4.4% | 3.6% | 3.1% | |

3% | 11.4% | 6.5% | 5.0% | 4.2% | 3.8% | |

4% | 11.9% | 7.1% | 5.6% | 4.9% | 4.5% | |

5% | 12.3% | 7.6% | 6.2% | 5.6% | 5.2% | |

6% | 12.8% | 8.2% | 6.9% | 6.3% | 6.0% |

While the allowance for wealth depletion characterizes the baseline assumption used in retirement income planning, Exhibit 2 moves us in the direction of preserving assets for indefinite use. Where Exhibit 1 allowed all assets to be depleted at the end of the horizon, Exhibit 2 aims to preserve 50% of assets (in inflation-adjusted terms) by the end through lower spending rates.

The intuition is most basic with a 0% return. With the desire to keep half of the initial wealth (adjusted for inflation), sustainable spending rates are cut in half. Now 5% is only sustainable for ten years, and 1% lasts fifty years. As return assumptions increase, the degree of differences between the two exhibits gets smaller.

For instance, with a 5% real return, the sustainable spending rate over fifty years falls from 5.2% to 5%. This small reduction to sustainable spending reflects just how sensitive remaining wealth is to small differences in spending rates over longer periods of time, at least when returns are high.

Within the context of the 4% rule, real compounded returns would need to be a bit above 3% to sustain a 4% spending rate over thirty years with an additional objective to preserve 50% of the purchasing power of the initial endowment.

Exhibit 2Sustainable Spending Rates for Different Time Horizons and Investment Returns Objective: Preserve 50% of Wealth (Inflation-Adjusted) at End of Horizon | ||||||

Spending Horizon (in Years) | ||||||

10 | 20 | 30 | 40 | 50 | ||

Inflation-Adjusted Investment Return | 0% | 5.0% | 2.5% | 1.7% | 1.3% | 1.0% |

1% | 5.7% | 3.2% | 2.4% | 2.0% | 1.8% | |

2% | 6.4% | 4.0% | 3.2% | 2.8% | 2.5% | |

3% | 7.1% | 4.7% | 3.9% | 3.6% | 3.3% | |

4% | 7.9% | 5.5% | 4.7% | 4.4% | 4.2% | |

5% | 8.5% | 6.2% | 5.5% | 5.2% | 5.0% | |

6% | 9.2% | 6.9% | 6.3% | 6.0% | 5.8% |

Exhibit 3Sustainable Spending Rates for Different Time Horizons and Investment Returns Objective: Preserve 100% of Wealth (Inflation-Adjusted) at End of Horizon | ||||||

Spending Horizon (in Years) | ||||||

10 | 20 | 30 | 40 | 50 | ||

Inflation-Adjusted Investment Return | 0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% |

1% | 1.0% | 1.0% | 1.0% | 1.0% | 1.0% | |

2% | 2.0% | 2.0% | 2.0% | 2.0% | 2.0% | |

3% | 2.9% | 2.9% | 2.9% | 2.9% | 2.9% | |

4% | 3.8% | 3.8% | 3.8% | 3.8% | 3.8% | |

5% | 4.8% | 4.8% | 4.8% | 4.8% | 4.8% | |

6% | 5.7% | 5.7% | 5.7% | 5.7% | 5.7% |

Finally, Exhibit 3 includes the objective that the full inflation-adjusted purchasing power of the initial endowment must be preserved at the end of the planning horizon.

With 0% returns and a desire to preserve the portfolio, the sustainable spending rate is obviously 0% regardless of the planning horizon. Nothing may be spent because the portfolio would be unable to make up the difference.

As for other investment returns, sustainable spending rates fall a bit below the investment return due to the assumption that spending is taken from the portfolio at the start of each year. For instance, regardless of horizon, the sustainable spending rate is 4.8% when the return is 5%. Again, this is only slightly less than the value found in Exhibit 2.

The investment return must be a bit higher than the spending rate so the portfolio balance can return to its initial level by year-end. Had spending been taken at the *end* of each year, the spending rate would equal the investment return, as you could indefinitely sustain a plan that spent each year’s investment return.

It is important to fully internalize how dependent spending rates are on investment returns. Naturally, lower returns allow for less spending. This is a key lesson to keep in mind for subsequent discussion. Next time, we will move away from assumptions about fixed market returns in order to further consider the impacts of market volatility.

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