Taking distributions from an investment portfolio amplifies the impacts of portfolio volatility, making retirement income planning particularly tricky as distributions tend to be the primary income source for retirees. We can use Monte Carlo simulations to show the increase of money-weighted investment returns in retirement, which has important implications about the choice for a fixed portfolio return assumption that should be used when creating financial plans within a spreadsheet.
Implied investment returns are usually not shown with Monte Carlo simulation output, but they exist underneath the hood. Which implied portfolio return supported a 90% chance for success? We have to reverse engineer Monte Carlo simulations to find out. The implied return will be lower than the average returns inputted in the simulation, and I find support for portfolio return assumptions for the post-retirement period being more conservative than for the pre-retirement period.
Consider three scenarios:
- An individual investing a lump-sum amount for thirty years,
- An individual saving a fixed percentage of a constant inflation-adjusted salary at the end of each year over a thirty-year accumulation period, and
- An individual withdrawing the maximum sustainable constant inflation-adjusted amount from a portfolio at the start of each year over a thirty-year retirement period.
Exhibit 1 below provides the distribution of results for the simulations. These simulations are based on a standard 50/50 portfolio using historical Morningstar data for the S&P 500 and intermediate-term government bonds. For the lump-sum investment, the numbers represent the distribution of average compounded returns over the 100,000 thirty-year periods. For the accumulation phase, the distribution of outcomes is for the internal rate of return when making thirty annual contributions at the end of each year relative to the final accumulated wealth at the end. For the retirement phase, the distribution of results is for the internal rates of return on the portfolio when withdrawing the maximum sustainable amount over a thirty-year period with distributions taken at the start of each year.
Exhibit 1
Distribution of Compounded Real Returns Over 30 Years
Monte Carlo Simulations For a 50/50 Asset Allocation
Based on SBBI Data, 1926-2015, S&P 500 and Intermediate-Term Government Bonds
Lump Sum | Accumulation | Retirement | |
1st Percentile | 0.7% | 0.2% | -0.1% |
5th Percentile | 2.0% | 1.6% | 1.3% |
10th Percentile | 2.6% | 2.4% | 2.0% |
25th Percentile | 3.8% | 3.7% | 3.4% |
Median | 5.1% | 5.1% | 4.9% |
75th Percentile | 6.4% | 6.6% | 6.6% |
90th Percentile | 7.6% | 7.9% | 8.2% |
95th Percentile | 8.3% | 8.7% | 9.3% |
99th Percentile | 9.7% | 10.2% | 11.3% |
Mean | 5.1% | 5.2% | 5.1% |
Std. Deviation | 1.9% | 2.2% | 2.5% |
Source: Own calculations with 100,000 Monte Carlo Simulations for 30-year periods for a portfolio with a 5.6% arithmetic real return and 10.8% volatility. |
In all three cases, the median return was close to 5.1%, which was the assumed compounded return for the simulations. However, most clients would probably shy away from using this number to develop a financial plan in a spreadsheet, because the probability the median can be achieved is only 50%. When choosing a number to plug into a spreadsheet, a conservative client might be more comfortable using something like the return in the 25th percentile—or even the 10^{th}—of the distribution. These numbers would correspond with 75% or 90% probabilities of success, respectively.
Financial planning software does not usually show the implied returns, but the exhibit does just that through a reverse engineering process. With the lump-sum investment, the compounded real return at the 25^{th} percentile is 3.8% over thirty years. For an accumulator, the 25^{th} percentile return is 3.7%, while it is 3.4% for the retiree. At the 10^{th}percentile, realized compounded real returns were 2.6% for the lump-sum investment, 2.4% for the accumulator, and 2% for the retiree.
These numbers are naturally lower to provide a greater chance of success, and sequence of returns risk pushes these numbers even lower for accumulators and retirees than with the lump-sum investment that does not experience sequence risk. The volatility of outcomes increases as we transition from a lump-sum (standard deviation of 1.9%) to accumulation (2.2%) to retirement (2.5%).
Monte Carlo simulations generally present results in terms of a probability for success. For instance, retirees may aim for a 90% rate of success or higher. An implied rate of return on the portfolio is connected to a given probability of success, though Monte Carlo simulations generally do not express their output in this way.
Higher rates of success would be connected with lower portfolio returns, since this return hurdle must be exceeded by the portfolio for the financial plan to be successful. In this discussion, I am tackling Monte Carlo from a different direction—using Monte Carlo simulations first to get a rate of return for the portfolio, then to simulate a financial plan using a fixed rate of return. Conservative investors will want to work with lower assumed returns, implying a need to save more today.
Individuals accumulating or spending assets will have different experiences than someone using a lump-sum investment. Accumulation effectively places greater importance on the returns earned late in your career when a given return impacts contributions longer.
With new contributions each year, the timing of returns matters, as later returns impact more contributions and have a larger impact on final wealth accumulations. This is sequence-of-returns risk as it applies in the accumulation phase. With greater importance placed on a shorter sequence of returns, we should expect a wider distribution of outcomes.
As for retirement, the impacts are even bigger as sequence risk further amplifies the impact of investment volatility. Retirees experience heightened sequence-of-returns risk when funding a constant spending stream from a volatile portfolio. While you may not be withdrawing more money, as your portfolio declines, your withdrawals become a larger percentage of your remaining assets.
This digs a hole for your portfolio that can be difficult to emerge from. The distribution of internal rates of return during retirement will be even wider because of the heightened importance placed upon the shorter sequence of post-retirement returns. A conservative retiree seeking a return assumption for retirement should use a lower value than pre-retirement.
This is another reason why individuals may want to use different return assumptions pre- and post-retirement. For example, a conservative client might be willing to use the 25^{th}percentile return during accumulation (calibrated to a 75% chance for success) but only the 10^{th} percentile during retirement (90% chance).
If the client were comfortable with the arithmetic real return and volatility of 5.6% and 10.8%, this would suggest using a 3.7% compounded real return assumption in the spreadsheet for accumulation and a 2% compounded real return assumption in their spreadsheet for retirement, even though the “best guess” about the compounding return they will experience is 5.1%.
Because of sequence-of-returns risk, conservative investors will want to use lower fixed return assumptions than just the compounded return assumed for a lump-sum investment. Sequence of returns risk is relevant for both the accumulation and retirement phases. Assumed returns should be lower in both cases.
The impact is even greater for retirement. Conservative clients will not want to use the “expected return” for their portfolios when developing lifetime financial plans. This is a really important point to remember and internalize when working in environments that require a return assumption but not an accompanying volatility.
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