E.  Withdrawal Rates

Figure 6 compares the distribution of the ending values for the two portfolios at the current 3% withdrawal rate.

 Figure 6

 Simulated Ending Value Percentiles
at the End of a 20 Year Horizon
3% Annual Withdrawal Rate

Rick noted across the entire distribution the Proposed portfolio had higher simulated ending values after twenty years than the IPS portfolio.8  As expected, these results were consistent with his construction of the Proposed portfolio with a higher expected return than the IPS portfolio.  The figure also indicated the Proposed portfolio had a wider range of possible outcomes, reflecting its higher risk.

F.  Target Expected Ending Values 

Rick’s targets for the simulation were a series of expected ending values for the Proposed portfolio at different withdrawal rates that bracketed the expected ending value of the IPS portfolio ($94,321,375) at the 3% withdrawal rate.  He knew that as the withdrawal rate increased the expected ending value naturally falls.  Figure 7 shows Rick’s simulation results with different withdrawal rates.

Figure 7

Distributions of Possible Ending Values for the Proposed Portfolio
at Different Withdrawal Rates
at the end of a 20 Year Horizon

In reviewing Figure 7, Rick observed that with a 4% withdrawal rate the simulation produced an expected ending value of $98.6 million for the Proposed portfolio.  With a 4.25% withdrawal rate it produced an expected ending value of $93.6 million.  The IPS  portfolio’s ending expected value is $94.3 million with a 3% withdrawal rate.  Therefore, a withdrawal rate between 4% and 4.25% from the Proposed portfolio would provide Roger with additional income while leaving the sons no worse off in terms of the expected ending portfolio value twenty years hence.  Thus, the crossover rate is between 4% and 4.25%.

V. The Crossover Rate

A.  Identifying the Crossover Rate

Rick next created Figure 8, summarizing the simulations.  It shows the expected ending values of the IPS and Proposed portfolios under different withdrawal rate assumptions.   

      Figure 8

               Determination of the Crossover Rate
              Based on Different Withdrawal Rates
              and Expected Proposed Portfolio Values
          at the end of a 20 Year Horizon

At a withdrawal rate of 4.2125% the expected ending value of the Proposed portfolio was equal to $94.3 million, the ending value of the IPS portfolio with a 3% withdrawal rate.  Rick elected to recommend to Roger that he employ the Proposed portfolio and a 4% withdrawal rate.  Rick had two reasons for recommending a withdrawal rate slightly less than the crossover rate.  First, the increase in the withdrawal rate from 3% to 4% represented a significant, immediate increase in annual income for Roger of $150,000 or 33% from his current proposed level.  Rick knew Roger’s spending pattern and felt the income level provided by the 4% withdrawal rate from the Proposed portfolio met  Roger’s needs.  Second, Roger’s sons would have a portfolio with an expected value of $98.6 million in twenty years which would be almost $4.3 million ($98.6 - $94.3) larger at a 4% withdrawal rate than the expected value of the Proposed portfolio with a 4.2125% withdrawal rate.

B.  Another Advantage of the Proposed Portfolio

Rick noted Figure 8 also underscored one of the advantages of moving to the Proposed portfolio.  If the IPS portfolio is instituted and the withdrawal rate increased to 4%, the expected value twenty years hence falls to $76.7 million from $94.3 million with the Proposed portfolio, almost an $18 million decline.  Changing the portfolio composition from the IPS portfolio to the Proposed portfolio avoids the problem of increasing the withdrawal rate to satisfy Roger’s income needs and the resulting negative impact on his sons.

VI.   Periodic Review

A.  Annual Reviews

Rick realized implementation of the Proposed portfolio and the revised withdrawal rate should not be put into practice and forgotten.  Over time capital markets change.  What appears to be appropriate policy given currently available information may not hold into the future.  Therefore, he planned to recommend a formal review of the portfolio’s asset allocation and the withdrawal rate be undertaken, preferably each year.9

B.  Potential Adjustments to the Withdrawal Rate

Rick also intended to stress to Roger the importance of explaining to his sons what might happen in the future.  For example, if capital markets declined for an extended period, then several possible events might occur: a) Roger would have to accept a lower withdrawal rate, b) the sons would have to realize there will be a lower ending expected value, c) the portfolio’s composition would have to be reconstructed resulting in a higher level of expected return and risk, or d) a combination of the above. 

VII. Communication

Roger finished reading Rick’s report and was quite pleased with the quality and clarity of the presentation.  The problem of better balancing his income needs and the interests of his sons appeared to be addressed by the report.  He was willing for the trust portfolio to experience a slightly higher level of expected risk in order to achieve the higher expected rate of return.  Roger was satisfied the 4% withdrawal rate or $600,000 to be received initially from the trust would allow him to maintain his desired lifestyle and if the trust’s portfolio performed as expected the dollar amount of withdrawal would grow over time.

Roger recognized as trustee of the revocable trust he had the freedom to invest and withdraw funds from the portfolio as he saw fit.  Over the years Roger’s relationship with his sons had been somewhat uneven.  Since the death of his wife and their mother, the sons had become even less communicative.  Roger had observed among his friends a number of instances of dysfunctional families, especially when large sums of money were involved.  He therefore decided to sit down with his sons and explain his intentions.  He also planned to share with them the trust document, the revised IPS to reflect Rick’s report, and the report itself.  He was particularly pleased that the charts in Rick’s report were, for the most part, formulated in terms of dollars.  Roger felt that explaining outcomes to financially unsophisticated people, which his sons were, in dollar figures had much more meaning than percentages. Roger was hopeful the discussion would be informative for the sons and reduce any potential acrimony toward him as he enjoyed his lifestyle.