Authors’ Note

Modern Portfolio Theory has become a customary tool used by investment professionals and, as such, constitutes an industry standard that investment decision makers cannot ignore.  This academic theory has become the bedrock of investment practice.  We have elected to publish three articles in consecutive editions of Wealth Strategies Journal to provide its readership with an understanding of Modern Portfolio Theory and the application of this theory to pertinent issues surrounding the administration and formulation of portfolios.  Sequential publication eliminates the need to redevelop Modern Portfolio Theory and other concepts in each article.  Wealth Strategies Journal readers will have the option of reviewing earlier articles to clarify any points of interest in subsequent articles.

This first article in this series, “Developing and Defining a Well Managed Portfolio – A Primer on Modern Portfolio Theory”, provided a foundation for understanding the underpinnings of Modern Portfolio Theory.  The second article described the usefulness to an investment decision maker of developing an investment policy statement and how the statement can be used to develop a portfolio’s appropriate risk level.  This final article in the series employs Modern Portfolio Theory and the investment policy statement as guides in helping determine an appropriate withdrawal rate for a portfolio. A useful tool in withdrawal rate decision making is the determination of the crossover rate:  the withdrawal rate such that at the end of the investment horizon period  the value of a more aggressive (higher risk) portfolio with a high withdrawal rate is the same as the value of a less aggressive (lower risk) portfolio with a lower withdrawal rate.    

I. Introduction

It was a hot, humid day in July 2007 and Roger Dowling was totally exhausted.  He had just spent the entire day with his attorney in an estate planning session.  Roger’s wife had died six months ago and her death necessitated a new will and a complete review of his estate plan.  Since Roger’s net worth was sizeable, the attorney, who also had worked considerably with experienced financial planners, had devised a will and estate plan that met his charitable and other intentions upon his death as well as minimized the potential estate and generation skipping transfer tax.  Roger, at the age of 65 and with a life expectancy of 20 years, had no intention of remarrying.

One of the issues Roger and his attorney had spent a considerable amount of time developing was the creation of a $15 million revocable trust with Roger as the trustee during his lifetime.  Upon his death, the trust becomes irrevocable with a corporate trustee.  The income beneficiaries of the irrevocable trust will be his two sons, William, age 28, and Milton, age 26.  The remainder beneficiaries of the irrevocable trust will be certain charities and, upon default in the exercise of their general power of appointment, the children of William and Milton, per stripes.

Much of Roger’s net worth consisted of non income producing raw land and since he recently retired he would be depending on the revocable trust for most of his living expenses.  During the planning session with his attorney, Roger had developed a preliminary investment policy statement (IPS) to be used as a guide for the administration of the revocable trust.  Included in the IPS was a rather conservative allocation to specific asset classes and a specified 3% withdrawal rate from the trust for Roger to meet his spending needs. 
           
As Roger reviewed the IPS he had a feeling of uneasiness.  On the one hand he felt the 3% withdrawal rate was not sufficient to maintain his current standard of living.  He planned to travel the world and maintain the second home in Florida.  On the other hand he wanted very much to have the corpus of the trust large enough upon his death to provide considerable income to his sons.  When he reached a final decision with respect to the management of the trust he planned to sit down with his sons and discuss the situation with them.
           
Roger decided to consult with his trusted financial consultant, Rick Hetterington.  During their conversation, Rick requested Roger send to him a copy of the trust document and the trust’s proposed IPS.  Rick promised to provide Roger an analysis within the next three weeks. 

The remainder of this article traces the thought process Rick followed to construct his recommendations.  The steps in the process were: select a feasible set of asset classes; construct an Efficient Frontier; analyze the portfolio planned in the IPS relative to that Efficient Frontier; investigate alternative portfolios with higher risk and return; use a simulation to determine the effect of different withdrawal rates on both the Proposed and IPS portfolios; and arrive at a recommended withdrawal rate.  A by-product of this process is the crossover rate – the withdrawal rate that produces the same projected ending wealth for two portfolios.  In Rick’s case he determined the withdrawal rate for the Proposed portfolio that produced the same ending wealth as was projected for the IPS portfolio.  We conclude with some observations on reasonable portfolio management practices and the importance of communication.

II. The Feasible Set and the Resulting Efficient Frontier

A.  The Feasible Set

Upon receiving and reviewing the information from Roger, Rick’s first step was to create an Efficient Frontier as of the end of June 2007.  He determined the asset classes and their corresponding benchmark indexes, shown in Figure 1, which Rick determined to be appropriate as the feasible set for constructing the Efficient Frontier.

Figure 1

Feasible Set
Asset Classes and their Benchmark Indexes

B.  The Efficient Frontier 

The Efficient Frontier that results from the feasible set is shown in Figure 2.

Figure 2

Feasible Set of Indexes and Their Efficient Frontier
as of June 2007

III. The IPS and Proposed Portfolio

A.  The IPS Portfolio – Expected Return and Risk

Next, Rick read the IPS prepared by Roger.  He paid particular attention to the sections of the IPS dealing with strategic asset allocation and the portfolio’s target rate of return.  The IPS portfolio’s strategic asset allocation is shown in Figure 3.  Using historical total return data for the asset classes and the percentage portfolio allocations indicated in the IPS, Rick estimated the expected return and standard deviation (risk) of the IPS portfolio as shown in Figure 3.  He noted the portfolio’s expected return of 13.03% was within the IPS’s target rate of return range of 12.5% to 13.5%.  The IPS was less specific with respect to the appropriate level of risk, stating only that the portfolio “should have a moderate level of risk.”  Given Roger’s apparent satisfaction with the proposed risk level associated with the proposed asset allocation under the IPS, Rick interpreted this to mean the portfolio should have less risk than an all equity portfolio but more risk than a purely fixed income portfolio.  He noted the IPS portfolio with a standard deviation of 10.11% met this criterion.

Figure 3

IPS and Proposed Portfolio Allocations
as of June 2007

Note: Percentages are rounded.

B. The Proposed Portfolio – Expected Return and Risk

While Rick was reasonably satisfied with the IPS portfolio’s expected return and risk, he was confident he could create a portfolio with a significantly higher expected return with only a modest increase in expected risk.  He was aware that Modern Portfolio Theory (MPT) suggests the most efficient portfolios lie on the Efficient Frontier.  That is, at a particular level of risk the portfolio with the highest level of expected return will be on the Efficient Frontier.  He also knew that MPT is a mechanical algorithm that produces efficient portfolios without regard to any criteria other than expected return, standard deviation, and correlation.  These allocations are efficient but do not necessarily reflect the investment experience, knowledge, or judgment of an experienced investor.  Thus, portfolios near the efficient frontier will often be more suitable for a portfolio than strictly efficient portfolios.1

Rick elected to duplicate Figure 2 but exclude all of the constituent asset classes with the exception of the most risky (Fama-French Small Value Stocks) and least risky (US 30-day TBill) asset classes.   This less cluttered Efficient Frontier is shown as Figure 4.  Rick then located the IPS portfolio based on its expected return and standard deviation relative to the Efficient Frontier.  As shown in Figure 4 the IPS portfolio is near but below the Efficient Frontier.
Given the desire for a moderate level of risk as expressed in the IPS and the slope of the Efficient Frontier, Rick investigated a number of portfolios on or just slightly below the Efficient Frontier at levels of risk greater than 10.11%.  Through an iterative process he decided on the Proposed portfolio allocation shown in Figure 3 and plotted relative to the Efficient Frontier in Figure 4.  The Proposed portfolio with an expected return of 14.45% and a standard deviation of 10.92% is very close to the Efficient Frontier and with a small increase in risk relative to the IPS portfolio offers a significantly higher expected rate of return.  Rick also noted the Proposed portfolio is a better diversified portfolio than the IPS portfolio. 2 

Figure 4

IPS and Proposed Portfolios Relative to the Efficient Frontier
as of June 2007

IV.  Simulation of Investment Returns

A.  Preparing for the Simulation

Rick’s next step was to compare the IPS and Proposed portfolios by simulating returns over a twenty year investment horizon – Roger’s life expectancy.  In preparing the simulation Rick noted the IPS indicated the trust would be managed in a tax-efficient manner such that all capital gains would be offset by capital losses and the trust would not incur capital gains taxes.  Though perhaps slightly unrealistic, for illustrative purposes Rick assumed the trust would not be liable for capital gains taxes.3  Also, it was assumed the trust would not be liable for income taxes as it was expected all net income would be distributed within the anticipated withdrawal amount.  He also gathered statistics (expected returns, standard deviations, and correlations) on the performance of the asset classes in Figure 3 for the period 1976 through June 2007.4

B.  Purpose of the Simulation
 
Rick used a simulation to help him compare the IPS and Proposed portfolios and to determine a new withdrawal rate that balances Roger’s need for income and at the same time preserves the corpus of the trust for his children.  Towards this end Rick’s simulation was designed to identify the maximum withdrawal rate, or crossover rate, such that the expected ending value of the Proposed portfolio is not less than the expected ending value of the IPS portfolio at a 3% withdrawal rate.  Rick realized that to generate a crossover rate the Proposed portfolio must offer a higher expected return and, thus, risk than the IPS portfolio.  Rick’s Proposed portfolio, shown in Figures 3 and 4, met this requirement.

C.  Inputs to the Simulation

Because an investment return simulation requires values for each constituent asset class to describe a portfolio’s future path, Rick used the historical asset class statistics to build forecasts.  He knew asset class returns should not be forecast independently, however, because MPT recognizes the importance of the relationships between them.5  Rick simulated short-term interest rates and used the relationship between those short-term rates and the asset classes in the feasible set to build scenarios of returns for the IPS and Proposed portfolios over twenty years.6

D.  Simulation Results

Rick’s simulation produced 500 return scenarios.7  Figure 5 summarizes these scenarios by listing the 95th through the 5th percentile of the returns to the two portfolios over the 500 scenarios.  As Rick expected, the Proposed portfolio’s returns outperformed the IPS portfolio’s returns at every percentile.
 

Figure 5

Simulated Return Percentiles
20 Year Horizon

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.