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
|
IPS
Portfolio |
|
Proposed Portfolio |
|
Change |
Asset Class |
$ |
% |
$ |
% |
% |
US Large Cap Growth |
1,500,000 |
10 |
900,000 |
6 |
-4 |
US Large Cap Value |
4,500,000 |
30 |
750,000 |
5 |
-25 |
US Small Cap Growth |
|
|
750,000 |
5 |
5 |
US Small Cap Value |
1,500,000 |
10 |
3,045,000 |
20 |
10 |
International Equities |
|
|
2,516,000 |
17 |
17 |
Real Estate |
3,000,000 |
20 |
2,562,000 |
17 |
-3 |
U.S. Bonds |
3,000,000 |
20 |
3,077,000 |
21 |
1 |
U.S. Cash Equivalent |
1,500,000 |
10 |
1,400,000 |
9 |
-1 |
Total |
15,000,000 |
100 |
15,000,000 |
100 |
|
Expected Return |
13.03% |
|
14.45% |
|
|
Standard Deviation |
10.11% |
|
10.92% |
|
|
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
Percentile |
IPS,% |
Proposed,% |
95th |
16.31 |
17.93 |
75th |
14.00 |
15.44 |
67th |
13.47 |
14.92 |
50th |
12.56 |
13.90 |
33rd |
11.67 |
12.91 |
25th |
11.17 |
12.37 |
5th |
9.10 |
10.18 |
1. The first article in this series, published in July 2007, discusses this concept in detail.
2. A number of different Proposed portfolios are possible in this scenario. The purpose here is to demonstrate the impact of one of these possible portfolios on expected returns with only a modest increase in risk.
3. This assumption has very little, if any, impact on the simulation results. The portfolio’s asset class allocations will be made up of individual assets. In order to generate liquidity beyond the income generated by the portfolio to meet Roger’s withdrawal needs, only a relatively small amount, in dollar terms, of asset sales would have to be undertaken on an annual basis. Thus, matching capital gains and losses from these transactions is quite possible. Further, periodic rebalancing of the portfolio can also be undertaken in a similar tax-efficient manner.
4. The historical record of the indexes varies. In this case the shortest index began in 1976.
5. For example, the simulation assumes small cap stocks will have a higher expected risk and return than large cap stocks. Though large cap stock returns might be higher than small cap stock returns in any one period, they should not be systematically higher over time. Similarly bonds are assumed to have a lower average expected risk and return than stocks. The simulation also assumes that all assets have correlations that are stable on average.
6. Many possible simulation techniques exist to take account of all these relationships. Most of the investment-oriented simulations use a variation of the Monte Carlo approach, so named because it uses a random number generator (like a Roulette wheel) to create investment scenarios. Our goal is not to explain the detailed calculations of the simulation – different experts may very well come to different results because they use different inputs – but to show how the results of a simulation can be used.
7. In general the more scenarios the more accurate is the simulation in terms of reducing the variability of results. The number of scenarios used here is reasonable for expository purposes and should be determined on a case-by-case basis.
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