BUCKET INVESTING with Dynamically Risk-Managed Portfolios by Tim Hanna, Ansh Chaudhary, and Jerry C

800-347-3539 | flexibleplan.com

BUCKET INVESTING With Dynamically Risk-Managed Portfolios By Tim Hanna, Ansh Chaudhary, and Jerry C. Wagner Flexible Plan Investments, Ltd. January 2021*

Summary We compare bucket investing to other common asset-allocation approaches—the traditional systematic withdrawal approach, in particular—for stocks and bonds. Our study analyzes some of the advantages and criticisms of the bucket investing approach. We conclude that using active management within the bucket approach can address some of the challenges of the method, which include sequence-of-returns and time-diversification issues. The bucket method with active management—specifically using different Multi-Strategy Core and Explore suitability profiles—shows the potential for much higher returns and can have greater psychological appeal to investors when compared to more traditional systematic withdrawal methods.

*Originally authored by Jerry C. Wagner, David Varadi, and Z. George Yang (September 2014). Jerry C. Wagner, J.D., is the founder and president of Flexible Plan Investments, Ltd., a U.S. registered investment advisory firm. The views and opinions are those of the authors only and do not necessarily represent those of Flexible Plan Investments or any of its affiliates. The authors are responsible for any errors. The authors also acknowledge the assistance of Renee Toth, Tiffany Wagner, and Jason Teed, and the programming assistance of Gayan Nagoda on data processing and statistics. The rise of bucket investing

It can be argued that the most important job for an investment adviser or financial planner is simply to protect investors from themselves. Creating an asset-allocation approach that can keep them invested and avoid selling risky investments at the wrong time is a difficult challenge. The “bucket” approach to investing has emerged as a popular asset-allocation methodology in the financial planning and advisory community because it is specifically designed to account for actual investor behavior.1

Designing an asset-allocation approach to meet a client’s financial objectives is often cited as the most important component of the investment advisory process. Despite the advent of Harry Markowitz’s modern portfolio theory, this process cannot be easily reduced to a financial engineering problem. Economists have long made a key assumption within their models that is highly flawed for the purposes of simplifying the mathematical implementation: They assume that human beings only make rational decisions.

Tim Maurer, a renowned financial adviser, speaker, and author, often states, “Personal finance is more personal than it is finance.” In that regard, economist Meir Statman has suggested that investors are neither irrational nor rational, but rather “normal”—that is, they display elements of both characteristics.2

The challenge of investor behavior

Empirical evidence has shown that investors are indeed far from rational. In a classic study by Dalbar, the average equity mutual fund investor made a return of 4.25%, while the S&P 500 made 6.02% over the same 20-year period. The 1.77% return differential could not be explained by financial theory and was famously dubbed “the behavior gap.” Investors lost over 60% of the returns available to them through poor market timing that was driven by emotional decision-making.3

The bucket investing approach seeks to address some of that emotional investor behavior with a combination of safety and a sense of control. It lets financial advisers set aside a portion of the investments to grow over time, assuring a steady income stream.4 Furthermore, it is highly compatible with the traditional financial-planning objectives that require matching assets to meet future liabilities.

What is bucket investing?

The bucket approach essentially divides a client’s portfolio assets into several pools, or “buckets.” Each bucket is assigned different planned goals, needs, or time horizons, and then a separate asset-allocation policy is designed for each. An individualized bucket approach also reflects financial planners’ and advisers’ emphasis on tailored solutions for their fee-paying clients.

Asset allocation using the bucket approach assigns each bucket a different asset type (such as bonds for income/capital preservation, or equities/stocks for capital appreciation). The simplest implementation of bucket investing would use only two buckets: bonds or cash to meet short- term expenses, and stocks for long-term growth5 (see illustration on the following page).

Bucket Investing | 800-347-3539 | flexibleplan.com 2 Different systems of bucket investing Simple Bucket Approach

Many different systems of bucket investing exist to address the specific needs and goals of different investors. Different tax brackets, opportunities to shelter income from taxation, unique planning objectives, and other factors all come into play. For example, some investors have relatively short-term objectives, while others may have longer- term goals such as saving for college tuition, retirement spending, or estate planning.

More complicated bucket strategies include those that use three to six buckets.6 Intermediate “buffer buckets” can have more refined planning time horizons designed for growth or spending goals and thus be targeted at layered return objectives. From an investment-management standpoint, a more complex bucket approach could use Wasting Bucket Approach different portfolios for each bucket, and these portfolios could be formed using either assets or strategies (or both) with either a passive or active management overlay.

Another example of a bucket approach commonly used by financial advisers is the “waterfall” bucket approach, in which the income bucket is replenished with flows from the longer-term buckets.

This study uses a “wasting” bucket approach whereby we drain the income bucket of its assets by withdrawing a fixed percentage annually for 10 years before turning to the stock bucket to generate the returns needed to make the annual withdrawal.

Common criticisms of the bucket investing approach

Though bucket investing addresses some of the negative investor behaviors previously described, it has drawn some criticism on its performance compared to other allocation strategies and for its capacity to manage risk over time and address sequence-of-returns risk.

Bucket Investing | 800-347-3539 | flexibleplan.com 3 Poor performance vs. static allocation strategies

A common criticism of the bucket approach is that it performs poorly when compared to static allocation strategies. However, many of the studies that advocate for one method or the other were conducted with a narrow set of historical data.7 Removing time-period biases leads to similar results under both strategies, which is illustrated by the case studies presented later in this paper.

Part of the reason the bucket approach has gained popularity in the investment advisory and planning community is the anecdotal evidence from peers that it improves client communication and retention. Behavioral finance proponents attribute this success mainly to the fact that most investors have a “mental accounting” bias.

Paraphrased from academic researcher Richard Thaler, who first coined the term, “mental accounting” describes a person’s tendency to categorize and evaluate economic outcomes by grouping their assets into a number of nonfungible (distinct) “mental accounts.”8 People may alter their perspective on money and investment according to the surrounding circumstances and make irrational decisions due to such a framing bias.

Behavioral life-cycle theory states that people mentally allocate wealth across three classifications: current income, current assets, and future income. As people tend to prefer spending now, rather than saving for later, the time-horizon-based bucket approach for wealth management was designed to address the psychological need for investors to have near-term liquidity, as well as continue working toward the goal of long-term growth of wealth.9

In practice, a floor level of assets designated as a short-term “spending bucket” is often kept as cash or in short-term securities that have little or no investment risk. Further, from a portfolio management perspective, planning “buckets” of capital under the framework of “goals-based investing”10 does institute beneficial risk discipline into the investment process.

Time diversification is a myth

One supposed benefit of using the bucket approach is that it aims to provide “time diversification.” According to the concept of time diversification, investments in higher-risk assets (such as stocks) are less risky over longer periods than shorter ones.

In a traditional two-bucket approach, the least-risky asset—typically, short-term bonds—is held in the bucket used to service immediate income needs. Meanwhile, the riskier portion of the portfolio—typically invested in stocks—is held in the bucket used for longer-term growth and aims to stay invested for a sufficient time to overcome any “bad luck” in terms of the start date (i.e., beginning of a bear versus the start of a bull market).

Some in the academic community debate the assertion that sufficient time will reduce the riskiness of stocks (see, for example, “What Practitioners Need to Know … About Time Diversification” by Mark Kritzman, “Stocks for the Long-Run” by Jeremy Siegel, and “The Long-Term Case for Equities—and How It Can Be Oversold” by Paul Samuelson). However, the numbers and the math are fairly straightforward and suggest that this matter is much more settled than in question.

Bucket Investing | 800-347-3539 | flexibleplan.com 4 Kritzman notes that the key point of confusion is that the probability of losing money—which is mathematically and empirically supported to be lower over time—does not consider the magnitude of the potential losses. Like any investment, the “expectation” is a function of both the probability of winning or losing and the ratio of the size of profits to losses. The dispersion of compound return percentages does shrink over time, but the variability of ending portfolio wealth (terminal wealth—the dollar value) actually increases over time.11 All of this is captured in financial options theory and pricing—and, in fact, the cost of option premiums does increase over time, which reflects the truth that time diversification is illusory.12 Failure to understand this can lead to some faulty construction of the longer-term buckets.

To illustrate this concept, we performed a series of Monte Carlo simulations using Brownian motion, which is a typically accepted practice for modeling a financial time series. Figure 1 shows the distribution of compound returns for five-year simulations, assuming that the market has a return of 8% and a standard deviation of 20%. We performed 25,000 simulations.

Figure 1 Distribution of Compound Returns for a 5-Year Stock Simulation

Source: Flexible Plan Investments Research

Notice that there is considerable variability when holding stocks for such a short time period. While the distribution is skewed, the absolute values of the maximum and minimum return values are nearly identical.

Subsequently, we performed a simulation using a long time period instead. In this case, to make the results clear, we chose 100 years (Figure 2).

Bucket Investing | 800-347-3539 | flexibleplan.com 5 Figure 2 Distribution of Compound Returns for a 100-Year Stock Simulation

The Spread Narrows

Source: Flexible Plan Investments Research It is easy to see that, as more time passes, returns at almost every point in the distribution become positive.

The problem is that investors do not get 100-year returns. Instead, they must compound them over a shorter time period. In other words, every year they must, in effect, re-invest their portfolio and have their entire wealth fluctuate as a function of the next year’s investment return. This is why risk management is so important, because a 50% loss can erase more than 10 years of investment gains.

In the next set of simulations, we show the distribution of terminal wealth (ending portfolio wealth) as a function of an investor’s holding period using the same set of assumptions.

Dispersion of terminal wealth for simulated stock time series

Figure 3 $100,000 “Grows” to Ending Balance Over 5-Year Holding Period

Source: Flexible Plan Investments Research

Bucket Investing | 800-347-3539 | flexibleplan.com 6 Figure 4 Distribution of Terminal Wealth 20-Year Holding Period

The Spread Widens

Source: Flexible Plan Investments Research

Figure 5 Distribution of Terminal Wealth 100-Year Holding Period

The Spread Gets Even Wider

Source: Flexible Plan Investments Research

Notice that the maximum terminal wealth is just over $750,000, while the minimum is close to $20,000. For comparison, we ran the same study using a 20-year and then a 100-year time frame (Figures 4 and 5).

In both the 20-year and 100-year holding periods, there are multiple instances of portfolios that have an ending wealth that is below $10,000 (i.e., a loss of more than 90%), and in some cases close to zero! Of course, the magnitude of the possible gains is also substantially higher than for the five-year portfolio, with billions of dollars being earned in the 100-year portfolio in some cases.

The variation in the outcomes of terminal wealth increases substantially over time, but the center of the distribution of terminal wealth outcomes tends to shift higher the longer the holding period. This highlights how a longer holding period tends to increase the likelihood of higher terminal wealth and decrease the likelihood of the portfolio experiencing a loss.

Bucket Investing | 800-347-3539 | flexibleplan.com 7 The “sequence of returns” dilemma

The sequence of returns is essential to Table 1 A simulation of asset allocation determining ending portfolio wealth and over time for the bucket approach whether or not an investor will be successful in achieving desired results. Finance professor Moshe Milevsky claims in his article “Can Buckets Bail-Out a Poor Sequence of Investment Returns?” that using the bucket approach or any other type of time-based asset-allocation methodology is, in fact, just an illusion.13

Using the bucket approach cannot protect an investor from a poor sequence of returns; although, it can potentially shift the risk to a different point in time, depending on when the investor is most exposed to equities.

The key point that Milevsky makes is that, without doing more, the asset allocation of an investor using the bucket methodology will change substantially over time. For example, in Table 1, we perform a 20-year simulation with stocks and bonds with a 4% withdrawal rate using a two-bucket approach, with each bucket given a 10-year time horizon.

Starting with a 50/50 portfolio of stocks and bonds, the bucket investor eventually shifts to 100% stocks. In this simulation, the average allocation was actually 77% in stocks and 23% in bonds—which is a significant departure from the original 50/50 portfolio. The actual average asset allocation and timing of the shifts will depend on the underlying market performance, the number of buckets, and the length of each bucket’s Source: Flexible Plan Investments Research. Assumes an 8% compound annual growth rate (CAGR) and a 20% standard deviation for the stock time horizon. basket and a 5% CAGR and 6% standard deviation for the bond basket. Correlation was assumed to be zero and 4% was withdrawn annually. 25,000 simulations were performed. This implies that the bucket approach is not easily comparable to a withdrawal strategy with, for example, a constantly rebalanced portfolio. However, as a general statement, the bucket approach is most exposed to equity risk at the end of the period and somewhat less exposed to risk at the beginning of the investment period.

Bucket Investing | 800-347-3539 | flexibleplan.com 8 At the outset, withdrawals will be taken from the less risky asset and therefore create less dependency on equity volatility than a systematic withdrawal approach from a constantly rebalanced portfolio. This can present problems, depending on when equity or fixed-income risk increase and losses are incurred.

A solution to address this criticism, which is discussed later in this paper, would be to use actively managed buckets, in which the overall exposure in each bucket mimics that of stocks and bonds, but the actively managed strategies help to reduce the exposure to risk during volatile periods, reducing the “sequence of returns” risk more than a passive allocation to equities and bonds would potentially produce.

Case studies: Simulations of the bucket approach versus systematic withdrawal methods

To better illustrate the benefits of using a bucket approach over a traditional asset-allocation approach, and counter some of the criticisms of the bucket approach, we ran a series of case studies using Monte Carlo simulations.

We compare three basic methods:

1. A simple two-bucket approach (50% in bonds for the first bucket and 50% in stocks for the second bucket) where the first bucket was liquidated and shifted to the next bucket at the end of its respective time horizon. We chose 10 years as the time horizon for each bucket. 2. A systematic withdrawal (SW) approach that assumes a constantly rebalanced portfolio fixed at 50% in stocks and 50% in bonds. 3. A systematic-withdrawal time-weighted (SW/TW) approach designed to be more comparable to the average asset allocation of the bucket approach. We used 2/3 in stocks and 1/3 in bonds in this approach to reflect the fact that the bucket method has an investment in the stock portfolio that is twice as long as the investment in bonds.

We made the following assumptions, which we believe to be reasonable from a historical standpoint:

• That stocks would have an 8% return with a 20% standard deviation. • That bonds would have a 5% return and a 6% standard deviation. • That the correlation between stocks and bonds was zero. • That the investor would withdraw 4% annually for a total time period of 20 years.

Using the bucket approach, each bucket lasted 10 years; the first bucket contained bonds, and the second contained stocks. To make accurate conclusions, we ran 25,000 different simulations and averaged the results.

One of the key metrics that we used to evaluate “success” for the investor was the Omega statistic (for more about the Omega statistic, see “A Universal Performance Measure” by Con Keating and William Shadwick, as well as the Appendix at the end of this paper). This statistic is used in option pricing and is a comprehensive risk measure that captures the upside versus the downside given a threshold return. The Omega ratio is a relative measure of the likelihood

Bucket Investing | 800-347-3539 | flexibleplan.com 9 of achieving a given return, such as a minimum acceptable return or a target return (see the Appendix for a deeper discussion of the Omega ratio and the formula we used to calculate it).

For our simulations, we randomly generated one-year returns until we had a 20-year sample. To calculate Omega, we used the annualized returns of each simulation as returns in the inputs into the function.

Base case: Bucket approach identical to systematic withdrawal using the same asset class

For a base case (Table 2), we wanted to see if there was any difference between the bucket approach and systematic withdrawal under the assumption that one uses the same asset in each bucket. If there is no difference, this implies that creating different time horizons or liquidation schedules has no impact on performance. In all cases, “ATV” represents the average terminal value and “MAR” represents the annualized return relative to the maximum drawdown (MDD).

Table 2 Base Case Example: 10% Return/10% Risk and 5% Withdrawal

Same Asset Used in Bucket and SW

i etun isk eg SW $384,554.66 $2,253,507.00 0.02% 6.18% 9.78% 15.48% 88.14 0.399 Bucket $384,727.21 $2,039,599.02 0.02% 6.18% 9.77% 15.46% 87.39 0.400

Source: Flexible Plan Investments Research

Notice that the statistics are nearly identical i betweenetun the SWisk and bucket approaches.eg This is toSW be expected$197,905.00 since it is$1,174,852.57 the same investment0.14% with2.38% the same10.00% level of26.61% risk and return.4.81 In the0.090 nextBucket case, we$244,748.07 show a more$3,711,944.47 realistic example0.88% using1.58% reasonable16.20% assumptions42.67% for1.81 both stocks0.040 andSW/TW bonds. $223,627.30 $2,195,026.81 0.95% 1.60% 13.03% 35.17% 1.90 0.050

Case 1: Comparing the bucket approach i withetun systematicisk withdrawal usingeg stocks and bondsSW $142,471.00 $1,024,537.00 0.22% 0.62% 12.00% 35.88% 1.53 0.020 Bucket $52,478.61 $776,498.00 5.97% -10.70% 21.68% 74.49% 0.02 -0.140 SW/TW $141,390.09 $1,182,058.76 1.23% -0.94% 15.39% 47.56% 0.65 -0.020 When we again compare the bucket approach to systematic withdrawal (fixed-weighted 50/50 and time-weighted 25/75) but use different asset classes in each bucket, one holding stocks and the other bonds (Table 3), we see that i the fixed-weightedetun isk 50/50 SW approacheg has the highestSW Omega$101,907.70 value. This$1,085,982.00 implies that2.22% it is the best-3.34% choice11.60% for achieving45.87% a 4% 0.23withdrawal-0.070 rate inBucket the long run.$116,801.71 The time-weighted$1,977,583.65 (25/75)4.34% systematic-5.51% withdrawal16.11% had54.45% the next 0.20best Omega,-0.100 SW/TW $85,240.70 $1,494,050.00 12.00% -14.36% 13.89% 61.00% 0.06 -23.540 followed by the bucket approach. The reward-to-risk rankings for the three approaches in this case is the same for MAR and Omega. i etun isk eg SW $384,554.66 $2,253,507.00 0.02% i etun6.18% 9.78%isk 15.48% eg88.14 0.399 BucketSW Table$384,727.21$196,688.06 3 Case 1:$2,039,599.02 $620,924.18 Stocks and Bonds0.02%0.00% in 50/50,6.18%2.87% 8% Return/20%9.77%8.55% 15.46%20.19% Risk for 87.390.32Stocks, 0.4000.142 Bucket $161,941.455% Return/6% $476,706.59 Risk for Bonds,0.00% 0 Correlation,2.00% 6.41% and 4%16.91% Withdrawal0.09 0.118 SW/TW $201,338.00 $1,039,394.40 0.50% 1.77% 11.59% 32.17% 0.26 0.055 i etun isk eg SW $197,905.00 $1,174,852.57 0.14% 2.38% 10.00% 26.61% 4.81 0.090 Bucket $244,748.07 $3,711,944.47 0.88% i etun1.58% 16.20%isk 42.67% eg1.81 0.040 SW/TWSW $223,627.30$492,773.37 $2,195,026.81 $1,602,079.57 0.95%0 1.60%7.62% 13.03%10.61% 35.17%14.48% 26.011.90 0.5260.050 Bucket $964,548.59 $8,498,561.31 0 10.54% 15.85% 21.80% 48.75 0.483 Source: Flexible Plan Investments Research i etun isk eg BucketSW Investing$142,471.00 | 800-347-3539$1,024,537.00 | flexibleplan.com0.22% 0.62% 12.00% 35.88% 1.53 0.020 10 Bucket $52,478.61 $776,498.00 5.97% -10.70% 21.68% 74.49% 0.02 -0.140 SW/TW $141,390.09 $1,182,058.76 1.23% -0.94% 15.39% 47.56% 0.65 -0.020 MSCC-MSLV 122.4 20.3 3.5 0.7 0.1 0.0 MSCM-MSLC 443.4 93.6 22.1 5.8 1.5 0.3 MSCB-MSSE 2.2 i etun isk eg MSCG-MSET 607.7 213.0 66.0 24.9 6.8 2.7 SW $101,907.70 $1,085,982.00 2.22% -3.34% 11.60% 45.87% 0.23 -0.070 MSCA-MSET 478.1 167.8 61.5 19.1 8.0 Bucket $116,801.71 $1,977,583.65 4.34% -5.51% 16.11% 54.45% 0.20 -0.100 S&P 500 0.0 0.0 0.0 0.0 0.0 0.0 TreasurysSW/TW (10-year)$85,240.70 $1,494,050.00 12.00%0.2 -14.36%0.0 13.89%0.0 61.00%0.0 0.060.0 -23.5400.0 60/40 S&P 500 and Treasurys 0.3 0.1 0.0 0.0 0.0 0.0

i etun isk eg MSCC-MSLVSW $196,688.06 $620,924.18 0.00% 2.87% 8.55%0.81 20.19%0.46 0.180.32 0.142-0.03 MSCM-MSLCBucket $161,941.45 $476,706.59 0.00%1.42 2.00%1.13 6.41% 16.91%0.60 0.370.09 0.1180.13 MSCB-MSSESW/TW $201,338.00 $1,039,394.40 0.50%1.12 1.77%0.97 11.59%0.83 32.17% 0.26 0.055 MSCG-MSET 0.81 0.73 0.65 0.57 0.46 0.33 MSCA-MSET 0.73 0.67 0.62 0.54 0.46 0.34 S&P 500 -0.16 i etun-0.31 -0.47isk -0.59 eg-0.70 -0.79 TreasurysSW (10-year) $492,773.37 $1,602,079.57 0.280 7.62%0.13 10.61%0.02 14.48%-0.07 26.01-0.26 0.526-0.54 60/40Bucket S&P 500 $964,548.59 and Treasurys $8,498,561.31 0.100 10.54%0.03 15.85%-0.09 21.80%-0.26 48.75-0.47 0.483-0.66

e in MSCC-MSLV 100.00%122.4 100.00%20.3 100.00%3.5 100.00%0.7 99.97%0.1 99.02%0.0 MSCM-MSLC 100.00%443.4 100.00%93.6 100.00%22.1 100.00%5.8 99.92%1.5 99.13%0.3 MSCB-MSSE 100.00% 100.00% 100.00% 99.99% 99.86% 99.21%2.2 MSCG-MSET 100.00%607.7 100.00%213.0 99.96%66.0 99.87%24.9 99.50%6.8 98.37%2.7 MSCA-MSET 100.00%478.1 99.99%167.8 99.94%61.5 99.70%19.1 99.26%8.0 98.17% S&P 500 90.87%0.0 80.57%0.0 67.66%0.0 54.46%0.0 41.62%0.0 31.39%0.0 Treasurys (10-year) 100.00%0.2 100.00%0.0 99.97%0.0 98.82%0.0 89.36%0.0 60.44%0.0 60/40 S&P 500 and Treasurys 99.98%0.3 99.58%0.1 96.73%0.0 88.29%0.0 71.84%0.0 50.98%0.0 e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.98% 99.06% MSCM-MSLC 100.00% 100.00% 100.00% 99.99% 99.95% 99.17% MSCB-MSSE 100.00% 100.00% 100.00% 99.97% 99.83% 99.30% MSCC-MSLV 0.81 0.46 0.18 -0.03 MSCG-MSET 100.00% 100.00% 99.98% 99.83% 99.44% 98.40% MSCM-MSLC 1.42 1.13 0.60 0.37 0.13 MSCA-MSET 100.00% 99.98% 99.95% 99.70% 99.24% 99.82% MSCB-MSSE 1.12 0.97 0.83 S&P 500 90.76% 80.21% 67.29% 53.98% 42.15% 31.06% MSCG-MSET 0.81 0.73 0.65 0.57 0.46 0.33 Treasurys (10-year) 100.00% 100.00% 99.98% 98.93% 89.48% 60.97% MSCA-MSET 0.73 0.67 0.62 0.54 0.46 0.34 60/40 S&P 500 and Treasurys 99.98% 99.60% 96.72% 88.44% 71.80% 51.07% S&P 500 -0.16 -0.31 -0.47 -0.59 -0.70 -0.79 Treasurys (10-year) 0.28 0.13 0.02 -0.07 -0.26 -0.54 60/40 S&P 500 and Treasurys 0.10 0.03 -0.09 -0.26 -0.47 -0.66

e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.97% 99.02% MSCM-MSLC 100.00% 100.00% 100.00% 100.00% 99.92% 99.13% MSCB-MSSE 100.00% 100.00% 100.00% 99.99% 99.86% 99.21% MSCG-MSET 100.00% 100.00% 99.96% 99.87% 99.50% 98.37% MSCA-MSET 100.00% 99.99% 99.94% 99.70% 99.26% 98.17% S&P 500 90.87% 80.57% 67.66% 54.46% 41.62% 31.39% Treasurys (10-year) 100.00% 100.00% 99.97% 98.82% 89.36% 60.44% 60/40 S&P 500 and Treasurys 99.98% 99.58% 96.73% 88.29% 71.84% 50.98% e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.98% 99.06% MSCM-MSLC 100.00% 100.00% 100.00% 99.99% 99.95% 99.17% MSCB-MSSE 100.00% 100.00% 100.00% 99.97% 99.83% 99.30% MSCG-MSET 100.00% 100.00% 99.98% 99.83% 99.44% 98.40% MSCA-MSET 100.00% 99.98% 99.95% 99.70% 99.24% 99.82% S&P 500 90.76% 80.21% 67.29% 53.98% 42.15% 31.06% Treasurys (10-year) 100.00% 100.00% 99.98% 98.93% 89.48% 60.97% 60/40 S&P 500 and Treasurys 99.98% 99.60% 96.72% 88.44% 71.80% 51.07% What is interesting is that the probability of failure for the bucket approach is lower than the SW/TW approach. This is consistent with the literature that uses probability-of-failure approaches to justify the use of the bucket approach. However, as we have indicated, the Omega statistic is a more comprehensive measure to evaluate success.

Another predictable outcome was that the bucket approach had the highest average terminal value (ATV) among the different approaches. The maximum portfolio wealth was also substantially higher for the bucket approach. This reflects the following:

1. The bucket method has a higher average stock allocation over time. 2. Withdrawals are deferred from the equity bucket for 10 years, which shields the compound returns from the damaging effects of withdrawing early under volatile conditions. 3. By avoiding rebalancing between stocks and bonds, the equity allocation is allowed to compound over time and grow within the portfolio.

Still, since the bucket exposure to equity is greater, it is obvious that despite the higher end value, the risk assumed to reach that end is the highest of the methods reviewed. Both risk and maximum drawdown are substantially higher than the other two methods.

In summary, while using the bucket approach with traditional asset classes can potentially increase the return to investors, it does so at the cost of exposing them to more risk and a potentially lower chance of financial-planning success (i.e., reaching their expected annual goal).

Cases 2 and 3: Comparing a bear market at the beginning and end of the holding period

The previous case studies only tell part of the story. As discussed, sequence of return can be problematic for bucket investing. To examine the impact of the sequence of returns, we take a look at two different circumstances, the first with bad luck at the end of the period in the form of a 50% bear market in stocks in the last year (Table 4), and the other where the bear market occurs in the first year the portfolio is invested i (Tableetun 5). isk eg SW $384,554.66 $2,253,507.00 0.02% 6.18% 9.78% 15.48% 88.14 0.399 SinceBucket the bucket$384,727.21 approach$2,039,599.02 is 100% in 0.02%stocks after6.18% the first9.77% 10 years,15.46% we would87.39 predict that0.400 it would be more adversely impacted by bad luck or a protracted bear market near the end than a systematic withdrawal approach. i etun isk eg SW $197,905.00 $1,174,852.57 0.14% 2.38% 10.00% 26.61% 4.81 0.090 Bucket $244,748.07 Table$3,711,944.47 4 Case 2: 0.88%Bad Luck 1.58%at the End16.20% of the Period42.67% 1.81 0.040 SW/TW $223,627.30 $2,195,026.81 0.95% 1.60% 13.03% 35.17% 1.90 0.050 50% Bear Market in Stocks in the Last Year

i etun isk eg SW $142,471.00 $1,024,537.00 0.22% 0.62% 12.00% 35.88% 1.53 0.020 Bucket $52,478.61 $776,498.00 5.97% -10.70% 21.68% 74.49% 0.02 -0.140 SW/TW $141,390.09 $1,182,058.76 1.23% -0.94% 15.39% 47.56% 0.65 -0.020

Source: Flexible Plan Investments Research i etun isk eg SW $101,907.70 $1,085,982.00 2.22% -3.34% 11.60% 45.87% 0.23 -0.070 Bucket $116,801.71 $1,977,583.65 4.34% -5.51% 16.11% 54.45% 0.20 -0.100 SW/TW $85,240.70 $1,494,050.00 12.00% -14.36% 13.89% 61.00% 0.06 -23.540

Bucket Investing | 800-347-3539 | flexibleplan.com 11 i etun isk eg SW $196,688.06 $620,924.18 0.00% 2.87% 8.55% 20.19% 0.32 0.142 Bucket $161,941.45 $476,706.59 0.00% 2.00% 6.41% 16.91% 0.09 0.118 SW/TW $201,338.00 $1,039,394.40 0.50% 1.77% 11.59% 32.17% 0.26 0.055

i etun isk eg SW $492,773.37 $1,602,079.57 0 7.62% 10.61% 14.48% 26.01 0.526 Bucket $964,548.59 $8,498,561.31 0 10.54% 15.85% 21.80% 48.75 0.483

MSCC-MSLV 122.4 20.3 3.5 0.7 0.1 0.0 MSCM-MSLC 443.4 93.6 22.1 5.8 1.5 0.3 MSCB-MSSE 2.2 MSCG-MSET 607.7 213.0 66.0 24.9 6.8 2.7 MSCA-MSET 478.1 167.8 61.5 19.1 8.0 S&P 500 0.0 0.0 0.0 0.0 0.0 0.0 Treasurys (10-year) 0.2 0.0 0.0 0.0 0.0 0.0 60/40 S&P 500 and Treasurys 0.3 0.1 0.0 0.0 0.0 0.0

MSCC-MSLV 0.81 0.46 0.18 -0.03 MSCM-MSLC 1.42 1.13 0.60 0.37 0.13 MSCB-MSSE 1.12 0.97 0.83 MSCG-MSET 0.81 0.73 0.65 0.57 0.46 0.33 MSCA-MSET 0.73 0.67 0.62 0.54 0.46 0.34 S&P 500 -0.16 -0.31 -0.47 -0.59 -0.70 -0.79 Treasurys (10-year) 0.28 0.13 0.02 -0.07 -0.26 -0.54 60/40 S&P 500 and Treasurys 0.10 0.03 -0.09 -0.26 -0.47 -0.66

e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.97% 99.02% MSCM-MSLC 100.00% 100.00% 100.00% 100.00% 99.92% 99.13% MSCB-MSSE 100.00% 100.00% 100.00% 99.99% 99.86% 99.21% MSCG-MSET 100.00% 100.00% 99.96% 99.87% 99.50% 98.37% MSCA-MSET 100.00% 99.99% 99.94% 99.70% 99.26% 98.17% S&P 500 90.87% 80.57% 67.66% 54.46% 41.62% 31.39% Treasurys (10-year) 100.00% 100.00% 99.97% 98.82% 89.36% 60.44% 60/40 S&P 500 and Treasurys 99.98% 99.58% 96.73% 88.29% 71.84% 50.98% e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.98% 99.06% MSCM-MSLC 100.00% 100.00% 100.00% 99.99% 99.95% 99.17% MSCB-MSSE 100.00% 100.00% 100.00% 99.97% 99.83% 99.30% MSCG-MSET 100.00% 100.00% 99.98% 99.83% 99.44% 98.40% MSCA-MSET 100.00% 99.98% 99.95% 99.70% 99.24% 99.82% S&P 500 90.76% 80.21% 67.29% 53.98% 42.15% 31.06% Treasurys (10-year) 100.00% 100.00% 99.98% 98.93% 89.48% 60.97% 60/40 S&P 500 and Treasurys 99.98% 99.60% 96.72% 88.44% 71.80% 51.07% As expected, the bucket approach is severely impacted by a bear market in stocks that occurs at the end of the period. The same results i wouldetun be true to iska similar extent if theeg bear market SW $384,554.66 $2,253,507.00 0.02% 6.18% 9.78% 15.48% 88.14 0.399 occursBucket at any$384,727.21 point near $2,039,599.02the end of an 0.02%investor’s 6.18%time horizon.9.77% 15.46% 87.39 0.400

The average terminal value of the bucket method is nearly a third of the value for either SW or

SW/TW. Note that the average return for ithe bucketetun approachisk across simulationseg is actually higherSW than for$197,905.00 SW or SW/TW,$1,174,852.57 yet the expectation0.14% 2.38% (Omega)10.00% is substantially26.61% lower4.81 due to 0.090the presenceBucket of $244,748.07adverse outcomes.$3,711,944.47 The percentage0.88% 1.58%of failure rate16.20% where42.67% an investor1.81 runs out0.040 of moneySW/TW is an$223,627.30 alarming 5.97%,$2,195,026.81 which is much0.95% higher1.60% than the13.03% SW/TW35.17% approach.1.90 In terms 0.050of planning success, the Omega ratio for the bucket approach is substantially lower than both systematic withdrawal methods. i etun isk eg SW $142,471.00 $1,024,537.00 0.22% 0.62% 12.00% 35.88% 1.53 0.020 Bucket $52,478.61 $776,498.00 5.97% -10.70% 21.68% 74.49% 0.02 -0.140 SW/TW $141,390.09Table$1,182,058.76 5 Case 3: Bad1.23% Luck at -0.94%the Beginning15.39% of the47.56% Period 0.65 -0.020 50% Bear Market in Stocks in the First Year i etun isk eg SW $101,907.70 $1,085,982.00 2.22% -3.34% 11.60% 45.87% 0.23 -0.070 Bucket $116,801.71 $1,977,583.65 4.34% -5.51% 16.11% 54.45% 0.20 -0.100 SW/TW $85,240.70 $1,494,050.00 12.00% -14.36% 13.89% 61.00% 0.06 -23.540

Source: Flexible Plan Investments Research

In contrast to the previous example, we would i expectetun that “badisk luck” at the beginningeg of the investmentSW period$196,688.06 would $620,924.18be more favorable 0.00% for the2.87% bucket 8.55%method. 20.19%This is because0.32 the stock0.142 bucketBucket is shielded$161,941.45 from withdrawals $476,706.59 for0.00% 10 years,2.00% giving it a6.41% chance 16.91%to recover 0.09without having0.118 toSW/TW withdraw $201,338.00too much proportionately $1,039,394.40 at0.50% the wrong1.77% time. It11.59% is arguably32.17% even more0.26 favorable0.055 for the bucket method in real life because the stock market exhibits predictable mean-reversion tendencies. Let’s examine the performance on the simulated time series (Table 5). i etun isk eg SW $492,773.37 $1,602,079.57 0 7.62% 10.61% 14.48% 26.01 0.526 AsBucket expected, $964,548.59 when the “bad $8,498,561.31 luck” occurs 0 early, 10.54%the performance15.85% of 21.80%the bucket48.75 approach0.483 is superior in terms of average terminal value and, relatively speaking, the Omega is roughly on par with SW. This is in contrast to the case in which the “bad luck” occurs later. In that case, the Omega for SW is much higher than the bucket approach. This implies that SW is hurt much more by initial bad luck, and this is consistent across both SW and SW/TW. MSCC-MSLV 122.4 20.3 3.5 0.7 0.1 0.0 MSCM-MSLC 443.4 93.6 22.1 5.8 1.5 0.3 InMSCB-MSSE fact, the SW/TW approach demonstrates the major disadvantage of bad luck at the 2.2 beginningMSCG-MSET of the period. The probability607.7 of running213.0 out of money66.0 is nearly24.9 three 6.8times that2.7 of theMSCA-MSET bucket approach. Furthermore, the 478.1Omega for167.8 SW/TW is61.5 less than19.1 a third of8.0 the bucket approach.S&P 500 0.0 0.0 0.0 0.0 0.0 0.0 Treasurys (10-year) 0.2 0.0 0.0 0.0 0.0 0.0 60/40 S&P 500 and Treasurys 0.3 0.1 0.0 0.0 0.0 0.0 These results are likely to be true regardless of whether a bear market starts in year one or in the subsequent years that follow—of course, with a lesser magnitude of severity. TheMSCC-MSLV bottom line is that the bucket approach is likely to be superior0.81 to0.46 a traditional0.18 systematic-0.03 MSCM-MSLC 1.42 1.13 0.60 0.37 0.13 withdrawalMSCB-MSSE approach that is more heavily1.12 weighted0.97 in equities0.83 (like a traditional 60/40 portfolio) whenMSCG-MSET there is “bad luck” early in the investment0.81 period.0.73 This0.65 supports0.57 the use of0.46 the bucket0.33 approach.MSCA-MSET However, when the “bad luck”0.73 comes late,0.67 if the 0.62bucket approach0.54 is0.46 invested 0.34in traditionalS&P 500 asset classes on a buy-and-hold-0.16 basis,-0.31 the approach-0.47 is not-0.59 as effective.-0.70 -0.79 Treasurys (10-year) 0.28 0.13 0.02 -0.07 -0.26 -0.54 60/40 S&P 500 and Treasurys 0.10 0.03 -0.09 -0.26 -0.47 -0.66

Bucket Investing | 800-347-3539 | flexibleplan.com 12 e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.97% 99.02% MSCM-MSLC 100.00% 100.00% 100.00% 100.00% 99.92% 99.13% MSCB-MSSE 100.00% 100.00% 100.00% 99.99% 99.86% 99.21% MSCG-MSET 100.00% 100.00% 99.96% 99.87% 99.50% 98.37% MSCA-MSET 100.00% 99.99% 99.94% 99.70% 99.26% 98.17% S&P 500 90.87% 80.57% 67.66% 54.46% 41.62% 31.39% Treasurys (10-year) 100.00% 100.00% 99.97% 98.82% 89.36% 60.44% 60/40 S&P 500 and Treasurys 99.98% 99.58% 96.73% 88.29% 71.84% 50.98% e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.98% 99.06% MSCM-MSLC 100.00% 100.00% 100.00% 99.99% 99.95% 99.17% MSCB-MSSE 100.00% 100.00% 100.00% 99.97% 99.83% 99.30% MSCG-MSET 100.00% 100.00% 99.98% 99.83% 99.44% 98.40% MSCA-MSET 100.00% 99.98% 99.95% 99.70% 99.24% 99.82% S&P 500 90.76% 80.21% 67.29% 53.98% 42.15% 31.06% Treasurys (10-year) 100.00% 100.00% 99.98% 98.93% 89.48% 60.97% 60/40 S&P 500 and Treasurys 99.98% 99.60% 96.72% 88.44% 71.80% 51.07% i etun isk eg SW $384,554.66 $2,253,507.00 0.02% 6.18% 9.78% 15.48% 88.14 0.399 Bucket $384,727.21 $2,039,599.02 0.02% 6.18% 9.77% 15.46% 87.39 0.400

i etun isk eg SW $197,905.00 $1,174,852.57 0.14% 2.38% 10.00% 26.61% 4.81 0.090 Bucket $244,748.07 $3,711,944.47 0.88% 1.58% 16.20% 42.67% 1.81 0.040 SW/TW $223,627.30 $2,195,026.81 0.95% 1.60% 13.03% 35.17% 1.90 0.050

i etun isk eg CaseSW 4: Using$142,471.00 historical$1,024,537.00 return data from0.22% 19980.62% through12.00% 2020 35.88% 1.53 0.020 Bucket $52,478.61 $776,498.00 5.97% -10.70% 21.68% 74.49% 0.02 -0.140 Let’sSW/TW now look$141,390.09 at a case $1,182,058.76study using some1.23% real-life-0.94% examples15.39% to better47.56% illustrate0.65 the point-0.020 (Table 6). In this case, we will use actual stock (S&P 500 Index) and bond (10-year Treasurys) annual return data and run a simulation to i compareetun the bucketisk approach to theeg two different systematicSW withdrawal$101,907.70 methods.$1,085,982.00 We use2.22% equally -3.34%sized buckets11.60% for the45.87% time period0.23 and, again,-0.070 a 50/50Bucket portfolio$116,801.71 of stocks$1,977,583.65 and bonds at 4.34%inception-5.51% for all strategies.16.11% 54.45% 0.20 -0.100 SW/TW $85,240.70 $1,494,050.00 12.00% -14.36% 13.89% 61.00% 0.06 -23.540

Table 6 Case 4: Actual Stock and Bond Data (January 1998-December 2020)

i etun isk eg SW $196,688.06 $620,924.18 0.00% 2.87% 8.55% 20.19% 0.32 0.142 Bucket $161,941.45 $476,706.59 0.00% 2.00% 6.41% 16.91% 0.09 0.118 SW/TW $201,338.00 $1,039,394.40 0.50% 1.77% 11.59% 32.17% 0.26 0.055

Source: Flexible Plan Investments Research i etun isk eg InSW this case, $492,773.37the bucket approach $1,602,079.57 falls between0 both7.62% systematic10.61% withdrawal14.48% methods26.01 in 0.526terms ofBucket annualized $964,548.59 return and MAR$8,498,561.31 ratio. The bucket0 10.54%approach 15.85%also has a21.80% lower risk48.75 and max0.483 drawdown when compared to both the systematic withdrawal methods, but shows lower average terminal values.

This is because the correlation between stocks and bonds is highly negative over the time MSCC-MSLV 122.4 20.3 3.5 0.7 0.1 0.0 period,MSCM-MSLC so a constantly rebalanced portfolio443.4 will have93.6 a higher22.1 return than5.8 the same1.5 portfolio0.3 mixMSCB-MSSE allowing for drifting allocations. In either case, the bucket approach shows superior 2.2 planning-successMSCG-MSET metrics than the industry-standard,607.7 213.0 stock-heavy,66.0 time-weighted,24.9 6.8 static,2.7 systematic-withdrawalMSCA-MSET portfolio. 478.1 167.8 61.5 19.1 8.0 S&P 500 0.0 0.0 0.0 0.0 0.0 0.0 Treasurys (10-year) 0.2 0.0 0.0 0.0 0.0 0.0 The60/40 bucket S&P 500 and approach Treasurys and active0.3 management0.1 0.0 0.0 0.0 0.0

One of the key failures of static asset-allocation approaches is that all of them fail to be responsiveMSCC-MSLV to different market environments. As we have seen,0.81 bear markets0.46 have0.18 been -0.03 devastatingMSCM-MSLC to all forms of static allocation—especially1.42 1.13 if they happen0.60 at the wrong0.37 time. 0.13This isMSCB-MSSE true regardless of whether one employs1.12 a constantly0.97 rebalanced0.83 approach (which is nearly impossibleMSCG-MSET to implement) or the bucket 0.81approach.0.73 The key difference0.65 0.57 between 0.46these two0.33 methodsMSCA-MSET is that when buying and holding0.73 traditional0.67 asset classes,0.62 the0.54 bucket 0.46approach 0.34is S&P 500 -0.16 -0.31 -0.47 -0.59 -0.70 -0.79 mostTreasurys affected (10-year) by bear markets that occur0.28 toward 0.13the end of0.02 the investor’s-0.07 time-0.26 horizon, while-0.54 the60/40 constantly S&P 500 and rebalanced Treasurys approach (with0.10 systematic0.03 withdrawal)-0.09 is most-0.26 impacted-0.47 by bear-0.66 markets that occur at the beginning.

From a practical perspective, since both of these methods were designed for retirement e in planning,MSCC-MSLV the bucket approach has more100.00% psychological100.00% appeal.100.00% In theory,100.00% people99.97% that have99.02% just retiredMSCM-MSLC are most sensitive when it comes100.00% to their100.00% nest egg 100.00%and may 100.00%make rash99.92% decisions99.13% if they encounterMSCB-MSSE a bear market early on. They100.00% are less100.00% likely to be100.00% concerned99.99% about 99.86%what may99.21% happen if MSCG-MSETthey run out of money at some point100.00% in the very100.00% distant future.99.96% Human99.87% nature99.50% is to focus98.37% on theMSCA-MSET shorter term (recency bias). However,100.00% the cost99.99% of running99.94% out of money99.70% can99.26% be severe—this98.17% S&P 500 90.87% 80.57% 67.66% 54.46% 41.62% 31.39% canTreasurys mean (10-year) having no financial options100.00% at a point100.00% of greatest99.97% need, when98.82% the client89.36% is unlikely60.44% to be60/40 able S&P to 500 return and Treasurys to work. The bucket approach99.98% is99.58% more sensitive96.73% to 88.29%this outcome,71.84% especially50.98% when employing a traditionale in buy-and-hold approach. Yet, as Milevsky stated, bucketing cannotMSCC-MSLV bail you out of a poor sequence100.00% of returns.100.00% 100.00% 100.00% 99.98% 99.06% MSCM-MSLC 100.00% 100.00% 100.00% 99.99% 99.95% 99.17% MSCB-MSSE 100.00% 100.00% 100.00% 99.97% 99.83% 99.30% BucketMSCG-MSET Investing | 800-347-3539 | flexibleplan.com100.00% 100.00% 99.98% 99.83% 99.44% 98.40% 13 MSCA-MSET 100.00% 99.98% 99.95% 99.70% 99.24% 99.82% S&P 500 90.76% 80.21% 67.29% 53.98% 42.15% 31.06% Treasurys (10-year) 100.00% 100.00% 99.98% 98.93% 89.48% 60.97% 60/40 S&P 500 and Treasurys 99.98% 99.60% 96.72% 88.44% 71.80% 51.07% Active management—in contrast to traditional buy-and-hold investing, which penalizes the bucket approach for “bad luck” in the later years—provides a solution to the sequence-of- returns dilemma. It is designed to respond to trends in return and volatility by shifting asset allocation throughout the holding period.

Most active management approaches that are based on trend following will outperform buy and hold in an extended bear market. As a trade-off, they may trail on the upside in bull markets. However, in aggregate, they produce a smoother return profile that is ideal for financial planning since it typically is not as sensitive to “bad luck.” By using active management with the bucket approach, it is possible to produce a “best of both worlds” solution designed to keep investors invested over the long term while protecting them from events in the future that may devastate their portfolios.

Case 5: Combining Multi-Strategy Core and Multi-Strategy Explore with the bucket approach

Multi-Strategy Core (MSC) is one of the turnkey, multi-strategy, dynamically risk-managed solutions available at Flexible Plan Investments. MSC dynamically combines multiple actively managed strategies with traditional asset classes into one portfolio to diversify risk across many strategies. The goal is to provide a risk-managed solution that provides the potential for superior returns for five client suitability profiles: conservative, moderate, balanced, growth, and aggressive.

Flexible Plan has also created a group of four turnkey Multi-Strategy Explore (MSE) solutions, which are designed to be added to the core portfolio as a “satellite” allocation. Each MSE solution allocates among strategies that take advantage of different market environments:

• Multi-Strategy Low Volatility (MSLV) has a universe of strategies available to it that tend to be more conservative. • Multi-Strategy Low Correlation (MSLC) has strategies that tend to have a low correlation to the overall market. • Multi-Strategy Special Equity (MSSE) is a more aggressive strategy that takes advantage of certain patterns in the markets. • Multi-Strategy Equity Trends (MSET) is another aggressive strategy that attempts to take advantage of market trends by taking on leveraged and inverse positions.

Typically, we advise our clients to use 60% MSC, coupled with a 40% allocation to MSE, to create a dynamic portfolio based on risk suitability. We also usually recommend combining the core and explore offerings that best match the level of risk undertaken by each: MSC Conservative with MSLV, MSC Moderate with MSLC, MSC Balanced with MSSE, MSC Growth with MSET, and MSC Aggressive with MSET.

In all, MSC and MSE draw on a universe of more than 50 different dynamically risk-managed strategies and suitability profiles.

Our Multi-Strategy Core and Explore offerings respond to trends in returns and risk and also to the correlations between strategies and asset classes to dynamically shift portfolio allocations at least monthly. These offerings are the financial equivalent of “cruise control” in your car: If the car starts accelerating above the target speed, the cruise control tells the car to slow down; likewise, if the car is going too slow, the cruise control tells the car to speed up.

Bucket Investing | 800-347-3539 | flexibleplan.com 14 i etun isk eg SW $384,554.66 $2,253,507.00 0.02% 6.18% 9.78% 15.48% 88.14 0.399 Bucket $384,727.21 $2,039,599.02 0.02% 6.18% 9.77% 15.46% 87.39 0.400

For this paper, we will focus on the most conservative and the most aggressive ends of the Multi-Strategy Core and Explore offerings i (theetun performanceisk breakdown ofeg all five of the differentSW suitability$197,905.00 profiles$1,174,852.57 can be found0.14% in the Appendix).2.38% 10.00% The MSC26.61% Conservative4.81 coupled0.090 with MSLVBucket and MSC$244,748.07 Aggressive$3,711,944.47 coupled with0.88% MSET will1.58% be used16.20% to fill the42.67% investment1.81 needs0.040 of the SW/TW $223,627.30 $2,195,026.81 0.95% 1.60% 13.03% 35.17% 1.90 0.050 fixed-income and stock buckets, respectively.

Using the MSC-MSE profiles on the two iextremesetun of the spectrumisk is comparableeg to a standard two-bucketSW $142,471.00approach that$1,024,537.00 uses a very conservative0.22% 0.62% investment12.00% such35.88% as bonds 1.53in the first0.020 bucketBucket and equities$52,478.61 in the$776,498.00 second bucket5.97% for maximum-10.70% capital21.68% appreciation.74.49% In0.02 the simulations-0.140 SW/TW $141,390.09 $1,182,058.76 1.23% -0.94% 15.39% 47.56% 0.65 -0.020 (Table 7, Figure 6, Table 8), we use the historical performance of MSC from February 1, 2001, when the research results for MSC begin. Starting on April 1, 2004, when the research results for MSE begin, we use the MSC-MSE blends i throughetun to Decemberisk 31, 2020. egWe use a 4% withdrawalSW rate,$101,907.70 which is$1,085,982.00 consistent with2.22% our previous-3.34% simulations.11.60% 45.87% 0.23 -0.070 Bucket $116,801.71 $1,977,583.65 4.34% -5.51% 16.11% 54.45% 0.20 -0.100 SW/TW $85,240.70 $1,494,050.00 12.00% -14.36% 13.89% 61.00% 0.06 -23.540 In Case 5, the buckets were divided into two nearly equal-sized portfolios over the period. In Table 7, we compare a traditional systematic withdrawal approach that maintains a 50% constantly rebalanced allocation (SW) to both MSC Conservative/MSLV and MSC Aggressive/ MSET, with a standard two-bucket approach i (Bucket).etun isk eg SW $196,688.06 $620,924.18 0.00% 2.87% 8.55% 20.19% 0.32 0.142 Bucket $161,941.45 $476,706.59 0.00% 2.00% 6.41% 16.91% 0.09 0.118 SW/TW $201,338.00Table 7 Case $1,039,394.40 5: MSC Conservative/MSLV 0.50% 1.77% and11.59% MSC Aggressive/MSET32.17% 0.26 0.055 Using the Bucket Approach vs. SW (February 2001–December 2020)

i etun isk eg SW $492,773.37 $1,602,079.57 0 7.62% 10.61% 14.48% 26.01 0.526 Bucket $964,548.59 $8,498,561.31 0 10.54% 15.85% 21.80% 48.75 0.483

Source: Flexible Plan Investments’ Hypothetical Research Reports (2/2001-12/2020). Strategy returns are shown after a 2.25% advisory fee less any applicable fee credits. Any index shown is not tradable. These results were achieved by means of retroactive application of a computer model and may not represent the results of actual trading. PAST PERFORMANCE DOES NOT GUARANTEE FUTURE RESULTS. UnlikeMSCC-MSLV our previous simulations, the Omega122.4 is now20.3 higher for3.5 the bucket0.7 approach0.1 versus0.0 the MSCM-MSLC 443.4 93.6 22.1 5.8 1.5 0.3 systematicMSCB-MSSE withdrawal approach. The average maximum drawdown for the bucket approach2.2 wasMSCG-MSET a very tolerable 21.80%—which is 607.7less than 213.0half of the 66.0maximum24.9 drawdown6.8 of the S&P2.7 500MSCA-MSET over the same time period. Most investors478.1 can167.8 tolerate 61.5drawdown19.1 levels of8.0 about 20%. S&P 500 0.0 0.0 0.0 0.0 0.0 0.0 Treasurys (10-year) 0.2 0.0 0.0 0.0 0.0 0.0 Noteworthy60/40 S&P 500 is and the Treasurys failure statistic shown 0.3in Table 7.0.1 By adding0.0 active management0.0 0.0 to the 0.0 simulation, the failure rate goes to zero, regardless of whether systematic withdrawal or the bucket approach is used. Given that the investment is being preserved under either approach (our primary objective), we can move on to comparing the difference in returns between the twoMSCC-MSLV methods. 0.81 0.46 0.18 -0.03 MSCM-MSLC 1.42 1.13 0.60 0.37 0.13 MSCB-MSSE 1.12 0.97 0.83 TheMSCG-MSET bucket approach has an annualized0.81 compound0.73 return that0.65 is about0.57 3.0% higher,0.46 and0.33 an averageMSCA-MSET terminal wealth that is almost 100%0.73 higher,0.67 than the0.62 systematic0.54 withdrawal0.46 approach.0.34 TheS&P Multi-Strategy 500 Core and Explore solution-0.16 is an-0.31 active management-0.47 -0.59 approach-0.70 that is -0.79 Treasurys (10-year) 0.28 0.13 0.02 -0.07 -0.26 -0.54 designed60/40 S&P to500 maximize and Treasurys returns per unit of0.10 risk. The0.03 cost of using-0.09 the bucket-0.26 approach-0.47 and-0.66 letting the aggressive portfolio “ride” while starting to withdraw from the conservative bucket is mitigated significantly through this risk management in our study.

e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.97% 99.02% MSCM-MSLC 100.00% 100.00% 100.00% 100.00% 99.92% 99.13% MSCB-MSSE 100.00% 100.00% 100.00% 99.99% 99.86% 99.21% MSCG-MSET 100.00% 100.00% 99.96% 99.87% 99.50% 98.37% BucketMSCA-MSET Investing | 800-347-3539 | flexibleplan.com100.00% 99.99% 99.94% 99.70% 99.26% 98.17% 15 S&P 500 90.87% 80.57% 67.66% 54.46% 41.62% 31.39% Treasurys (10-year) 100.00% 100.00% 99.97% 98.82% 89.36% 60.44% 60/40 S&P 500 and Treasurys 99.98% 99.58% 96.73% 88.29% 71.84% 50.98% e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.98% 99.06% MSCM-MSLC 100.00% 100.00% 100.00% 99.99% 99.95% 99.17% MSCB-MSSE 100.00% 100.00% 100.00% 99.97% 99.83% 99.30% MSCG-MSET 100.00% 100.00% 99.98% 99.83% 99.44% 98.40% MSCA-MSET 100.00% 99.98% 99.95% 99.70% 99.24% 99.82% S&P 500 90.76% 80.21% 67.29% 53.98% 42.15% 31.06% Treasurys (10-year) 100.00% 100.00% 99.98% 98.93% 89.48% 60.97% 60/40 S&P 500 and Treasurys 99.98% 99.60% 96.72% 88.44% 71.80% 51.07% In Figure 6, we compare a constantly rebalanced systematic withdrawal approach (SW—50/50 initial allocation, 4% withdrawal) using the MSC Conservative/MSLV and MSC Aggressive/MSET values (orange line) versus the SW approach using the traditional, buy-and-hold S&P 500 and Treasurys portfolio (yellow line). Additionally, we display the two-bucket approach first using traditional assets (gray line) and then with MSC Conservative/MSLV replacing bonds and MSC Aggressive/MSET replacing stocks (blue line). The results are summarized in the table in Figure 6.

Figure 6 Case 5: The Bucket Approach vs. Systematic Withdrawal with Active vs. Passive Portfolios (February 2001–December 2020)

Based on historical returns, whether using active or passive management, the drawdowns for the bucket approach are higher than for the systematic withdrawal method, but the MSC-MSE blend actively managed bucket approach has a more tolerable 22.37% drawdown versus the nearly 30% drawdown with the passive portfolio.

History provides a good example of how the bucket approach can survive being unlucky, even if faced with a bear market near the end of the period. Investors in a passive portfolio would have been exposed 100% to stocks when the 2008 bear market began, which is why the resulting drawdown was so severely felt by them. Few investors would be able to sustain that level of drawdown (almost 60%) and continue with the same asset allocation. The aggressive MSC-MSE blend experienced a maximum drawdown of about a third of that level.

In Figure 7, we compare the historical performance of the bucket approach and systematic withdrawal using active and passive management with a bear market at the beginning of the investment period. As shown earlier in Case 3, a bear market at the beginning of the investment period tends to help the performance of the bucket approach compared to systematic withdrawal. The slight outperformance of the bucket approach using passive allocations in Figure 7 confirms the conclusions made in Case 3. Using our actively managed strategies, the bucket approach performed significantly better than the systematic withdrawal approach using actively managed strategies.

Bucket Investing | 800-347-3539 | flexibleplan.com 16 Figure 7 The Bucket Approach vs. Systematic Withdrawal with a Bear Market at Beginning of Period (October 2007–December 2019)

In Figure 8, we do the same thing, except the bear market is now placed at the end of the investment period. As discussed in Case 2, a bear market at the end of the investment period tends to help systematic withdrawal over the bucket approach. Figure 8 confirms this, as the systematic withdrawal approach using only asset classes slightly outperforms the bucket approach using passive allocations (yellow versus gray lines). However, when incorporating actively managed strategies with both approaches, we can see that the bucket approach now outperforms the systematic withdrawal approach when the bear market is placed at the end of the investment period.

Figure 8 The Bucket Approach vs. Systematic Withdrawal with a Bear Market at End of Period (January 2003–February 2009)

Bucket Investing | 800-347-3539 | flexibleplan.com 17 i etun isk eg SW $384,554.66 $2,253,507.00 0.02% 6.18% 9.78% 15.48% 88.14 0.399 Bucket $384,727.21 $2,039,599.02 0.02% 6.18% 9.77% 15.46% 87.39 0.400

i etun isk eg SW $142,471.00$384,554.66 $1,024,537.00$2,253,507.00 0.22%0.02% 0.62%6.18% 12.00%9.78% 15.48%35.88% 88.141.53 0.3990.020 Bucket $384,727.21$52,478.61 $2,039,599.02$776,498.00 5.97%0.02% -10.70%6.18% 21.68%9.77% 15.46%74.49% 87.390.02 -0.1400.400 FiguresSW/TW 7 and$141,390.09 8 both help$1,182,058.76 to show the benefits1.23% -0.94%of using active15.39% management47.56% coupled0.65 with-0.020 the bucket asset-allocation approach.

i etun isk eg WhichSW MSC-MSE$197,905.00$101,907.70 blend$1,174,852.57$1,085,982.00 profile for which0.14%2.22% bucket?-3.34%2.38% 10.00%11.60% 26.61%45.87% 4.810.23 -0.0700.090 Bucket $244,748.07$116,801.71 $3,711,944.47$1,977,583.65 0.88%4.34% -5.51%1.58% 16.20%16.11% 42.67%54.45% 1.810.20 -0.1000.040 WeSW/TW performed$223,627.30$85,240.70 25,000 simulations$2,195,026.81$1,494,050.00 to determine12.00%0.95% which-14.36%1.60% MSC-MSE13.03%13.89% blend35.17%61.00% suitability1.900.06 profiles-23.5400.050 were best for different levels of targeted returns (withdrawal rates). We compared these profiles to stocks (S&P 500), bonds (Treasurys), and i a 60/40etun portfolio ofisk stocks and bonds.eg In this case, SW $142,471.00 $1,024,537.00 0.22% 0.62% 12.00% 35.88% 1.53 0.020 we used a standard systematic withdrawal i methodetun since thereisk was only one suitabilityeg profile Bucket $52,478.61 $776,498.00 5.97% -10.70% 21.68% 74.49% 0.02 -0.140 usedSW in each$196,688.06 of the groups $620,924.18 in the simulations. 0.00% The2.87% purpose8.55% was to determine20.19% which0.32 MSC-MSE0.142 SW/TW $141,390.09 $1,182,058.76 1.23% -0.94% 15.39% 47.56% 0.65 -0.020 blendBucket suitability$161,941.45 index would $476,706.59 be ideal for0.00% a bucket2.00% with a given6.41% target16.91% return. 0.09 0.118 SW/TW $201,338.00 $1,039,394.40 0.50% 1.77% 11.59% 32.17% 0.26 0.055

Table 8 illustrates that by using MSC Balanced i (MSCB)/MSSEetun isk (bolded results)eg one can achieve theSW highest probability$101,907.70 of$1,085,982.00 success (the highest2.22% Omega-3.34% value).11.60% 45.87% 0.23 -0.070 Bucket $116,801.71 $1,977,583.65 4.34% i etun-5.51% 16.11%isk 54.45% eg0.20 -0.100 SW/TWSW $492,773.37$85,240.70 $1,494,050.00 $1,602,079.57 12.00%0 -14.36%7.62% 13.89%10.61% 61.00%14.48% 26.010.06 -23.5400.526 BucketTable 8 Omega $964,548.59 Statistic $8,498,561.31Comparison of Different0 10.54% MSC-MSE15.85% Suitability21.80% Profiles to48.75 Standard0.483 Asset Classes and Portfolios at Different Target Returns/Withdrawal Rates (Using 2001–2020 Data)

i etun isk eg SW $196,688.06 $620,924.18 0.00% 2.87% 8.55% 20.19% 0.32 0.142 MSCC-MSLVBucket $161,941.45 $476,706.59 0.00%122.4 2.00%20.3 6.41%3.5 16.91%0.7 0.090.1 0.1180.0 MSCM-MSLCSW/TW $201,338.00 $1,039,394.40 0.50%443.4 1.77%93.6 11.59%22.1 32.17%5.8 0.261.5 0.0550.3 MSCB-MSSE 2.2 MSCG-MSET 607.7 213.0 66.0 24.9 6.8 2.7 MSCA-MSET 478.1 167.8 61.5 19.1 8.0 i etun isk eg S&P 500 0.0 0.0 0.0 0.0 0.0 0.0 SW $492,773.37 $1,602,079.57 0 7.62% 10.61% 14.48% 26.01 0.526 Treasurys (10-year) 0.2 0.0 0.0 0.0 0.0 0.0 Bucket $964,548.59 $8,498,561.31 0 10.54% 15.85% 21.80% 48.75 0.483 60/40 S&P 500 and Treasurys 0.3 0.1 0.0 0.0 0.0 0.0

e in MSCC-MSLV 100.00% 100.00% 100.00%0.81 100.00%0.46 99.97%0.18 99.02%-0.03 MSCM-MSLC 100.00%1.42 100.00%1.13 100.00% 100.00%0.60 99.92%0.37 99.13%0.13 MSCB-MSSE 100.00%1.12 100.00%0.97 100.00%0.83 99.99% 99.86% 99.21% MSCG-MSET 100.00%0.81 100.00%0.73 99.96%0.65 99.87%0.57 99.50%0.46 98.37%0.33 MSCA-MSET 100.00%0.73 99.99%0.67 99.94%0.62 99.70%0.54 99.26%0.46 98.17%0.34 S&P 500 90.87%-0.16 80.57%-0.31 67.66%-0.47 54.46%-0.59 41.62%-0.70 31.39%-0.79 Treasurys (10-year) 100.00%0.28 100.00%0.13 99.97%0.02 98.82%-0.07 89.36%-0.26 60.44%-0.54 60/40 S&P 500 and Treasurys 99.98%0.10 99.58%0.03 96.73%-0.09 88.29%-0.26 71.84%-0.47 50.98%-0.66 Source: Flexible Plan Investments’e Hypothetical in Research Reports (2/2001-12/2020). Strategy returns are shown after a 2.25% advisory feeMSCC-MSLV less any applicable fee credits. Any index shown is not100.00% tradable. These100.00% results were100.00% achieved 100.00%by means of retroactive99.98% appli99.06%cation of a computerMSCM-MSLC model and may not represent the results of100.00% actual trading.100.00% PAST PERFORMANCE100.00% DOES99.99% NOT GUARANTEE99.95% FUTURE 99.17%RESULTS. MSCB-MSSE e in 100.00% 100.00% 100.00% 99.97% 99.83% 99.30% MSCC-MSLVMSCG-MSET 100.00% 100.00% 100.00%99.98% 100.00%99.83% 99.97%99.44% 99.02%98.40% MSCM-MSLCMSCA-MSET 100.00% 100.00%99.98% 100.00%99.95% 100.00%99.70% 99.92%99.24% 99.13%99.82% BucketMSCB-MSSES&P 500 Investing | 800-347-3539 | flexibleplan.com100.00%90.76% 100.00%80.21% 100.00%67.29% 99.99%53.98% 99.86%42.15% 99.21%31.06% 18 MSCG-MSETTreasurys (10-year) 100.00% 100.00% 99.96%99.98% 99.87%98.93% 99.50%89.48% 98.37%60.97% MSCA-MSET60/40 S&P 500 and Treasurys 100.00%99.98% 99.99%99.60% 99.94%96.72% 99.70%88.44% 99.26%71.80% 98.17%51.07% S&P 500 90.87% 80.57% 67.66% 54.46% 41.62% 31.39% Treasurys (10-year) 100.00% 100.00% 99.97% 98.82% 89.36% 60.44% 60/40 S&P 500 and Treasurys 99.98% 99.58% 96.73% 88.29% 71.84% 50.98% e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.98% 99.06% MSCM-MSLC 100.00% 100.00% 100.00% 99.99% 99.95% 99.17% MSCB-MSSE 100.00% 100.00% 100.00% 99.97% 99.83% 99.30% MSCG-MSET 100.00% 100.00% 99.98% 99.83% 99.44% 98.40% MSCA-MSET 100.00% 99.98% 99.95% 99.70% 99.24% 99.82% S&P 500 90.76% 80.21% 67.29% 53.98% 42.15% 31.06% Treasurys (10-year) 100.00% 100.00% 99.98% 98.93% 89.48% 60.97% 60/40 S&P 500 and Treasurys 99.98% 99.60% 96.72% 88.44% 71.80% 51.07% i etun isk eg SW $384,554.66 $2,253,507.00 0.02% 6.18% 9.78% 15.48% 88.14 0.399 Bucket $384,727.21 $2,039,599.02 0.02% 6.18% 9.77% 15.46% 87.39 0.400

i etun isk eg SW $101,907.70 $1,085,982.00 2.22% -3.34% 11.60% 45.87% 0.23 -0.070 Bucket $116,801.71 $1,977,583.65 4.34% -5.51% 16.11% 54.45% 0.20 -0.100 SW/TW $85,240.70 $1,494,050.00 12.00% -14.36% 13.89% 61.00% 0.06 -23.540

i etun isk eg SW $492,773.37 $1,602,079.57 0 7.62% 10.61% 14.48% 26.01 0.526 Bucket $964,548.59 $8,498,561.31 0 10.54% 15.85% 21.80% 48.75 0.483

TableMSCC-MSLV 10 adds time horizon into the index to discover the probability0.81 of0.46 success0.18 for MSC-MSE-0.03 blendsMSCM-MSLC and traditional asset classes in meeting1.42 both1.13 the withdrawal needs0.60 and 0.37the requisite0.13 timeMSCB-MSSE horizon. All of the MSC-MSE blend1.12 profile indexes0.97 demonstrate0.83 a probability of success of MSCG-MSET 0.81 0.73 0.65 0.57 0.46 0.33 moreMSCA-MSET than 90%. By contrast, the buy-and-hold0.73 asset0.67 classes0.62 and 60/400.54 portfolio0.46 seriously0.34 lag. S&P 500 -0.16 -0.31 -0.47 -0.59 -0.70 -0.79 TreasurysTable (10-year)10 Comparison of Probability of0.28 Success0.13 of Different0.02 MSC-MSE-0.07 Suitability-0.26 Profiles-0.54 to 60/40 S&P 500 and Treasurys 0.10 0.03 -0.09 -0.26 -0.47 -0.66 Standard Asset Classes and Portfolios at Different Target Returns/Withdrawal Rates Over 5-Year and 20-Year Time Horizons (Using 2001–2020 Data)

e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.97% 99.02% MSCM-MSLC 100.00% 100.00% 100.00% 100.00% 99.92% 99.13% MSCB-MSSE 100.00% 100.00% 100.00% 99.99% 99.86% 99.21% MSCG-MSET 100.00% 100.00% 99.96% 99.87% 99.50% 98.37% MSCA-MSET 100.00% 99.99% 99.94% 99.70% 99.26% 98.17% S&P 500 90.87% 80.57% 67.66% 54.46% 41.62% 31.39% Treasurys (10-year) 100.00% 100.00% 99.97% 98.82% 89.36% 60.44% 60/40 S&P 500 and Treasurys 99.98% 99.58% 96.73% 88.29% 71.84% 50.98% e in MSCC-MSLV 100.00% 100.00% 100.00% 100.00% 99.98% 99.06% MSCM-MSLC 100.00% 100.00% 100.00% 99.99% 99.95% 99.17% MSCB-MSSE 100.00% 100.00% 100.00% 99.97% 99.83% 99.30% MSCG-MSET 100.00% 100.00% 99.98% 99.83% 99.44% 98.40% MSCA-MSET 100.00% 99.98% 99.95% 99.70% 99.24% 99.82% S&P 500 90.76% 80.21% 67.29% 53.98% 42.15% 31.06% Treasurys (10-year) 100.00% 100.00% 99.98% 98.93% 89.48% 60.97% 60/40 S&P 500 and Treasurys 99.98% 99.60% 96.72% 88.44% 71.80% 51.07%

Summing up our findings, what is striking about the results displayed in Tables 8–10 is that all five MSC-MSE blend profiles outperform the asset classes and a 60/40 portfolio at all levels of return/withdrawal rates. As expected, as the target return/withdrawal rates increase, the optimal MSC-MSE blend risk level also increases. However, since the maximum target return/ withdrawal rates are modest when compared to the historical returns of MSC-MSE blends, MSC Balanced/MSSE is the most aggressive portfolio required to maximize the probability of planning success even at the 8% target return level. In addition, the use of even more aggressive MSC-MSE blend portfolios in pursuit of higher returns may also be justified, as these blends using the bucket system still outperformed the use of traditional buy-and-hold asset classes or portfolios in the study.

Conclusion

In this paper, we compared the bucket approach with a more traditional systematic withdrawal approach with a constantly rebalanced portfolio (summarized in the following table).

Bucket Investing | 800-347-3539 | flexibleplan.com 19 Bucket Investing vs. Traditional Portfolio Management

Systematic Withdrawal Bucket Investing from a Single Portfolio

• Multiple portfolios • Single portfolio • Each with a different time • Meant to last the length horizon of the longest investment time horizon • Matches assets to future liabilities • Single investment policy • Always reallocates to the • Needs to be very diversified shorter-term buckets • Needs to constantly rebalance • Always withdraws from the shortest-term bucket • Withdrawals taken from a single portfolio on a systematic basis

Our study also analyzes some of the advantages and criticisms of the bucket investing approach (summarized in the following table).

Bucket investing

Advantages Disadvantages

• Moves in tune with investor • The myth of time diversification psychology • Wide range of outcomes • Takes advantage of “mental possible accounting” • Time and discipline needed • Each portfolio customized for for reallocation a specific time horizon • Timing of losses • Focuses on survival of principal • Allows long-term investments to compound longer

Bucket Investing | 800-347-3539 | flexibleplan.com 20 We show through simulation that the bucket approach is a trade-off that can increase returns versus a traditional approach and tends to reduce the impact of bad luck at the beginning of the investment period. Yet it is also more sensitive to the impact of bad luck at the end of the planning period.

In general, if one simply implements bucket investing with passively held asset classes, the traditional systematic withdrawal approach tends to have a higher probability of planning success. This is because diversification is maximized and risk is minimized by rebalancing to a constant mix.

However, our studies showed that this conclusion can be reversed if passive asset class investments are replaced by actively managed portfolios. Figure 6 shows that the results of both methodologies are improved by the use of turnkey, multi-strategy, dynamically risk- managed strategies instead of passive asset classes. And bucket investing is shown to be superior to systematic withdrawal when dynamic risk management of the investments is chosen.

Importantly for financial advisers and their clients, the likelihood of success, preservation of capital, and the risk of failure also all improve by (1) using actively managed portfolios over passive asset classes, and (2) with the use of bucket investing instead of the systematic withdrawal methodology.

In our simulations, active management outperformed whether using the traditional systematic method or the more psychologically appealing bucket approach. Furthermore, in implementing the bucket approach, we found that using different MSC-MSE suitability profiles for different target-return buckets proved to be a promising method to maximize the outcome of applying the bucket approach to financial planning.

Bucket Investing | 800-347-3539 | flexibleplan.com 21 Appendix: Definitions and methods

Monte Carlo simulation

To build simulations of potential portfolio outcomes, we generated 25,000-plus bucket system portfolios using a simulation application designed specifically to model the bucket system. We used the algorithms outlined in Figures A and B to generate each portfolio’s yearly returns. Each equity path represents the portfolio’s year-end price streams. (Table A shows one simulated equity path using end-of-year prices.)

Table A Simulated Equity Path

Source: Flexible Plan Investments’ Hypothetical Research Reports (2/2001-8/2020). Strategy returns are shown after a 2.25% advisory fee less any applicable fee credits. Any index shown is not tradable. These results were achieved by means of retroactive application of a computer model and may not represent the results of actual trading. PAST PERFORMANCE DOES NOT GUARANTEE FUTURE RESULTS.

To illustrate this concept, we performed a series of Monte Carlo simulations, which is a widely accepted practice for modeling financial time series within the industry. Monte Carlo simulation uses what is known as risk-neutral valuation to generate return simulations. We used stochastic differential equations with geometric Brownian motion to generate a random time series based on a given mean and standard deviation. A stochastic process (St) is calculated using a percentage drift (μ, or mu), percentage volatility (σ, or sigma), and Brownian motion factor (dWt). The variable dt is the time step used for mu and sigma values (Figure A). The analytical solution for Figure A is Figure B.

Figure A Stochastic Differential Equation Using Brownian Motion dS = µS dt + σS dW dSt = µStdt + σStdWt

Figure B Analytical Solution for Figure A σ2 S = S exp µ – —σ t + σW t 0 2 t Bucket Investing | 800-347-3539 | flexibleplan.com 22 Z = R cos(�) = –2lnU cos(2πU ) Z0 = R cos(�) = –2lnU1 cos(2πU2) Z = R sin(�) = –2lnU sin(2πU ) Z1 = R sin(�) = –2lnU1 sin(2πU2)

2 x = z And x = pz + 1 – p z x1 = z1 x2 = pz1 + 1 – p z2

∫ (1 – F(x))dx Ω(r) = ∫ F(x)dx dSt = µStdt + σStdWt

The Box-Muller transformation (Figure C) is used to generate normally distributed random numbers using independent random numbers: U1 and U22 are independent random numbers that are uniformly distributed between 0 and 1. We thenσ use the Mersenne Twister, a high-quality, pseudo-random Snumber = generationS exp algorithmµ to – generate — theset independent, + σW random numbers. t 0 2 t Figure C Box-Muller Transformation

Z0 = R cos(�) = –2lnU1 cos(2πU2)

dSt = µStdt + σStdWt Z1 = R sin(�) = –2lnU1 sin(2πU2)

This gives you two independent random numbers, Z0 and Z1, each with a standard normal distribution. 2 2 x = z And x = pzσ + 1 – p z To generate a complete1 St =1 time S0 series,exp we recursively2µ – call— the1 algorithmt + previouslyσWt described2 for the required number of data points. We use yearly CAGR2 and standard deviation for mu and sigma where the time step is one year and the initial portfolio value is 100,000 for all simulations.

Bucket return correlation

In the realZ world,0 = single R bucketcos( returns�)∫ have = (1 some –– degree2lnU F(x))dx of correlation1 cos( to 2theπ otherU 2buckets.) To simulate this importantΩ(r) feature, = we used the Cholesky decomposition, or Cholesky factor- ization algorithm, to integrate correlations into our individual simulations, for example, using the equations in Figure D to generate random returns∫ forF(x)dx two correlated assets. Z1 = R sin(�) = –2lnU1 sin(2πU2) Figure D Equation to Generate Random Returns for 2 Correlated Assets

2 And x1 = z1 x2 = pz1 + 1 – p z2

X1 and X2 are normally distributed, correlated random numbers, while Z1 and Z2 are normally distributed, uncorrelated random numbers. In applying the lower-upper (LU) decomposition algorithm to the correlation matrix to an uncorrelated sample, we can generate a randomly correlated financial time series for the∫ buckets. (1 – F(x))dx Ω(r) = Omega values for the probability of success∫ F(x)dx The Omega ratio is a relative measure of the likelihood of achieving a given return, such as a minimum acceptable return or a target return. Omega represents a ratio of the cumulative probability of an investment’s outcome above an investor’s defined return level (a threshold level), to the cumulative probability of an investment’s outcome below an investor’s threshold level.

Bucket Investing | 800-347-3539 | flexibleplan.com 23 dSt = µStdt + σStdWt

2 S = S exp µ – —σ t + σW t 0 2 t

The Omega concept neatly captures the notion of continuous expectation on investment. It divides expectedZ0 = returns R cos( into two �parts—upside) = returns–2lnU (good) 1andcos( downside2 returnsπU 2(bad).) The higher the Omega value is, the greater the probability that a given return will be met or exceeded.

To calculate Omega on these portfolios, we calculate the CAGR for each simulation using year- end pricesZ for1 each= R bucket sin( system� portfolio.) = –2lnU1 sin(2πU2)

The formulae of Omega (Figure E, where F(x) is the probability density function of return x) is implemented as Omega = Excess Sum of All CAGR Values Above Threshold / Deficiency Sum 2 of All CAGR Values Below ThresholdAnd Geometric Omega, or GOmega = Excess Average of All CAGR Valuesx Above1 = zThreshold1 / Deficiencyx2 =Average pz of1 All+ CAGR1 Values – pBelowz 2Threshold.

Figure E Equation for the Omega Statistic ∫ (1 – F(x))dx Ω(r) = ∫ F(x)dx

We also use a yearly percentage ranking of all simulations (year-end price series) to generate the 20th, 50th, and 80th percentile of equity paths.

Figure F Normal Investment Simulation vs. Bucket Investment Simulation for 20-Year Period (Monte Carlo Simulations)

• 0.5 correlation between all buckets • 5% systematic withdrawal • 4% threshold for Omega • 10% CAGR and 10% risk for all buckets • $100,000 initial investment equally weighted to each bucket • 10,000 simulations for each system

Bucket Investing | 800-347-3539 | flexibleplan.com 24 Source: Flexible Plan Investments Research

Performance breakdown of the different suitability profiles of MSC-MSE Blends

The performance metrics of the MSC-MSE blends from February 2001 through December 2020 are provided in Table B. The two suitability profiles used throughout the paper are MSC-MSLV in place of the fixed-income bucket and MSA-MSET in place of the equity bucket.

Table B Performance Metrics of the MSC-MSE Blends (February 2001 through December 2020)

Bucket Investing | 800-347-3539 | flexibleplan.com 25 Works Cited

1. Benjamin, Jeff. March 27, 2011. “Bucket Strategies Provide a Pot of ‘Safe Money.’” Invest- ment News. https://www.investmentnews.com/bucket-strategies-provide-a-pot-of-safe- money-35240. 2. Statman, Meir. 2019. “Behavioral Finance: The Second Generation.” CFA Institute Research Foundation. https://www.cfainstitute.org/en/research/foundation/2019/behavioral-finance-the-second-generation. 3. Dalbar. 2020. “Dalbar QAIB: Investors Are Still Their Own Worst Enemy.” https://www.ifa. com/articles/dalbar_2016_qaib_investors_still_their_worst_enemy/. 4. Light, Larry. February 23, 2020. “Why the Bucket Strategy Is the Best for Retirement With- drawals.” Forbes. https://www.forbes.com/sites/lawrencelight/2020/02/23/why-the-bucket- strategy-is-the-best-for-retirement-withdrawals/#663a05036909. 5. Evensky, Harold, and Deena B. Katz, eds. 2006. “Retirement Income Redesigned: Master Plans for Distribution–An Adviser’s Guide for Funding Boomers’ Best Years.” New York: Bloomberg Press. 6. Beaudoin, William. May 2013. “Sample Case.” Private Communication. Integrated Financial Partners. 7. Tomlinson, Joe. April 20, 2020. “Bucket Strategies—Challenging Previous Research.” Advi- sor Perspectives. https://www.advisorperspectives.com/articles/2020/04/20/bucket-strategies-challenging-previous-research. 8. Thaler, Richard H. July 19, 1999. “Mental Accounting Matters.” Journal of Be- havioral Decision Making 12, no. 3: 183–206. https://doi.org/10.1002/(SICI)1099- 0771(199909)12:3%3C183::AID-BDM318%3E3.0.CO;2-F. 9. Shefrin, Hersh M., and Richard H. Thaler. October 1988. “The Behavioral Life-Cycle Hy- pothesis.” Economic Inquiry 26, no. 4: 609–43. https://doi.org/10.1111/j.1465-7295.1988. tb01520.x. 10. Nevins, Daniel. January 2004. “Goals-Based Investing: Integrating Traditional and Behav- ioral Finance.” The Journal of Wealth Management 6, no. 4: 8–23. https://doi.org/10.3905/ jwm.2004.391053. 11. Kritzman, Mark P. January/February 2015. “What Practitioners Need to Know … About Time Diversification.” Financial Analysts Journal 71, no. 1: 14–18. https://doi.org/10.2469/ faj.v71.n1.4. 12. Merton, Robert C., and Zvi Bodie. 1995. “A Conceptual Framework for Analyzing the Finan- cial Environment.” In “The Global Financial System: A Functional Perspective,” by Dwight B. Crane, Kenneth A. Froot, Scott P. Mason, André Perold, Robert C. Merton, Zvi Bodie, Erik R. Sirri, and Peter Tufano, 3–31. Boston: Harvard Business School Press. 13. Milevsky, Moshe A. 2006. “Can Buckets Bail-Out a Poor Sequence of Investment Returns?”

Bucket Investing | 800-347-3539 | flexibleplan.com 26 Further Reading

Bengen, William P. October 1994. “Determine Withdrawal Rates Using Historical Data.” Journal of Financial Planning 7, no. 4: 171–80. Benz, Christine. August 22, 2013. “We Put the Bucket System Through a Longer Stress Test.” https://www.morningstar.com/articles/608619/we-put-the-bucket-system-through-a-longer- stress-t. Benz, Christine. August 30, 2012. “A Sample Retirement Portfolio Using the Bucket Ap- proach.” https://www.morningstar.com/articles/566257/a-sample-retirement-portfolio-using-the-bucket-approach. Black, Fischer, and Andre F. Perold. 1992. “Theory of Constant Proportion Portfolio Insurance.” Journal of Economic Dynamics and Control 16, nos. 3–4: 403–26. Brunel, Jean L.P. 2003. “Revisiting the Asset Allocation Challenge Through a Behavior- al Finance Lens.” The Journal of Wealth Management 6, no. 2 (Fall): 10–20. https://doi. org/10.3905/jwm.2003.320479. Brunel, Jean L.P. 2006. “How Sub-Optimal—If At All—Is Goal-Based Asset Allocation?” The Journal of Wealth Management 9, no. 2 (Fall): 19–34. https://doi.org/10.3905/ jwm.2006.644216. Campbell, John Y., and L. Viceira. 2002. “Strategic Asset Allocation.” New York: Oxford Univer- sity Press. Cooley, Phillip, Carl Hubbard, and Daniel T. Walz. April 2011. “Portfolio Success Rates: Where to Draw the Line.” Journal of Financial Planning 24, no. 4: 48–60. Das, Sanjiv, Harry Markowitz, Jonathan Scheid, and Meir Statman. April 2010. “Portfolio Opti- mization with Mental Accounts.” The Journal of Financial and Quantitative Analysis 45, no. 2: 311–34. https://www.jstor.org/stable/27801487. Dybvig, Philip H. April 1995. “Dusenberry’s Ratcheting of Consumption: Optimal Dynamic Consumption and Investment Given Intolerance for Any Decline in Standard of Living.” The Review of Economic Studies 62, no. 2: 287–313. https://doi.org/10.2307/2297806. Dybvig, Philip H. January/February 1999. “Using Asset Allocation to Protect Spending.” Finan- cial Analysts Journal, 55, no. 1: 49–62. https://www.jstor.org/stable/4480138. Frank, Larry R., John B. Mitchell, and David M. Blanchett. November 2011. “Probability-of- Failure-Based Decision Rules to Manage Sequence Risk in Retirement.” Journal of Financial Planning 24, no. 11: 44–53. Grossman, Sanford, and Zhongquan Zhou. July 1993. “Optimal Investment Strate- gies for Controlling Draw-downs.” Mathematical Finance 3, no. 3: 241–76. https://doi. org/10.1111/j.1467-9965.1993.tb00044.x. Guyton, Jonathan T. October 2004. “Decision Rules and Portfolio Management for Retirees: Is the ‘Safe’ Initial Withdrawal Rate Too Safe?” Journal of Financial Planning 17, no. 10: 54–62. Guyton, Jonathan T., and William J. Klinger. March 2006. “Decision Rules and Maximum Initial Withdrawal Rates.” Journal of Financial Planning 19, no. 3: 48–58.

Bucket Investing | 800-347-3539 | flexibleplan.com 27 Horan, Stephen M. November 2006. “Optimal Withdrawal Strategies for Retirees with Multiple Savings Accounts.” Journal of Financial Planning 19, no. 11: 62–75. Investment Company Institute. August 2010. “The U.S. Retirement Market, First Quarter 2010.” Research Fundamentals 19, no. 3: 1–33. Keating, Con, and William Shadwick. May 2002. “A Universal Performance Measure.” London, The Finance Development Centre. Markowitz, Harry. March 1952. “Portfolio Selection.” The Journal of Finance 7, no. 1: 77–91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x. Merton, Robert C. 1971. “Optimal Consumption and Portfolio Rules in a Continuous Time Model.” Journal of Economic Theory 3: 373-413. Merton, Robert C. August 1969. “Lifetime Portfolio Selection Under Uncertainty: The Con- tinuous-Time Case.” Review of Economics and Statistics 51, no. 3: 247–57. https://doi. org/10.2307/1926560. Michaud, Richard O. 2003. “A Practical Framework for Portfolio Choice.” Journal of Investment Management 1, no. 2: 1–16. Perold, Andre F., and William F. Sharpe. January/February 1988. “Dynamic Strategies for Asset Allocation.” Financial Analysts Journal 44, no. 1: 16–27. Pfau, Wade D. December 2010. “An International Perspective on Safe Withdrawal Rates: The Demise of the 4 Percent Rule?” Journal of Financial Planning 23, no. 12: 51–61. Samuelson, Paul A. August 1969. “Lifetime Portfolio Selection by Dynamic Stochastic Pro- gramming.” The Review of Economics and Statistics 51, no. 3: 239–46. https://doi. org/10.2307/1926559. Samuelson, Paul. A. 1994. “The Long-Term Case for Equities—and How It Can Be Oversold.” Journal of Portfolio Management, 21: 15–24. Scott, Jason S., and John G. Watson. 2013. “The Floor-Leverage Rule for Retirement.” Finan- cial Analysts Journal 69, no. 5: 45–60. https://doi.org/10.2469/faj.v69.n5.2. Shefrin, Hersh, and Meir Statman. June 2000. “Behavioral Portfolio Theory.” The Journal of Financial and Quantitative Analysis 35, no. 2: 127–51. https://doi.org/10.2307/2676187. Siegel, Jeremy. 2014. “Stocks for the Long-Run: The Definitive Guide to Financial Market Re- turns & Long-Term Investment Strategies.” 5th ed. McGraw-Hill Education. Wagner, Jerry. August 2003. “Rethink Risk.” Financial Planning Magazine. https://www.flexibleplan.com/Portals/2/PDF/article-rethink-risk-0803.pdf Woerheide, Walter, and D. Nanigian. December 2011. “Sustainable Withdrawal Rates from Retirement Portfolios: The Historical Evidence on Buffer Zone Strategies.” SSRN working paper. http://dx.doi.org/10.2139/ssrn.1969021. Yang, Z. George, and Liang Zhong. 2013. “Towards Optimal Portfolio Strategy to Control Maximum Drawdown—The Case of Risk Based Dynamic Asset Allocation.” China Finance Review International 3, no. 2: 131–63.

Bucket Investing | 800-347-3539 | flexibleplan.com 28 Disclosures

This white paper is provided for information purposes ically and make appropriate changes. In those cases only and should not be used or construed as an indica- where a Universe Component does not have sufficient tor of future performance, an offer to sell, a solicitation price history, a substitute, including in the case of an- to buy, or a recommendation for any security. Flexible nuities, a mutual fund, research report result, or market Plan Investments, Ltd., cannot guarantee the suitability index after which the sub-account was “cloned,” may or potential value of any particular investment. Infor- be used in order to create a longer history from which mation and data set forth herein has been obtained to test. When this occurs, the daily value of the sur- from sources believed to be reliable, but that cannot be rogate may differ from the NAV of the actual Universe guaranteed. Before investing, please read and under- Component used prospectively due to different internal stand Flexible Plan Investments, Ltd., Brochure Form expenses. If the expenses are lower or in the case of ADV Part 2A and Form CRS. PAST PERFORMANCE indexes used, non-existent, the result of their use will DOES NOT GUARANTEE FUTURE RESULTS. Inherent be to overstate returns. Conversely, higher internal in any investment is the potential for loss as well as expenses will understate returns. profit. A list of all recommendations made within the immediately preceding 12 months is available upon Advisors Preferred LLC (“AP”). Pursuant to a contract written request. with AP, Flexible Plan Investments, acting in the capacity of a sub-adviser, provides investment advisory ser- Research Report results are hypothetical and were vices for investing in select equity, income, derivative achieved by means of retroactive application of a and ETF Investments which Flexible Plan Investments computer model, with the benefit of hindsight, and may also may use in selected strategies, regardless of the not represent the results of actual trading. Therefore, Investments described as being utilized elsewhere Research Report results are NOT represented as actual in this information. If these Investments are used in trading or client experience and they do not reflect the Client’s portfolio, since Adviser would receive a fee for impact on decision making or economic or market fac- its sub-adviser activities, Clients will receive a pro-rata tors experienced during actual management of funds. credit on their billing. AP is a federally registered in- The investment return and principal value of an invest- vestment adviser and is the adviser of The Gold Bullion ment may be lower or higher than the performance Strategy Fund, Gold Bullion Strategy Portfolio, and the quoted; and investors’ shares, when redeemed, may Quantified family of funds. Flexible Plan Investments, be worth more or less than their original cost. Annual Ltd., serves as investment sub-adviser to The Gold returns are compounded monthly Bullion Strategy Fund and the Quantified Funds, distributed by Ceros Financial Services, Inc. (member FINRA/ Expenses of the funds are included to the extent they SIPC). AP is the Funds’ investment adviser and is a are reflected in the NAV. Sub-accounts of variable wholly-owned subsidiary of Ceros Financial Services, annuities, in addition to the expenses of a mutual fund, Inc. AP is compensated by the Funds in its role as have mortality, administrative and other charges. Other investment adviser to the funds on the basis of assets fees may apply. Distributions have been reinvested. under management in the Funds. When provided, dividends are reinvested for indexes. In those cases where indexes do not provide dividend The principal risks of investing in the Funds are risks of information, those returns would be understated. As in- the sub-adviser’s investment strategy, risks of aggres- dividual tax rates vary, taxes have not been considered. sive investment techniques, high portfolio turnover, risk of investing in derivatives, risks of investing in The strategies, mutual funds, exchange-traded funds ETFs, risks of investing in other investment companies, (ETFs), or annuity sub-accounts drawn for investment leverage risk, taxation risk, concentration risk, gold risk, (the Universe Components) may be reduced or added wholly-owned corporation risk, risk of non-diversifica- to from time to time due to closures and other opera- tion and interest rate risk. “Gold Risk” includes volatility, tional considerations. The list represents the universe in price fluctuations over short periods, risks associated use at the time of this report and may differ from prior with global monetary, economic, social, and political periods. We review the Universe Components period- conditions and developments, currency devaluation

Bucket Investing | 800-347-3539 | flexibleplan.com 29 and revaluation and restrictions, trading and transac- Strategy and asset allocation decisions may not always tional restrictions. be correct and may adversely affect account performance. The use of leverage may magnify this risk. You may obtain a Prospectus and SAI through the Leverage and funds employing derivatives carry other following contact information: risks that may result in losses, including the effects of unexpected market shifts, default, and/or the potential illiquidity of certain derivatives. Fund The Gold Bullion Strategy Fund Active investment management may involve more http://www.goldbullionstrategyfund.com frequent buying and selling of assets. The majority of Quantified Alternative Investment Fund Flexible Plan strategies utilize no-load mutual funds Quantified Managed Income Fund with no transaction charges. Best efforts are employed Quantified Market Leaders Fund Quantified STF Fund to avoid short-term redemption charges, however, Quantified Tactical Fixed Income Fund actively managed strategies can still result in charges, Quantified Evolution Plus Fund especially when entering or exiting a strategy. Addi- Quantified Common Ground Fund tionally, any commissioned investments will reflect the Quantified Pattern Recognition Fund impact of more frequent buying and/or selling of assets. http://www.quantifiedfunds.com If investing within a non-tax-deferred investment, Inves-

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If this presentation is calculated with the maximum Advisor may predicate some strategies on trading current management fee, the maximum current signals furnished by non-affiliated firms. In such management fee in effect is 2.25% (1.75% for group instances, the non-affiliated firm is under contract to retirement plans). Strategic Solutions and Managed Adviser to provide, and in certain instances, implement Solutions fees are deducted in arrears at the rate of management of Client accounts in such strategies. 2.25% annually, with pro-ration of partial periods. Actu- Flexible Plan by necessity relies on information, data, al management fees will vary between 1.0% and 2.25% and software provided by third parties, the reliability of annually. Returns for certain programs/product families which, while believed to be accurate, cannot be guar- are shown before withdrawal of a maximum establish- anteed and losses may result from reliance upon them. ment fee of 1.2% unless the selected date range in- These are normal risks for which Flexible Plan takes cludes the inception date (start date) and if the solicitor no responsibility beyond use of reasonable care in its firm allows the use of an establishment fee. All mutual selection of the third party. fund fees and expenses are included to the extent they are reflected in net asset value; other fees may apply. For many strategies, Adviser provides suitability-based profiles with names such as, without limitation, Conser- Results are shown after fees at the rate indicated and, vative, Moderate, Balanced, Growth, and Aggressive if applicable, subject to a credit for use of any FPI or with numerical designations such as 25, 40, 60, 80, sub-advised funds (primarily used in QFC Strategies). and 100. Clients should draw no conclusions from These fees are not taken into account in computing such titles. Rather, they are simply a way of designating Annualized risk, Beta, or Maximum loss (daily). Since the hierarchical ranking of Adviser’s Profiles within a monthly maximum loss is after fees, there may be an strategy. They are not meant to imply any ranking within occasion when monthly max loss may exceed dai- some universal risk measure or benchmark, nor are they ly max loss. The maximum investment advisory fee equivalent to a Client’s subjective concept of the term. is 2.25% yearly (1.75% for group retirement plans),

Bucket Investing | 800-347-3539 | flexibleplan.com 30 dependent upon assets under management, and is de- (or the failure to intervene) by US or foreign gov- ducted pro-rata in arrears. For the Strategic Solutions, ernments or central banks, or by currency controls as well as Schwab, Nationwide MarketFLEX Advisor or political developments. Long / Short Directional: VA, and Jefferson National Monument Advisor strat- Portfolio may invest in derivative investments such egies, an establishment fee of up to 1.2% has been as futures, contracts, options, swaps, and forward deducted at inception. currency exchange contracts that may be illiquid or increase losses due to the use of leveraged po- ASSET CLASS RISK CONSIDERATIONS sitions. US and Global Equities: In addition to the foreign investment risks noted above, the principal US and Global Bonds: All investments involve risk. risks associated with equities include market, port- Special risks associated with investing in bonds folio management, and sector risks. Downside Pro- include fluctuations in interest rates, inflation, tection: The use of cash, short-term investments, declining markets, duration, call, and credit risk. inverse funds, and hedging strategies may help miti- Special risks are associated with foreign investing, gate the overall risk of the portfolio and offer some including currency fluctuations, economic insta- downside protection. bility, and political developments. Investments in developing markets involve heightened risks related Investors should consider carefully information to the same factors, in addition to those associated contained in the prospectus, including investment with these markets’ smaller size and lesser liquidity. objectives, risks, charges, and expenses. You can Commodities: Concentrating investments in natural request a prospectus by contacting your financial resources industries can be affected significantly by advisor. Please read the prospectus carefully be- events relating to those industries, such as varia- fore investing. Investment value will fluctuate, and tions in the commodities markets, weather, disease, shares, when redeemed, may be worth more or less embargoes, international, political, and economic than original cost. developments, the success of exploration projects, tax and other government regulations, and other PAST PERFORMANCE DOES NOT factors. US and Global Real Estate: Investments GUARANTEE FUTURE RESULTS. in Real Estate are subject to changes in economic conditions, credit risk, and interest rate fluctuations Please read Flexible Plan Investments’ Brochure Form Global Currencies: Foreign currency exchange ADV Part 2A carefully before investing. rates may fluctuate significantly over short periods of time. They generally are determined by supply As supplemental information, a listing of all recom- and demand in the foreign exchange markets and mendations made within the immediately preceding relative merits of investments in different countries, 12 months, all assumed trades, and other data used actual or perceived changes in interest rates, and to generate the referenced results is available upon other complex factors. Currency exchange rates request. Inherent in any investment is the potential for also can be affected unpredictably by intervention loss as well as the potential for gain.

Bucket Investing | 800-347-3539 | flexibleplan.com 31