Because the past is known and fixed, it’s relatively easy to calculate the outcomes of various choices that investors might have made. But sometimes this analysis is too simplistic for making useful choices that will apply to the future.

Even when actual yearly returns are known, the sequence or order of those returns plays a huge role in determining the outcomes during both the accumulation and distribution phases of investing. Unfortunately, this sequence is outside the control of investors.

On the other hand, investors do have at least some control over a number of important choices that savers and retirees make about their money.  These include how much they save, when they start saving, how they allocate their investment assets, when they retire and how much they take from their portfolios in retirement.

In this article we examine the effects of the order in which returns happen, using simulations based on actual results from the years 1970 through 2008. We then look at how investors can make choices that are likely to improve their odds of successfully retiring without running out of money.

To follow the twists and turns of this discussion, we use the example of a 35-year-old investor who is just beginning to build her nest egg and who wants to retire at age 65.

Distribution Tables Show Historic Returns

In the article “How much money can you prudently take out of your investments in retirement?” we show six tables of potential distributions. These tables show one sequence of returns, which are the actual annual returns from 1970 through 2008.

The future is not certain. Future returns could be very different from those of the past, and the order in which they occur will have substantial impacts on the portfolio value and the resulting distributions.

Investors can get a more robust view of potential outcomes by looking at a variety of potential sequential returns, with some scenarios starting with low or negative returns, and other scenarios starting with higher returns.

Bootstrapping – Shows Multiple Return Possibilities

We accomplish this by using bootstrapping, a technique described in “Bootstrapping: Another way to assess potential investment outcomes.”

The concept of bootstrapping, as we use it, starts with actual returns for all years from 1970 through 2008. We then generate multiple potential future scenarios by rearranging the historic returns. One obvious potential sequence of returns starts with 1970 and goes through 2008. Another starts with 1971, goes through 2008, and then loops back again to 1970. A third starts with 1972, continues through 2008, and then loops back to include the returns from 1970 and 1971 at the end of the sequence, to get the 39 years. And so on.

We can start with any year from 1970 to 2008, take all the sequential returns from that year forward through 2008, then loop back to 1970 and continue to the starting point, giving us 39 scenarios.

Here are three examples:

Figure 1 

With these multiple possible scenarios, we can look at the outcome under each scenario, and then calculate the probability of success, which we’ll define here as not running out of money during retirement.

In our calculations, each year’s contribution or distribution increases by the change in the Consumer Price Index for the previous year.

Variables which Impact Ending Wealth

We will look at both the accumulation phase and the distribution phase, and analyze the impact that different return scenarios and other variables may have on the outcome.

The variables we will look at during the accumulation phase include the number of years of savings, the periodic amount saved and asset allocation. In the distribution phase, we will look at varying the asset allocation, initial portfolio value, retirement age, distribution amount and longevity.

Accumulation Phase

To demonstrate how these factors apply to an individual, let’s assume a 35 year old woman with no savings who wants to retire at 65. At age 35, the first year of our calculations, she saves $3,000. In subsequent years she increases that amount every year to keep up with inflation.

Her equity allocation should be determined by her risk preferences, loss tolerance and her desired portfolio value at retirement, which can be done in consultation with her financial advisor. Let’s assume she chooses a portfolio which is 70 percent equity and 30 percent fixed-income (with the equity and bond component similar to Merriman’s recommendations). How much might she have when she retires?

If her returns were identical to those of 1970 through 1999 (30 years), she would have a portfolio worth almost $1.68 million at retirement. But what if the sequence of returns was very different than those of 1970 through 1999? Over 30 years, depending on the year of her first investment, using our 39 return scenarios her ending portfolio could have been as low as $360,000 or as high as $1.68 million, with an average of $1.05 million.

Figure 2 shows the range of potential outcomes for the 39 scenarios. Each bar represents the estimated ending portfolio value if the investment returns started with the year indicated. The horizontal line is the average forecasted portfolio value at the start of retirement.

Figure 2: Accumulation Phase, Base Case

Click here for a larger version of this table

Why is there such a large potential range of outcomes? If she begins investing in 1984, the portfolio grows nicely until it is worth almost $403,000 at the end of 2007; then it gets hit by the turbulence of 2008, leading to a 26 percent decline. Given the way these bootstrapping scenarios work, after 2008 the returns loop back and start again with the returns from 1970. The last two years before her retirement are 1973 and 1974, both of which had negative returns. This scenario highlights the large risk an investor faces in the last few years before retirement from a substantial market decline.

Conversely, if she first invests in 1970, the portfolio hits the bad years of 1973 and 1974 early on, when she has relatively few dollars at stake. Since her time horizon is 30 years, the portfolio will miss the terrible 2008 market, and she will start her retirement with a large nest egg.

Now let’s ask another question. What if she wanted to start her retirement with a portfolio worth $1.5 million at the age of 65? To achieve this, there are various things she could have done. She could have started saving earlier, saved more each year or had a higher equity allocation in her portfolio.

Let’s look at each of these variables, one at a time, to get to an average forecasted portfolio value at the beginning of retirement of around $1.5 million, and then look at combinations of changes she could make.

If she starts saving three years earlier, at age 32, she ends up at 65 with a portfolio which averages $1.45 million. Alternatively, she could start saving at 35, but save more aggressively. If her initial investment is $4,300, she ends up with a portfolio worth an average of $1.51 million at retirement.

Since stocks have historically returned more than bonds over time, she could instead increase her allocation to stocks. Even if she invests the entire portfolio in stocks (which we would not necessarily recommend due to the higher risk), she ends up with an average of $1.37 million over the 39 return scenarios, assuming she starts saving $3,000 per year at age 35.

Now, let’s see the impact of changing several things at the same time. Instead of starting to save at 35, she starts at 34. Instead of $3,000, her initial investment is $3,500. And instead of a 70 percent stock allocation she chooses 80 percent. She ends up with an average portfolio, over the 39 scenarios, of $1.51 million.

To summarize her choices, she invested for 31 years instead of 30, an increase in years of 3.3 percent. She boosted the initial amount saved from $3,000 to $3,500, an increase of 17 percent. And she increased her stock allocation from 70 percent to 80 percent. The combination of all these increased her average forecasted portfolio value at retirement by 44 percent, from $1.05 million to $1.51 million. This shows the potentially large impact over time of relatively modest changes to a savings and investment discipline.

Figure 3 summarizes these examples, with the changes from the base case in bold.

Figure 3

Based on all the actual returns from 1970 through 2008, Figure 4 shows the range of potential portfolio values at the start of retirement for a 34 year old who starts saving $3,500 per year, with subsequent investments adjusted for inflation, who saves for 31 years and has an equity allocation of 80 percent in her portfolio.

Figure 4: Accumulation Phase, Modified Case

Click here for a larger version of this table

Notice that, even after making these changes, she could still end up with much less than her goal of $1.5 million.

Distribution Phase

Now, let’s assume that our hypothetical retired investor, at the age of 65, has a portfolio worth $1.05 million. She has some control over how much she takes out of the portfolio each year and she also has control over her equity allocation. By taking good care of her health, she may have some control over her longevity.

Let’s say that she has determined that, taking into account Social Security and her pension, she needs $52,500 from her portfolio each year, adjusted for inflation, to finance her desired lifestyle. This is equal to 5 percent of her portfolio value. She wants to decrease her stock allocation after she retires to be more conservative. Let’s assume she’ll live to the ripe old age of 100.

What is the probability that she can live to 100 without running out of money ? Figure 5 shows this, for each of several different equity allocations.

Please note that our measure of success is that the portfolio avoids running out of money. While the odds of success in this case do not increase much past 60 percent equity, her average ending portfolio size will increase with higher stock allocations, though with increased risk of periodic loss.

Figure 5: Distribution Phase, Chances of Success

Click here for a larger version of this table

With an equity allocation of 50 percent, there is a 69 percent chance the portfolio will not run out of money by the time she is 100. If she can tolerate a bit more risk, she can increase the chances of success to 82 percent by choosing a 60 percent equity allocation.

If her goal is to maximize the chances of not running out of money in retirement while controlling her level of risk, then a 60 percent allocation to equities looks reasonable.

The outcome of these assumptions is still heavily dependent on what year we assume she retires. The range of potential outcomes for a 60 percent equity allocation is shown in Figure 6. The horizontal line is now the average portfolio value at the end of her life, at age 100.

Figure 6: Distribution Phase, 60 Percent Equity, Outcomes for 39 Different Scenarios

Click here for a larger version of this table

Now even though the 82 percent success rate is not foolproof, it is good to note that, in many of the scenarios where she runs out of money, the ending balance is only slightly negative. Minor modifications of her spending over time can solve much of that problem. However, she would have run out of money (shown by a negative bar) if, within five years of retiring, she hit the turbulence of 2008 followed several years later by the poor returns of 1973 and 1974.

What if, through earlier or more diligent saving, or better returns, she retires with a portfolio of $1.5 million, and still needs to withdraw $52,500 in her first retirement year? In this case, her odds of success are much higher, as you will see in Figure 7.

Figure 7: Distribution Phase, 60 Percent Equity, $1.5 million portfolio

Click here for a larger version of this table

In this case, no matter which of the 39 potential return scenarios is run, the portfolio never runs out of money! This is because the initial distribution rate of 3.50 percent ($52,500 from the $1.5 million portfolio) is quite conservative.

Let’s go back to the first retirement scenario, where she has $1.05 million. How can she improve the odds that her portfolio will not run out of money during her lifetime?

Her options include postponing retirement, taking out less money, and increasing her equity allocation. While we think a good practice is to run the portfolio out to age 100, relatively few people live that long.

What if she delays retirement? Instead of working for 30 years and retiring at 65, she could work (and save) for 31 years and retire at 66. Postponing retirement has at least four important benefits. First, additional years on the job will let her add more to her savings. Second, her portfolio has more time to potentially grow before it has to start paying her. Third, her portfolio will have fewer years that it must pay out. Fourth, delaying Social Security can make those payments permanently higher.

While the postponement of retirement is not to be taken lightly, the potential benefits are large enough to consider.  Delaying retirement by one year, and investing for 31 years instead of 30, increases the average forecasted portfolio size from $1.05 million to $1.17 million, at her original 70 percent global equity allocation. The portfolio now has to last only 34 years instead of 35. Since she will start taking money out of the portfolio one year later, her initial distribution will be $54,890 instead of $52,500, reflecting the average annual inflation rate of 4.55 percent.

Figure 8 shows the odds of success for different asset allocations.

Figure 8: Start Retirement One Year Later, Chances of Success

Click here for a larger version of this table

Compare Figure 8 with Figure 5. In Figure 5, the portfolio value started at $1.05 million, the initial distribution was $52,500, and the portfolio had to last 35 years. In Figure 8, the portfolio starts at $1.17 million, the initial distribution is $54,890, and the portfolio has to last 34 years. At a 60 percent equity allocation, the odds of success in Figure 5 are 82 percent while in Figure 8 the chances of success are 90 percent. So, by working one additional year, she increases the chances of not running out of money from 82 percent to 90 percent. Figure 8 also shows that increasing her equity allocation beyond 50 percent won’t really change her chances of success (but it will increase the average ending portfolio value). This gives her the additional flexibility of choosing a lower equity allocation without raising the risk that she will run out of money.

Now let’s look again at the original retirement portfolio of $1.05 million. Instead of taking an initial $52,500, or 5 percent, from the portfolio, assume that she takes $49,875, or 4.75 percent. This is a decrease of $2,625 or 5 percent from $52,500.

Figure 9: Distribution Phase, Lower Distributions, Chances of Success

Click here for a larger version of this table 

With this change, the odds of success go from 82 percent to 90 percent, at 60 percent equity.

Finally, what if, after a judicious and conservative assessment of how long she might live, our retiree decides that she wants to assume that the portfolio will have to last only until she is 95 instead of 100? The starting portfolio is still $1,050,000 and the initial distribution is $52,500. The decreased expected longevity will increase the chances of not running out of money in the 60 percent equity case from 82 percent to 90 percent.

In summary, the lessons of these charts amount to a kind of good news, bad news. The longer you live, the more chance you have of outliving your money. Generally speaking, a healthy person with long-lived parents should be very diligent about saving towards retirement, based on the increased chance of living a longer life.

Note that we have just shown various probabilities of success for only 39 different return scenarios, none of which is likely to happen in the future. People have no control over what the markets will return over time.

However, this exercise shows the impacts of things over which investors and retirees do have control. These factors can positively impact the amount of money that’s available in retirement.

Here’s my advice, in three parts:

First, to paraphrase from the political arena, save early and save often. Save enough to help finance what hopefully will be a long and fruitful retirement.

Second, time your retirement and calibrate your distributions so you can enjoy life and still have enough to maintain your desired lifestyle for the rest of your expected lifetime.

Finally, get professional help to be sure you have made the right choices. Financing your retirement is a balancing act involving multiple issues that work together. Only you can determine the answers that are best for you. But a good advisor can make sure you have asked all the right questions.

Larry Katz is research director of Merriman.

Disclaimer and Disclosure
This report has been prepared by Merriman, a registered investment advisor, (the Company”) and contains calculations and analyses based on various data and assumptions.  These calculations and analyses are necessarily dependent on the reasonableness and accuracy of the data and assumptions used.  While reasonable efforts have been made to ensure the accuracy of the calculations included in this report, the Company is not responsible for any computational error. 

Unless otherwise noted, all reported or projected results (1) assume reinvestment of interest and dividends; (2) are net of any applicable management fees and transaction costs (except for the S&P 500 returns, which are based on an index); and (3) do not reflect any effect of taxes.

Actual results may differ from the results presented in this report and past performance and results may not be indicative of future results.  You should not assume that future performance of any specific investment, security, strategy, or other product or service directly or indirectly referred to in this report will be profitable or equal the indicated performance level.  Different types of investments, investment strategies, and investment products involve varying degrees of risk, and there can be no assurance that any specific investment will either be suitable or profitable for you or your investment portfolio.

Due to various factors, including rapidly changing market conditions, the enclosed report may not be reflective of current positions and/or recommendations. This or a similar report should be completed at least annually to best reflect your individual circumstances and market conditions.  You should not assume that this report serves as the receipt of, or a substitute for, personalized advice from a financial advisor or other investment professional.  No portion of the report content should be interpreted as legal, accounting or tax advice.  You are solely responsible for determining whether any investment, security, strategy, or any other product or service, is appropriate or suitable for you based on your investment objectives and personal and financial situation. You should consult with an investment professional, or an attorney or tax professional regarding your specific investment, legal or tax situation.

You, as our client or prospective client, agree, as a condition precedent to your use of this report to release and hold harmless the Company, its officers, directors, owners, employees and agents from any and all adverse consequences resulting from any of the Company’s actions and/or omissions which are independent of your receipt of personalized individual advice from the Company.

This document contains hypothetical results, including annual return sequences which did not take place.  Hypothetical performance is potentially misleading.  Hypothetical data does not represent actual performance and should not be interpreted as an indication of actual performance.  This data is based on transactions that were not made.  Instead, the trades were simulated, based on knowledge that was available only after the fact and thus with the benefit of hindsight. Past returns are not indicative of future results.

Data Sources: 

The following data sources were used to develop the tables and figures in this presentation.  Note that many of our return series rely on academic simulations gathered and developed by Dimensional Fund Advisors (DFA).  All performance data are total returns including interest and dividends. Simulated data subtracts the current expense ratio for the comparable fund.

Equities                                               
   
Emerging Markets                         DFEMX to May 1994, DFA simulation back to Jan 1987.

Emerging Market Core                   DFCEX from May 2005.   

Emerging Market Small Cap           DEMSX back to 1999, DFA simulation back to Jan. 1987.
       
Emerging Market Value                  DFEVX back to 1999, DFA simulation back to Jan. 1987.

International Large Cap                 DFALX back to 1992, MSCI EAFE back to 1970.
           
International Large Cap Value        DFIVX back to Mar 1994, DFA simulation back to 1975.   
 
International Small Cap                  DFISX back to Oct. 1996, DFA simulation back to 1970.
        
International Small Cap Value        DISVX back to 1995.               

Large Cap                                      DFLCX back to 1991, S&P 500 back to 1970.
       
Large Cap Value                            DFLVX back to 1994, simulation back to 1927.   

Micro Cap (or Small Cap)               DFSCX back to 1983, Dimensional US Micro Cap Index to 1970.

Real Estate Investment Trusts    DFREX back to Jan. 1993, Don Keim REIT Index 1975-1992, NAREIT 1972-1974.

S&P 500                                        1926 - 1989.  Stocks, Bonds, Bills, and Inflation 2003 Yearbook, Ibbotson Associates, Chicago (annually updated); 1990 – Present S&P 500 Index, provided by Standard & Poor's Index Services Group.   

Small Cap Value                          DFSVX back to 1994, DFA simulation back to 1927.


Bonds & Inflation

Lehman U.S. TIPs                                    Back to March 1997, Morningstar.

DFA Intermediate Government Bonds    DFIGX, Morningstar

Vanguard Short-Term Treasuries            VFISX, Morningstar.
               
Tables & Charts (Global Balanced Portfolio)

•    Monthly rebalancing
•    1% Management Fee included
•    Fixed Income Allocation: 50% in Intermediate Term Government, 30% in Short-term Treasuries and 20% in TIPs
•    U.S. Equity Allocation: 20% each in LC, LCV, SC, SCV, and REITs
•    International Equity Allocation is:   
1970-1974:  50% Int. LC, 50% Int. SC
1975-1986:  25% Int. LC, 25% Int. LCV, 50% Int. SC
1987-1994:  20% Int. LC, 20% Int. LCV, 10% EM, 5% EMS, 5% EMV, 40% Int. SC
1995-2005:  20% Int. LC, 20% Int. LCV, 10% EM, 5% EMS, 5% EMV, 20% Int. SC, 20% Int. SCV
2006 - 2007: 20% each in Int. LC, Int. LCV, Int. SC, Int. SCV, and EM Core
•    Fees are calculated based on Schwab custodial fees which average around 10 bps and the Merriman asset-based fee schedule, imposed yearly.
•    Distribution is at the beginning of the year.
•    A fixed amount will be distributed each year and increased annually by the inflation rate for the previous year.