Lifetime Investment Phases

Generally speaking, there are two basic phases in a lifetime of investing: accumulation and distribution.

Accumulation Phase

In the first phase, which is the accumulation phase, investors start to work, and hopefully contribute an increasing amount of savings each year to their portfolio as they reach their peak earning years. The goal is to have a portfolio at retirement which will allow sufficient distributions such that, when combined with social security, pensions, and other income sources, it gives the retiree a more than adequate amount of income to enjoy retirement while not running out of money.

During the accumulation phase, the portfolio is expected to grow over time from periodic savings and investment returns. The portfolio’s ultimate size at retirement will depend on the size of the investments, the returns on those investments and the length of time before withdrawals begin.

The key output for the accumulation phase is the ending portfolio value at the start of retirement.

Distribution Phase

The second phase in an investor’s life is the distribution phase, when the (typically retired) investor is taking money out his or her portfolio. The portfolio will still be generating investment returns, but these gains will be tempered by the periodic withdrawals, which could lead to one of multiple scenarios.

Through some combination of modest portfolio size at the beginning of the distribution phase, high withdrawals, high inflation and/or investor longevity, the portfolio may eventually decline, and may even run out of money during the investor’s lifetime.

Conversely, through some beneficial combination of larger initial portfolio value at retirement, modest withdrawals, low inflation and favorable investment returns, the portfolio value may ultimately stabilize, such that the growth in the portfolio each year covers all the withdrawals. Even better, the portfolio might generate returns which are higher than the necessary withdrawals, leading to a comfortable retirement and possibly a sizable estate.

Key outputs for the distribution phase are:
-    The probability of success, which is the probability of not running out of money over the retiree’s lifetime; and
-    The ending portfolio value at the end of the person’s life.

Distribution Tables

The fixed distribution tables used in the article "How much money can you prudently take out of your investments in retirement?" show the impact of the distribution phase on portfolio values. Starting with a portfolio of $1 million, the tables show the impact on the portfolio for a variety of asset allocations, using different withdrawal rates adjusted for annual inflation, for the returns which actually took place between 1970 and 2008.

Sequence of Investment Returns

For both the accumulation and distribution phases, the sequence of investment returns is very important. In the accumulation phase, the investor is not hurt very much by poor market performance in the early years, since any negative returns impact a relatively small portfolio, and the investor could take advantage of the resulting low stock prices by investing more, and by taking advantage of the many more years to invest.

The situation is just the reverse in the distribution phase. Negative portfolio returns in the last years leading up to retirement and the first few years of retirement can have a disproportionate negative impact on the ultimate ending value of the portfolio. This is because the portfolio value, which typically declines in the distribution years, may be biggest at the beginning of retirement. A poor investment environment at the outset of retirement would have the greatest negative impact when the portfolio is at its biggest. In addition, the retiree will not have the earning capacity to contribute more to the portfolio to take advantage of lower stock prices, and won’t have the benefit of lots of time to have the portfolio grow.

Our fixed distribution tables show one sequence of returns, which are the historic returns which occurred from 1970 to 2008. Going forward, the sequence of returns that will take place will be different than what has already occurred. Investors could get a more robust view of potential outcomes if they could see a variety of sequential returns, with some scenarios starting with low or negative returns, and other scenarios starting with higher returns.

Monte Carlo Analysis

One way to show the results using a large number of potential portfolio return sequences is to use Monte Carlo analysis. This is a mathematical simulation which draws portfolio returns from a statistical distribution, and then generates hundreds, or even thousands, of potential outcomes.

Monte Carlo analysis could be quite useful in analyzing potential outcomes. However, it is not a panacea.

The returns for the Monte Carlo analysis come from a theoretical distribution which is based on historical returns. However, the returns for any given year in any given scenario are not necessarily linked by economic reality to the returns generated for the previous year. Also, any Monte Carlo analysis is sensitive to the assumptions used. While it is typical to use a fixed set of correlations between asset classes, correlations tend to increase during times of market stress, making the assumption of fixed correlation somewhat suspect.

Reasonable Compromise

There is a reasonable compromise between the one scenario shown using the historic returns and the hundreds or thousands of scenarios which could be shown using the more theoretical Monte Carlo analysis. That is to use bootstrapping.

Bootstrapping

Bootstrapping, as we use it, starts with the actual returns for all the years between 1970 and 2008. We then generate a number of return scenarios based on the number of years of returns we have, in this case 39. The first potential sequence of returns is the actual historical returns, starting with 1970 and going through 2008. Another possible set of returns starts with 1971, goes through 2008, and then loops back again to 1970. A third possible set of returns starts with 1972, continues through 2008, and then loops back to 1970 and 1971 at the end of the sequence, to get the 39 years.

The generalization is to start with any year between 1970 and 2008. Take all the sequential returns from that year through 2008, then loop back to 1970 and the years following to get the necessary number of years desired in the analysis.

Here are three examples of the 39 possible scenarios:

For each scenario, we assume that contributions or distributions increase by the Consumer Price Index for the associated year.

Note that the time horizon we use could be less than the number of scenarios. For example, even though there will always be 39 scenarios if we use historical information from 1970 – 2008, we could use a shorter time horizon, of, for example, 30 years, for each scenario.

Benefits of Bootstrapping

- With bootstrapping, there are as many scenarios as there are years for historic returns.

- Bootstrapping is more robust than the static distribution table, and can be used to quickly answer various questions, such as:

-    “What happens to my ending portfolio value in the distribution stage if I start with the poor returns from 2008?”

-    “On average, over 39 scenarios, with a 60/40 asset allocation and a given initial distribution, would I end up with a positive balance at the end of 30 years?”

- Each year’s returns follow the previous year’s, so that the sequential returns are in synch with the economic cycle (with one exception, that 1970 always follows 2008).

- Returns of different asset classes within a portfolio move appropriately relative to each other.

Negative Balances

In the distribution tables using the returns from 1970 - 2008, any ending portfolio value less than zero is blanked out.  For bootstrapping purposes, we want to be able to calculate the average ending portfolio value over the 39 scenarios, so we need an ending portfolio value for each scenario, even if it is negative. We have the option of applying a borrowing cost to negative balances (such as the cost of a reverse mortgage or a home equity line of credit), or we could assume no interest cost to fund negative balances.

Bootstrapping Example

Let’s take a 30 year old who is starting to build a portfolio, works until the age of 65, and then wants his portfolio to last until age 100.

Results – Accumulation Phase

The first year, he saves $5,000. Each year, his annual savings increase by the inflation rate for the applicable year. He is in the workforce for 35 years. What is the average amount of money he might accumulate over the 39 scenarios, using different asset allocations?

The graph shows that, over the 35 remaining years that the investor is working, his average total contribution for the 39 scenarios would be $415,713. His total portfolio, including the compounded earnings on the total portfolio, would vary depending on his asset allocation mix. If he invested solely in the S&P, he would end up with around $2.72 million at the age of 65.

He would be able to achieve just about the same result of $2.72 million at the age of 65 with less overall equity exposure if he invested in a portfolio comprised of 60% global equity and 40% fixed income.

Results – Distribution Phase

Now our investor is ready to retire at the age of 65. He chose a 60/40 allocation during his earning years, now has $2.72 million, and wants the portfolio to last until he is 100 years old. Let’s assume he shifts to a 50/50 allocation and that he needs annual distributions starting at $136,000. This is equal to an initial distribution of 5.00% of the portfolio (on a $1 million portfolio, the equivalent withdrawal would be $50,000 per year, similar to a “moderate” withdrawal rate).

While a withdrawal of $136,000 per year sounds like a lot of money, the first withdrawal is 35 years from now. If we assume inflation of 3.5% per year, that’s the equivalent of taking out $40,800 today.

What is the likelihood of the portfolio being able to sustain this withdrawal rate, over the 39 scenarios?

This next graph shows the probability of ending up with a portfolio value greater than 0, through age 100, for different asset allocations, over 39 scenarios.

Click here for a larger version of this table

You could see that for equity allocations of 40% and less, the odds of ending up with a positive portfolio value are less than 80%. In other words, there is no way to avoid some risk. Investors who think stocks are too risky, and allocate a large percentage of the portfolio to bonds, may face a higher probability of running out of money during their lifetime.

At 50% equity, using the 39 scenarios, there is around an 87% chance that the portfolio won’t run out of money. Compare this to the portfolio invested 100% in the S&P500, which has a 56% chance of success.

This next graph shows the average ending portfolio value, in the investor’s 100th year, for different asset allocations.

Click here for a larger version of this table

Notice that for very low stock allocation of up to 20%, the expected ending portfolio value is close to or below zero, meaning that there is a high likelihood the portfolio would not be able to sustain that withdrawal rate, and would run out of money. At 50% equity, the average ending portfolio value across all the simulations is $14.69 million 70 years from now. This is the equivalent of around $1.32 million in today’s dollars, assuming annual inflation of 3.5%.

The final graph shows the impact of changing the sequence of returns, for a given asset allocation of 50% equity and 50% fixed income. It shows the ending portfolio value, assuming different starting years.

For example, if the retiree endured the negative return of 2008 in the first year of retirement, the portfolio would have been hit hard, and the portfolio would not have lasted for the full retirement. In fact, the portfolio would have run out of money if the first year of retirement had returns started with any of the years 2004 – 2008, due to two reasons: The first reason is having a very bad year (2008) within five years of the beginning of retirement.

The second reason is that since the bootstrapping adds the years starting in 1970 after 2008, and the years 1973 and 1974 were also bad, portfolios starting in the years 2004 - 2008 faced the double whammy of a terrible 2008, followed in the simulation by poor years soon after that, corresponding to 1973 and 1974.

If the investor was fortunate enough to begin retirement with a portfolio worth $2.72 million using 1975 as the first year, a particularly good year for stocks (which also had positive returns for the portfolio for the next 14 years after that, allowing the portfolio to grow quickly before having to sustain losses), he would have ended up with a whopping $47 million in future value at age 100. The horizontal line across the graph shows the average $14.69 million of all the scenarios.

Click here for a larger version of this table

Conclusion

Of course, the future will in all likelihood be different than the average of any group of bootstrapping scenarios, and the actual ending portfolio value and probability of success for any individual may not end up being within the range shown in the bootstrapping simulations. We are dealing with very long time frames, and small changes in assumptions can lead to larger changes in results.

That said, bootstrapping can be a valuable addition to the analytic tools we offer clients to assess the likelihood their portfolio will last through retirement. Clients can ask their financial advisor for more details.

A future article will look at the impact of changing the various parameters, such as the periodic amount saved, number of years of saving, retirement age, and longevity.

Larry Katz is director of research at Merriman.

Disclaimer and Disclosure
This report has been prepared by Merriman, a registered investment advisor, (the Company”) and contains calculations and analyses based on the data and assumptions provided by you as our client or prospective client.  These calculations and analyses are necessarily dependent on the reasonableness and accuracy of the data and assumptions you have provided.  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 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 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 that year.