Absent investment chicanery, every portfolio is going to have positive returns at times and negative returns at other times. Does the order of these gains and losses actually matter?

To understand the impact of the market's ups and downs, let's examine the annual performance of 12 different asset classes over a 15-year period from Jan. 1, 1998 to Dec. 31, 2012. These asset classes are shown in two tables on the following pages: Forward Performance Sequence and Reversed Performance Sequence. They are the same numbers, but one table starts with the earliest performance data and works forward. The other starts with the most recent years and works backward, to highlight the role played by sequence. In both tables, the negative annual performance is highlighted by a yellow background.

The analysis also covers two portfolios: a balanced portfolio of 60% large-cap U.S. stocks and 40% U.S. bonds, and a multi-asset balanced portfolio in which all 12 individual asset classes are weighted equally and rebalanced annually.

The analysis leads to an important conclusion: For a lump sum investment that is allowed to grow undisturbed over a number of years, the sequence of returns does not matter mathematically. But it likely matters to clients prone to emotional reactions, just not in terms of raw math.

Click for chart

DISTRIBUTION PORTFOLIO

Where the math gets interesting is in the performance differences within a distribution portfolio, in which money is withdrawn each year. For simplicity's sake, assume the starting balance is \$100,000, an initial withdrawal is 5% (or \$5,000) and the annual withdrawal increases by 3%. A total of \$92,995 is withdrawn over the 15-year period.

When comparing the results for distribution portfolios using the Forward and Reversed performance sequences, the largest differences in the internal rate of return and ending account value are generally associated with assets that have a high standard deviation of return.

This is particularly noticeable in emerging markets stocks and real estate. Within a distribution portfolio, the ending account values differed by almost \$30,000, based on the sequence of returns. Negative returns in the initial years of a distribution phase are highly destructive to the portfolio account value. In the case of emerging markets stocks, the better result occured when using reversed returns because the Forward Performance Sequence had negative results in four of the first five years.

This same phenomenon played out in real estate. The results were better when positive returns occurred in the first several years of the distribution period, as happened for real estate in the Reversed Performance Sequence.

The differences between sequences were less pronounced in fixed income, however. Three of the fixed-income assets (U.S. bonds, TIPS and non-U.S. bonds) had very similar results whether returns were forward or reversed.

Yet cash, interestingly, was quite sensitive to sequence of returns - as shown by the results using the Reversed Performance Sequence, in which the low cash returns in recent years (2009 to 2012) occurred at the beginning of the sequence. These anemic initial returns could not support the portfolio as money was withdrawn each year. When a portfolio is hurt in the early years, it becomes difficult to recover.

SEEKING STABILITY

The 60/40 portfolio and the 12-asset portfolio had very similar results whether returns were forward or reversed, suggesting that both have a return pattern that is more stable - as also shown by their relatively low standard deviation of return. This is a key and perhaps intuitive point: When a portfolio (or single asset class) has a more stable return pattern, its performance is less vulnerable to variation in the sequence of returns.

The overall results of the analysis are shown in the Performance Summary table on page 72. The first section of the table shows the standard deviation for all 12 asset classes as well as for the 60/40 portfolio and the 12-asset portfolio.

The next segment of the table shows the 15-year annualized return for the forward sequence of returns (1998-2012) and the reversed sequence of returns (2012-1998), assuming a lump-sum investment. The returns are identical, as might be expected. The last section of the table shows the results of an additional test: running the withdrawal portfolio (and its various components) through 15 randomized return sequences. The variation in ending account balances was astonishing.

For large-cap U.S. stocks, the average ending balance was a bit more than \$53,000, with a high balance of \$96,586 (following large positive returns in the early years) and a low balance of \$3,314 (after the initial years were marked by negative returns).

But the differential in U.S. large stocks was pedestrian compared with the differential in ending account value for emerging markets stocks. The average was \$159,101, the maximum was \$302,426 and the minimum was a loss of \$33,925. Obviously, a negative balance is not possible - when an account hits a zero balance, it's done - but this simulation was allowed to go into the negative to demonstrate how dramatic the difference can be in a distribution portfolio based solely on sequence of returns.

Once again, the fixed-income asset classes had much tighter results because their returns are less volatile and seldom involve negative annual results.

Across 15 simulations the 60/40 portfolio had an average ending balance of nearly \$86,000, whereas the multi-asset portfolio had an average ending balance of about \$148,000. In fact, the multi-asset portfolio had one of the highest minimum ending account balances in the randomized return sequences.

It proves that the sequence of returns matters when building a distribution portfolio for retirees, in which a client draws money systematically. It's crucial to a portfolio's longevity.

Diversification is a key element in stabilizing the sequence of returns, while also producing a level of return that can sustain a retirement portfolio for several decades.

Craig L. Israelsen, Ph.D., is a Financial Planning contributing writer inSpringville, Utah, and an associate professor at Brigham Young University. He is author of 7Twelve: A DiversifiedInvestment Portfolio With a Plan.