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Sequence Of Return Risk During The Accumulation Phase

In one of Mike Nadle's recent articles, "The Dividend Growth 50 Scores a Total Return 'Upset'

(found here: seekingalpha.com/article/3963392-dividend-growth-50-scores-total-return-upset)

in the comments section there was a discussion regarding the risk of sequence of returns while in the accumulation phase of building your retirement portfolio.

One camp holds that "Sequence of return risk only applies to when income is being taken from an investment."

Another camp holds that "Though most definitions may only apply sequence of returns affects to distributions the affect is not only on distributions it will affect the size of your retirement portfolio going into retirement as well, which will ultimately determine how long it lasts."

Before considering which is correct, a definition of what we mean when we talk about sequence of return risk. For the purpose of this Instablog Sequence of Return Risk exists if the order in which annual returns are realized impacts the terminal value of an investment program. In other words, given two investment plans that are identicle in all respects except for the order in which the annual returns are realized, then if at maturity the value of the two portfolios are different , then sequence risk exists.

Both camps in this debate reference a paper by Blackrock (found here : http://bit.ly/22G0lbz). This paper shows that given three investors who each deposit $1,000,000 at age 40 and none of them add to or withdraw from their portfolio over the subsequent 25 years, then regardless of the sequence of the annual returns, the values at age 65 are all the same. Thus the conclusion "The sequence of returns has no impact on the final portfolio value when you are saving".

This paper is correct in it's conclusion given the scenario as it was presented. This can be easily verified by remembering the cummutative property of multiplication; the order in which you multiply a sequence of numbers has no impact on the result.

While this is a correct result, it is so limited as to be virtually useless. Why? Because it only applies in a very specific circumstance, that being those few case where neither additions or withdrawals are made at any time over the investment time frame. A more interesting examination would be for those cases where either (or both) additions or withdrawals are made. Under these conditions, does the sequence of returns impact the terminal value?

Starting from the table provided by Blackrock consider Mrs. Jones, Mr. Smith and Mr. Brown, and just to keep the numbers from getting too large, assume each deposits $100 at the end of each year. What we get when we do the calculations is shown in the following table:

  Mrs. Jones Mr. Smith Mr. Brown
Year ROR Balance at end of Year ROR Balance at end of Year ROR Balance at end of Year
0   $100.00   $100.00   $100.00
1 22.0% $222.00 -7.0% $193.00 7.6% $207.60
2 15.0% $355.30 -4.0% $285.28 7.6% $323.38
3 12.0% $497.94 12.0% $419.51 7.6% $447.95
4 -4.0% $578.02 15.0% $582.44 7.6% $582.00
5 -7.0% $637.56 22.0% $810.58 7.6% $726.23
6 22.0% $877.82 -7.0% $853.84 7.6% $881.42
7 15.0% $1,109.49 -4.0% $919.68 7.6% $1,048.41
8 12.0% $1,342.63 12.0% $1,130.05 7.6% $1,228.09
9 -4.0% $1,388.93 15.0% $1,399.55 7.6% $1,421.43
10 -7.0% $1,391.70 22.0% $1,807.45 7.6% $1,629.46
11 22.0% $1,797.88 -7.0% $1,780.93 7.6% $1,853.29
12 15.0% $2,167.56 -4.0% $1,809.70 7.6% $2,094.14
13 12.0% $2,527.66 12.0% $2,126.86 7.6% $2,353.30
14 -4.0% $2,526.56 15.0% $2,545.89 7.6% $2,632.15
15 -7.0% $2,449.70 22.0% $3,205.98 7.6% $2,932.19
16 22.0% $3,088.63 -7.0% $3,081.56 7.6% $3,255.04
17 15.0% $3,651.93 -4.0% $3,058.30 7.6% $3,602.42
18 12.0% $4,190.16 12.0% $3,525.30 7.6% $3,976.21
19 -4.0% $4,122.55 15.0% $4,154.09 7.6% $4,378.40
20 -7.0% $3,933.97 22.0% $5,167.99 7.6% $4,811.16
21 22.0% $4,899.45 -7.0% $4,906.23 7.6% $5,276.81
22 15.0% $5,734.37 -4.0% $4,809.98 7.6% $5,777.84
23 12.0% $6,522.49 12.0% $5,487.18 7.6% $6,316.96
24 -4.0% $6,361.59 15.0% $6,410.26 7.6% $6,897.05
25 -7.0% $5,916.28 22.0% $7,820.52 7.6% $7,521.22

These results can easily be replicated by building a fairly simple spreadsheet. (You can also verify the average ROR as 7.6% using the Blackrock numbers). I'm only showing the accumulation case as it would seem the the risk during the withdrawal phase in agreed to by all.

Looking at the terminal values for each of our investors shows the following: Mrs. Jones has $5,916, Mr. Smith has $7,821 and Mr. Brown has $7,521. Mrs Jones' portfolio is worth $1,905 less (or almost 25%) than Mr. Smith. This is not an insignificant difference.

I would suggest that in fact for the majority of portfolios in the accumulation phase where new funds are being constantly added, sequence of return risk does exist. The question of what to do about is however another matter.

Glen