## Tuesday, September 24, 2013

### Sequence of Returns Risk and Payouts

As I mentioned in previous posts, the web is replete with columns about sequence of returns (SOR) risk showing that the order in which we experience market returns matters when we begin spending constant-dollar amounts from our portfolios.

I previously showed how you can eliminate the SOR risk from terminal portfolio values (TPV) — the amount of money in your portfolio at the end of retirement — by basing your retirement spending on a constant percentage of remaining portfolio balance. But, I didn’t talk about the payouts of spending strategies, which is an important point missed by every other SOR risk column I have read.

Using the six annual returns:

 -19.76% -9.37% 7.96% -0.86% 27.33% 14.88%

let’s look at both TPV’s and their payouts from both spending strategies (constant-dollar withdrawals and percentage of remaining balance withdrawals) using the 720 possible orders of these six returns.

In the first scenario, a retiree has a stock portfolio valued at \$1M and she withdraws \$25,000 a year. The second is identical, except the retiree withdraws 2.5% of her portfolio’s remaining balance every year.

Here are the results[i] for the 720 sequences for \$25,000 withdrawals in graph format.

With constant-dollar withdrawal amounts, the annual payout is always \$25,000 (by definition) but the terminal portfolio value depends on the order of returns.  TPV’s ranged from \$931,049 to \$1,015,467.

Remember what we are doing here is not looking at different sets of market returns, but at the 720 different ways this set of six returns can be ordered.

And, here are the results[ii] for 2.5% withdrawals of remaining portfolio balance each year.

With percentage withdrawals, TPV is \$979,537 no matter how the annual returns are ordered, but annual payouts range from \$16,553 to \$36,986 and the present values (PV) of those annual payouts discounted at 2% range from \$108,000 to \$182,000.

SOR risk affects payouts but not terminal portfolio values when spending is based on remaining portfolio balance.  It affects terminal portfolio values but not payouts when spending is based on anything else. So, SOR risk is going to show up somewhere.

We get to decide which place by picking a spending strategy.

You might expect that eliminating SOR risk with respect to terminal portfolio values simply generates the same amount of wealth while varying the payouts and holding the TPV’s constant, instead of the reverse.

It doesn’t.

When we transfer SOR risk from terminal portfolio value to payouts, we don’t transfer an equal amount of risk. Here’s an example.

Since both terminal portfolio values and annual payouts are important, I measure retirement wealth as the present value (PV) of all payouts in retirement plus the present value of the terminal portfolio, as if it were paid back to the retiree after 30 years. I use a 2% discount rate and consider the two scenarios above (2.5% withdrawals and \$25,000 withdrawals).

First, I looked at all 720 possible sequences of the six annual market returns.

PRESENT VALUE OF RETIREMENT WEALTH WITH ALL PERMUTATIONS OF SIX ANNUAL RETURNS

 PV of Terminal Portfolio PV of Payouts Total PV Average Total NPV Std. Dev. 2.5% Withdrawals 869,801 107,853 to 182,068 977,654 to 1,051,869 1,010,627 16,621 \$25,000 Withdrawals 826,745 to 901,705 140,036 966,780 to 1,041,741 1,008,407 16,789

The ranges of outcomes are the result of SOR risk. They use the same 6 annual market returns, but in every possible combination. In particular, look at the Total PV column. These are the ranges of 720 possible outcomes as measured by the combined present values of payouts and terminal portfolio values.

The results aren’t very different after 6 years. Percentage withdrawals do only a little better by every measure. But recall from my earlier post that SOR risk grows exponentially with time and these differences might be much more pronounced over longer periods.

Next, I looked at a thirty-year sequence. Fortunately, we don’t have to run all 2.65 x 1032 permutations of 30 years of returns (when is the D-Wave quantum laptop hitting the market?) because we know the best-case scenario is when the annual returns are ordered highest to lowest and the worst-case scenario is the reverse.

I looked at the sequence of real market returns from 1979 to 2008 from Robert Shiller’s website and ran both spending strategies with that data for the best-  and worst-case sequence of returns. Here is what I found:

PRESENT VALUE OF RETIREMENT WEALTH
BEST- AND WORST-CASE SEQUENCES FOR MARKET RETURNS 1979 TO 2008

 PV of Terminal Portfolio PV of Payouts Total PV of Retirement Wealth Worst Sequence of Returns 2.5% Withdrawals 3,100,060 487,892 3,587,951 \$25,000 Withdrawals 431,240 559,911 991,151 Best Sequence of Returns 2.5% Withdrawals 3,100,060 4,893,631 7,993,691 \$25,000 Withdrawals 5,604,748 559,911 6,164,660

Percentage withdrawals are significantly better in both the best and worst cases.

Now, a couple of important points. First, while I had been using 4.5% and \$45,000 in previous examples, I had to change the withdrawals to 2.5% and \$25,000 in this step because the constant withdrawal portfolio failed in its twelfth year with \$45,000 withdrawals in the worst case.

This brings out an important point regarding the two strategies. The constant-dollar withdrawal strategy, as is well advertised, leaves the retiree flat broke before retirement ends 5% to 10% of the time. Percentage withdrawals never do, though payouts will decline as the portfolio values drops.

This is the worst case of SOR risk. Not that constant-dollar withdrawal strategies cost more, or that we aren’t compensated for the risk, but that portfolio failure[iii] is a real possibility.

Second, I am not trying to show that one of these two spending strategies outperforms the other. There is plenty of research to show that constant-dollar withdrawal strategies underperform. At these two extremes, in this specific example, percentage withdrawals look much better, but there are plenty of sequences in the middle where constant-dollar withdrawal shows better results, including the actual 1979 to 2008 order, where \$26,842 withdrawals generated a PV of  \$5M compared to \$4.7M for 2.5% withdrawals.

I will note, however, that I have tried many 30-year sequences of returns and I am yet to find a set of returns where percentage withdrawals did not dominate constant-dollar withdrawals in the best and worst-case sequences using present value of combined payouts and TPV’s.

What I am trying to show is that shifting SOR risk from terminal portfolio values to annual payouts isn’t a wash.

Given the 30 annual market returns in this example, 2.5% withdrawals provided outcomes from \$3.6M in the worst case to \$8M in the best. That’s the range of outcomes if we remove SOR risk from terminal portfolio value.

\$25,000 withdrawals generated about \$1M in the worst case and \$6.1M in the best. So, switching from constant-dollar to percentage withdrawals not only switched SOR risk from TPV to payouts, it provided higher value and lower risk. And it completely avoided portfolio failure.

That’s consistent with the many studies that show constant-dollar withdrawal strategies underperform.

Notice that the differences in sequence of returns risk is much more pronounced at 30 years than at six. Since SOR risk is partially the result of the uncertainty of stock prices along the path (it isn’t present in a buy and hold strategy) that is what we should expect.

So, we can eliminate SOR risk from terminal portfolio values, or eliminate it from annual payouts, but not both. If we eliminate it from annual payouts, we introduce the risk of portfolio failure.

By basing our spending strategy on a constant percentage of remaining portfolio values, we can shift SOR risk to annual payouts, where it seems to do less harm.

Personally, I’d prefer risking my annual income to risking the source of all future annual income, even if it were an even trade, but it is not.

Next up: Sequence of Returns Risk or Something Else?

CONSTANT-DOLLAR WITHDRAWALS OF \$25,000 ANNUALLY

 Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Market Return -19.76% -9.37% 7.96% -0.86% 27.33% 14.88% Portfolio Balance 1,000,000 777,400 679,558 708,650 677,556 837,732 937,387 Payout 25,000 25,000 25,000 25,000 25,000 25,000

[ii] 2.5% OF REMAINING BALANCE WITHDRAWALS

 Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Market Return -19.76% -9.37% 7.96% -0.86% 27.33% 14.88% Portfolio Balance 1,000,000 777,400 685,123 722,530 698,253 871,630 979,537 Payout 25,000 19,435 17,128 18,063 17,456 21,791

[iii] By “portfolio failure” in this case, I’m referring to depleting a portfolio before the end of retirement.

1. Mr. Cotton,
Wonderful explanation. I was wondering what your thoughts might be about the possibility of increasing the constant percentage withdrawal to compensate for the payout fluctuations. Seems like this could be done and still be safe from portfolio failure.
Michael

1. I did notice while I was comparing 4.5% withdrawals with \$45,000 withdrawals that I could increase the percentage a bit and still come out ahead. For example, 5% withdrawals might favorably compare with \$45,000 withdrawals.

I chose 4.5%/\$45,000 solely because they are numbers familiar to the SWR crowd.

Increasing the percentage would be fine, of course, if the market mostly goes up. If you increase the percentage and the market doesn't go up enough to justify it, you will primarily be shifting payout value from the end to the beginning of retirement because you will later be taking that same larger percentage of a declining portfolio. A larger percentage is going to reduce the value of your terminal portfolio, which might not be a bad thing.

It will still be safer than constant-dollar withdrawals, and cheaper, because you're less likely to go broke.

I would have to add, though, that my gut feeling is that efforts to fix the problems with spending down a volatile portfolio of stocks in retirement by either method will ultimately be unsatisfying.

As Wade Pfau once told me, "You simply can't expect to spend a consistent amount periodically from a volatile portfolio."

You might get away with it, but you shouldn't expect it.

Thanks for the question!

--Dirk