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?

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[i]

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.

Clarifying Sequence of Returns Risk (Part 2, with Pictures!)

My last post, Clarifying Sequence of Returns Risk (Part 1), was a bit heavy on the math for some people (that is to say, it contained some math), so I thought I would summarize it with some pictures and a few additional comments before moving on to a broader view of large losses early in retirement and a different kind — to my way of thinking — of sequence of returns (SOR) risk.

An important point from Part 1 is that the impact of the sequence of market returns on our investment results depends on the investment policies we choose.

From its peak in October 2007 through September 2013, the S&P 500 returned an average of 2.19% a year. Those six annual returns might have arrived in any of 6! (6 factoral) different orders, which is to say by one of 720 different paths. But if you invested $1,000,000 in the S&P 500 at the 2007 peak and still held those stocks at the end of six years, you ended up with $1,138,544 no matter which of those paths the market might have taken. 

(My charts show only 50 representative paths of the 720 so the graph doesn’t turn into a blob.)

The actual order of annual returns from 2007 to 2013 was:

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

Reverse this sequence of returns, turn them upside down, shake them up, arrange them in alphabetical order according to height — it doesn’t change the portfolio value at the end of the six years. In other words, the stock market has no SOR risk, and consequently, neither does a Buy and Hold strategy. (SOR risk arises from buying and selling at uncertain prices at the 5 points in the middle of a 6-year period.)

Safe withdrawal rate (SWR) strategies, which sell a constant dollar amount of stocks periodically, do have SOR risk. Here’s a graph of an SWR strategy over the time period mentioned above in which the investor started with a million dollar portfolio and withdrew $45,000 a year.

Again, there are actually 720 annual return paths the market could possibly have taken, given all permutations of 6 annual returns. Those paths end up in different places when you withdraw fixed dollar amounts periodically. The actual path the returns followed during this time period went from a million dollars to $776,461 in this scenario.

The worst path (returns ordered smallest to largest) would have taken the portfolio to $765,052 by October 2013, and the best (the opposite order) to $917,005. And that’s risk as finance defines it: uncertainty of outcomes. For this time period, only 8 of the 720 possible paths led to worse returns than the actual outcome.

Today, I’m looking at the risk associated with terminal portfolio values and not the annual payouts, which also differ by spending strategy[1]. I’m less concerned with fluctuations in annual payouts than I am with depleting the source of those payouts.

I showed algebraically in my last post that an investor can avoid this SOR risk by selling a constant percentage of remaining portfolio value periodically, for example, selling 4.5% of remaining portfolio value each year instead of a constant $45,000. The same is true of buying in the accumulation phase.

Here’s what those paths look like.

There are 720 possible paths with this strategy, too, but notice a big difference between this and the previous chart: all paths end up in the same place — $866,008 in our example. When you withdraw a constant percentage of remaining portfolio balance annually, you have no SOR risk. The ultimate portfolio value doesn’t depend on the order of market returns.

We can eliminate SOR risk to our portfolio’s terminal value by basing withdrawals on remaining portfolio balance, but this does not eliminate SOR risk from our portfolio payout. In fact, we cannot eliminate SOR risk from the payouts of any strategy that spends down a portfolio of stocks and bonds. We simply cannot expect to safely withdraw a constant amount from a volatile portfolio.

This brings me to what I believe to be a critical point: when you buy and hold, or buy or sell a constant percentage of your remaining portfolio balance periodically, you are gambling that stock prices will be higher in the future. That’s market risk.

But when you withdraw (or invest) constant dollar amounts periodically, or random dollar amounts, or changing percentages of remaining portfolio balance, you are placing a large side bet on which path those market returns will take to get there.

You’re adding a significant amount of risk to your investment, as can be seen by the single outcome for percentage withdrawals and a wide range of outcomes for constant dollar withdrawals. The constant dollar withdrawal policy had a range of outcomes of nearly $152,000 for a portfolio that started out with a million dollars.

We get compensated (over the long term) for taking market risk. Sequence of returns risk, however, is not market risk, but risk that an investor may add with her investment policy. The market cannot reward you for that risk. Investors with SOR risk add additional risk that is not diversifiable and with no expectation of additional reward.

What strategies escape sequence of returns risk? Many of the columns I have read recently suggest that the only way to avoid SOR risk is to avoid volatile assets like stocks, or at least to reduce your exposure to stocks to reduce SOR risk. Though that will certainly do it, that doesn’t appear to be the only way.

Buy and Hold is a special case of percentage withdrawal strategies where the percentage sold simply equals zero. There is no SOR risk. Though I have not done the math, I would expect Value Averaging to avoid SOR risk. As I have shown above, withdrawing a constant percentage of remaining portfolio balance has no SOR risk.

Dollar Cost Averaging and Safe Withdrawal Rate strategies are both exposed to SOR risk — they buy or sell constant dollar amounts — and perhaps that is why they underperform in most studies[2] that compare strategies.

Lastly, the number of possible market return paths increases by a factorial every period. Given its source, you would expect SOR risk to be cumulative and to grow rapidly with the number of interim transactions, and it does. I ran a 30-year set of S&P 500 annual returns from 1983 to 2012 and found that the best and worst possible outcomes for a $1M investment and $45,000 annual withdrawals ranged from about $39,000 to $42,000 after ten years. After thirty years, the range grew to $50,000 to $200,000.

So, here are my take-away’s from this post.

Sequence of return risk comes from our investment policies, not from the market. It is the result of the uncertainty of prices at the interim buy/sell transactions after the initial investment. There is no SOR risk with Buy and Hold because there are no interim transactions. There is also no SOR risk when we buy or sell amounts based on remaining portfolio balance, as I showed algebraically in my last post.

SOR risk increases dramatically over longer time periods because there are far more interim transactions that introduce more price risk.

SOR risk cannot be diversified away, nor are we compensated for it.

Choosing an accumulation or spending strategy that introduces additional risk that is un-diversifiable and uncompensated cannot be an optimal approach in either phase.

There's more to Sequence of Return risk and it's going to take a few more posts to cover it. I hope you'll stick with me for the next post on this topic, Sequence of Returns Risk and Payouts.