Sequence of Returns Risk
Dirk Cotton
SVIA Fall Forum
Dirk Cotton
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Retiree since 2005
Retirement Researcher
Retirement Financial Advisor
Thought Leader at Advisor Perspectives
Blogger (?) at The Retirement Café (www.theretirementcafe.com)
Three Ways to Fund Retirement
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Insurance and safe bonds
Volatile investment portfolio
Some combination of the two
Insurance and Safe Bonds Guarantee Income
with No Upside
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Social Security retirement benefits (OASI)
Fixed annuities
Treasury Inflation-Protected Securities, or TIPS, held to maturity
Volatile Investment Portfolios Provide Upside
but No Guarantees
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Stocks and bonds
Mutual funds and ETFs
Commodities, real estate investments trusts and other volatile assets
Combinations of the Two Seek a Compromise
Between Safety and Upside
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“Floor-and-Upside” Retirement Income Strategy
Floor covers minimum lifestyle spending or non-discretionary spending
Volatile portfolio “upside” offers the possibility of improving standard of
living or bequest
Like putting your plane ticket home in the hotel safe in Vegas
Stable Value Has A Role in Both
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In floor portfolio for stable income for short periods (inflation risk)
In volatile portfolio along with bonds to dampen volatility
Upside Portfolio is Subject to “Sequence of
Returns” Risk
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Most define SOR Risk as the probability that a retiree’s portfolio will be
prematurely depleted by a series of poor returns just before or just after
retirement.
It is actually a little more complicated than that.
The Basic Math
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Consider a 5-year series of stock market returns:
The Basic Math
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No matter how we order
the returns, the terminal
portfolio value remains
$1.03
This is simply the
commutative law from
high school math: a x b = b
xa
As long as we are not
buying or selling, the order
of returns doesn’t matter.
The Basic Math
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Algebraically, we could write the the terminal portfolio value with no
spending or savings as:
TPV = ( $100) (1.10 ) (1.02 ) ( 0.88) (1.08) ( 0.97)
TPV = $103.44
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We can order those terms any of the 720 possible orders and the TPV
will always be $103.
We can order the five market returns in 120 different ways
The Basic Math
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When we sell from this portfolio annually, however, the
equation becomes quite different. Spending $12 at the
beginning of every year, we get:
TPV =0.97 (1.08 (0.88 (1.02 (1.1 ($100 - 12) - 12) - 12) - 12) - 12)
= $44.47
The Basic Math
The Basic Math
What is the best of the 120 sequences of returns?
Sorted from best to worst.
The Basic Math
What is the worst of the 120 sequences of returns?
Sorted from worst to best.
SOR Risk and Accumulation
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We mostly discuss SOR Risk in the context of the post-retirement Spending
phase. Is SOR Risk also present when we are saving for retirement?
Yes, and we can see this by simply changing the sign of the spending amount
in our example above. Let’s change the plus $12 we spend to a minus $12
we save.
SOR Risk and Accumulation
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Algebraically, we simply change this:
TPV =0.97 (1.08 (0.88 (1.02 (1.1 ($100 - $12) - $12) - $12) - $12) - $12)
to this:
TPV =0.97 (1.08 (0.88 (1.02 (1.1 ($100 + $12) + $12) + $12) + $12) + $12)
SOR Risk and Accumulation
Where does SOR Risk come from?
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It isn’t there when we don’t buy or sell, so it must appear when we do.
It doesn’t exist with Social Security benefits, pensions, bond ladders or other
non-volatile sources of income – we only see it with volatile portfolios.
We don’t see it with buy-and-hold stock portfolios, even though they are
volatile.
SOR Risk is the uncertainty of the prices of assets in a volatile portfolio when
we will make future purchases or sales of those assets.
Why is SOR Risk so dangerous near retirement
age?
We’ve seen that it stems from price volatility, but it is exacerbated. . .
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By the fact that we can’t run a negative balance.
By the time value of money.
 When we lose $1 early in retirement, we lose its compounded earnings
for perhaps 30 years
 When we lose it late in retirement, we only lose a few years of its
compounded earnings
And. . .
Why is SOR Risk so bad a decade before and
after retirement?
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Because around retirement age is
when we are able to place our
largest bets.
Why is SOR Risk so bad a decade before and
after retirement?
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SOR Risk is dangerous in early
retirement because our portfolio
is large and losses are
compounded for perhaps 30
years
In Accumulation, it is less
dangerous because the bets with
long-term impact occur when the
portfolio is small.
Does SOR Risk go away after the first 10 years of
retirement?
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No, but it diminishes exponentially with the expected remaining years in
retirement.
No!
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Does the market reward SOR Risk?
Most investment risk has an upside – higher returns.
SOR Risk is not diversifiable and the market cannot compensate us for it.
How can you mitigate SOR Risk?
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You can completely avoid it by funding retirement with Social Security
benefits, TIPS bond ladders and life annuities.
As the Sustainable Withdrawal Rates (SWR) studies show, you mitigate SOR
Risk by spending less from your risky portfolio.
 However, doing so will lower your standard of living and increase the
probability that you will leave a large unspent portfolio at the end of life
that could have raised that standard of living.
You mitigate SOR Risk by selling a percentage of your remaining portfolio
balance each year, rather than a constant dollar amount based on a
percentage of your initial portfolio value.
How can you mitigate SOR Risk?
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You can keep your risky portfolio’s equity allocation between about 35% and
70%.
You can mitigate SOR risk with a Floor-and-upside strategy that provides
safe income to cover non-discretionary expenses and invests the rest in a
risky portfolio of assets.
Probability of Ruin and Probability of
Outliving Your Portfolio
Cumulative Incidence of Death and Ruin
How many ways can 30 years of annual market
returns in retirement be ordered?
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If we knew our future annual portfolio returns in advance, which of course
we can’t, there is still a huge range of possible outcomes depending on their
order.
We could know the best possible outcome (they arrive sorted largest to
smallest) and the worst (sorted smallest to largest), but the range would be
so gigantic as to be useless.
There would be 30! possible orders of those returns and predicting the
order is impossible.
How big is 30! ?
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It’s pretty big:
 2.65 x 1032
 265,252,800,000,000,000,000,000,000,000,000
What is the probability that you will experience
the worst sequence of returns for 30 years?
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1/30!
0.0000000000000000000000000000000038
Same probability as the best sequence
But how big is 30!?
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2.65 x 1032 (30!) is a lot smaller than a googol. That’s 1 x 10100 or about 70!.
Researchers at the University of Hawaii (where else?) estimate that there
are 7.5 x 1018 grains of sand (roughly 20!) on all the beaches on earth
combined.
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30! is 14 orders of magnitude greater.
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On a clear night we might see 2,500 of them.
Scientists estimate that there are a septillion (1 x 1024) stars in the
observable universe (call it 24!).
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30! is about 48 million times greater than 24!.
And that’s why I use 5-year periods for my examples
instead of 30-year periods.