Recently, I reviewed the economist’s argument for the
existence of an annuity
puzzle. Buried inside that post is something rather important, which didn’t
receive proper consideration since it was secondary to the annuity issue. I’d
like to return to that.
A general assumption in safe withdrawal rate research
is that people plan to spend a constant inflation-adjusted amount for as long
as they live. That is intuitive and it is connected to the idea of consumption
smoothing. People like to spend the same amount over time and don’t want to
experience reductions to their standard of living.
However, this spending plan is actually not optimal for
any reasonable set of preferences about the tradeoff between spending now and
later, even if we assume that future market returns are known in advance.
Before explaining why, I do want to make one point
clear: there is an unrelated issue that retirees may gradually wish to reduce
spending as they age for other reasons. They just slow down with time and don’t
get out as much. I reviewed evidence about that in a recent
column at Advisor Perspectives. But please ignore that for now. It is a
completely separate matter from what I am about to discuss. (Or maybe it isn’t,
perhaps people are just behaving rationally after all with a plan to reduce
spending)
The issue today is: since your survival probabilities
decline with time, it is rational to spend more earlier on while you are more
likely to be alive, and to spend less later on when the probability of still
being alive is lower. You should intentionally plan to decrease spending as you
age to account for the lower probability of living to each subsequent age.
Financial economists have known this for a long time,
but I don’t think the message about it has gotten out very well because the
result is usually obscured in a mathematical equation rather than being written
out with words. We only see it if we try to graph those old equations.
So it is optimal to reduce spending as you age, but by
how much? The answer to that depends on
what financial economists call risk
aversion, but which I would like to rename as spending flexibility for the retirement period. How flexible are
you about letting your spending decrease?
Are you willing to spend more now with an understanding you may have to cut
back later, or would you be willing to spend less now to help ensure you can
spend just as much later? Generally people want to smooth their consumption,
but again the hangup is that this may not always make sense when the
probability of survival declines over time. A larger number for spending
flexibility means the retiree is less flexible and wants greater consumption
smoothing, as retirees care less about upside and really wish to maintain as
high of spending as possible even in the low probability event that they happen
to live a very long time.
I will assume retirement date wealth of $100. This
amount doesn’t impact the results. I assume a male retiree at 65 and use the
Social Security Administration 2007 Period Life Tables to obtain survival rates
past this age. At retirement, retirees choose their annual spending amounts for
ages 65-100. Financial markets are simplified to one asset which always and
forever provides the same fixed return. Since retirees know the future
investment returns, making these plans is easy to do. They don’t know how long
they will live, but they can decide on how much they will spend each year
should they still be alive.
There are now two competing tradeoffs: you want to
spend the same amount every year for as long as you live to get the most
lifetime value from your spending, but you also want to frontload your spending
to early retirement when you have the highest chance for survival.
The following figure shows the optimal spending path
for different degrees of spending flexibility when asset returns are 0%.
Someone with flexibility of 1 is quite willing to let
their spending decrease over time to reflect the low probability of survival as
they age. Spending starts higher but declines to very low levels by one’s 90s.
With flexibility of 2, more effort is made toward keeping a smooth level of
spending. But again, it is still optimal to frontload spending. You can also
see for coefficients of 5 and 10 how we obtain greater smoothing even in the
face of the decreasing survival probabilities. How much lower would you let
your spending fall in your 90s to allow more spending in your 60s? It’s an important and highly personal question.
But if you want something even flatter than the spending flexibility=10 case,
it means you are quite risk averse about spending reductions. The constant
inflation-adjusted spending assumption creates very extreme inflexibilities and
risk aversion on the part of the retiree, and it may not be what retirees
really want! Do you want it?
As the market return increases, you know that your
remaining portfolio will grow at a faster rate, allowing you to spend more earlier
in retirement. At the same time, you have some incentive to delay spending a
bit so that you leave more wealth in your portfolio to grow at the higher rate and
support even more spending later. Here we can see the spending pattern when
asset returns are 4%:
Naturally as well, the less flexible you are about
letting your spending fall, the more valuable a fixed income annuity becomes. As
I discussed in the previous
blog post, some with flexibility=10 case would require 90% more wealth to
be just as happy with not annuitizing as if they had just annuitized in the
first place (under the basic assumptions I used). For those with more
flexibility, the value of annuities is less than this.
A
key point here is: The assumptions of constant inflation-adjusted spending used
in safe withdrawal rate studies, though intuitively appealing, is not optimal
even in the case that there is no uncertainty about future market returns.
It will be great to move more and more toward combining
the theoretical insights and rigorous methods used by finance academics with
the real world practicalities and understandings of people and financial
planners developing retirement solutions. I think this is a good example of
where there is some ample ground for the cross-fertilization of ideas.
