What is “Enough” Retirement Saving

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					    Factors that Make a Difference for Financial Well-Being During Retirement

Executive Summary: Economists have developed good answers to the question of how
much an individual or couple should be saving for retirement, but these answers depend
on many details of the family’s situation. It matters a lot

      how old they are when they begin saving for retirement
      when they plan to retire
      what kind of Social Security checks they can expect
      how high the interest rate is above inflation
      how fast their wages will grow
      how big their mortgage payments are and when the mortgage will be paid
      how much they are saving for college and how much college debt they will end
       up with
      how well they insure against bad events
      how well diversified their assets are
      how much diversified risk they take on
      how well they avoid high mutual fund fees.

The key idea that allows one to put all these factors together and calculate the appropriate
level of saving is the concept of “consumption smoothing.” This is the principle that one
should save enough to be able to maintain one’s level of spending from now until the day
one dies, unless after careful thought one really intends to spend less later on than now.
Free online calculators are available to come up compute this number based on the details
of a family’s situation. Even a rough calculation is likely to be much better than one’s
best guess without doing any calculations. Therefore, it is essential to tackle the possibly
painful task of making such a calculation. Examples are given in this article which
provide some guidance about reasonable macroeconomic assumptions to put into a
retirement saving calculation.

Other than the generosity of Social Security, the key factors that can reduce the amount
of saving needed to make a given level of consumption sustainable are starting to save
early and planning to retire late, high interest rates in comparison with inflation, wage
growth, a large drop in mortgage payments in the near future, saving for college in
advance so that one will not carry too much debt afterwards, good insurance, taking on a
lot of well-diversified risk and holding funds with low fees.

In addition to explaining the factors that make a difference for financial well-being
during retirement, this article tries to communicate some of the kinds of reasoning that
economists use in thinking about these issues. Although some of the recommendations
here may be overturned by future economic research, they will be overturned by deeper
and more subtle use of the kinds of reasoning illustrated here.
How Much is Enough Retirement Saving? In a recent article (Skinner, 2007),
Dartmouth economist Jonathan Skinner shows how complicated it is to determine the
right amount of retirement saving for a given family. Many factors need to be taken into
account. The only good way to get an answer that takes into account all the key factors
in your own situation is to use (often free) software designed for that purpose1 or to
design one’s own spreadsheet. Even then different software packages will not always
agree, and using the software packages often requires making macroeconomic predictions
where the right answer is not obvious.

Without knowing the specific details of your finances, I cannot hope to do as well as one
of those software packages in giving a number for an adequate level of retirement saving.
What I can do in this article is to give some background behind these numbers and my
own views about the macroeconomic predictions to plug into such a software package.
Even more importantly, I hope to persuade you that making even an imperfect calculation
of how much you should be saving for retirement will be better than just trying to guess.
Economists have been thinking hard about retirement saving for more than 50 years now,
when Franco Modigliani and Milton Friedman along with their coauthors did the work on
life-cycle saving that earned them Nobel prizes in Economics. I feel that the approach
economists use for life-cycle saving gives some persuasive answers to the question of
how much is enough retirement saving.

“Consumption Smoothing.” The key concept economists use to judge if someone has
enough retirement saving goes by the name of “consumption smoothing.” “Consumption
smoothing” is the idea that, generally speaking, people want to spend at a steady rate over
time. There are some obvious reasons to modify this, such as the expenses of taking
children that one might hope will go down over time, or health care expenses that are
likely to go up as one gets older. But it is important to understand the basic force of the
consumption-smoothing argument.

Suppose you are worried about whether you have enough retirement saving, but you
don’t want to really think about it. One way you might reassure yourself is to say “I can
probably make it in retirement even if I don’t have much money.” But if you can make
it on without much money later, you can probably make it without spending much money

To illustrate the principle of consumption smoothing, consider a hypothetical couple, the
Andersons. In doing the calculations, we will use a trick economists use to make long-
run projections that are immune to changes in inflation: adjusting all numbers for
inflation from the get go. Economists call inflation-adjusted quantities “real” quantities.

                                         The Andersons

       Two adults, no children.

 One prominent example of such a software package is ESPlanner, which was developed by the Boston
University economist Laurence Kotlikoff and the Cato Institute economist Jagadeesh Gokhale.
      Both 45 years old.
      No savings yet.
      Planning to retire at Social Security’s normal retirement age of 67.
      Planning as if they will both live to age 95 (in order to make sure they don’t
       outlive their money in an era of improving medicine.
      Assuming a real rate of return 3% per year above the rate of inflation. (For
       example, if inflation will hover around 2% per year, a rate of return of 5% per
       year will be 3% above the rate of inflation.)
      Currently making $3000 per month after taxes.
      Planning as if their wages in the future will barely keep up with inflation (that is,
       they assume their real salaries will be flat.)
      On Social Security, assuming that Social Security will survive, but will have
       significant cuts. So they look at the documents they get every year from Social
       Security every year (which by law will be adjusted for inflation), and reduce the
       amounts by about 15% to allow for some cuts and for taxes on the Social Security
       payments get an estimate of $1638 per month of after-tax Social Security.

Given this couple’s situation, here is how an economist might go about figuring out how
much they can afford to spend according to the logic of consumption smoothing. The
idea is to add up the total lifetime value of each stream of money and then distribute that
total value evenly over the course of a lifetime. At a 3% real interest rate, $1638 per
month adjusted for inflation, going from 22 years in the future (age 67 minus age 45) to
50 years in the future (age 95 minus age 45) is worth about $182,000. For comparison, at
$3000 per month for 22 years, the total value of all the after-tax wages this couple will
earn from now until retirement is worth about $772,000. Both of these numbers come
from what is called a “present-discounted-value” calculation. Thus, they have a total
value of about $651,000 to work with. At a 3% real interest rate, this will support real
spending of about $2485 per month, adjusted for inflation. This number for how much
monthly spending they can afford given these resources comes from a calculation similar
to calculations of mortgage payments for loans of a given size, duration and interest rate.
In this case, since the couple will live 50 years and everything is done in real terms, it is
what the payment would be for a 50-year mortgage at a 3% interest rate, on a loan of
$772,000.) Spending $2485 per month, this couple will be saving $515 per month.

What happens if the Andersons spend more than $2485 per month now? Then in
retirement, it will end up spending less than $2485 per month, after adjusting for
inflation. At a 3% real interest rate, after adjusting all amounts for inflation, every $100
per month more spent in the 22 years before retirement will reduce affordable spending
by $106 per month every month for the longer 28 year period from retirement until age

Do people want to smooth consumption out over their lifetimes? Following on some
earlier work with Robert Barsky and Thomas Juster (Barsky, Juster, Kimball and
Shapiro, 1997), Claudia Sahm, Matthew Shapiro and I arranged to collect data on how a
representative sample of Americans over 50 who were willing and able to do an online
survey felt about consumption smoothing (Kimball, Sahm and Shapiro,2007). We asked
them to imagine that their financial planner had calculated a variety of plans for spending
before and after retirement that they could afford. They had to choose. We found that,
regardless of the interest rate they were faced with, most people chose very similar levels
of consumption before and after retirement in this scenario. People were a little more
likely to choose spending the went up over time than spending that went down over time,
even though that required a sacrifice of spending early on. Thus, when the choice is
spelled out, most people are willing to sacrifice to keep their spending after retirement
roughly equal to their spending before retirement.

There can be a temptation to stick one’s head in the sand and just hope everything will be
all right. But if spending at one’s current rate is unsustainable, it makes sense to spread
the pain evenly across the years. And among the readers of this newletter many will
discover after careful calculations that they can afford to spend more than they are
currently spending.

The Importance of the Age of Retirement. The planned age of retirement makes a
huge difference to the level of spending one can afford according to the consumption
smoothing logic. In the example above of the Andersons, if they could both work until
the age of 70, they could afford to spend $2692 per month and would only need to save
$308 per month to smooth consumption. This is not only because they would earn
money in those last three years of work between when they are both age 67 and when
they are both 70, but also because—as shown on the Social Security document received
each year--Social Security rules adjust the size of the monthly Social Security benefit
upward if one retires later (to a $2399 per month Social Security check in their case).
That higher Social Security check will be especially valuable since they are planning to
live a long time. Even if they do plan to retire at 67, they might want to put off drawing
Social Security in order to get the fatter Social Security checks. On the other hand, if the
Anderson’s retire when they are both 62, they lose five years of income and get smaller
Social Security checks (only 1140 per month in Social Security). This reduces the level
of consumption they can afford under the consumption smoothing logic to $2097 per
month. This means they would need to save $902 per month.

Of course, in choosing a planned retirement date, it is important to be realistic about how
long one will be physically able to work and whether one’s employer is likely to
downsize. But many people can realistically plan to work until they are 67 or 70 years
old. This is especially attractive if one has a relatively pleasant job. Thus, one of the
nicest ways to improve one’s likely financial well-being in retirement is to find a line of
work one is willing to continue to work at until a later age.

Adjustments: Houses, Children and Medical Care. Let me illustrate a little more the
principles behind figuring out the level of sustainable spending. First, certain types of
spending naturally go up or down over time. Jonathan Skinner (Skinner, 2007) points out
several factors that can make spending go up or down in ways that do not disturb one’s
lifestyle. First, if you own a house, when the mortgage is paid off, you won’t have to
make mortgage payments anymore. It makes sense to smooth the spending on things
other than the mortgage, which means that it is OK to plan for spending including the
mortgage payment to drop at that point. Second, the amount of money needed to support
the children may go up when they begin college and then fall after that. Third, in early
retirement, it is probably possible to save some money by careful shopping and by
cooking for oneself rather than going out to eat as often, but in later retirement, out-of-
pocket health costs are likely to go up substantially.

Let me give a concrete illustration of the simplest of these cases--the effect of mortgage
payments on appropriate saving. Suppose the Andersons described above were paying
$1000 per month of their after-tax income on their mortgage, which would be paid off at
around the time they retire at age 67. Then they can afford to save $378 a month less
each month (so that they only need to save $137 each month for retirement instead of
$515 each month). The key here is that the mortgage payment is making them
accustomed to a low level of other spending, which they can continue to manage on
during retirement. There are two cautions here. First, the adjustment is only for the
mortgage payment part of the house payment that will go away after the loan is paid off
($1000 a month in this example), not the money escrow payments for property taxes,
which will not go away after the loan is paid off. Second, if the home loan will not be
paid off until well into retirement, the adjustment will be much less.

Insurance: An Essential Part of a Saving Program. Second, insurance is important.
The need for other saving to take care of the future will be less if one has good insurance.
Economists view insurance as another form of consumption smoothing—a way to keep
one’s ability to spend in bad circumstances roughly equal to one’s ability to spend in
good circumstances. For those with low incomes, Medicaid and the survivor and spousal
benefits of Social Security can go a long way towards providing this insurance, but for
those with higher incomes, it will be necessary to purchase additional insurance.

Medicare has large copayments and deductibles, out-of-pocket medical costs in
retirement can be large unless one has good medigap insurance from a former employer
or from a private purchase. However, the biggest financial risk in retirement is the risk
that one will need to pay for a nursing home. Getting the government to pay for a
nursing home requires first using up one’s wealth other than the house and often settling
for a lower quality nursing home. Thus, long-term-care insurance is something to think
about seriously.

Before retirement, the biggest financial risk people typically face is the risk of long-term
disability. If long-term disability insurance is available through one’s employer, it is
wise to take advantage of it. This is one risk that people are almost never allowed to buy
as much insurance as they should want.2 So when it is offered on fair terms, one should
take as much as possible.

The next biggest financial risk before retirement is the risk of dying. When someone
dies, their earning power usually dies with them. Life insurance cannot bring someone

 The reason is that there are always problems with some people feigning disability—problems that can
never be entirely eliminated.
back to life, but it can replace the money that they would have earned had they lived.
Some of the rules of thumb I have heard for life insurance (usually some number of years
worth of income) make no sense from the perspective of consumption smoothing. My
rule of thumb would be that one should have enough term life insurance3 to replace lost
earnings all the way through planned retirement, minus the spending reduction because
the number of people spending is one less. For married couples with a single earner, or
one spouse who earns a large share of the family’s income, this can be a very large
amount of life insurance. I can easily imagine someone balking at this large amount of
life insurance, imagining that they will make do if the worst happens, but a little sacrifice
when things are OK can avoid a lot of pain in the worst case when things go wrong. We
are used to seeing those left behind by a death take a big financial hit. This is not the
nature of things. It is a sign of too little life insurance. It doesn’t need to happen.

In addition to general confusion about life insurance, two bad arguments get in the way of
people having enough life insurance. First is the argument “We can’t afford it.” Most
difficult financial situations that make it hard to afford life insurance would also make the
loss of a key income-earner especially painful, making life insurance all the more
imperative. Second is the argument that since a death is so unlikely, one doesn’t need to
prepare for such a contingency. Here the key fact is that since a death is so unlikely,
fairly priced life insurance premiums are inexpensive compared to the size of the benefit
the life insurance delivers in the event of a death.

Why term life insurance? The alternative, whole life insurance, often has high fees. Its
only benefit over term life insurance is that it might be one of many ways to commit to
save. Investment advisors often talk about “Buy Term and Invest the Difference” as a
superior alternative to whole life insurance as long as enough discipline or other
commitment mechanism for saving can be found.

The one time when people sometimes have too much life insurance is near retirement and
after retirement. The rule of thumb to have enough term life insurance to replace the lost
income until retirement means that while the amount of life insurance one needs can be
quite large when one is young, near retirement it declines in close to a straight line. Once
one is retired and so has no future earnings to replace, life insurance is unnecessary
(except perhaps as part of an exotic tax or bequest strategy). Even before retirement,
realizing that one will not need life insurance after retirement allows one to save money
on premiums by getting a guaranteed level of premiums only up to the time of one’s
planned retirement. All of these statements, of course, are for a context in which one is
saving for retirement in other ways so that there is some wealth for the one left behind to
fall back on. If however, one has serious problems with one’s saving discipline and
commitment, second and third-best saving vehicles may be better than nothing. But in
general, life insurance addresses a consumption smoothing issue that has a dramatically
different profile than retirement saving addresses.

  So-called “whole life insurance” is a strange bundling of pure life insurance with a bond of sorts, and
typically involves large fees.
Rates for term life insurance vary widely. It is worth doing some careful comparison
shopping. I had a good experience with the online life insurance broker
They helped me find life insurance with significantly cheaper rates than I had been
paying. Finding out the lowest rate one can get can go a long way toward making life
insurance seem affordable.

High Real Interest Rates are Your Friend. The third principle behind consumption
smoothing calculations is that for a serious saver, the higher the interest rate is above
inflation, the more he or she will be able to spend. When young, we are used to paying
more interest than we make, but for anyone who plans to retire, consumption smoothing
usually requires enough asset accumulation that one will earn a lot more interest over a
lifetime than one will pay.

The effect of the interest rate one assumes on the amount of saving required for
consumption smoothing can be dramatic. One can lull oneself into a false sense of
security by plugging in too high an interest rate into a retirement saving calculator. It is
probably not safe to assume that the interest rate will beat inflation by more than 3% per
year. Consider the Anderson’s again. Following their original plan of both retiring at
age 67, assuming a 4% real interest rate (that is, an interest rate 4% above inflation), they
could afford to consume $2560 per month (up from $2485 per month at a 3% real interest
rate), reducing their saving to $440 per month from the $515 per month needed for
consumption smoothing at a 3% real interest rate. On the other hand, assuming a 2.5%
real interest rate, they could only afford to consume $2446 per month, and would need
to save $554 per month in order to smooth consumption.

The uncertainty of future interest rates is a real issue. Low future real interest rates
(interest rates only a little above inflation) are one of the big dangers retirement savers
face. While government budget deficits in the United States might push interest rates up
compared to inflation, budget surpluses and extremely high saving rates in China and
other East Asian countries might push interest rates down. This uncertainty of future
interest rates makes holding money in short-term assets like Treasury Bills and money
market funds that do not lock in future interest rates quite risky. In view of the generally
lower interest rates on short-term assets compared to long-term assets, this means that
there is little reason to hold significant short-term assets beyond a money-market fund for
the purpose of writing checks. The one exception is if one is willing to make a big bet
that interest rates will go up in the future.

Indeed, when saving for retirement, it makes sense to treat long-term bonds as the safe
asset and to compare the returns of all other assets to those long-term bonds. More
specifically, Treasury bonds with a maturity on the order of one’s remaining life
expectancy are the closest thing to a safe asset in the context of retirement saving, since
the idea is to support consumption throughout the remainder of one’s life. Here, there is
room for more innovation on the part of financial services firms such as TIAA-CREF to
have a range of long-term bond funds with different, clearly labeled maturities (or to be
more technical, different “durations”—a measure of how long it is until the average
payout of a bond). This would make it easer for participants to put their savings into
bonds that will pay out when the money is needed.

Long-term bonds were not always a safe asset. In the past, inflation risk was a big danger
to the real value of long-term bonds. The good news there is that now, much of the
senior staff of the Federal Reserve system is made up of professionally trained
economists who have read an academic literature that puts a premium on inflation
stabilization. I would not be surprised to see the Federal Reserve declare an official long-
run inflation target of about 2 percent per year in the near future, as the European Central
Bank has done, or a semi-official long-run inflation target in the form of the Federal
Reserve’s inflation “forecast” several years down the road. Also, TIAA-CREF, like
several other financial services companies, offers an inflation-linked bond fund to protect
against this risk.

One way to think of why the level of interest rates matters is to calculate what stream of
payments over the course of 30 years (say for retirement years from age 65 to age 95) a
given amount of money can finance. In making these calculations, I will assume that you
want the stream of payments to go up gradually with inflation, so that only the part of the
interest rate beyond inflation goes into the calculation. At a continuously-compounded
3% beyond inflation, each $100,000 one has accumulated can support $421 per month
indexed for inflation. At 4% beyond inflation, each $100,000 can support $477 per
month (indexed for inflation). But at 2 ½ % beyond inflation, each $100,000 can only
support $395 (indexed for inflation).

Interest rates are even more important if one is able to do some saving well in advance of
retirement. Financial professionals often learn the power of compound interest through
the “rule of 72.” This is a useful approximation that says that if the interest rate (in this
case the part of the interest rate beyond inflation) times the number of years multiplies to
72%, then with compounding, the money actually doubles--an overall increase of 100%.
For example, 3% per year for 24 years will double one’s money. Thus, at a 3% rate of
interest beyond inflation, $100,000 that you have saved by the age of 41 will support
$842 per month from age 65 to age 95, indexed for inflation. At a 4% rate of interest
beyond inflation, it only takes 18 years to double the purchasing power of one’s money.
But at a 2 ½ % rate of interest beyond inflation, it will take 29 years to double the
purchasing power of one’s money.

Fees Matter. The annual fees of mutual funds are often stated in percentage terms,
which makes them sound smaller than they really are. So far, the financial services
industry has been able to beat back the regulatory requirement that financial statements
give fees in dollar terms, you will need to do your own multiplication. For example, I
find to my dismay that I have almost $400,000 in a fund that charges a 0.45% annual fee,
as compared to the rest of my retirement savings, which is in a “Spartan” fund with a
0.1% annual fee. The difference between 0.45% and 0.1% on $400,000 means that I am
paying $1400 extra in fees every year on that $400,000. Having finally done the
multiplication, the desire to save this $1400 per year is enough to motivate me to do the
paperwork necessary to transfer this money into a fund that has a low one tenth of one
percent annual fee. Even if only $50,000 were involved, the total cost of the extra fees
would add up to $1400 over the course of 8 years—well worth trying to avoid.

The other way to illustrate the importance of fees is to realize that half a percent per year
in extra fees has the same effect on the retirement saving one can finance as a half a
percent reduction in the interest rate. The examples above about the effect of a drop in
the interest rate beyond inflation from 3% per year to 2.5% per year illustrate how
important this is. Indeed, earning 3% per year beyond inflation and paying 0.5% per
year extra in fees is exactly like earning 2.5% per year beyond inflation with lower fees.
One half percent per year in fees is taking a full one-sixth of the 3% one is earning
beyond inflation. In the case of the Anderson’s the calculations reported above about the
effects of changes in the real interest rate apply. A half percent higher annual fee that
reduces the after-fee rate of return from 3% to 2.5% will reduce affordable spending by
$39 every month for the rest of their lives. That means that they will be devoting more
than 1.5% of what would otherwise be their affordable spending to totally unnecessary
fees. In other words, because they pay fees year after year, If the Andersons learn how
to shop for fees that are lower by half a percent per year on their savings will do them as
much good as if they each received a permanent 1.5% raise not only in their wages in
their Social Security as well.

Incredibly, the average level of fees people pay for their mutual funds is almost 1% per
year. As I mentioned above, it is possible to find funds that have fees only a tenth that.
Can you imagine paying ten times as much as you have to for a car? But mutual fund
fees over a lifetime can easily add up to more than the price of a car.

Many people think they are getting something by paying for higher fees. But academic
research has shown that overall, high fee funds do not have any better performance to
make up for their high fees. High fees are not a good indication of high quality in the
mutual fund world. Indeed, overall, high-fee funds seem to do somewhat worse, even
before the higher fees are taken into account.

Taking on More Risk to Increase Returns. Given the leverage high interest rates have
in raising one’s level of sustainable spending, it is worth considering taking significant
risks in order to raise the effective interest rate one is earning. There is a fundamental
tradeoff between the level of return one earns from bearing risk and the amount one
needs to save each month in order to be able to spend in retirement on a par with one’s
current spending.

The only kind of risk worth taking on is fully diversified risk in broadly based funds.
Some people are tempted to try to earn supernormal returns above those available from
the broad market indexes. This is a very difficult and potentially dangerous thing to try
to do. Any attempt to earn supernormal returns runs against two big problems. First, you
are competing in the market against professionals who notice what is going on faster than
you do. By the time you see what is going on, it will be too late to take advantage of it.
Second, you are likely to be your own worst enemy. Some economists (most famously,
John Campbell and Robert Shiller, 1988) believe that one can earn supernormal returns
by being a contrarian—that is, by selling when everyone else’s buying has pushed up the
price/dividend ratio and buying when everyone else’s selling has pushed down the
price/dividend ratio. It is said that Warren Buffett has done well by being just such a
contrarian for individual firms. But if the market or a particular stock is ever overvalued,
it is because there is some attractive and seemingly compelling idea out there for why it
should be valued so much. Similarly, if the market or a particular stock is ever
undervalued, it is because there is some attractive and seemingly compelling idea out
there for why it should be valued so little. If you try to time the market--or even worse,
try to play individual stocks--you are much more likely to be swept up in the attractive
false idea du jour than you are to see through that idea and act as a contrarian. You may
hear stories of people who were successfully at trying to play the market in various ways,
but all such stories should taken with this grain of salt: when people take large risks in
different ways, some of them are bound to get lucky.

How should one diversify? Besides using broadly based funds within the U.S., and
looking at a variety of types of risky assets, in order to diversify fully, there is a strong
argument to be made for holding a large share of one’s risky assets in international or
global funds. In our jobs, most of us depend a lot on how well the United States does
economically. It is putting too many eggs in one basket to hold only U.S. stock funds.
Holding only U.S. stock funds is a milder version of the horrible mistake some people
make of holding large quantities of stock in their own companies, which puts them in
danger of having their retirement savings evaporate exactly when they have lost their job.

How much of one’s retirement saving should one put into broadly-based, low-fee stock
mutual funds? The basic answer is “a lot.” Many people have caught on to the benefits
of stock-holding. This has pushed up the price of stocks. Because they are pricier now
than they were historically, stocks are not likely to do as well in the future as they have
historically. But many economists still think that stocks can be expected to earn, say, 3%
per year more than bonds. Even if this is an overestimate, another important fact is
that—despite the recent crisis from subprime housing loans—stocks don’t seem to be as
risky as they used to be. Finally, a serious argument has been advanced by Raj Chetty
(Chetty 2006) that people act more risk averse than they should according to the logic of
consumption smoothing. What all of this means is that, contrary to conventional wisdom,
it is not unreasonable to consider putting 100% of one’s assets into diversified assets such
as broadly-based, low-fee stock mutual funds. Not everyone will want to do this, but it is
a reasonable thing to do.

Putting all or most of one’s investable funds into diversified high-yielding risky assets is
often called for if one has many years to retirement and one’s job is safe and not sensitive
to the fluctuations of the stock market. Many in academia are in exactly this situation.
For example, outside of economics and finance (where salaries do go up and down with
the stock market), a tenured professorship has many of the financial characteristics of a
bond. To the extent one’s earning power acts like a bond, even very large amounts of
risky asset holdings are balanced out by that bond-like earning power for those some
ways away from retirement. Thinking of one’s earning power as an asset to which the
rest of one’s portfolio should be adapted is a powerful idea that will be a commonplace of
financial planning in the future, but it is not yet universally understood by even good
financial planners.

Let’s see how such risk-taking reasoning works for the Anderson’s. Suppose they
assume that a broad-based stock index can be expected to earn 3% more than long-term
bonds (after accounting for the lowest fees they can find, around .1% per year), and that
the price of a broad-based stock index relative to long-term bonds will have unpredictable
movements of about 15% annually (“annual standard deviation” of 15% would be the
technical description). They consider their jobs very safe, with essentially no relationship
between their pay and how well the stock market does. They are not willing to be scared
of risk itself, but only about the concrete comparison of how much a dollar will mean to
them after bad fortune as compared to how much a dollar will mean to them after good
fortune. Therefore, they assess their own justified risk aversion at a relative risk aversion
of 1.5. Formal calculations from an advanced economic model of optimal consumption
in the face of rate of return risk (see Robert Merton, 1971, and Laurie Pounder, 2007)
indicate that with this level of willingness to bear risk, the Andersons now do not need to
save at all! In fact, the sophisticated, yet still grossly simplified, calculations say they can
now afford to spend $3137 each month, which is $137 more than they earn! The catch is
that, in the model, with zero current savings, they need to borrow $744,540 at the
Treasury bond rate to invest in stocks.

Obviously, the recommendation to borrow $744,540 at the Treasury bond rate and invest
it in the stock market because no one would lend this much money to them at the
Treasury bond rate to do this. (For one thing, there is no legal way to put up one’s future
wage income and Social Security income as collateral.) But what it indicates is that the
Andersons should be as heavily into low-fee broad-based index funds as heavily as
practicable. It does not make sense for them to hold any bonds. All of their savings
should be in stock. Moreover, since the higher interest rate at which they would be able
to borrow would probably eat up all of the 3% they estimate stocks can earn above
bonds, they need to save a lot right away so that they are able to invest heavily low-fee
stock index funds without borrowing. In the face of a higher borrowing interest rate
than the Treasury bond rate, formal calculations become extremely difficult (worthy of a
chapter in a Ph.D. dissertation). The optimal level of saving in this situation will be
determined in important measure by the need to get some savings to invest in the low-fee
stock index funds to take advantage of the huge opportunity that a high-risk, high-return
strategy represents.

To get a recommendation for saving, a reasonable approximation for families who are in
this situation of being limited to investing only 100% of their financial wealth in stocks
would be start by inputting a 6% real interest rate (the 3% bond rate plus the 3% extra
for stocks) into a retirement saving calculator as if it were a safe interest rate. Then they
can adjust the level of recommended saving upward and recommended spending
downward to account for two factors. First, the return should be adjusted for risk,
especially if the total amount of stock held is large relative to what the family would
ideally like to hold if it faced no borrowing constraints. Second, the need to build up
wealth to be able to hold stock argues for saving now and deferring spending until later.
Without having done the extremely difficult calculations mentioned above, my educated
guess is that the optimal level of spending and saving after accounting for these two
factors is likely to be in between what the retirement saving calculator would recommend
with a 6% safe rate and what the retirement saving calculator would recommend with a
4.5% safe rate—halfway in between the expected return on stocks and the return on the
safe asset, long-term bonds.

Here there is yet another area where financial innovation would be appropriate. Although
most couples cannot borrow at the Treasury bond rate, it is possible for financial firms to
engineer leveraged financial derivatives that, say, go up by 4% every time a broad stock
market index goes up 1% and go down 4% every time the broad stock market index goes
down 1%. Such leveraged derivatives currently exist, but carry relatively high fees.
Low-fee versions of such leveraged derivatives provided by would be very valuable in
allowing people with modest savings to take advantage of a high-risk high-return strategy
in a big way. (Warnings about how much risk people were taking on would need to be
very clear, but the risk would have a good chance of being well-rewarded.)

Anyone who chooses a high-risk, high-return strategy needs to be prepared for a bumpy
ride. Psychologically this strategy may be easier if one doesn’t look at one’s portfolio too
often. (See Benartzi and Thaler, 1995, for a discussion and analysis of how “looking” too
often can scare people from a lucrative high-risk, high-return strategy.) If the target share
of financial risky assets stays at 100%, there is no need for rebalancing anyway, since the
share will naturally stay at 100% whatever the fluctuations in the value.

It is important to emphasize that it is only very broad-based diversification across all the
broad categories of risky assets one can invest in throughout the world that makes the
high-risk high-return strategy truly worthwhile. The more diversified your portfolio is,
the more risky assets you can afford to take on.

Final Thoughts. Rather than trying to summarize everything written above, let me
emphasize some of the advice I am giving that I think goes beyond or differs from what
many financial planners might say. First, it seems dangerous to me to assume that
interest rates in the future will do much better than 3% above the inflation rate, which
with a 2% inflation rate would be a 5% interest rate Locking in a higher interest rate (or
if need be, a 5% interest rate) with long-term bonds makes a lot of sense. In general,
money market funds, checking accounts, savings accounts, short-term bonds and
Treasury bills should only be held for transactions purposes and are not appropriate for
retirement saving. Second, it is crucial to personally check the annual fee of all the
mutual funds that you hold and any you are thinking of holding, and look for funds with
fees of only a few tenths of one percent. Third, it is perfectly reasonable to consider
putting 100% of one’s financial wealth into low-fee stock index funds or other broadly-
based, low-fee funds. Fourth, an important aspect of diversification is holding some
international stock. Fifth, especially when there is a primary income earner in the family,
it can make sense to have very large amounts of term life insurance, well beyond the
typical rules of thumb, but one must do a lot of comparison shopping to get the best rates
for term life insurance. Finally, one of the best ways to improve one’s financial situation
in retirement is to choose a career one is willing and able to continue working at until
well past the usual retirement age.


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Campbell, John and Robert Shiller, 1988. “The Dividend-Price Ratio and
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Kimball, Miles, Claudia Sahm and Matthew Shapiro, 2007. “Measuring Time
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