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A B C D E F G
1 Retirement Years Income Growth Rate of Inflation Savings Rate ROR rROR Extra-Cons
2 25 0.07 0.03 0.15 0.06 0.0291 40,000
3 Age Income Deflator Savings Cumulative Savings rConsumption Expenditures
4 30 50,000 1.00 7,500 7,500 42,500 0
5 31 53,500 1.03 8,025 15,975 44,150 0
9 35 70,128 1.16 10,519 61,658 51,419 0
19 45 137,952 1.56 20,693 308,859 75,264 0
22 48 168,997 1.70 25,349 375,099 84,378 68,097
23 49 180,826 1.75 27,124 354,588 87,654 70,140
24 50 193,484 1.81 29,023 260,397 91,058 144,489
25 51 207,028 1.86 31,054 158,252 94,595 148,824
26 52 221,520 1.92 33,228 124,331 98,268 76,644
27 53 237,026 1.97 35,554 88,401 102,084 78,943
28 54 253,618 2.03 38,043 131,748 106,049 0
29 55 271,372 2.09 40,706 180,359 110,167 0
39 65 533,829 2.81 80,074 1,090,888 161,257 0
40 Total 1,116,851 Real Annuity 22,048




of the loss of interest on the funds that would have been saved. If you change the input in G2
to $25,000 (reflecting the cost of a public college), the retirement annuity falls to $32,405, a
loss of “only” 35% in the standard of living.


>
10. What if anything should you do about the risk of rapid increase in college tuition?
Concept
CHECK
18.8 HOME OWNERSHIP:
THE RENT-VERSUS-BUY DECISION
Most people dream of owning a home and for good reason. In addition to the natural desire for
roots that goes with owning your home, this investment is an important hedge for most fami-
lies. Dwelling is the largest long-term consumption item for most people and fluctuations in
the cost of dwelling are responsible for the largest consumption risk they face. Dwelling costs,
in turn, are subject to general price inflation, as well as to significant fluctuations specific to
geographic location. This combination makes it difficult to hedge the risk with investments in
securities. In addition, the law favors home ownership in a number of ways, chief of which is
tax deductibility of mortgage interest.
Common (though not necessarily correct) belief is that the mortgage tax break is the major
reason for investing in rather than renting a home. In competitive markets, though, rents will
reflect the mortgage tax-deduction that applies to rental residence as well. Moreover, homes
are illiquid assets and transaction costs in buying/selling a house are high. Therefore, pur-
chasing a home that isn™t expected to be a long-term residence for the owner may well be a
speculative investment with inferior expected returns. The right time for investing in your
home is when you are ready to settle someplace for the long haul. Speculative investments in
real estate ought to be made in a portfolio context through instruments such as Real Estate
Investment Trusts (REITs).
With all this in mind, it is evident that investment in a home enters the savings plan in two
ways. First, during the working years the cash down payment should be treated just like any
other large extra-consumption expenditure as discussed earlier. Second, home ownership
affects your retirement plan because if you own your home free and clear by the time you
retire, you will need a smaller annuity to get by; moreover, the value of the house is part of
retirement wealth.
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Essentials of Investments, Management Investment Strategy Companies, 2003
Fifth Edition




645
18 Taxes, Inflation, and Investment Strategy



<
11. Should you have any preference for fixed versus variable rate mortgages?
Concept
CHECK
18.9 UNCERTAIN LONGEVITY
AND OTHER CONTINGENCIES
Perhaps the most daunting uncertainty in our life is the time it will end. Most people consider
this uncertainty a blessing, yet, blessing or curse, this uncertainty has economic implications.
Old age is hard enough without worrying about expenses. Yet the amount of money you may
need is at least linear in longevity, if not exponential. Not knowing how much you will need,
plus a healthy degree of risk aversion, would require us to save a lot more than necessary just
to insure against the fortune of longevity.
One solution to this problem is to invest in a life annuity to supplement Social Security
life annuity
benefits, your base life annuity. When you own a life annuity (an annuity that pays you in-
come until you die), the provider takes on the risk of the time of death. To survive, the An annuity that pays
provider must be sure to earn a rate of return commensurate with the risk. Except for wars and you income until
natural disasters, however, an individual™s time of death is a unique, nonsystematic risk.13 It you die.
would appear, then, that the cost of a life annuity should be a simple calculation of interest
rates applied to life expectancy from mortality tables. Unfortunately, adverse selection comes
in the way.
adverse selection
Adverse selection is the tendency for any proposed contract (deal) to attract the type of
party who would make the contract (deal) a losing proposition to the offering party. A good The tendency for any
example of adverse selection arises in health care. Suppose that Blue Cross offers health cov- proposed deal to
erage where you choose your doctor and Blue Cross pays 80% of the costs. Suppose another attract the type of
party who would
HMO covers 100% of the cost and charges only a nominal fee per treatment. If HMOs were
make the deal a
to price the services on the basis of a survey of the average health care needs in the population
losing proposition
at large, they would be in for an unpleasant surprise. People who need frequent and expensive to the offering party.
care would prefer the HMO over Blue Cross. The adverse selection in this case is that high-
need individuals will choose the plan that provides more complete coverage. The individuals
that the HMO most wants not to insure are most likely to sign up for coverage. Hence, to stay
in business HMOs must expect their patients to have greater than average needs, and price the
policy on this basis.
Providers of life annuities can expect a good dose of adverse selection as well, as people
with the longest life expectancies will be their most enthusiastic customers. Therefore, it is
advantageous to acquire these annuities at a younger age, before individuals are likely to know
much about their personal life expectancies. The SS trust does not face adverse selection
since virtually the entire population is forced into the purchase, allowing it to be a fair deal on
both sides.
Unfortunately we also must consider untimely death or disability during the working years.
These require an appropriate amount of life and disability insurance, particularly in the early
stage of the savings plan. The appropriate coverage should be thought of in the context of a
retirement annuity. Coverage should replace at least the most essential part of the retirement
annuity.
Finally, there is the need to hedge labor income. Since you cannot insure wages, the least
you can do is maintain a portfolio that is uncorrelated with your labor income. As the Enron
case has taught us, too many are unaware of the perils of having their pension income tied to
their career, employment, and compensation. Investing a significant fraction of your portfolio
in the industry you work in is akin to a “Texas hedge,” betting on the horse you own.
13
For this reason, life insurance policies include fine print excluding payment in case of events such as wars,
epidemics, and famine.
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Essentials of Investments, Management Investment Strategy Companies, 2003
Fifth Edition




646 Part SIX Active Investment Management



>
12. Insurance companies offer life insurance on your children. Is this a good idea?
Concept
CHECK
18.10 MATRIMONY, BEQUEST, AND
INTERGENERATIONAL TRANSFERS
In the context of a retirement plan we think of risk in terms of safety first, where mean-
variance analysis is inadequate. We have already touched on this issue earlier, in the context
of (1) raising the ROR with risky investments, (2) avoiding savings plans that rely too heav-
ily on savings in later years, and (3) acquiring life insurance and including life annuities in the
savings portfolio.
One sort of insurance the market cannot supply is wage insurance. If we could obtain wage
moral hazard insurance, a savings plan would be a lot easier to formulate. Moral hazard is the reason for
this void in the marketplace. Moral hazard is the phenomenon whereby a party to a contract
The phenomenon
(deal) has an incentive to change behavior in a way that makes the deal less attractive to the
whereby a party to
other party.14 For example, a person who buys wage insurance would then have an incentive
a contract has an
incentive to change to consume leisure at the expense of work effort. Moral hazard is also why insuring items for
behavior in a way that
more than their market or intrinsic value is prohibited. If your warehouse were insured for lots
makes the contract
more than its value, you might have less incentive to prevent fires, an obvious moral hazard.
less attractive to
In contrast, marriage provides a form of co-insurance that extends also to the issue of
the other party.
longevity. A married couple has a greater probability that at least one will survive to an older
age, giving greater incentive to save for a longer life. Put differently, saving for a longer life
has a smaller probability of going to waste. A study by Spivak and Kotlikoff (1981)15 simu-
lated reasonable individual preferences to show that a marriage contract increases the dollar
value of lifetime savings by as much as 25%. Old sages who have been preaching the virtue
of matrimony for millennia must have known more about economics than we give them
credit for.
Bequest is another motive for saving. There is something special about bequest that differ-
entiates it from other “expense” items. When you save for members of the next generation
(and beyond), you double the planning horizon, and by considering later generations as well,
you can make it effectively infinite. This has implications for the composition of the savings
portfolio. For example, the conventional wisdom that as you grow older you should gradually
shift out of stocks and into bonds is not as true when bequest is an important factor in the
savings plan.
Having discussed marriage co-insurance and bequest, we cannot fail to mention that
despite the virtues of saving for the longest term, many individuals overshoot the mark. When
a person saves for old age and passes on before taking full advantage of the nest egg, the estate
is called an “involuntary, intergenerational transfer.” Data shows that such transfers are wide-
spread. Kotlikoff and Summers (1981)16 estimate that about 75% of wealth left behind is ac-
tually involuntary transfer. This suggests that people make too little use of the market for life
annuities. Hopefully you will not be one of them, both because you will live to a healthy old
age and because you™ll have a ball spending your never-expiring annuity.


>
13. If matrimony is such a good deal, but you haven™t yet found a soul mate, should
Concept
you rush to surf the Web for a potential spouse?
CHECK
14
Moral hazard and adverse selection can reinforce each other. Restaurants that offer an all-you-can-eat meal attract
big eaters (adverse selection) and induce “normal” eaters to overeat (moral hazard).
15
Laurence J. Kotlikoff and Avia Spivack, “The Family as an Incomplete Annuities Market,” Journal of Political
Economy, 89, no. 2 (April 1981), pp. 372“91.
16
Laurence J. Kotlikoff and Lawrence H. Summers, “The Role of Intergenerational Transfers in Aggregate Capital Ac-
cumulation,” The Journal of Political Economy, 89, no. 4. (August, 1981), pp. 706“32.
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Essentials of Investments, Management Investment Strategy Companies, 2003
Fifth Edition




647
18 Taxes, Inflation, and Investment Strategy


• The major objective of a savings plan is to provide for adequate retirement income. SUMMARY
• Even moderate inflation will affect the purchasing power of the retirement annuity.
Therefore, the plan must be cast in terms of real consumption and retirement income.
• From a standpoint of smoothing consumption it is advantageous to save a fixed or rising
fraction of real income. However, postponement of savings to later years increases the risk
of the retirement fund.
• The IRA-style tax shelter, akin to a consumption tax, defers taxes on both contributions
and earnings on savings.
• The progressive tax code sharpens the importance of taxes during the retirement years.
High tax rates during retirement reduce the effectiveness of the tax shelter.
• A Roth IRA tax shelter does not shield contributions but eliminates taxes during
retirement. Savers who anticipate high retirement income (and taxes) must examine
whether this shelter is more beneficial than a traditional IRA account.
• 401k plans are similar to traditional IRAs and allow matched contributions by employers.
This benefit should not be foregone.
• Capital gains can be postponed and later taxed at a lower rate. Therefore, investment in
low-dividend stocks is a natural tax shelter. Investments in interest-bearing securities
should be sheltered first.
• Social Security benefits are an important component of retirement income.
• Savings plans should be augmented for large expenditures such as children™s education.
• Home ownership should be viewed as a hedge against rental cost.
• Uncertain longevity and other contingencies should be handled via life annuities and
appropriate insurance coverage.

KEY
401k plans, 637 moral hazard, 646 Social Security, 639
TERMS
adverse selection, 645 progressive tax, 633 tax shelters, 632
flat tax, 630 real consumption, 628 traditional IRA, 635
life annuity, 645 retirement annuity, 626
longevity, 642 Roth IRA, 635

PROBLEM
1. With no taxes or inflation (Spreadsheet 18.1), what would be your retirement annuity if
SETS
you increase the savings rate by 1%?
2. With a 3% inflation (Spreadsheet 18.2), by how much would your retirement annuity
grow if you increase the savings rate by 1%? Is the benefit greater in the face of
inflation?
3. What savings rate from real income (Spreadsheet 18.3) will produce the same retirement
annuity as a 15% savings rate from nominal income?
4. Under the flat tax (Spreadsheet 18.4), will a 1% increase in ROR offset a 1% increase in
www.mhhe.com/bkm


the tax rate?
5. With an IRA tax shelter (Spreadsheet 18.5), compare the effect on real consumption
during retirement of a 1% increase in the rate of inflation to a 1% increase in the tax rate.
6. With a progressive tax (Spreadsheet 18.6), compare an increase of 1% in the lower tax
bracket to an increase of 1% in the highest tax bracket.
7. Verify that the IRA tax shelter with a progressive tax (Spreadsheet 18.7) acts as a hedge.
Compare the effect of a decline of 2% in the ROR to an increase of 2% in ROR.
8. What is the trade-off between ROR and the rate of inflation with a Roth IRA under a
progressive tax (Spreadsheet 18.8)?
9. Suppose you could defer capital gains income tax to the last year of your retirement
(Spreadsheet 18.9). Would it be worthwhile given the progressivity of the tax code?
Bodie’Kane’Marcus: VI. Active Investment 18. Taxes, Inflation, and © The McGraw’Hill
Essentials of Investments, Management Investment Strategy Companies, 2003

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