Morningstar Magazine - February/March 2018 - 44

Strategies

Investing Over the Lifecycle, Part III
When it comes to choosing the
right insurance products, there's a gap
between theory and practice.

QUANT U

Paul D. Kaplan

In this series, I have presented models of rational
behavior that address decisions that
individual investors need make over the course of
their financial lives regarding savings, spending,
and insurance. This final installment brings
investing in risky assets into the picture. Space
prohibits me from presenting a complete
model that addresses investment decisions over
the lifecycle. Instead, I will give a brief
overview of what such a model would cover and
go into a few selected details.
Lifecycle Investing With Uncertain Returns

The option to invest in risky assets provides
investors with the opportunity to grow their
portfolios by earning returns that exceed what is
available with riskless securities alone.
Of course, doing so subjects investors to risk.
As postulated by Harry Markowitz, among efficient
portfolios, there is a trade-off between risk
and expected return. Facing this trade-off, a
rational investor selects a portfolio on the efficient
frontier based on risk tolerance. When
the constituents of the portfolios are broad asset
classes, this is the asset-allocation decision.
Essential Consumption, Lifestyle Consumption, and
Asset Allocation
In lifecycle models, asset allocation can be a
two-step process. Because certain types
of consumption are essential consumption (such as
food, clothing, and housing), the funds for them
should not be subject to risk. Therefore, in the
first step of asset allocation, the investor allocates

44

Morningstar February/March 2018

enough of wealth to riskless investments. These
investments can take the form of conventional
riskless securities, as well as immediate
fixed annuities, as I discussed in the December/
January 2018 issue of Quant U.
If assets are available after funding essential
consumption, the investor can invest them in an
efficient portfolio of risky assets to fund
lifestyle consumption. The choice of the portfolio
depends on the risk tolerance of the investor. This
is the second step in asset allocation. In the
lifecycle model, this step is simply equity exposure.
E X H I BI T 1 shows how the two-step process results
in an overall equity exposure.
The combination of riskless and risky assets
that the investor holds as financial assets depends
in part on where he or she is in the lifecycle.
Net total wealth consists of financial wealth and
human capital less liabilities. (By liabilities, I mean
the present value of essential consumption
and term life insurance premiums to cover the
fixed bequest, which I discuss below.) The investor
divides his or her financial wealth between
the portfolio of risky assets and riskless assets,
so that net total wealth has the same asset
allocation as the portfolio of risky assets. Over time,
as human-capital-less-liabilities declines,
the investor increases the allocation percentage
of financial wealth to maintain the allocation
of net total wealth to risky assets. The resulting
decline in the percentage of equity allocation
is the glide path.
Just as the allocation to riskless assets is
composed of conventional riskless securities and
immediate fixed annuities, the allocation to risky

assets is composed of conventional risky assets
and immediate variable annuities. Using variable
annuities, the investor can create a lifetime stream
of income that varies with the value of a risky
portfolio. I explain immediate variable annuities in
some detail below and how in lifecycle models
they help fund lifestyle consumption.
Bequests and Fixed and Variable Life Insurance
As in the riskless model that I presented in
the last issue of Quant U, in a lifecycle model with
risky returns, there can be bequests. Just as
there can be both fixed essential consumption and
variable lifestyle consumption in a lifecycle model,
there also can be fixed and variable bequests.
For the fixed bequest, the investor purchases term
life insurance and accumulates riskless
assets, reducing life insurance as assets grow,
until accumulated assets are sufficient to
meet the desired fixed bequest. The investor uses
some of the income generated from the assets to
help fund essential consumption.
In principle, the variable bequest should work
the same way. The investor should purchase
"variable term" life insurance, accumulate
risky assets, and use some of the return generated
by the assets to pay for lifestyle consumption.
By "variable term" life insurance, I mean a policy
each year, the insured pays a premium,
and that should the insured die in the following
year, the insurance company pays the beneficiaries
an amount that depends on the value of
a risk portfolio.
The problem is that while variable-term life
insurance makes perfect sense in a model, it is not
available in the real world, at least not as a
separate insurance product. Instead, insurance
companies offer different types of variable life
insurance products, which bundle together
investment portfolios, term life insurance, variable
death benefits, and other features.
Immediate Variable Annuities
In the last issue of Quant U, I showed that

immediate fixed annuities play an important role
in providing guaranteed lifetime income in a fixed
amount. In a model with uncertain returns,
investors also desire lifestyle consumption, which
varies with the value of a portfolio of risky assets.



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