Niko

An Asset Allocation Puzzle
By NIKO CANNER, N. GREGORY MANKIW, AND DAVID N. WEIL *
This paper examines popular advice on portfolio allocation among cash, bonds,
and stocks. It documents that this advice is inconsistent with the mutual-fund
separation theorem, which states that all investors should hold the same com-
position of risky assets. In contrast to the theorem, popularadvisors recommend
that aggressive investors hold a lower ratio of bonds to stocks than conservative
investors. The paper explores various possible explanations of this puzzle and
finds them unsatisfactory. (JEL GI l)
How should an investor's attitude toward
risk influence the composition of his port-
folio? A simple and elegant answer to this
question comes from themutual-fund separa-
tion theorem. This theorem, a building block
of the most basic Capital Asset Pricing Model
(CAPM), is taught regularly to undergradu-
ates and business students. According to the
theorem, more risk-averse investors should
hold more of their portfolios in the riskless as-
set. The composition of risky assets, however,
should be the same for all investors.Popular financial advisors appear not to fol-
low the mutual-fund separation theorem. When
these advisors are asked to allocate portfolios
among stocks, bonds, and cash, they recommend
more complicated strategies than indicated by
the theorem. Moreover, these strategies differ
from the theorem in a systematic way. Accord-
ing to these advisors, more risk-averse investors
shouldhold a higher ratio of bonds to stocks.
This advice contradicts the conclusion that all
investors should hold risky assets in the same
proportion.
The purpose of this paper is to document
this popular advice on portfolio allocation and
attempt to explain it. We begin in Section I by
reviewing the basic mutual-fund separation
theorem. We consider the conditions under
whichall investors should hold stocks and
bonds in the same proportion. We also present
a numerical example of the optimal mutual
fund based on the historical distribution of
stock and bond returns.
In Section II we document the nature of
popular financial advice regarding portfolio al-
location. We show that this advice contrasts
starkly with the predictions of themutual-fund
separation theorem. Moreover, the deviations
from the theorem are systematic. In the rest of
the paper we take this popular advice on port-
folio allocation as the "data" to be explained.
In Section III we consider whether such ad-
vice might be optimal. We consider various
deviations from the assumptions that underlie
the basic mutual-fund separation theorem. Inparticular, we consider the absence of a risk-
less asset; preferences that depend on more
than the mean and variance of returns; port-
folio choice in dynamic settings; and the ex-
istence of nontraded assets. Although we
cannot rule out the possibility that popular ad-
vice is consistent with some model of rational
behavior, we have so far been unable to find
such amodel.
The difficulty in explaining popular ad-
vice suggests that investors (or investment
advisors) are not fully rational. But how far
from full rationality are the recommended
portfolios? In Section IV we examine the
costs of holding nonoptimal portfolios. We
show that these portfolios are not far from
*
Canner: McKinsey & Company, 55 East 52ndStreet,
New York, NY 10055; Mankiw: Department of Econom-
ics, 223 Littauer Center, Harvard University, Cambridge,
MA 02138; Weil: Department of Economics, Box B,
Brown University, Providence, RI 02912. The authors are
grateful to John Campbell, Tony Lancaster, and the ref-
erees for comments, to Michael Rashes for research assis-
tance, and to the National Science Foundation...