Edwin J. Elton, Martin J. Gruber
ABSTRACT
In a recent article in this journal, Canner, Mankiw and Weil (CMV)
argue that in general popular investment advice, and in particular the
investment advice of four investment advisors, is inconsistent with modern
portfolio theory and is irrational. As CMV state, since portfolio theory
is so well known and easy to implement, finding irrationality here has
serious implications for the assumption of rationality throughout
economics. As part of their analysis, CMV assert that investment advice
can only be viewed as rational if the ratio of bonds to stocks either
remains constant or increases as the investor seeks higher return (takes
on more risk). As evidence of advisor irrationality, CMV point out that
investor advisors frequently advocate decreases in the ratio of bonds to
stocks to obtain higher returns. They state, "Although we cannot rule out
the possibility that popular advice is consistent with some model of
rational behavior, we have so far been unable to find such a model."1
In this comment we show that in the absence of a riskless asset the rationality test of CMV is not a result of the efficient set mathematics of Modern Portfolio Theory (MPT), but rather that their results require both data with particular properties and the assumption that unrestricted short sales are allowed. If short sales are allowed the efficient set mathematics must result in the ratio of bonds to stocks monotonically changing as risk increases, but the monotonic relationship can be either decreasing or increasing depending on the inputs used. If short sales are not allowed, the ratio of bonds to stock must be decreasing for the high range of expected returns as risk increases.
Furthermore, we show that under relevant assumptions the specific advice given by investment advisors is consistent with modern portfolio theory (MPT). As part of their analysis CMW analyze the portfolio problem when short sales are forbidden but riskless lending and borrowing exists and when a riskless asset does not exist but short sales are allowed. We argue that the realistic problem involves no short sales and no riskless lending and borrowing (in real terms), that this is the problem the advisors are solving, and that their advice is rational in this framework.
We proceed in three steps. We first review some of the basic tenets of MPT, discuss alternative formulations of the problem, and examine which of these alternatives is appropriate for the problem being analyzed. Then, using efficient set mathematics, we show that CMK's criteria to test for rationality do not hold. Finally we show that the specific asset allocations proposed by each of the investment advisors selected by CMW are consistent with MPT under realistic estimates of inputs to the portfolio optimization problem.
1 Canner et al (1997), page 181.
Subject : Economics, Investments, Portfolio Choice(Empirical/Theoretical)
Elton: (212) 998-0361
eelton@stern.nyu.edu
Gruber: (212) 998-0333
gruber@stern.nyu.edu
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