Fallacy of the log-normal approximation to optimal portfolio decision

108 Pages·2008·2.18 MB·English

by  Merton, Robert C

LIBRARY
OFTHE
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY

Dewey
'^.INST.Tfc;^
JAN 9 1973
FALLACY OF THE LOG-NORMAL APPROXIMATION
TO OPTIMAL PORTFOLIO DECISION-MAKING OVER MANY PERIODS
Robert C. Merton
Paul A. Samuelson
623-72
November 1972
Sloan School of Management and Department of Economics
MASSACHUSETTS
INSTITUTE 01
50 MEMORIAL DRIVE
JAMBRIDGE. MASSACHUSETTS 021

MA<:s. INST.TfCH.
DEC 7 1972
dimi Ll'dKARY
FALLACY OF THE LOG-NORMAL APPROXIMATION
TO OPTIMAL PORTFOLIO DECISION-MAKING OVER MANY PERIODS
Robert C. Merton
Paul A. Samuelson
623-72
November 1972
Sloan School of Management and Department of Economics
M.I.T.
JAN 9 1973
FALLACY OF THE LOG-NORMAL APPROXIMATION
TO OPTIMAL PORTFOLIO DECISION-MAKING OVER I4ANY PERIODS*
Robert C. Merton
Paul A. Samuelson
Sloan School of Management and Department of Economics
Massachusetts Institute of Technology
I. Introduction
Thanks to the revival by von Neumann and Morgenstern,maximization
of the expected value of a concave utility function of outcomes has for the
last third of a century generally been accepted as the "correct" criterion
for optimal portfolio selection. Operational theorems for the general
case were delayed in becoming recognized, and it was appropriate that the
seminal breakthroughs of the 1950's be largely preoccupied with the special
case of mean-variance analysis.— Not only could the fruitful Sharpe-Lintner-
Mossin capital asset pricing model be based on it, but in addition, it gave
rise to simple linear rules of portfolio optimizing. In the mean-variance
model, the well-known Separation or Mutual-Fund Theorem holds; and with suit-
able additional assumptions, the model can be used to define a complete micro-
economic framework for the capital market, and a number of empirically test-
able hypotheses can be derived. As a result, an overwhelming majority of the
2/
literature on portfolio theory have been based on this criterion.—
Unfortunately, as has been pointed out repeatedly, the mean-variance
criterion is rigorously consistent with the general expected-utility approach
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