3-Milestones Page 81 Wednesday, February 4, 2004 12:47 PM
Milestones in Financial Modeling and Investment Management 81fied and options are inherently risky. Option pricing theory again mir-
rors the setting of insurance premiums.
Lundberg’s work went unnoticed by the actuarial community for
nearly 30 years, though this did not stop him from enjoying a successful
career as an insurer. Both Bachelier and Lundberg were in advance of
their time; they anticipated, and probably inspired, the subsequent
development of probability theory. But the type of mathematics implied
by their work could not be employed in full earnest prior to the devel-
opment of digital computers. It was only with digital computers that we
were able to tackle complex mathematical problems whose solutions go
beyond closed-form formulas.THE PRINCIPLES OF INVESTMENT: MARKOWITZ
Just how an investor should allocate his resources has long been
debated. Classical wisdom suggested that investments should be allo-
cated to those assets yielding the highest returns, without the consider-
ation of correlations. Before the modern formulation of efficient
markets, speculators widely acted on the belief that positions should be
taken only if they had a competitive advantage in terms of information.
A large amount of resources were therefore spent on analyzing financial
information. John Maynard Keynes suggested that investors should
carefully evaluate all available information and then make a calculated
bet. The idea of diversification was anathema to Keynes, who was actu-
ally quite a successful investor.
In 1952, Harry Markowitz, then a graduate student at the University
of Chicago, and a student member of the Cowles Commission,^7 published a
seminal article on optimal portfolio selection that upset established wis-
dom. He advocated that, being risk adverse, investors should diversify their
portfolios.^8 The idea of making risk bearable through risk diversification
was not new: It was widely used by medieval merchants. Markowitz under-
stood that the risk-return trade-off of investments could be improved by
diversification and cast diversification in the framework of optimization.(^7) The Cowles Commission is a research institute founded by Alfred Cowles in 1932.
Originally based in Colorado Springs, the Commission later moved to the University
of Chicago and thereafter to Yale University. Many prominent American economists
have been associated with the Commission.
(^8) See Harry M. Markowitz, “Portfolio Selection,” Journal of Finance (March 1952),
pp. 77–91. The principles in Markowitz’s article were then expanded in his book
Portfolio Selection, Cowles Foundation Monograph 16 (New York: John Wiley,
1959).