232 THE HANDBOOK OF PORTFOLIO MATHEMATICS
parameters change quite quickly from one time period to another, optimal
portfolio mixes change very slowly (as do optimalfvalues). Generally, the
correlations between market systems tend to remain constant. This is good
news to a trader who has found the optimal portfolio mix, the optimal di-
versification among market systems.
The Markowitz Model
The basic concepts of modern portfolio theory emanate from a monograph
written by Dr. Harry Markowitz.^1 Essentially, Markowitz proposed that
sound portfolio management has to do with composition, not individual
stock selection.
Markowitz argued that diversification is effective only to the extent that
the correlation coefficient between the markets involved is negative. Recall
the linear correlation coefficient from Chapter 1. If we have a portfolio
composed of one stock, our best diversification is obtained if we choose
another stock such that the correlation between the two stock prices is
as low as possible. The net result would be that the portfolio, as a whole
(composed of these two stocks with negative correlation), would have less
variation in price than either one of the stocks alone (see Figure 7.1).
The portfolio shown in Figure 7.1 (the combination of Market Systems
A and B) will have variance at least as high as the individual market systems
since the market systems have a correlation of+1.00 to each other.
The portfolio shown in Figure 7.2 (the combination of Market Systems
A and C) will have less variance than either Market System A or Market
System C since there is a negative correlation between Market Systems A
and C.
Markowitz proposed that investors act in a rational manner and, given
the choice, would opt for a portfolio with the same return as the one they
have, but with less risk, or opt for a portfolio with a higher return than the
one they have but with the same risk. Further, for a given level of risk there is
an optimal portfolio with the highest yield; likewise, for a given yield there
is an optimal portfolio with the lowest risk. Investors with portfolios where
the yield could be increased with no resultant increase in risk or investors
with portfolios where the risk could be lowered with no resultant decrease
in yield are said to haveinefficientportfolios.
(^1) Markowitz, Harry.Portfolio Selection—Efficient Diversification of Investments.
New Haven, CT: Yale University Press, 1959.