Similarly in trying to make variance small it is not enough to invest
in many securities. It is necessary to avoid investing in securities with
highcovariances among themselves. We should diversify across industries
because firms in different industries, especially industries with
different economic characteristics, have lower covariances than firms within an industry.
The concepts \financial
writings. Usually if the term \were replaced by \
yield\of return,\
change of apparent meaning would result.
Variance is a well-known measure of dispersion about the expected.
If instead of variance the investor was concerned with standard error,
a = Tv, or with the coefficient of dispersion, a/E, his choice would
still lie in the set of efficient portfolios. Suppose an investor diversifies between two portfolios (i.e., if he puts
some of his money in one portfolio, the rest of his money in the other.
An example of diversifying among portfolios is the buying of the shares
of two different investment companies). If the two original portfolios
haveequal variance then typically12 the variance of the resulting (compound)
portfolio will be less than the variance of either original port-
12. In no case will variance be increased. The only case in which variance will not be
decreased is if the return from both portfolios are perfectly correlated. To draw the isovariance curves as ellipses it is both necessary and sufficient to assume that no two distinct
portfolios have perfectly correlated returns.
90 The Journal of Finance folio. This is illustrated by Figure 7. To interpret Figure 7 we note that
a portfolio iP) which is built out of two portfolios P' = (x:,x:)and
P\= (xi::xi')is of the form P = XP' + (1 - h ) ~ \= (AX:+
(1 - X)XI ,AX:+ (1 - x)x:'). P is on the straight line connecting
P' and P\The E-V principle is more plausible as a rule for investment behavior
as distinguished from speculative behavior. The third moment13 M8 of
the probability distribution of returns from the portfolio may be connected
with a propensity to gamble. For example if the investor maximizes
utility(U)which depends on E and V(U = U(E, V), d U/aE> 0, aU/dE<0) he will never accept an actuarially fair14 bet. But if
13. If R is a random variable that takes on a finite
number of values 71,.. . ,m with
probabilities*I, . . . , gnrespectively, and expected value E, then = 2*i(ri- El3 i=l
14. One in which the amount gained by winning the bet times the ~robabilitvof winning
Port)olio Selection 9I
U = U(E, V, Mg) and if dU/dM3 # 0 then there are some
fair bets
which would be accepted.
Perhaps-for a great variety of investing institutions which consider
yield to be a good thing; risk, a bad thing; gambling, to be
avoided-E, V efficiency is reasonable as a working hypothesis and a working maxim.
Two uses of the E-V principle suggest themselves. We might use it
in theoretical analyses or we might use it in the actual selection of portfolios.
In theoretical analyses we might inquire, for example, about the
various effects of a change in the beliefs generally held about a firm,
or a general change in preference as to expected return versus variance
of return, or a change in the supply of a security. In our analyses the
Xi might represent individual securities or they might
represent aggregates
such as, say, bonds, stocks and real estate.15 To use the E-V rule in the selection of securities we must have procedures
for finding reasonable pi and aij. These procedures, I believe,
should combine statistical techniques and the judgment of practical
men. My feeling is that the statistical computations should be used to
arrive at a tentative set of pi and aij. Judgment should then be used
in increasing or decreasing some of these pi and uij