马克维茨投资组合选择(7)

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

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