CHAPTER 1

INTRODUCTION

The Analysis of Portfolios

This monograph is concerned with the analysis of portfolios containinglarge numbers of securities. Throughout we speak of "portfolio selection"rather than "security selection." A good portfolio is more than a longlist of good stocks and bonds. It is a balanced whole, providing theinvestor with protections and opportunities with respect to a wide range ofcontingencies. The investor should build toward an integrated portfoliowhich best suits his needs. This monograph presents techniques ofPortfolio Analysis directed toward determining a most suitable portfoliofor the large private or institutional investor.

A portfolio analysis starts with information concerning individualsecurities. It ends with conclusions concerning portfolios as a whole.The purpose of the analysis is to find portfolios which best meet theobjectives of the investor.

Various types of information concerning securities can be used as theraw material of a portfolio analysis. One source of information is thepast performance of individual securities. A second source of informationis the beliefs of one or more security analysts concerning future performances.When past performances of securities are used as inputs, theoutputs of the analysis are portfolios which performed particularly well inthe past. When beliefs of security analysts are used as inputs, the outputsof the analysis are the implications of these beliefs for better and worseportfolios.

This introductory chapter discusses broad principles upon which thetechniques of portfolio analysis are based. The next chapter discusses theinputs, outputs, and objectives of illustrative portfolio analyses. Subsequentparts of the monograph go more deeply into the techniques by whichinformation concerning securities is transformed into conclusions concerningportfolios.

The Uncertainty of Security Returns

Uncertainty is a salient feature of security investment. Economicforces are not understood well enough for predictions to be beyond doubtor error. Even if the consequences of economic conditions were understoodperfectly, non-economic influences can change the course of generalprosperity, the level of the market, or the success of a particular security.The health of the President, changes in international tensions, increases ordecreases in military spending, an extremely dry summer, the success of aninvention, the miscalculation of a business management—all can affect thecapital gains or dividends of one or many securities.

We are expecting too much if we require the security analyst to predictwith certainty whether a typical security will increase or decrease in value.Even if he could assemble all information, including information availableonly to the managers of the corporation and information available only toits competitors, the security analyst might still be forced to conclusionssuch as:

This security may be expected to do well if securities in general do well. Itmust be expected to do poorly if securities in general do poorly. Even thisfollowing of the market is not certain. There are weaknesses which may causeit to do poorly even though securities in general are performing well: Thepossibility of a labor dispute or of an aggressive competitor cannot be ignored.On the other hand, there are potentialities which may bring success greater thaneven the corporation management dares hope. The new styling of the product,the (not inexpensive) advertising campaign, and the expansion of productionfacilities may prove to be a magic combination, fulfilling all expectationsfor it.

Only the clairvoyant could hope to predict with certainty. Clairvoyantanalysts have no need for the techniques of this monograph.

The existence of uncertainty does not mean that careful security analysesare valueless. The security analyst may be expected to arrive at reasonableopinions to the effect that:

The return (including capital gains and dividends) on security A is lessuncertain than that on security B; the return on security C is more closelyconnected to the course of the general market than is that on security D; thegrowth of security E is more certain but has less potential than that of securityF; only if the demand for their industry's product continues to expand (as itis likely, but not certain, to do) will the return on securities G and H besatisfactory.

Carefully and expertly formed judgments concerning the potentialities andweaknesses of securities form the best basis upon which to analyze portfolios.

Correlation among Security Returns

A second salient feature of security investment is the correlation amongsecurity returns. Like most economic quantities, the returns on securitiestend to move up and down together. This correlation is not perfect:individual securities and entire industries have at times moved against thegeneral flow of prosperity. On the whole, however, economic good andill tend to spread, causing periods of generally high or generally loweconomic activity.

If security returns were not correlated, diversification could eliminaterisk. It would be like flipping a large number of coins: we cannot predictwith confidence the outcome of a single flip; but if a great many coins areflipped we can be virtually sure that heads will appear on approximatelyone-half of them. Such canceling out of chance events provides stabilityto the disbursements of insurance companies. Correlations amongsecurity returns, however, prevent a similar canceling out of highs andlows within the security market. It is somewhat as if 100 coins, about tobe flipped, agreed among themselves to fall, heads or tails, exactly as thefirst coin falls. In this case there is perfect correlation among outcomes.The average outcome of the 100 flips is no more certain than the outcomeof a single flip. If correlation among security returns were "perfect"—ifreturns on all securities moved up and down together in perfect unison—diversificationcould do nothing to eliminate risk. The fact that securityreturns are highly correlated, but not perfectly correlated, implies thatdiversification can reduce risk but not eliminate it.

The correlation among returns is not the same for all securities. Wegenerally expect the returns on a security to be more correlated with thosein the same industry than those of unrelated industries. Business connectionsamong corporations, the fact that they service the same area, acommon dependence on military expenditures, building activity, or theweather can increase the tendency of particular returns to move up anddown together.

To reduce risk it is necessary to avoid a portfolio whose securities are allhighly correlated with each other. One hundred securities whose returnsrise and fall in near unison afford little more protection than the uncertainreturn of a single security.

Objectives of a Portfolio Analysis

It is impossible to derive all possible conclusions concerning portfolios.A portfolio analysis must be based on criteria which serve as a guide to theimportant and unimportant, the relevant and irrelevant.

The proper choice of criteria depends on the nature of the investor.For some investors, taxes are a prime consideration; for others, such asnon-profit corporations, they are irrelevant. Institutional considerations,legal restrictions, relationships between portfolio returns and the cost ofliving may be important to one investor and not to another. For eachtype of investor the details of the portfolio analysis must be suitablyselected.

Two objectives, however, are common to all investors for which thetechniques of this monograph are designed:

1. They want "return" to be high. The appropriate definition of"return" may vary from investor to investor. But, in whatever sense isappropriate, they prefer more of it to less of it.

2. They want this return to be dependable, stable, not subject to uncertainty.No doubt there are security purchasers who prefer uncertainty,like bettors at a horse race who pay to take chances. The techniques inthis monograph are not for such speculators. The techniques are for theinvestor who, other things being equal, prefers certainty to uncertainty.

The portfolio with highest "likely return" is not necessarily the one withleast "uncertainty of return." The most reliable portfolio with anextremely high likely return may be subject to an unacceptably high degreeof uncertainty. The portfolio with the least uncertainty may have anundesirably small "likely return." Between these extremes would lieportfolios with varying degrees of likely return and uncertainty.

If portfolio A has both a higher likely return and a lower uncertainty ofreturn than portfolio B and meets the other requirements of the investor,it is clearly better than portfolio B. Portfolio B may be eliminated fromconsideration, since it yields less return with greater uncertainty than doesanother available portfolio. We refer to portfolio B as "inefficient."After eliminating all such inefficient portfolios—all such portfolios whichare clearly inferior to other available portfolios—we are left with portfolioswhich we shall refer to as "efficient." These consist of: the portfolio withless uncertainty than any other with a 6% likely return, the portfolio withless uncertainty than any other with a 7% likely return, and so on. Itcannot be said of two efficient portfolios "the first is clearly better than thesecond since it has a larger likely return and less uncertainty." All suchcases have been eliminated.

The proper choice among efficient portfolios depends on the willingnessand ability of the investor to assume risk. If safety is of extreme importance,"likely return" must be sacrificed to decrease uncertainty. If agreater degree of uncertainty can be borne, a greater level of likely returncan be obtained. An analysis of the type presented in this monograph:

first, separates efficient from inefficient portfolios;

second, portrays the combinations of likely return and uncertainty ofreturn available from efficient portfolios;

third, has the investor or investment manager carefully select thecombination of likely return and uncertainty that best suits his needs; andfourth, determines the portfolio which provides this most suitablecombination of risk and return.

CHAPTER 2

ILLUSTRATIVE PORTFOLIO ANALYSES

Inputs to an Illustrative Portfolio Analysis

The nature and objectives of portfolio analyses may be illustrated by asmall example concerned with portfolios made of one or more of ninecommon stocks and cash. The nine securities, listed in Figures la to li,include a utility, a railroad, a large and a small steel company, and severalother manufacturing corporations. Cash is included in the analysis as atenth "security." No special significance should be attached to this listof securities other than that it will be used in illustrating principles ofportfolio analysis.

An actual portfolio analysis would start from a much longer list ofpromising securities. Not all these securities would appear in the finaldesirable portfolio. They enter the analysis as candidates for a place inthe desirable portfolio.

The returns on the nine securities, during the years 1937-54, are presentedin Table 1 and illustrated in Figure 1. The return during a year is definedto be

(the closing price for the year) minus

(the closing price for the previous year) plus

(the dividends for the year) all divided by

(the closing price of the previous year).

For example, the return in 1948 is

(closing price, 1948) - (closing price, 1947) + (dividends, 1948)/(closing price, 1947)

This is the amount which an investor would have made or lost if he invested51.00 at the end of 1947, collected the dividends declared in 1948, and soldat the closing price of 1948. A loss is represented by a negative return.For example, if the closing price of 1947 were 50, that of 1948 were 45, and$2 of dividends were declared during 1948, then the return in 1948 would be

45 - 50 + 2/50 = -.06,

or a loss of 6 % per dollar invested.

Our example portfolio analysis will consider performances of portfolioswith respect to "return" thus defined. This assumes that a dollar ofrealized or unrealized capital gains is exactly equivalent to a dollar ofdividends, no better and no worse. This assumption is appropriate forcertain investors, for example, some types of tax-free institutions. Otherways of handling capital gains and dividends, which are appropriate forother investors, are discussed later.

Our nine securities differed in the amount of return which they yieldedon the average. For example, the average of the annual returns onUnited States Steel Common Stock was 14.6 cents per dollar invested;that on Coca-Cola Common was 5.5 cents per dollar invested. On theaverage the return on U.S. Steel was higher than that on Coca-Cola.

Securities also differ with respect to their stability of return. Forexample, the greatest loss incurred on A. T. & T. was 18 cents per dollarinvested (in 1941). On the other hand, the greatest loss on Sharon Steelwas 43 cents per dollar in vested .(in 1937). In three other years SharonSteel showed losses exceeding 20 cents per dollar. Clearly, A. T. & T.showed less variability of return than did Sharon Steel.

Portfolio selection should be based on reasonable beliefs about futurerather than past performances per se. Choice based on past performancesalone assumes, in effect, that average returns of the past are good estimatesof the "likely" return in the future; and variability of return in the past isa good measure of the uncertainty of return in the future. Later we shallsee how considerations other than past performances can be introducedinto a portfolio analysis. For the present it is convenient to discuss ananalysis based on past performances alone.

Suppose that a portfolio consisted of 20 cents' worth of Atchison,Topeka & Santa Fe per dollar invested, plus 80 cents' worth of Coca-Colaper dollar invested. The return in 1954 on such a portfolio would be

(.2) times (the return of A. T. & Sfe in 1954) plus

(.8) times (the return of Coca-Cola in 1954)

= (.2)(.469) + (.8)(.077)

= .155.

Return can be calculated similarly for any combination of securities inany year.

The average return on the portfolio consisting of 80% Coca-Cola and20% A. T. & Sfe was equal to

(.8) times (the average return on Coca-Cola) plus

(.2) times (the average return on A. T. & Sfe)

= (.8)(.055) + (.2)(.198)

= .084.

This is higher than the average return on Coca-Cola and lower than theaverage return on A. T. & Sfe. Inevitably the average return on a portfoliolies somewhere between the highest and the lowest average return onthe securities contained in the portfolio.

One might conjecture that the variability of return on a portfolio can,similarly, be no smaller than that of the least variable security in theportfolio. But this is not so. The return on A. T. & Sfe was ratherunstable during the period 1937-54 (showing a maximum loss of 45 centson the dollar). The return on Coca-Cola was more stable, showing amaximum loss of only 25 cents. The return on the 80 %-20 % combinationof Coca-Cola and A. T. & Sfe, respectively, was still more stable. Itsmaximum loss was only 18 cents on the dollar. In Figure 2 we haveplotted the annual returns on the portfolio consisting of 80 cents Coca-Cola,20 cents A. T. & Sfe. For comparison we have also plotted the return onCoca-Cola.

"Largest loss" is not the only possible measure of variability. Anothermeasure, better for our purposes, is discussed later. In terms of thismeasure also, the variability of A. T. & Sfe is greater than that of Coca-Cola,while that of Coca-Cola is, nevertheless, greater than that of theportfolio. For the present we assume that Figure 2 and the reader's eyeconfirm the statement that the variability of the particular portfolio wasless than that of either of the securities contained in it.

Our 20%-80% portfolio had both a higher average return and a lowervariability of return than a portfolio consisting of 100% Coca-Cola. Onthe whole, the "diversified" portfolio was both more profitable and morestable than Coca-Cola alone. One might wonder whether or not there wassome other portfolio—some other combination of our ten securities (ninesecurities and cash)—which had both greater average return and greaterstability than even the 20%-80% mixture. Or perhaps there was aportfolio with greater average return and the same stability; or greaterstability and the same average return.