The purpose of this study is to measure and evaluate the objectives, risk, and return of 123 American mutual funds using monthly returns in the period 1960–1969. The paper considers five questions: How were stated fund objectives related to risk and return, as measured over the subsequent decade? How did funds of various objectives perform in terms of return and return-to-risk measures? Did average excess return increase with risk? Was the return-to-risk performance of the average mutual fund better or worse than that of the stock market as a whole? How did the slope of the mutual fund line of returns versus beta compare to the capital market line; i.e., did funds at one end of the risk spectrum appear to “outperform” those at the other end?

This paper develops a credit-analysis model encompassing the accuracy of analytical methods, quality of applicants, cost of acquisition and analysis, profit from good loans, and losses from bad loans. Information generally available to the lending institution and subjective estimates can then be used to select from among alternative credit-granting systems the system with the greatest expected net present value. Each institution is thus able to find the credit granting system most appropriate for its particular market and analytical abilities.

The model's profit maximizing objective and broad scope make it useful for setting credit department standards of performance. Costs can be compared with theoretical values of performance computed from loss rates, acceptance rates, and market information. The conditional probabilities, the chances of making the correct decision, can also be estimated for use in comparing methods of analysis or individual analysts. Unlike the loss rate, the conditional probability is an independent, unbiased measure of a method's accuracy.

The example presented dealt with consumer installment loans, but the formulation is applicable to direct lending of any type. It provides the means for comparing loans with differing initial costs as well as widely varying risk classes and maturities. Financial institutions making direct loans add substantial values to capital supplied by the money and capital markets. The model is a theoretical formulation of the relationship between the cost and output of credit analysis.

Since the Second World War the corporate pension trust has become a prominent method of provision for employees' retirement income. The continuing liberalization of pension provisions and pressures to match pension trust liabilities with assets has established pension contributions as a significant component of corporate cash outlays. Asset accumulation in pension trusts has rendered such institutions a major source of capital funds.

The results obtained for accounts payable contrast with those for accounts receivable. With receivables, it appears that the level is determined more or less automatically by sales, linear trend, and season of the year. In the case of payables, it seems that trend and season are unimportant, and that the level of payables is determined instead by not only the level of purchases, but by capital requirements. Further, the current obligation on bank term-loans plays an important role in determining the response of payables to the need for working capital.

However, it was shown that fairly simple models are sufficient to account for most of the variance in accounts payable. Although it was anticipated that monetary variables would be significant for accounts payable, this was not borne out. As for accounts receivable, most of the variance in accounts payable for the Lumber and Wood Products Industry can be associated with microeconomic (i.e., industry variables) and time variables alone.

Several tentative conclusions concerning trade credit in the Lumber and Wood Products Industry may be listed:

1. Receivables can be accounted for almost entirely by sales, trend, or season.

2. Payables are not directly influenced by trend or season.

3. The direct influences of money supply and interest rates on accounts payable are not significant.

4. The effect of working capital on payables is adequately captured by treating current assets and current liabilities as separate independent variables.

5. The current obligation on long-term bank loans is more important in determining the level of payables than are short-term bank loans or the level of long-term debt.

The FINSIM model provides a fundamental and analytical basis for security evaluation. The methodology presented includes the relevant economic and firm variables in an efficient computational scheme and is useful for:

1. reducing the analysts' judgments about the future to a specific stock price (the model described does not replace the analyst, rather it provides the analyst with a vehicle to determine the implications of his critical assumptions);

2. testing the probable impact of changed expectations concerning the firm and/or the level of the market on stock value;

3. getting at what “the markets” expectations must be to justify the current price;

4. determining the value of additional information (are results changed significantly to pay for the expense of refined estimates?);

5. determining the impact of alternative growth horizons on value; and

6. determining what the actual growth rate of total earnings must be to overcome the dilution effects of financing with external equity.

While the security analyst still faces the problems associated with decision making under uncertainty, the methodology presented facilitates the use of sensitivity analysis to study the implications of uncertain knowledge of parameters.

Industry analysis has long been a cornerstone in both the academic and professional segments of the investment community. Concepts such as “an industry providing downside protection” or “another is certain to outperform the market” have been prevalent throughout the profession. The importance of industry analysis in terms of stock price changes has been suggested by King, while the influence of the industry factor on corporate earnings changes has been documented by Brown and Ball. These studies and others have indicated that industry analysis has been an important part of security valuation.

The Markowitz model for the efficient diversification of investments [12] has, over the years since its original formulation, provided the basis for many investigations into the question of portfolio selection. Amongst the more notable contributions to the theory are the works of Fama [6] and Mandelbrot [11], Smith [17], Latané [10], Arditti [1], and Blume [2].

The normative procedures of Markowitz [4], Sharpe [6], and others can be utilized to determine an optimal portfolio (set of security holdings) given estimates of risk, relevant constraints, and expected returns on securities. Building on these foundations, the positive models of Sharpe [7], Lintner [3], Mossin [5], and others assume that investors form portfolios as if they were following such procedures. We observe considerable differences in portfolio composition, some of which undoubtedly stem from differences in expectations. Yet the predictions of most investors are either made implicitly or, if made explicitly, are jealously guarded and hence cannot be observed by outsiders.

Intuitively, a risk averter diversifies between two investments if there is some sort of negative interdependence. In [3], Samuelson gives the example of buying shares in a coal company and an ice company. It is of interest to characterize this concept of negative interdependence more sharply.

Certainly, the concept of skewness of returns and its role in the context of portfolio analysis has gained increasing attention in recent literature. Witness the studies by Alderfer and Bierman [1], Arditti [2, 3], Jean [4], and Simonson [5]. Each of these studies has treated skewness as the third moment of a series expansion—accordingly, skewness has been measured and interpreted as a logical extension of the traditional two-dimensional return-versus-standard deviation analysis of security evaluation.

Econometric research in the past two decades has vitnessed a considerable use of dummy variables in regression analysis. The analysis of covariance has long been a standard statistical technique to test the equality of coefficients in linear regressions. While students and researchers are generally aware of the close relationship between the two methods, they are often frustrated at choosing one method instead of the other in practice and wonder whether the two methods lead to the same test results. This note shows that the two methods are equivalent from the point of view of hypothesis testing.

It has been said [2,4,5,6,7, and 8], and it seems to be widely accepted, that the geometric mean of the price relatives of a group of securities can be interpreted as the return which would have been earned on a portfolio of those securities, managed continuously over time to maintain an equal money investment in each security. This is a theoretical concept which could not be implemented literally by a portfolio manager, but it can still be treated rigorously in a mathematical sense. In a recent paper in this journal Rothstein [8] defined continuous reallocation as the limiting case of a policy which does have an operational definition. He showed that the index corresponding to a policy of the equalization of dollar investments approaches the geometrically averaged index as its limiting value. We shall argue that this interpretation of the geometric mean is a misleading one, since it depends upon assumptions which imply serious market inefficiencies.

The authors, Hodges and Schaefer, of the preceding paper [2], taking up where my own article [3] left off, have contributed to a better understanding of the geometric mean index of stock price relatives. Their basic point is that, if in any practical situation a portfolio were managed according to a policy of periodic reallocation, the wealth relative of the portfolio would not be approximated by the geometric index. This is demonstrated through simulation, using randomly generated price sequences as well as empirical data. In addition, they have presented a verbal characterization of the hypothetical portfolio policy whose wealth relative is measured by the mth-order power mean of price relatives discussed in my paper. This policy, as I had stated, is not an intuitively simple one like “maintain equal dollar amounts at all times” or “buy and hold.”