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Economic analysis based on the Theory of the Firm shows that the exporting firm can be conceptualized as a discriminating monopolist, facing several demand curves. The analysis shows that under these conditions, and assuming certainty, the larger the firm, the higher the ratio of exports to total sales. When uncertainty is introduced into the model, the conclusion regarding the relationship between size and the ratio of exports to sales is reinforced. Large firms can afford to assume more risks than small ones; in addition, their risks from foreign operations are less than those of small firms because the large firms benefit from economies of scale in foreign marketing. Consequently, the risk premium demanded by large firms from foreign marketing is less than the premium insisted upon by small firms. Large firms therefore tend to export a higher share of their output. These theoretical constructs are confirmed by empirical analysis performed on a sample of several hundred firms from six industries in Denmark, Holland and Israel. The figures confirm, with few exceptions, that the size of firms is indeed positively correlated with the ratio of exports to sales. The normative conclusion which can be drawn from the above is that economic policy-makers who wish to increase the export potential of industrial firms, should adopt policies which will encourage large firms to come into being through mergers, take-overs or simply fast growth.

The interpretation of the duality conditions of linear programming in the determination of optimal investment programmes has definitively clarified the question of the ‘correct’ discount rate in the deterministic case (Chames, Cooper, Miller, 1959). A similar total analysis of the multiple expectations case facilitates superior indications of the nature of the present value calculation for a piecemeal approach to project appraisal. A controversial issue is the question of whether the expected values of net cash flows should be discounted with a ‘risk-adjusted’ rate or whether such flows should first be adjusted for risk and then be discounted at a ‘risk free’ rate.

One of the by-products of the literature which followed the publication of Phillips's (1958) well-known paper was the development and elaboration of models of individual behavior in labor-market disequilibrium (see Phelps [1969] for a survey). In retrospect this may be the most significant consequence of the Phillips curve analysis, since the labor-market models may suggest ways for tackling the wider problem of the adjustment to equilibrium which is still in a very messy state. In this paper we shall consider one aspect of the problem which has been neglected by the "new microeconomics," namely, the implications of attitudes toward risk for individual behavior in disequilibrium. Section II introduces the concept of a risk premium which is then used in Section III to analyze the relationship between individual behavior toward risk, job search, and the structure of wage offers by firms. Sections IV and V consider the relationship between the distribution of risk attitudes and the distribution of income and wealth among individuals. A concluding section points out some of the implications of the analysis for empirical research.

The rapid economic growth in the last decade and the fierce competition have forced industry to raise its output, to develop new manufacturing methods and, where possible, to lower the fixed costs per unit of output. Consequently bigger factories and warehouses have been and are being built. Furthermore increasing labour costs have speeded up rationalisation and the introduction of efficient machinery.Often, in the course of this development, too little attention has been paid to safety. This is reflected in the increasing number of Fire and Consequential Loss claims which have become so costly that the premium income has proved inadequate. Insurers have therefore adjusted their tariffs and increased their rates.Of course, this is no solution to the problem. Insurers have to insist on adequate fire prevention and fire protection measures. Progress in the right direction can certainly be expedited by realistic tariffs which take account of all the positive features (sprinklers, inspection reports, etc.) and the negative features of a given risk (in commerce or industry).Rating experts say that the tariffs of industrialized countries do not always point to the actual risk and claims fluctuations; one very important factor here, the size of the risk or of the building (i.e. its insured value, volume, surface area), brings me to the main theme of my today's talk.

THIS PAPER CONSIDERS how risk premiums on investments are likely to change over time. The analysis is based upon results derived by Sharpe, Lintner and others [2, 5, 6, 9, 11] for equilibrium in the market for risk assets. To simplify the analysis it is assumed all physical assets are owned by firms. This allows us to identify the national wealth with the total value of company assets. It is shown that for a constant rate of interest the secular trend in the cost of capital for an investment project of given riskiness depends upon the growth of national wealth and the growth of population. The first part of the paper examines secular trends in risk premiums. The question we are in effect asking is whether the compensation required for risktaking changes through time. Under a class of investor utility functions-the Bernoulli or logarithmic utility function-risk premiums would be constant through time. Under two classes of investor utility functions-the negative exponential and the quadratic utility function-risk premiums would be constant under conditions of economic stagnation. Under these latter classes of utility functions risk premiums would increase over time under conditions of growth in per capita national wealth. The second part examines secular trends in the Lintner-Mossin measure of the "market price of risk." Under growth in national wealth and population and reasonable assumptions on investor utility functions this is shown to decline secularly. However, it is argued that the secular decline in the "market price of risk" is unimportant from the perspective of economic allocation under uncertainty. The analysis uses comparative statics and the rate of growth of total wealth is treated as exogenous. The results may, however, have some significance for growth theory. If (as is possible) risk premiums increase as per capita wealth increases, this would be a factor in limiting the feasible rate of growth of output.

The author examines the question whether the allocation of insurances between different classes of risk, each with different multiplicatively increased probabilities of death, can depend on whether or not the risk premium is returned in the event of survival. The result of his examination is as follows

The long-standing controversy over whether speculators in a futures market earn a risk premium is analyzed within the context of the capital asset pricing model recently developed by Sharpe, Lintner, and others. Under that approach the risk premium required on a futures contract should depend not on the variability of prices but on the extent to which the variations in prices are systematically related to variations in the return on total wealth. The systematic risk was estimated for a sample of wheat, corn, and soybean futures contracts over the period 1952 to 1967 and found to be close to zero in all three cases. Average realized holding period returns on the contracts over the same period were close to zero.

The reinsurance to be treated in this note shall cover the excess over a certain limit Q of the total amount of claims for each accounting period paid by the ceding company. Regardless of the rule for the determination of the limit Q such a reinsurance shall in this context be called stop loss reinsurance.Generally, such a reinsurance is called either stop loss or excess of loss reinsurance depending on the rule for the determination of Q. The use of the term stop loss regardless of this rule is preferred here in order to avoid confusion with an excess of loss reinsurance which refers to the excess of the amount of one or more claims caused by an individual event.The total amount of claims paid by the ceding company c during the period t shall be denoted cXt. This random function constitutes for a fixed value of c a stochastic process with the discontinuous parameter t > o.(It may be remarked that for a fixed pair of values of c and tcXt can be regarded as a particular value of a sample function pertaining to the process of the continuous paramater τ generally considered in the collective theory of risk to which the total amount of claims up to time τ is attached, in this case o < τ ≤ 1. cXt can also be considered as the increments during the time interval t of the total amount of the claims up to τ.)

THE EFFECTS OF DIVERSIFICATION on portfolio efficiency have been examined extensively over the past decade since the pioneering works of Markowitz [10], and later Sharpe [12] and Lintner [7]. The great majority of the empirical work has been limited to common stocks in the U.S. capital market. Recently papers have begun to appear examining the merits of diversifying across international boundaries ([1], [2], [4], [5], [6], [11]). The purpose of this paper is to examine several theoretical implications of such international diversification, with particular attention to the effects of imperfections in international financial markets on risk premia for capital assets, the cost of capital to firms, and the efficiency with which capital is allocated.

Reinsurance forms can roughly be classified into proportional and non-proportional. The authors of this paper had planned to investigate the “efficiency” of two different reinsurance forms, one from each of these categories. Efficiency is here understood as reduction in the variance of the annual results of the risk business achieved per unit of ceded reinsurance risk premium. This investigation may be carried out in full later.This note will only deal with the interplay between surplus and excess of loss reinsurance; more specifically the effect of changes in the volume of surplus cessions on the excess of loss risk premium.The study came out of a practical Fire Reinsurance rating problem and will be carried through under very simplified assumptions. Thus we will ignore the conflagration hazard and the possibility of a wrongly taxed PML. This means that if amounts above a PML of M are ceded on a surplus basis the highest loss per event will be M, and an excess cover above a priority m will never pay more than M-m per event.The following notations will be usedR(M) ceded risk premium volume on surplus basis, the PML retention being M.πM(m) excess of loss risk premium if priority is m and surplus cessions are made above a PML of M.

In decision theory the concept denoted variously as “risk aversion increment” or “risk premium” has not been fully exploited, although it is neither new nor complex. In this paper we will show how the concept of the risk aversion increment can be used for developing an alternative to the explicit use of the utility function. For most people the use of a risk aversion increment provides a better conceptual reference than does the use of a utility function. To illustrate the usefulness of the concept as a basis for gaining insight into problem statements and their analysis, the following applications are developed: 1) general results for the exponential utility function. 2) estimation of utility functions. 3) general results for various combinations of utility functions and probability distributions. 4) use in sequential decisions. 5) application in the theory of incentives.

Besides its well known applications, the collective risk theory has recently also been applied to problems connected with the so called Experience Rating. This term is used to define a method of premium calculation in insurance business which is based partially or totally on the individual experience of the particular risk involved. It is obvious that Experience Rating is essentially applicable to collective insurances which contain no saving element. In practical applications various possibilities may be considered.The collective theory of risk provides an efficient calculus for the analysis of the various forms of Experience Rating and in paper [3] a particular form of Experience Rating for collective insurances is examined. It is there assumed that the collective risk premium is based on experience derived from non-individual observations. If any cost loading is disregarded, the net premium is given by the relation P′ = (I + λ) P, where λ is a security factor and P the part of the premium covering the expected claims cost.A premium refund is to be deducted from the basic net premium P′. In this formula α′ and β are suitable numerical values and S means the due sum to be paid out for claims. Hence the net cost to the group considered depends on the actual claims S and therefore takes into account the individual claims experience. It may be shown that for β = I the form of Experience Rating considered is equivalent to a stop loss cover. The general case with β ≠ I represents a combination of ordinary insurance cover and stop loss cover.

Within the Union of Swedish Local Fire Mutuals, whose members are responsible for the majority of rural fire insurance, stocks and losses are statistically studied since 1936.

ECONOMISTS have long agreed that the rate of interest on a loan depends on the risks the lender incurs. But how lenders estimate these risks has been left largely to conjecture. This paper presents and tests a hypothesis about the determinants of risk premiums on corporate bonds. By risk premium is meant the difference between the market yield on a bond and the corresponding pure rate of interest. My hypothesis is as follows: (1) The average risk premium on a firm's bonds depends first on the risk that the firm will default on its bonds and second on their marketability. (2) The "risk of default" can be estimated by a function of three variables: the coefficient of variation of the firm's net income over the last

Some months ago I had occasion to enquire of half-a-dozen offices what were their rates of single premium for a certain survivorship assurance. The highest rate quoted exceeded the lowest by 40 per-cent of the latter. This fact appears to me to afford a good illustration of the different estimates formed by actuaries of the value of the risk run under survivorship assurances. The discrepancy probably arises mainly from the use of different tables of mortality in calculating the risk premiums. It will be seen later on, that the differences in survivorship premiums as found from different mortality tables are in some instances very considerable. I am inclined to think, too, that some actuaries, through a feeling of uncertainty as to whether they have correctly estimated the risk premiums, load them very heavily in order to be on the safe side.

I THE EVIDENCE THAT is available shows that interest rates charged on business loans by commercial banks tend to vary inversely with the size of the loan being made and therefore with the size of the borrower making the loan, since smaller borrowers tend to make smaller loans.' Several explanations have been offered of this fact that interest rates charged small borrowers tend to be greater than interest rates charged large borrowers. One explanation is that the costs of making loans to small borrowers tend to be greater than the costs of making loans to large borrowers. Many costs tend not to vary with the size of loans; consequently, costs as a percentage of loan value decrease with loan size and therefore with the size of the borrower. In addition, the absolute size of the costs of investigating credit worthiness may be greater for small borrowers than for large borrowers.2 A second explanation is that lenders ask larger risk premiums on loans to small borrowers than on loans to large borrowers, other things the same. Professor Alhadeff has proposed a third explanation of the fact that smaller borrowers appear to pay higher interest rates than larger borowers, and it is with this explanation that the present paper is concerned.3 Alhadeff recognizes that differential costs and, perhaps, differential risk premiums undoubtedly play a role,4 but he maintains that, to explain fully the higher rates charged small borrowers, one must consider ". . . the nature of the market in which large borrowers deal." Alhadeff takes as the starting point of his analysis the observed

where ri, represents the total return of a company's security; ai measures the return arising from specific company effects; R1I represents the return of a broadly based pool of assets characteristic of general business, and 1int is a random variable with zero mean and zero intertemporal and intercompany covariance. When the assumptions of the capital asset pricing model are fulfilled a company's risk premium, i.e. its expected return less the pure rate of interest, is proportional to the risk premium of the market as a whole. P is the factor of proportionality for it can be shown that:2

The annual valuation of the policies in stock is probably the most cumbersome single task in a Life Office. It demands a great amount of labour and time. No wonder therefore, that during past times a lot of different methods have been devised to simplify and reduce this work.

The most important property of a distribution function to be used as a model for the distribution of one claim is of course that it fits the data well enough. If there is no natural truncation point in the data a more formal demand is that all the moments of the distribution function exist. Further, to be of a real value to the statistician, the chosen d.f. ought to be reasonably handy to use. As all the moments of the lognormal d.f. exist the first point to be checked is whether the lognormal d.f. fits the data. The other points on the list below are the qualities that I think are of the greatest value when using a distribution function, i.e. they reflect the handiness of the d.f.Does the lognormal d.f.1. Fit the data?2. Give an unbiased and efficient estimate of the mean? It is important that this estimate is not too difficult to compute.3. Give a practicable confidence interval of the mean?4. Give a known distribution function of the estimate of the risk premium?This paper is an attempt to give an affirmative answer to these questions. As the lognormal distribution function has been treated in the monograph “The lognormal distribution” by J. Aitchison and J. A. C. Brown (Cambridge University Press) the theory of this distribution function will not be dealt with more than necessary for the context.

The article examines first the functional relationship of premiums and reserves. It then proceeds to the development of reserves by accumulating gross dremiums less risk premiums and expenses on an experience basis, leading to reserves augmented by the surplus to the date of valuation. Finally the process is extended to include the effect of fluctuations in the value of the assets. It is shown that the methods described in the paper, which lend themselves to a prospective formulation, are particularly suitable for the administration of portfolins covered by assets subject to wide fluctuations in value.

For policies concluded to cover abnormal risks this essay demonstrates by means of some examples the development of the premium reserves, the changes in risk premiums if the sums assured are reduced and the supplemental premium reserve payments in those cases in which there is a reduction of the term of assurance. The essay also describes the process allowing the simple addition of two assurances with different excess mortality to give a single assurance. Finally the author shows that a policy concluded to cover an abnormal risk and providing for repayment of the risk premium at the end of the endowment period if the insured is then living bears the characteristics of an assurance payable in case of death if the risk premiums increase with increasing excess mortality.

In a paper [13] in this journal the author has further developed the ruin theory—first presented by E. Sparre Andersen [1] to the XVth International Congress of Actuaries, New York, 1957—in case the epochs of claims form a renewal process and the gross risk premium is positive. It turned out that much of the Cramer treatment [6] of the classical ruin theory (Poisson case) could be generalized to the more general situation. In the present paper the author points out that the identity shown by him in an earlier paper [12] for the Poisson case is also capable of being generalized. Some comments concerning the case with a negative gross risk premium are also included. I.a. the Cramer asymptotic formula for the ruin probability for an infinite period is generalized also in that case. Further information about the contents of the paper may be inferred from the following section headings. The paragraph 5.4 and the sections 6–7 are found in Part II to appear in SAT 1971:3–4.

This paper is a secondary analysis of the data from two risk taking gambling experiments to test the value of risk hypothesis. The value of risk hypothesis is said to be true if the value of taking a risk is positive and if the level of risk at maximum expected value shifts towards greater risk for groups compared with individuals. Based upon the task, a method for imputing the value of risk is presented and then used to test the hypothesis. Data support the assumption of a positive value for risk taking but do not support a shift in maximum expected value risk. Therefore, the data do not support the value of risk hypothesis.

On the assumption that the probability of death of an abnormal risk is subject to constant multiple extramortality the author gives the formulae for the risk premiums — with and without restitution at the end of the endowment period — and for the changes in the mathematical reserves arising from these risk premiums. He describes and formularises the problems resulting from changes in an endowment insurance concluded to cover an abnormal risk and thoroughly investigates the permanent shortening of the term of assurance by means of supplemental premium reserve payments. By way of example he shows that there is no need for changes in the risk premiums at least for certain graduated supplemental payments.

Few topics in our discipline rival the social rate of discount as a subject exhibiting simultaneously a very considerable degree of knowledge and a very substantial level of ignorance. Economists understand thoroughly just what this variable should measure: the opportunity cost of postponement of receipt of any benefit yielded by a public investment. They agree also on the components that should be considered in making up this figure: primarily the welfare foregone by not having these benefits available for immediate consumption or reinvestment and (perhaps) a premium corresponding to the risk incurred in undertaking government projects. Above all, economists are quite generally in accord on the view that a very serious misallocation of resources can result from the use of an incorrect estimate of the value of this variable in a cost-benefit calculation. Yet, while they agree that exernalities can play a significant role in the matter, there is some considerable question even about the direction of these effects. There is substantial obscurity and divergence of views in discussions of the implications of differences (if indeed there are any) in the degree of risk that is incurred when a given project is undertaken by a private firm on the one side and by government on the other.

In order to understand what determines people’s cash holdings and the prices of goods in terms of cash, we have to discuss more generally the causes making people hold idle stocks — of which cash balances are a particular case. This necessitates the application of Equilibrium Theory generalised to take account of time, imperfect competition and uncertainty. Our procedure is as follows.

If you find any Island or maine land populous, and that the people hath no need of cloth then you are to devise what com-modities they have to purchase the same withall.

0. Summary. The theory of collective risk deals with an insurance business, for which, during a time interval (0, t) (1) the total claim X(t) has a compound Poisson distribution, and (2) the gross risk premium received is Xt. The risk reserve Z(t) = u + Xt - X(t), with the initial value Z(O) = u, is a temporally homogeneous Markov process. Starting with the initial value u, let T be the first subsequent time at which the risk reserve becomes negative, i.e., the business is "ruined". The problem of ruin in collective risk theory is concerned with the distribution of the random variable T; this distribution has not so far been obtained explicitly except in a few particular cases. In this paper, the whole problem is re-examined, and explicit results are obtained in the cases of negative and positive processes. These results are then extended to the case where the total claim X(t) is a general additive process. 1. Introduction. The theory of collective risk, as developed by the Swedish actuary Filip Lundberg, deals with the business of an insurance company. Following a series of papers published by him during the years 1909-1934, a considerable amount of work has been done by Cram6r, Segerdahl, Tacklind, Sax6n, Arfwedson and many others; a survey of the theory from the point of view of stochastic processes was given by Cram6r [2], [3] and an excellent review has recently been given by Arfwedson [1]. Briefly, the mathematical model used in this theory can be described as follows. (a) The claims occur entirely "at random", that is, during the infinitesimal interval of time (t, t + dt), the probability of a claim occurring is dt and the probability of more than one claim occurring is of a smaller order than dt, these probabilities being independent of the claims which have occurred during (0, t). (b) If a claim does occur, the amount claimed is a random variable with the probability distribution dP(x) (-oo < x < m), negative claims occurring in the case of ordinary whole-life annuities. Under the assumptions (a) and (b), it is easily seen that the total amount X(t) of all claims which occur during (0, t) has the compound Poisson distribution given by

This paper was the basis of the paper entitled "Risk and the Rate of Return on Financial Assets: Some Old Wine in New Bottles," which was published in the Journal of Financial and Quantitative Analysis in December 1975. Differences between the two papers result from the refereeing process. This original working paper version is clearer and more complete. These papers were the first to document the lack of positive relationship between risk and return in the empirical cross-section of stock market returns.

The purpose of this paper is to re-examine some of the theoretical and empirical implications of existing ideas about the role of social overhead capital in the process of economic growth. In the course of this inquiry these ideas are found wanting in several important respects, and as a result, I have formulated some new hypotheses which are more general in scope and better able to explain the limited data available.

With the notable exception of Lintner, the comparative statics of security risk premiums in a mean-variance context has received sparse rigorous treatment in the published literature.' Lintner examines the implications of changing the number of individuals in the market, changing present market wealth, and redistributing wealth. Most of his analysis, however, is hampered by the unrealistic assumption of constant absolute risk aversion, failure to consider simultaneously several types of comparative statics changes, and an exogenous specification of a fixed risk-free rate of return. This essay attempts to remedy these deficiencies. In Section I, applying the mean-variance security valuation model developed formally in the Appendix, I isolate useful categories of comparative statics influences which have clear analogies in the more traditional capital theory under certainty. In Section II, "relative" risk premiums (ratios of one plus the expected rate of return on a portfolio to one plus the risk-free rate) are shown to depend on per capita wealth and social attitudes toward risk. For the special case of constant proportional risk aversion, single-period spot-rate relative risk premiums are constant over time, even with changes in population and changes in social wealth. In Sfction III, alternative definitions of the "market price of risk" and market measures of risk are compared on the basis of their comparative statics implications. The theoretical basis for many of the contributions of this essay is provided in the Appendix, in which the general relationship between the "market price of risk" and an aggregation of individual measurable utility functions is derived, assuming either normal probability distributions for security returns or quadratic utility. This new theorem motivates brief comments on measures of risk aversion and mean-variance efficiency analysis.

i. The futures price of a commodity is so closely connected with expectations as to its price in the future, that it is possible to make an estimate of how accurate these expectations are. The significance of such an estimate, however, can only be appreciated if the structure of prices in a futures market is understood. This structure is somewhat complicated. The price of every futures contract must satisfy the two conditions expressed in the following equations: (i) FP CP i + c'q (ii) EPFP= r where CP is the current or spot price of the commodity, FP is the price of the futures contract with a certain period to run before maturity,1 i and c' are the marginal interest and carrying charges for holding stocks for this period, and q is the marginal yield in convenience from holding stocks of this size for this period; and where EP is the representative expected price, and r the market risk premium. 2. A fuller discussion of these equations will be found in recent numbers of the Review of Economic Studies.2 There it was shown that the risk premium might take a negative sign either (i) if the risks that were to be hedged were predominantly negative risks, i.e. the sort of risks a man would face who had sold forward more than he owned; or (ii) if, when there was both buying and selling of futures by speculators, the bears were more averse to bearing risks than the bulls, and sufficiently so to outweigh the riskaversion of the hedgers. In a futures market for a raw

The purpose of this note is to demonstrate that the explicit introduction of consumption patterns alters the traditional relationship between expected return and variance presented by Markowitz, Tobin, Sharpe, Lintner, and others. Diversification, reducing risk by lowering the variance of the expected income, is the cornerstone of traditional capital asset value theory. Consumption is introduced as one undifferentiated commodity. However, income serves to satisfy consumption, and there are as many assets generating income as there are goods and services satisfying wants. The problem is, therefore, whether in a world of uncertainty the pattern of future expenditures should be considered in selecting investors' portfolios, even in a world of no transaction costs. The presumption here is that there is specialization in consumption (as well as in production) and that investors have different patterns of consumption expenditures. Consumers do not "consume" in general, but rather they consume specific goods and services, In other words, introducing expenditures on more than one asset raises the problem of different tastes and elasticities of demand, both with respect to price and income. These elasticities, for a given product, vary from person to person and with income, hence, there are two sources for risk-one resulting from uncertain prices and one due to uncertain income.

This paper reports the results of a simulation study undertaken to examine the validity of constant elasticity estimates. In the past decade there have been statistical studies almost too numerous to mention which have attempted to explain some aggregate aspect of money, income, interest, credit, liquidity, or the like; these are sometimes loosely categorized as "demand for money" studies. In many of these studies constant elasticity estimates are computed, and are used as the basis for policy recommendations. (Some examples are [4; 7; 8].) In addition, such methodology has been employed to estimate the cost of the draft [1], risk premiums on corporate bonds [2], industrial expansion in the nineteenth century [3], rates of return on production functions [6], etc. It is our purpose to illustrate that constant elasticity estimates are valid only for a special case (as everyone who has studied intermediate price theory knows but forgets), and to show the range of actual elasticities for various functional forms where the constant elasticity assumption does not hold. In addition, the accuracy of the estimation of (actually) constant elasticities based on logarithmic transformation is examined.

One of the problems which has plagued thouse attempting to predict the behavior of capital marcets is the absence of a body of positive of microeconomic theory dealing with conditions of risk/ Althuogh many usefull insights can be obtaine from the traditional model of investment under conditions of certainty, the pervasive influense of risk in finansial transactions has forced those working in this area to adobt models of price behavior which are little more than assertions. A typical classroom explanation of the determinationof capital asset prices, for example, usually begins with a carefull and relatively rigorous description of the process through which individuals preferences and phisical relationship to determine an equilibrium pure interest rate. This is generally followed by the assertion that somehow a market risk-premium is also determined, with the prices of asset adjusting accordingly to account for differences of their risk.

The general concern of Professor Horrigan's paper is said to be the investigation of the utility of accounting data in long-term credit administration, where the major problem is the determination of default risk on bonds. The specific question which he attempts to answer, however, is whether or not one year's financial data, viewed primarily in ratio form, can be used to predict corporate bond ratings. Because this question is rather limited in scope, at least relative to Horrigan's general concern, it seems appropriate to begin my comments by examining the logic which led him to choose it. On page 45, Professor Horrigan states that the ideal independent variable in a study of default risk would be "a measure which could be scaled on a continuum ranging from certain repayment through certain default." He then comments, however, that "such a variable obviously does not exist." Few, if any, students of the bond market would seriously question this last statement. However, it does not follow that all of them would immediately agree that the best possible surrogate measure of default risk is bond ratings. (I realize, of course, that Professor Horrigan does not say ratings are the best possible surrogate, but it also seems reasonable to assume that he regards them as a better surrogate than others which might just as easily have been used.) I would suggest, however, that an alternative and perhaps better measure of default risk might be bond yields themselves, or the risk premium on bonds, that is, the difference between bond yields and yields or long-term, default-free treasuries. After all, the market is assessing default risk too, and its assessments are considerably more continuous than those made by Moody's. I hasten to add that my remarks are not meant to imply that bond ratings are

the existing theory by establishing the economic significance of the partial relative risk aversion function. Let u(t) be a utility function for wealth. The functions A(t) = -u"(t)/u'(t) and R(t) -tu"(t)/u'(t) are the Arrow-Pratt absolute and relative risk aversion functions. The importance of A(t) arises when considering an individual's aversion to risk as wealth is varied but the risk remains unchanged, while R(t) becomes relevant when wealth and the risk are changed in the same proportion. We shall demonstrate that the partial relative risk aversion function P(t; w) = -tu"(t + w)/u'(t + w) is important when the risk is varied but wealth w remains fixed. In addition, we indicate the economic relationships between the functions A, R, and P; present some results about the behavior of P; and relate its behavior to that of A and R. The analysis in this paper is based on Pratt's risk premium which we feel is the only function which actually measures risk aversion for arbitrary risks.2 Our analysis differs from that of both Arrow and Pratt in that we do not use "infinitesimal" risks. Arrow and Pratt interpret A and R as "local" measures of absolute and relative risk aversion. The results of this paper show that the functions A, R, and P have a significance beyond their interpretation as "local" measures of risk aversion in that they determine the behavior of the risk premium in different comparative static contexts. In Section 2 basic concepts are briefly discussed. Section 3 contains our main results. In it the economic significance of A, R, and the new function P is established through their relationship with the risk premium, and we show how the behavior of these functions is relevant for the theory of risk aversion. Section 4 contains a comparison of our results with those of Arrow and Pratt, and indicates the usefulness of A, P, and R. for comparative static analysis of expected utility maximization models.

This paper reports in succinct form the findings of a study undertaken a number of years ago that sought to measure the relation between risk and rate of return and, thus, to determine an empirical basis for implementing several Supreme Court decisions (Bluefield Waterworks Case, 1923, for one) that a public utility is entitled to earnings sufficient to permit its rate of return on invested capital to be similar to those in "other business undertakings which are attended by corresponding risks and uncertainties." Defining "business" risk as functionally related to the variability of earnings, a number of hypotheses concerning rate of return and risk are tested statistically, and a reasonable and significant association is discovered between them for both a sample of industries and individual companies. The statistical model, however, explains only about a quarter of the variability in rates of return among industries and firms, suggesting that it has not captured some important determinants of business risk. The final section examines our results in the light of recent developments in the theory of financial risk.

This paper concerns utility functions for money. A measure of risk aversion in the small, the risk premium or insurance premium for an arbitrary risk, and a natural concept of decreasing risk aversion are discussed and related to one another. Risks are also considered as a proportion of total assets.

This paper compares several insurance experience variables under two major types of rating laws for five kinds of insurance in eleven states. Two major purposes of the article are to attempt to validate insurer opinions about rate regulation in these states and to help fill an empirical gap in the literature on the subject. For comparative purposes, t:he rating laws were classified as either (1) can use before filing, or (2) cannot use before filing. Although rate levels appear to have been more adequate in the CU states, it is dangerous to generalize as to the degree to which this would be true if more states were included in this category. Differences among individual states within the CNU group were considerably greater than those between the averages for the two groups of states. Thus it appears that the administration of the rating laws and other factors may be more significant than the type of law, per se. Nonetheless, the CU states generally had lower percentages of assigned risk premiums, less market penetration for major bureau affiliates, but greater overall market concentration and receptiveness to product innovation. With the trend to more liberal rating laws, the regulator's prime concem may be the prevention of monopolies. Representatives of fire and casualty insurers frequently have maintained that Gerald R. Hartman, Ph.D., F.C.A.S., C.P.C.U., C.L.U., is Associate Professor of Insurance at Temple University. This paper was submitted in February, 1969. The author wishes to acknowledge the support of the Cooperative League of the United States of America, including the folowing companies: Desjardins Mutual Life Insurance Company, Mutual Service Insurance Company, Cooperators Insurance Association, Co-operative Insurance Services, Ltd., La Societe d'Assurance des Caisses Populaires, Nationwide Insurance Company, and Leaguie Life Insurance Company. In addition, he desires to express his gratitude to the National Bureau of Casualty Underwriters, the Insurance Company of North America, the National Association of Independent Insurers and the University of Pennsylvania for their help with this study. The author acknowledges the computational assistance provided by Ed Rappaport, Tom Beam and Paul Eldridge, graduate students at the University of Pennsylvania. Finally, he expresses his appreciation to the State Insurance Departments that responded to his questionnaire and provided additional information as it was reauested. the type of rate regulatory law is a major determinant of insurance underwriting experience. Most persons familiar with the operation of rate regulation in the United States probably would concur, at first blush, with this view. There are so many factors which affect underwriting results, however, that after further reflection upon the subject one may wonder whether the type of rate regulatory law is a major determinant of undervriting results. Underwriting losses, especially in automobile liability insurance, have been attributed to the fact that insurance rates generally require prior approval by insurance departments before they may be used. Yet, to the writer's knowledge, only Mark Kai-Kee of the California Insurance Department has published data which specifically relate rating laws and underwriting results. Mr. Kai-Kee compared California and countywide loss ratios to

In a number of recent papers [11] [12],2 it has been shown that, for the United States, the behaviour of the term structure of interest rates can be explained remarkably well by combining the "Preferred Habitat" version of the Expectation Theory with a simple and readily tractable model of the formation of expectations, a model in which expected future rates are represented by a linear function of past rates. The purpose of the present paper is to generalize that approach and to strengthen the evidence supporting it in two major directions. First, we endeavour to broaden and refine the earlier analysis by making proper allowance for one additional factor, which is entirely consistent with the spirit of the model but was not duly taken into account, namely the effect of expectations of future changes in the price level. Evidence is provided that this additional factor is empirically important and that by allowing for it one can obtain a significant improvement in fit as well as a reduction in the serial correlation of the residual error. Some further improvement can also be achieved by introducing a variable intended to measure the effect of changes in the uncertainty about the future course of interest rates on the risk premium. Our second goal is to provide independent evidence in support of both the expectation theory and of our model of expectation formation and of the determinants of the risk premium, by exploring the relation between our model and the "rational expectation hypothesis". To this end we first derive expressions for the "optimal" (in the least square sense) linear forecast of all future rates, conditional upon the past history of rates of interest and rates of inflation. We show that the relation between the long rate and the history of short rates and prices which is estimated in the process of fitting our term structure equation is broadly similar to the relation that would hold if, in fact, (1) the long rate were an average of expected future rates-as called for by the expectation hypothesis-and (2) the expected future rates tended to represent optimal forecasts-as called for by the rational expectation hypothesis. These results provide strong evidence in support of both hypotheses, and of our term structure model built on them. Further