The demand for index bonds by households is studied in an inter-temporal optimization model in which households can choose a portfolio consisting of equity, nominal bonds, and index bonds. The rate of inflation is uncertain. In a setting where all income is from capital gains, it is shown that index bonds command a premium over nominal bonds only if equity is not a hedge against inflation; it is also shown that, if there are homogeneous expectations and no outside bonds, all lending and borrowing will be through index bonds with no nominal bonds existing. These conclusions are modified when individuals have income from human capital. The very stringent conditions under which a single index bond provides the household with the same utility as a full set of futures markets are examined in a model with many consumption goods.

The Demand for Index Bonds

The question 'when is a random variable Y riskier or more variable than another random variable X ?' has recently been answered in the literature in a manner that is consistent with expected utility theory This paper provides a similarly natural and theoretically sound definition for the statement that 'the random variables Y1 and Y2 are more correlated or positively interdependent than the random variables X1 and X2' The usefulness of the definition is demonstrated by applying it to the determination of the effects of increased correlation on behaviour in some standard economic models Correlation generalisee croissante: une definition et quelques implications economiques Recemment on a pu repondre a la question 'quand une variable aleatoire Y est-elle plus aleatoire ou plus variable qu'une variable al6atoire X?' d'une fagon qui est consistente avec la theorie de l'utilite basee sur l'esperance math6matique Ce memoire veut construire une definition tout aussi naturelle et theoriquement robuste pour la proposition 'les variables al6atoires Y, et Y2 sont davantage co-reliees ou davantage positivement interdependantes que les variables aleatoires X1 et X2' Les auteurs montrent l'utilite de cette d6finition en l'appliquant a la calibration des effets d'une correlation plus grande sur le comportement dans des modeles economiques conventionnels The question 'when is a random variable Y riskier or more variable than another random variable X?' has been answered in the literature in a manner consistent with expected utility theory (see for example Hanoch and Levy, 1969; Hadar and Russell, 1969; and especially Rothschild and Stiglitz (RS), 1970) These papers consider only scalar random variables (see, however, Brumelle and Vickson, 1975, and the references therein) Once the analysis is extended to a multivariate, and in particular a bivariate, framework it seems reasonable to ask whether a similarly natural and theoretically sound definition may be provided for the statement that 'the random variables Y1 and Y2 are more correlated (positively interdependent or interrelated) than the random variables X1 and X2' The research described in this paper was supported in part by grants from the Canada Council and the National Research Council This paper was presented at the Canadian Economic Theory Conference, Montreal, May 1978 Canadian Journal of Economics / Revue canadienne d'Economique, XIII, no I February / fevrier 1980 Printed in Canada / Imprime au Canada 0008-4085 / 80 / 0000-0016 $0150 / ?) 1980 Canadian Economics Association This content downloaded from 1575539138 on Sun, 26 Jun 2016 05:55:14 UTC All use subject to http://aboutjstororg/terms Increasing generalized correlation / 17 The formulation and theoretical justification of such a definition is the objective of the first part of this paper In the second part we demonstrate the usefulness of the definition by applying it to the determination of the effects of increased correlation on behaviour in some standard economic models The structure and approach of the first part are similar to those of RS We proceed as follows: the key notion of an elementary correlation increasing transformation (CIT) of a given bivariate probability distribution is defined and is used to motivate the first definition of greater correlation The CIT iS then used to define correlation-averse and correlation-affine utility functions They in turn are used to formulate the following plausible alternative definition of greater correlation: Y1 and Y2 are more correlated than X1 and X2 if all expected utility-maximizers who are correlation averters (lovers) prefer (disprefer) (X1, X2) to (Y1, Y2) The third section proves that the above two definitions of greater correlation are equivalent, and the fourth section compares them with others used in the literature In particular, we point out the limited theoretical validity of the linear (Pearsonian) correlation coefficient or the covariance as measures of the positive interdependence of two random variables Many of the notions and results described may be found in scattered references in the literature One contribution of this paper is to bring them into focus as the essential components of a natural and theoretically sound definition of greater correlation In addition, we feel that our approach to Theorem 6, via elementary correlation-increasing transformations, provides further insight and a new perspective regarding the definition of greater correlation The second part contains a more extensive analysis of the effects of increased correlation in an expected-utility framework than may be found in existing literature Portfolio diversification is discussed first, and then the analysis of portfolio diversification is extended to the case where future consumption good prices, as well as asset returns, are uncertain The use of an asset as a hedge against uncertain inflation is considered Finally, we analyse the effects of correlated price expectations in a two-period model of the behaviour of a competitive firm Proofs of the principal theorems in the text are collected in an appendix Proofs of most of the remaining theorems may be found in Epstein and Tanny (1978)

Increasing Generalized Correlation: A Definition and Some Economic Consequences

This paper is a review of the foundations and current state of mean-variance capital market theory. This work, whose foundations lie in the mean-variance portfolio model of Markowitz, deals with determination of the prices of capital assets under conditions of uncertainty. The Sharpe-Lintner capital asset pricing model which forms the core of this body of literature is an investigation of the implications of the normative Markowitz model for the equilibrium structure of asset prices. The essential characteristics of these models are reviewed along with the current state of the empirical evidence bearing on them. Many of the recent extensions of the theory are also reviewed and some attempt is made to integrate these extensions with the currently available empirical evidence.

Capital Markets: Theory and Evidence

WE ARE MEETING at a time when few matters are of more serious concern to students of finance and to members of the financial community than the impacts of inflation on our financial institutions and markets and its implications for investment policy. The evidence now available clearly indicates that substantial modifications and major new developments in our generally accepted models of security returns and capital market equilibria are going to be required to deal effectively with the impacts of inflation on our markets. The bulk of this address will be devoted to reviewing some of this evidence and suggesting some of the indicated modifications in our by-now conventional models and analytical frameworks. I will also advance some new theory which explains observed relations between inflation and equity market prices and returns, identify further effects of inflation on security markets and financial behavior, and suggest directions for further research on these issues. It will be useful, however, to view these further advances in our work in the perspective of a brief review of a few of the major landmarks in the development of our discipline. Although most of these basic earlier advances have not dealt specifically with inflation, they have provided a set of analytical frameworks and insights which form an essential base from which to develop a more probative understanding and analysis of the effects of inflation. Additional perspective comes from observing that-even though many of our central models and propositions as they stand are indeed seriously incomplete and biased, if not positively misleading, with respect to the impact of inflation on security returns-this earlier work has otherwise made very substantial and important advances in our understanding of financial markets and had a constructive impact on financial management and decision-making which should not be overlooked as we emphasize the need for further developments.

Inflation and security returns

Stock prices, inflation, and the term structure of interest rates

Financial assets produce no consumption goods. They cannot be used to satisfy such human desires as food or shelter. Instead, their value stems from claims on future consumption. As these claims fluctuate ln expected magnitude, in risk of being satisfied, and in the time until fulfillment, asset prices also vary. That much economists and men of affairs take for granted. But the precise relations between asset prices and individual expectations, risk preferences, and time preferences are not well understood. Economic tradition has assigned to financial assets the quality of"value storage." Money has received additional credit as a "medium of exchange," that is, a completely "liquid" asset; but both characteristics can be subsumed under the phrase, "claim on consumption." For example, the "liquidity" value of a currency arises from its immediate recognition.l C)ne can easily verify this by noting the differences in waiter response when paying for lunch with dongs in New York and Hanoi; or,

Assets, Money, and Commodity Price Inflation under Uncertainty

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Assets, Money, and Commodity Price Inflation under Uncertainty