It is shown that the class of elliptical distributions extend the Tobin [14] separation theorem, Bawa's [2] rules of ordering uncertain prospects, Ross's [12] mutual fund separation theorems, and the results of the CAPM to non-normal distributions, which are not necessarily stable. Further, the mean-covariance matrix framework is generalized to a mean-characteristic matrix framework in which the characteristic matrix is the basis for a spread or risk measure, and a generalized equilibrium pricing equation is arrived at. The implications to empirical testing of the CAPM and modeling the empirical distribution of speculative prices are discussed. THE PURPOSE OF THIS paper is to describe the class of elliptical distributions and delineate their relevance to portfolio theory and its empirical applications. The class of elliptical distributions contains the multivariate normal (multinormal, henceforth) distribution as a special case; as well as many non-normal multivariate distributions including the multivariate Cauchy, the multivariate exponential, a multivariate elliptical analog of Student's t-distribution (the multivariate t, henceforth1), and non-normal variance mixtures of multinormal distributions. We show that some of the general characteristics of all members in the class of elliptical distributions make them admissible candidates for generalizing the theory of portfolio choice and equilibrium in capital asset markets, as well as attractive alternatives for use in empirical studies. More specifically, elliptical distributions are characterized by two parameters and extend the Tobin's [14] separation theorem, Bawa's [2] rules of ordering uncertain prospects, Ross's [13] mutual fund separation theorems, and the results of the CAPM to non-normal distributions, which are not necessarily stable. The definitions and properties of elliptical distributions are in Section I. The main results are in Section II and the importance of elliptical distributions in empirical works is discussed in Section III. are greatly appreciated. Special thanks are extended to Stephen Brown for his comments and suggestions. Errors remain ours. 'This is the so called Dunnett-Sobel multivariate t; it is also called the central multivariate t; see Johnson and Kotz [9] p. 134. 2 This section relies on Kelker [10], Devlin et al., [6], and the references therein. 745 746 The Journal of Finance definite symmetric matrix. Then, a p-component random vector X = (X1, X2, *. . , Xp)' is said to be distributed elliptically, X e (A, Q): Definition (a) if and only if the characteristic function of X is of the form: EIEXP(it'X)} cx(t) = I(t'Qt)EXP(it'A); (E denotes the expectation operator, i = , and a prime denotes transpose, throughout). Thus, cx(t) depends only on the quadratic form t 'Q t. Definition (b) if and only if for all nonzero p-component scalar vectors a, all the univariate random variables a'X such that VAR(W'X) is constant, follow the same distribution.

It is shown that the class of elliptical distributions extend the Tobin [14] separation theorem, Bawa's [2] rules of ordering uncertain prospects, Ross's [12] mutual fund separation theorems, and the results of the CAPM to non‐normal distributions, which are not necessarily stable. Further, the mean‐covariance matrix framework is generalized to a mean‐characteristic matrix framework in which the characteristic matrix is the basis for a spread or risk measure, and a generalized equilibrium pricing equation is arrived at. The implications to empirical testing of the CAPM and modeling the empirical distribution of speculative prices are discussed.

Using a unique data set with detailed information on the derivative positions of upstream oil and gas firms during 1996–2008, we find that hedging intensity is positively related to factors that amplify chief executive officer (CEO) entrenchment and free cash flow agency costs. There is also robust evidence that hedging is motivated by the reduction of financial distress and borrowing costs, and that it is influenced by both intrinsic cash flow risk and temporary spikes in commodity price volatility. We present a comprehensive perspective on the determinants of corporate hedging, and the results are consistent with the predictions of the risk management and agency costs literatures.

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Building on theoretical asset pricing literature, we examine the role of market risk and the size, book‐to‐market (BTM), and volatility anomalies in the cross‐section of unlevered equity returns. Compared with levered (stock) returns, unlevered market beta plays a more important role in explaining the cross‐section of unlevered equity returns, even after controlling for size and BTM. The size effect is weakened, while the value premium and the volatility puzzle virtually disappear for unlevered returns. We show that leverage induces heteroskedasticity in returns. Unlevering returns removes this pattern, which is otherwise difficult to address by controlling for leverage in regressions.