Risky Returns Research Articles

A Comparative Study of Gini's Mean Difference and Mean Variance in Portfolio Analysis

Abstract:The methods traditionally used for comparing uncertain prospects are the mean variance and the stochastic dominance approaches. Yitzhaki has recently presented an alternative model based upon Gini's mean difference to compare uncertain prospects. The mean Gini model is similar in nature to the mean variance model in that it uses a two‐parameter statistic to describe the probability distribution of risky returns. Theoretically, the mean Gini model is consistent with the behaviour of investors under conditions of uncertainty for a wider class of probability distributions. Thus Gini's mean difference appears to be more adequate than variance as a measure of risk. This study firstly generated the mean Gini efficient frontier and secondly compared the mean variance efficient frontier with it. For the sample data employed, the mean variance model gave a very good approximation to the mean Gini model. Since the computational costs of the mean variance approach were a small fraction of those of the mean Gini approach, the theoretical advantage would not appear in this case to translate into a practical one.

Moral Hazard and Information Sharing: A Model of Financial Information Gathering Agencies

ABSTRACTWe propose a theory of information gathering agencies in a world of informational asymmetries and moral hazard. In a setting in which true firm values are certified by screening agents whose payoffs depend on noisy ex post monitors of information quality, the formation of information gathering agencies (groups of screening agents) is justified on two grounds. First, it enables screening agents to diversify their risky payoffs. Second, it allows information sharing. The first effect itself is insufficient despite the risk aversion of screening agents and the stochastic independence of the monitors used to compensate them.

Moral Hazard and Information Sharing: A Model of Financial Information Gathering Agencies

We propose a theory of information gathering agencies in a world of informational asymmetries and moral hazard. In a setting in which true firm values are certified by screening agents whose payoffs depend on noisy ex post monitors of information quality, the formation of information gathering agencies (groups of screening agents) is justified on two grounds. First, it enables screening agents to diversify their risky payoffs. Second, it allows information sharing. The first effect itself is insufficient despite the risk aversion of screening agents and the stochastic independence of the monitors used to compensate them.

Stochastic Dominance for Decreasing Absolute Risk Aversion

In recent years the expected-utility approach to decision making under risk has gained increasing acceptance among portfolio theorists. On the other hand, the mean-variance (MV) approach of Markowitz [13], which has dominated portfolio theory in the past, continues to enjoy great popularity. In MV theory, the investor is assumed to rank his preferences for risky returns solely in terms of their means and variances, with higher means and lower variances, being preferred. Tobin [20] showed that MV theory is consistent with expected utility theory in the special case of joint-normally distributed asset returns. The MV approach enjoys a ready acceptance among practitioners, and requires only modest informational and computational inputs. Perhaps its most attractive feature is its ability to decompose the overall portfolio problem into a sequence of much simpler problems: first, the “efficient” set of portfolios (which minimize variance for any given mean return) is calculated, and then the investor chooses one of the efficient portfolios in a manner consistent with his personal preferences. This efficient set is the same for all investors having the same mean-variance-covariance estimates of risky-asset returns, and can, in principle, be determined once and for all using parametric quadratic programming [12, 22] Despite these real advantages, the MV theory embodies certain problems of principle in the case of nonnormally distributed asset returns, and this fact has led to increasing emphasis on the presumably more rational expected-utility theory.

Certainty Equivalents and Timing Uncertainty

ing problems: the certainty equivalent method (CE), the risk-adjusted discount method (RAD) , and the probability distribution or Hillier-Hertz approach (PD, based on [4]). Each one of these methods evaluates the multiperiod stream of risky returns generated by an investment for given distributions of the returns 2 in each period. A common assumption for all three methods is the certainty of the occurrence of a given risky cash inflow (defined by its distribution) in a given time period. This assumption is probably derived from accounting practices. In references [8] and [9] the PD approach was generalized by removing the certain timing assumption. This paper examines the implications of random timing of cash returns within the framework of the better known CE method. There are many projects, in which it is clearly inappropriate to assume

A Note on Capital Gains Exemption and Risk Taking

In the August 1969 issue of this Journal, Stiglitz 1 has shown that a proportional tax on the asset alone (with no tax on the risky asset) will increase the demand for the risky asset if there is constant or increasing absolute risk aversion or, alternatively, if relative risk aversion is less than or equal to unity. Undoubtedly, this is a very restrictive result.2 In particular, if we take decreasing absolute risk aversion which, as we shall see, implies that the risky asset is a superior good as a reasonable behavioral postulate, Stiglitz's analysis does not provide any definite answer. In this note we modify the treatment of capital gains by asserting that the return on risky assets has two components a safe component (rL) and a pure capital gains (or loss) term (x). One possible way to conceptualize this idea is to refer to a bond that offers a known rate of return plus a liquidity premium in recognition of the uncertainty as to its end-of-period market value. Consequently, we examine the effects of exempting risky capital gains from taxation. Normally we would expect r1, the component of the risky return, to be at least as great as the return on the asset r. For generality, however, let us first consider the problem where r1 > r. In such a case, before-tax wealth W1 can be written as

Discussion of Auditor's Loss Functions Implicit in Consumption-Investment Models

I feel that Scott's paper is addressing a different type of problem than those presented previously at this conference. Others have been concerned with I consider technology issues, that is, how can auditor make better use of his resources? How can he bear less risk at same cost or bear same risk at a lower cost? But in all cases, auditor's loss function was taken as given, either explicitly or implicitly. Scott is addressing issue of what should this loss function be? In order to answer this question, we must consider role of auditor in society, his relationships with other actors in society, and technology is available to him. Scott suggests that we look at opportunity losses of a typical user due to auditor's errors, with hope that this loss function could be tied to a Bayesian approach to auditor's decisions. Of course, two researchers will seldom agree on exactly model is most appropriate, so I will not dwell on those model details that I could readily change if I were to try to implement model. Instead, I will point out three difficulties in Scott's approach that severely limit insights that I obtain from his analysis. Two difficulties have to do with model construction, third with approach in general. The first model construction problem arises because Scott includes only one risky asset. As pointed out in paper, the proportion of risky investment, kt, is very sensitive to specification of risky return, z, with result that loss function itself is also very sensitive. It would appear to me that proportion of wealth invested in an individual risky asset, and therefore loss function itself, would also be very sensitive to opportunities for user to diversify his portfolio. In fact, if we add a

Abstract--Valuation of Corporate Bonds, Leverage, and Security Yields

In recent capital-market equilibrium theories it has been customary to entertain the assumption that corporate bonds are riskless. Attention has therefore been directed to the valuation of shares, since it is trivial to deal with the valuation of bonds under the assumption of riskless bond yield. In order to study the effect of leverage on equity and bond yields at the equilibrium while removing the assumption of riskless bonds, one must first deal with a valuation model for risky bonds. Consequently, one must face the necessity of making explicit the stochastic relationships between the risky bond returns and the risky share returns. To do this, each firm decides a dollar amount to be paid to the bondholders at the end of a period during which it generates random gross yields. The total return to bondholders is a random variable since it is possible that a firm's gross yield may be less than the dollar amount promised, a case of default. The total return to shareholders as a random variable is therefore conditional upon the choice of the promised amount to the bondholders. In other words, the explicit stochastic relationships between the bond returns and share returns will be conditional upon the choice of promised returns to bondholders by all firms. Employing the usual assumptions found in the capital-market equilibrium theories and the negative exponential utility function of final wealth, the model then generates conditional equilibrium prices of bonds and shares, and the resulting conditional equilibrium leverage and expected yields.

Shifts to risk and reward.

The expected payoffs for the risky alternatives in a standard shift-to-risk experiment were investigated rather than controlled. As predicted, a significant shift to reward was found. The group expectations of the risky payoffs were higher than the means of the individual expectations. The shift to reward was significantly, but lowly, correlated with a cotemporaneous shift to risk. Implications of the shift to reward are discussed.