Mean-variance Setting Research Articles

Mean-variance sets for dietary choice models: simplicity in a complex world

This paper presents a series of simulations designed to determine optimal diet breadth under shortfall avoidance models. Profitability and encounter rate functions were varied, and means and variances of energy intake rate were generated using a simple simulation procedure. The resulting mean-variance sets assumed three distinct shapes: u-shaped, arched, and looped. These simulations show that certain mean-variance sets allow the forager to employ simple behavioural rules to determine the optimal diet breadth. This situation occurs when low ranking diet items have small handling times, and these conditions may be quite common. In other cases, mean-variance sets may be too complicated to allow for easy behavioural rules designed to minimize starvation probability. The ability to characterize foraging problems into a limited series of mean-variance set types benefits workers examining the evolution and maintenance of foraging strategies, since these sets have clear implications for the ability of animals to develop simple behavioural rules. Unfortunately data are lacking on the profitability and encounter rate distributions animals face in nature.

Additive and multiplicative risk premiums with multiple sources of risk

Abstract This paper considers the risk premium for one risk when other background risk is present. In a mean-variance setting, we examine the conditions under which the risk premium will be negative. These conditions consider the variance of the considered risk in relation to the covariance of the considered risk with the background risk. We consider the cases of both multiplicative and additive risks. A breakdown of the total risk premium into several components is established by removing each source of risk consecutively. The case of multiplicative risks is shown to be quite different from the additive-risk case in that the individual's total willingness-to-pay for the removal of all risk on a sequential basis does not necessarily equal the willingness-to-pay for removal of all risk simultaneously.

DISCOUNTING THE COMPONENTS OF AN INCOME STREAM: REPLY

THE PURPOSE OF [1] was to define conditions, consistent with the expected utility maxim, under which a project's present value could be calculated by application of the income-component discounting notion first introduced in [7]. The anlaysis focused on an individual decision-maker and unfortunately did not consider the corporation with stock trading in a perfectly competitive market. Before turning to the implications of market environment for my results, let us first consider Turnbull's certain world counter-example from which he reasons that my additivity condition does not necessarily hold. One can see that if Turnbull were true to his analysis or to my assumption, that any individual may borrow or lend at a riskless rate without affecting that rate (see [1], p. 995, second paragraph), the U(C1, C2) preference function and his corresponding analysis are irrelevant to this discussion. For if one does allow borrowing and lending at a single interest rate in a certain world-the perfect market assumption, then clearly for any preference function that gives rise to convex indifference curves in (C1, C2) then Pz = Px + Py. To see this draw, the Fisher diagram (Figure 1) where the absolute slope of the market opportunity line is one plus the interest rate, i. Then starting at (C*, C*) it is clear that if the individual is promised an additional Z dollars in period 2 then the maximum price, Pz, that he would be willing to pay in period 1 is Z/(l + i), for he could obtain that trade-off in the market place. Identical reasoning leads to Px= X/(l + i) and Py = Y/(l + i), consequently Pz = Px + Py. My interpretation of the remainder of Turnbull's comment is that the calculation of a project's net present value should simply yield the additions to a firm's future equilibrium stock price and if the market values of the stock's risky component income streams are additive, as they are when equilibrium is represented by a complete set of Arrow-Debreu securities, or in a mean-variance setting with a riskless asset and homogeneous expectations, then additivity holds for the present values or prices of the project's risky income streams. These observations by Turnbull are clearly valid. The additivity principle in the context of a competitive stock market also holds true for heterogeneous expectations, given, of course, equal and costless access to all information by all potential investors. (c.f. [5], and [6].) The common thread connecting these results is that in perfectly competitive security markets all participants achieve efficient portfolio diversification, and therefore equilibrium prices will consequently reflect all possible gains from risk reduction. Since I was negligent in considering the impact of market conditions in deriving my conclusions, some statement should have been made regarding the implications for my results of that other type of market, an imperfect one. If a merger affects