Little attention has been given to the behavior of option portfolio risk across different portfolio sizes, perhaps because many individuals view unhedged long option positions as too risky for rational investor consideration. It appears possible, however, to combine long option positions with less risky assets to produce portfolios with favorable risk-return characteristics [10].

The efficient estimation of econometric models with rational expectations by the substitution method usually entails the use of a non-linear simultaneous equations estimator and hence is not very attractive computationally. It is shown that for a wide class of problems efficient estimates can also be obtained with standard estimation methods if instead an errors in variables approach is used. For many other problems, although not providing fully efficient estimates because rationality is not imposed, the errors in variables method will still have a strong appeal because otherwise it uses all of the structural information in the model; unlike the substitution method, when an incomplete information set is used, it guarantees consistent estimates; and it is easy to compute.

It is often desirable to know whether or not a risky asset's beta coefficient has changed and, if so, at what point in time the change occurred. For example, this knowledge is of obvious importance to beta-using security analysts and portfolio managers. As another example, a given theory may imply that a particular firm's beta should have changed at different points in time. Investigators may want to test such a hypothesis. Furthermore, tests are frequently performed on the effects of events on residuals of the market model, tests requiring the assumption of beta stability. For these, and possibly other reasons, it is useful to be able to detect that a change in beta did, in fact, take place as well as, in some instances, identifying the point in time at which the change took place.

A number of studies have compared the investment risk of various industries and of various individual corporations in developed countries (DCs). The purpose of this paper is to compare investment risk in DCs with less developed countries (LDCs). The variance of returns to investment in common stocks provides a natural measure of investment risk and will be used in this study. Studies in LDCs include work of Levy and Sarnat [12], [13]. Errunza [3], [4], and Lessard [11]. Levy and Sarnat and Errunza found low economy-wide investment risk on an average for LDCs (relative to DCs), with stock indices being used as surrogates for economy-wide risk. These results are not unambiguous, however, because there are probable difficulties due to infrequent trading and averaging in the broad market indices used in the above studies. Hence, we use a sample of the largest corporations that suffer little, if at all, from thin trading and/or averaging.

A consumer faces list prices for commodities, but can buy one at a discount. Discounts vary randomly between sellers. The number of quotations sought depends on list prices, search costs and wealth. This function is homogeneous of degree zero, and, provided some sufficient conditions are satisfied, is; increasing in wealth; decreasing in search cost; independent of the list price of the discounted commodity if indirect utility is multiplicatively separable; increasing in the list price if the commodity is a necessity; increasing in the list price of substitutes. Slutsky's equation is generalized to include search.

This analysis suggests several distinctive policy recommendations about environmental problems. One is that some of the alarms about ecological catastrophes cannot simply be dismissed, even when some of those who sound the alarms seem almost fanatic. The information needed to be sure one way or another is simply lacking, and may not be attainable at reasonable cost for a long time. We are therefore left with inevitable risk. Ecological systems could also be incomparably more robust than the alarmists claim, so we might also be worrying needlessly. The implication for environmental and ecological research is that we should not exprect that it will produce conclusive information, but should fund a lot of it anyhow. If previous research has produced few compelling results, valid information about these problems is scarce and therefore more valuable. The harvest of research in the areas characterized by indivisibilities is then poor but precious knowledge. If it is important to be able to change behavior quickly, when and if we finally get the information that the ecosystem can't take any more, then it is important that we have the open-mindedness needed to change our views and policies the moment decisive information arrives. Those who shout wolfmore » too often, and those who are sure there are no wolves around, could be our undoing.« less