Andreas Löffler

Two remarks on the uniqueness of equilibria in the CAPM

In the standard ‘capital asset pricing model’ (CAPM) with a riskless asset we give a sufficient condition for uniqueness. This condition is a joint restriction on the agents’ endowments and their preferences which is compatible with non-increasing absolute risk aversion and which is in particular satisfied with constant absolute risk aversion. Moreover, in the CAPM without a riskless asset we give an example for multiple equilibria even though all agents have constant absolute risk aversion.

A μ-σ-Risk Aversion Paradox and Wealth Dependent Utility

We report a surprising property of mu-sigma-preferences: the assumption of nonincreasing relative risk aversion implies the optimal portfolio being riskless. We discuss a solution of that paradox using wealth dependent utility functions in detail. Using the revealed preference theory we show that (general, i.e. not necessary mu-sigma) wealth dependent utility functions can be characterized by Walds axiom. Copyright 2001 by Kluwer Academic PublishersWe report a surprising property of μ-σ-preferences: the assumption of nonincreasing relative risk aversion implies the optimal portfolio being riskless. We discuss a solution of that paradox using wealth dependent utility functions in detail. Using the revealed preference theory we show that (general, i.e. not necessary μ-σ) wealth dependent utility functions can be characterized by Walds axiom.

The structure of the distributions of cash flows and discount rates in multiperiod valuation problems

In capital budgeting problems future cash flows are discounted using the expected one-period returns of the investment. In this paper we relate this approach to the assumption that markets are free of arbitrage. Our goal is to uncover implicit assumptions on the set of cash flow distributions that are suitable for the capital budgeting method. Our results are twofold. First we obtain that for deterministic cost of capital the set of admissible cash flow distributions is large in the sense that no particular structure of the evolution of the distributions is implied. We give stylized examples that demonstrate that even strong assumptions on the return distributions do not restrain the shape of the cash flow distributions. This shows that Famas assertion that the distributions of one_-period single returns become more and more skewed cannot be generalized to multi_period budgeting problems. Secondly, in a subsequent analysis we characterize the cash flow distributions under the additional assumption of a deterministic dividend yield. In this case a linear relationship between returns and cash flows obtains.

Do taxes matter in the CAPM

The traditional literature on the CAPM assumes that investor’s tax payments simply vanish from the model. This assumption is not at all consistent with the actual behavior of the Treasury. The theory of general equilibrium states that an interest rate rf = 0 will not affect prices if taxes are introduced. We show that this result can be extended to the CAPM if the tax payments are redistributed among investors.

Why Total Beta Produces Arbitrary Valuations: A Violation of the “No-Arbitrage” Principle

Meaningful evaluation equations must be in line with the no-arbitrage principle. If they are not, one can derive any company value from them. This is unacceptable both for practitioners and for academics. This paper shows that total beta does not meet the no-arbitrage principle.

Debreu's decomposition and aggregate demand functions

Abstract We investigate whether Debreu’s (Journal of Mathematical Economics, 1 (1974) 15–23) decomposition can be used to characterize aggregate demand functions f: R 2 ++ → R 2 + on an arbitrary compact set K⊂ R 2 ++ . It is shown that in a special case a necessary condition obtained by Sonnenschein/Shafer and Koch will be sufficient.