Estimating the stochastic discount factor without a utility function

Using the Pricing Equation in a panel-data framework, we construct a novel consistent estimator of the stochastic discount factor (SDF) which relies on the fact that its logarithm is the serial-correlation ìcommon featureîin every asset return of the economy. Our estimator is a simple function of asset returns, does not depend on any parametric function representing preferences, is suitable for testing di§erent preference speciÖcations or investigating intertemporal substitution puzzles, and can be a basis to construct an estimator of the risk-free rate. For post-war data, our estimator is close to unity most of the time, yielding an average annual real discount rate of 2.46%. In formal testing, we cannot reject standard preference speciÖcations used in the literature and estimates of the relative risk-aversion coe¢ cient are between 1 and 2, and statistically equal to unity. Using our SDF estimator, we found little signs of the equity-premium puzzle for the U.S.

Options listing and the volatility of the underlying asset: a study on the derivative market function

Os mercados de derivativos são vistos com muita desconfiança por inúmeras pessoas. O trabalho analisa o efeito da introdução de opções sobre ações no mercado brasileiro buscando identificar uma outra justificativa para a existência destes mercados: a alteração no nível de risco dos ativos objetos destas opções. A evidência empírica encontrada neste mercado está de acordo com os resultados obtidos em outros mercados - a introdução de opções é benéfica para o investidor posto que reduz a volatilidade do ativo objeto. Existe também uma tênue indicação de que a volatilidade se torna mais estocástica com a introdução das opções.

Local concavifiability of preferences and determinacy of equilibrium

In this paper we consider strictly convex monotone continuous complete preorderings on R+n that are locally representable by a concave utility function. By Alexandroff 's (1939) theorem, this function is twice dífferentiable almost everywhere. We show that if the bordered hessian determinant of a concave utility representation vanishes on a null set. Then demand is countably rectifiable, that is, except for a null set of bundles, it is a countable union of c1 manifolds. This property of consumer demand is enough to guarantee that the equilibrium prices of apure exchange economy will be locally unique, for almost every endowment. We give an example of an economy satisfying these conditions but not the Katzner (1968) - Debreu (1970, 1972) smoothness conditions.

Equity-premium puzzle: evidence from Brazilian data

This paper uses 1992:1-2004:2 quarterly data and two di§erent methods (approximation under lognormality and calibration) to evaluate the existence of an equity-premium puzzle in Brazil. In contrast with some previous works in the Brazilian literature, I conclude that the model used by Mehra and Prescott (1985), either with additive or recursive preferences, is not able to satisfactorily rationalize the equity premium observed in the Brazilian data. The second contribution of the paper is calling the attention to the fact that the utility function may not exist if the data (as it is the case with Brazilian time series) implies the existence of states in which high negative rates of consumption growth are attained with relatively high probability.

A CAPM with higher moments: theory and econometrics

We develop portfolio choice theory taking into consideration the first p~ moments of the underIying assets distribution. A rigorous characterization of the opportunity set and of the efficient portfolios frontier is given, as well as of the solutions to the problem with a general utility function and short sales allowed. The extension of c1assical meanvariance properties, like two-fund separation, is also investigated. A general CAPM is derived, based on the theoretical foundations built, and its empirical consequences and testing are discussed

Dynamic hedging with stocastic differential utility

In this paper we study the dynamic hedging problem using three different utility specifications: stochastic differential utility, terminal wealth utility, and we propose a particular utility transformation connecting both previous approaches. In all cases, we assume Markovian prices. Stochastic differential utility, SDU, impacts the pure hedging demand ambiguously, but decreases the pure speculative demand, because risk aversion increases. We also show that consumption decision is, in some sense, independent of hedging decision. With terminal wealth utility, we derive a general and compact hedging formula, which nests as special all cases studied in Duffie and Jackson (1990). We then show how to obtain their formulas. With the third approach we find a compact formula for hedging, which makes the second-type utility framework a particular case, and show that the pure hedging demand is not impacted by this specification. In addition, with CRRA- and CARA-type utilities, the risk aversion increases and, consequently the pure speculative demand decreases. If futures price are martingales, then the transformation plays no role in determining the hedging allocation. We also derive the relevant Bellman equation for each case, using semigroup techniques.

A consumption CAPM with a reference level

We study an intertemporal asset pricing model in which a representative consumer maximizes expected utility derived from both the ratio of his consumption to some reference level and this level itself. If the reference consumption level is assumed to be determined by past consumption levels, the model generalizes the usual habit formation specifications. When the reference level growth rate is made dependent on the market portfolio return and on past consumption growth, the model mixes a consumption CAPM with habit formation together with the CAPM. It therefore provides, in an expected utility framework, a generalization of the non-expected recursive utility model of Epstein and Zin (1989). When we estimate this specification with aggregate per capita consumption, we obtain economically plausible values of the preference parameters, in contrast with the habit formation or the Epstein-Zin cases taken separately. All tests performed with various preference specifications confirm that the reference level enters significantly in the pricing kernel.

The polictical economy informed lobbies

We analize a discrete type version of a common agency model with informed principals of Martimort and Moreira (2005) in the context of lobby games. We begin discussing issues related to the common values nature of the model, i.e.the agent cares directly about the principal’s utility function. With this feature the equilibrium of Martimort and Moreira (2005) is not valid. We argue in favor of one solution, although we are not able to fully characterize the equilibrium in this context. We then turn to an application: a modification of the Grossman and Helpman (1994) model of lobbying for tariff protection to incoporate assimetric information (but disconsidering the problem of common values) in the lobbies objective function. We show that the main results of the original model do not hold and that lobbies may behave less agressively towards the police maker when there is private information in the lobbies valuation for the tariffs.

Assorted topics in monetary economics

Esta tese é uma coleção de quatro artigos em economia monetária escritos sob a supervisão do Professor Rubens Penha Cysne. O primeiro desses artigos calcula o viés presente em medidas do custo de bem-estar da inflação devido a não se levar em conta o potencial substitutivo de moedas que rendem juros, como depósitos bancários.[1] O segundo se concentra na questão teórica de se comparar os escopos dos tradicionais modelos money-in-the-utility-function e shopping-time através do estudo das propriedades das curvas de demanda que eles geram.[2] O terceiro desses trabalhos revisita um artigo clássico de Stanley Fischer sobre a correlação entre a taxa de crescimento da oferta monetária e a taxa de acumulação de capital no caminho de transição.[3] Finalmente, o quarto diz respeito à posição relativa de cada uma de seis medidas do custo de bem-estar da inflação (uma das quais é nova) em relação às outras cinco, e uma estimativa do erro relativo máximo em que o pesquisador pode incorrer devido a sua escolha de empregar uma dessas medidas qualquer vis-à-vis as outras.[4] This thesis collects four papers on monetary economics written under the supervision of Professor Rubens Penha Cysne. The first of these papers assesses the bias occuring in welfare-cost-of-inflation measures due to failing to take into consideration the substitution potential of interest-bearing monies such as bank deposits.[1] The second one tackles the theoretical issue of comparing the generality of the money-in-the-utility-function- and the shopping-time models by studying the properties of the demand curves they generate.[2] The third of these works revisits a classic paper by Stanley Fischer on the correlation between the growth rate of money supply and the rate of capital accumulation on the transition path.[3] Finally, the fourth one concerns the relative standing of each one of six measures of the welfare cost of inflation (one of which is new) with respect to the other five, and an estimate of the maximum relative error one can incur by choosing to employ a particular welfare measure in place of the others.[4] [1] Cysne, R.P., Turchick, D., 2010. Welfare costs of inflation when interest-bearing deposits are disregarded: A calculation of the bias. Journal of Economic Dynamics and Control 34, 1015-1030. [2] Cysne, R.P., Turchick, D., 2009. On the integrability of money-demand functions by the Sidrauski and the shopping-time models. Journal of Banking & Finance 33, 1555-1562. [3] Cysne, R.P., Turchick, D., 2010. Money supply and capital accumulation on the transition path revisited. Journal of Money, Credit and Banking 42, 1173-1184. [4] Cysne, R.P., Turchick, D., 2011. An ordering of measures of the welfare cost of inflation in economies with interest-bearing deposits. Macroeconomic Dynamics, forthcoming.

Alocação dinâmica ótima com momentos de ordem superior para a estratégia de carry trade

O objetivo do presente trabalho é verificar se, ao levar-se em consideração momentos de ordem superior (assimetria e curtose) na alocação de uma carteira de carry trade, há ganhos em relação à alocação tradicional que prioriza somente os dois primeiros momentos (média e variância). A hipótese da pesquisa é que moedas de carry trade apresentam retornos com distribuição não-Normal, e os momentos de ordem superior desta têm uma dinâmica, a qual pode ser modelada através de um modelo da família GARCH, neste caso IC-GARCHSK. Este modelo consiste em uma equação para cada momento condicional dos componentes independentes, explicitamente: o retorno, a variância, a assimetria, e a curtose. Outra hipótese é que um investidor com uma função utilidade do tipo CARA (constant absolute risk aversion), pode tê-la aproximada por uma expansão de Taylor de 4ª ordem. A estratégia do trabalho é modelar a dinâmica dos momentos da série dos logartimos neperianos dos retornos diários de algumas moedas de carry trade através do modelo IC-GARCHSK, e estimar a alocação ótima da carteira dinamicamente, de tal forma que se maximize a função utilidade do investidor. Os resultados mostram que há ganhos sim, ao levar-se em consideração os momentos de ordem superior, uma vez que o custo de oportunidade desta foi menor que o de uma carteira construída somente utilizando como critérios média e variância.

Tax filing choices for the household under separable spheres bargaining

If household choices can be rationalized by the maximization of a well defined utility function, allowing spouses to file individually or jointly is equivalent to offering the envelope of the two tax schedules. If, instead, household ’preferences’ are constantly being redefined through bargaining, the option to file separately may affect outcomes even if it is never chosen. We use Lundberg and Pollak’s (1993) separate spheres bargaining model to assess the impact of filing options on the outcomes of primary and secondary earners. Threat points of the household’s bargain are given for each spouse by the utility that he or she attains as a follower of a counter-factual off-equilibrium Stackelberg game played by the couple. For a benchmark tax system which treats a couple’s average taxable income as if it were that of a single individual, we prove that if choices are not at kinks, allowing couples to choose whether to file jointly or individually usually benefits the secondary earner. In our numeric exercises this is also the case when choices are at kinks as well. These findings are, however, quite sensitive to the details of the tax system, as made evident by the examination of an alternative tax system.

Testing consumption optimality using aggregate data

This paper tests the optimality of consumption decisions at the aggregate level taking into account popular deviations from the canonical constant-relative-risk-aversion (CRRA) utility function model-rule of thumb and habit. First, based on the critique in Carroll (2001) and Weber (2002) of the linearization and testing strategies using euler equations for consumption, we provide extensive empirical evidence of their inappropriateness - a drawback for standard rule- of-thumb tests. Second, we propose a novel approach to test for consumption optimality in this context: nonlinear estimation coupled with return aggregation, where rule-of-thumb behavior and habit are special cases of an all encompassing model. We estimated 48 euler equations using GMM. At the 5% level, we only rejected optimality twice out of 48 times. Moreover, out of 24 regressions, we found the rule-of-thumb parameter to be statistically significant only twice. Hence, lack of optimality in consumption decisions represent the exception, not the rule. Finally, we found the habit parameter to be statistically significant on four occasions out of 24.

Convexity in multidimensional mechanism design

The present article initiates a systematic study of the behavior of a strictly increasing, C2 , utility function u(a), seen as a function of agents' types, a, when the set of types, A, is a compact, convex subset of iRm . When A is a m-dimensional rectangle it shows that there is a diffeomorphism of A such that the function U = u o H is strictly increasing, C2 , and strictly convexo Moreover, when A is a strictly convex leveI set of a nowhere singular function, there exists a change of coordinates H such that B = H-1(A) is a strictly convex set and U = u o H : B ~ iR is a strictly convex function, as long as a characteristic number of u is smaller than a characteristic number of A. Therefore, a utility function can be assumed convex in agents' types without loss of generality in a wide variety of economic environments.

Reality check for volatility models

Asset allocation decisions and value at risk calculations rely strongly on volatility estimates. Volatility measures such as rolling window, EWMA, GARCH and stochastic volatility are used in practice. GARCH and EWMA type models that incorporate the dynamic structure of volatility and are capable of forecasting future behavior of risk should perform better than constant, rolling window volatility models. For the same asset the model that is the ‘best’ according to some criterion can change from period to period. We use the reality check test∗ to verify if one model out-performs others over a class of re-sampled time-series data. The test is based on re-sampling the data using stationary bootstrapping. For each re-sample we check the ‘best’ model according to two criteria and analyze the distribution of the performance statistics. We compare constant volatility, EWMA and GARCH models using a quadratic utility function and a risk management measurement as comparison criteria. No model consistently out-performs the benchmark.