Finding a maximum skewness portfolio - A general solution to three-moments portfolio choice

Considering the three first moments and allowing short sales, the efficient portfolios set for n risky assets and a riskless one is found, supposing that agents like odd moments and dislike even ones. Analytical formulas for the solution surface are obtained and important geometric properties provide insights on its shape in the three dimensional space defined by the moments. A special duality result is needed and proved. The methodology is general, comprising situations in which, for instance, the investor trades a negative skewness for a higher expected return. Computation of the optimum portfolio weights is feasible in most cases.

Do higher moments really matter in portfolio choice?

We present explicit formulas for evaluating the difference between Markowitz weights and those from optimal portfolios, with the same given return, considering either asymmetry or kurtosis. We prove that, whenever the higher moment constraint is not binding, the weights are never the same. If, due to special features of the first and second moments, the difference might be negligible, in quite many cases it will be very significant. An appealing illustration, when the designer wants to incorporate an asset with quite heavy tails, but wants to moderate this effect, further supports the argument.

Introducing higher moments in the CAPM: some basic ideas

We show how to include in the CAPM moments of any order, extending the mean-variance or mean-variance-skewness versions available until now. Then, we present a simple way to modify the formulae, in order to avoid the appearance of utility parameters. The results can be easily applied to practical portfolio design, with econometric inference and testing based on generalised method of moments procedures. An empirical application to the Brazilian stock market is discussed.

On certain geometric aspects of portfolio optimisation with higher moments

We discuss geometric properties related to the minimisation of a portfolio kurtosis given its first two odd moments, considering a risk-less asset and allowing for short sales. The findings are generalised for the minimisation of any given even portfolio moment with fixed excess return and skewness, and then for the case in which only excess return is constrained. An example with two risky assets provides a better insight on the problems related to the solutions. The importance of the geometric properties and their use in the higher moments portfolio choice context is highlighted.

Apreçamento da assimetria idiossincrática no mercado brasileiro de ações

Recent papers in finance presented models in which the idiosyncratic skewness is a priced component of security returns. More specifically, stocks with high expected idiosyncratic skewness should have low expected returns. Boyer, Mitton and Vorkink (2009) showed that it actually happens in the American stock market. The goal of this thesis is to verify if this actually happens in the Brazilian stock market. The result, however, was different than expected: stocks with high expected idiosyncratic skewness have high expected returns. Among the possible explanations for this behavior are the difficult to predict idiosyncratic skewness and even failures in the construction of estimates of idiosyncratic skewness, which are calculated from the residuals of the Fama-French three-factor model.

Essays on regulation and risk

In this thesis, we investigate some aspects of the interplay between economic regulation and the risk of the regulated firm. In the first chapter, the main goal is to understand the implications a mainstream regulatory model (Laffont and Tirole, 1993) have on the systematic risk of the firm. We generalize the model in order to incorporate aggregate risk, and find that the optimal regulatory contract must be severely constrained in order to reproduce real-world systematic risk levels. We also consider the optimal profit-sharing mechanism, with an endogenous sharing rate, to explore the relationship between contract power and beta. We find results compatible with the available evidence that high-powered regimes impose more risk to the firm. In the second chapter, a joint work with Daniel Lima from the University of California, San Diego (UCSD), we start from the observation that regulated firms are subject to some regulatory practices that potentially affect the symmetry of the distribution of their future profits. If these practices are anticipated by investors in the stock market, the pattern of asymmetry in the empirical distribution of stock returns may differ among regulated and non-regulated companies. We review some recently proposed asymmetry measures that are robust to the empirical regularities of return data and use them to investigate whether there are meaningful differences in the distribution of asymmetry between these two groups of companies. In the third and last chapter, three different approaches to the capital asset pricing model of Kraus and Litzenberger (1976) are tested with recent Brazilian data and estimated using the generalized method of moments (GMM) as a unifying procedure. We find that ex-post stock returns generally exhibit statistically significant coskewness with the market portfolio, and hence are sensitive to squared market returns. However, while the theoretical ground for the preference for skewness is well established and fairly intuitive, we did not find supporting evidence that investors require a premium for supporting this risk factor in Brazil.

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.

CAPM estendido para momentos superiores : um teste empírico

A inclusão de momentos superiores no apreçamento de ativos do modelo CAPM vem sendo bastante discutido nas últimas décadas. Esse trabalho realiza um teste empírico para o modelo CAPM estendido para os 3o e 4o momentos, no qual as assimetrias e curtoses dos ativos também são apreçadas. O teste foi realizado utilizando o Método Generalizado dos Momentos (MGM), em que todas as condições de momento derivam do modelo teórico. Os dados utilizados foram os retornos diários das ações mais negociadas na Bovespa entre 2004 e 2006.

Measuring core inflation as the common trend of prices

In recent years, many central banks have adopted inflation targeting policies starting an intense debate about which measure of inflation to adopt. The literature on core inflation has tried to develop indicators of inflation which would respond only to "significant" changes in inflation. This paper defines a measure of core inflation as the common trend of prices in a multivariate dynamic model, that has, by construction, three properties: it filters idiosyncratic and transitory macro noises, and it leads the future leveI of headline inflation. We also show that the popular trimmed mean estimator of core inflation could be regarded as a proxy for the ideal GLS estimator for heteroskedastic data. We employ an asymmetric trimmed mean estimator to take account of possible skewness of the distribution, and we obtain an unconditional measure of core inflation.

On impatience, education, returns, and inequality

In this paper we investiga te the impact of initial wealth anel impatience heterogeneities, as wcll as differential access to financia! markets on povcrty anel inequality, anel cvaluate some mechanisms that could be used to alleviate situations in which these two issues are alarming. To address our qucstion we develop a dynamic stochastic general cquilibrium modo! of educational anel savings choicc with heterogeneous agents, where individuais differ in their initial wealth anel in their discount factor. We find that, in the long run, more patient households tend to be wealthier anel more educated. However, our baseline model is not able to give as much skewness to our income distribution as it is rcquircd. We then propose a novel returns structure based on empírica! observation of heterogeneous returns to different portfolios. This modification solves our previous problem, evidencing the importance of the changes made in explaining the existing levels of inequality. Finally, we introducc two kinds of cash transfers programs- one in which receiving thc benefit is conditional on educating the household's youngster (CCTS) anel one frec of conditionalities (CTS) - in order to evaluate the impact of these programs on the variables of concern1 Wc fine! that both policies have similar qualitativo rcsults. Quantitatively, howcvcr, the CCTS outperforms its unconclitional version in all fielcls analyzecl, revealing itself to be a preferable policy.

Dois ensaios em finanças

In the first chapter, we test some stochastic volatility models using options on the S&P 500 index. First, we demonstrate the presence of a short time-scale, on the order of days, and a long time-scale, on the order of months, in the S&P 500 volatility process using the empirical structure function, or variogram. This result is consistent with findings of previous studies. The main contribution of our paper is to estimate the two time-scales in the volatility process simultaneously by using nonlinear weighted least-squares technique. To test the statistical significance of the rates of mean-reversion, we bootstrap pairs of residuals using the circular block bootstrap of Politis and Romano (1992). We choose the block-length according to the automatic procedure of Politis and White (2004). After that, we calculate a first-order correction to the Black-Scholes prices using three different first-order corrections: (i) a fast time scale correction; (ii) a slow time scale correction; and (iii) a multiscale (fast and slow) correction. To test the ability of our model to price options, we simulate options prices using five different specifications for the rates or mean-reversion. We did not find any evidence that these asymptotic models perform better, in terms of RMSE, than the Black-Scholes model. In the second chapter, we use Brazilian data to compute monthly idiosyncratic moments (expected skewness, realized skewness, and realized volatility) for equity returns and assess whether they are informative for the cross-section of future stock returns. Since there is evidence that lagged skewness alone does not adequately forecast skewness, we estimate a cross-sectional model of expected skewness that uses additional predictive variables. Then, we sort stocks each month according to their idiosyncratic moments, forming quintile portfolios. We find a negative relationship between higher idiosyncratic moments and next-month stock returns. The trading strategy that sells stocks in the top quintile of expected skewness and buys stocks in the bottom quintile generates a significant monthly return of about 120 basis points. Our results are robust across sample periods, portfolio weightings, and to Fama and French (1993)’s risk adjustment factors. Finally, we identify a return reversal of stocks with high idiosyncratic skewness. Specifically, stocks with high idiosyncratic skewness have high contemporaneous returns. That tends to reverse, resulting in negative abnormal returns in the following month.