Risky assets performance measures analysis: a study of potential investment, Sharpe ratio and generalized Sharpe ratio indexes. / Análise de medidas de desempenho de ativos de risco: um estudo dos índices de potencial de investimento, Sharpe e Sharpe generalizado

AUTOR(ES)
DATA DE PUBLICAÇÃO

2008

RESUMO

This master dissertation studies and compares the characteristics of Sharpe ratio and its variants, SRc and SRd, generalized Sharpe ratio (GSR) and investment potential (IP), both GSR and IP associated to any utility function. By the fact that GSR and IP are identical indexes, empiric tests were conducted between SRc and GSR. The indexes were evaluated theoretically under two different aspects: retrospective analysis, i.e., analyze the observed monthly log-returns, and prospective analysis, i.e., series to occur. Under prospective view, ex ante facto, SRc (Sharpe ratio with normal state variable) and SRd (Sharpe ratio with lognormal state variable), for being associated to the quadratic utility function, show the inherent problems to utility functions such as the bliss point and the pump money economic agent. The same happens in a retrospective view, ex post facto, with the GSR (performance potential with HARA utility function family) when the risk aversion coefficient equals minus one, gama=-1. Therefore, the GSR can be associated to different utility functions avoiding the undesirable effects. Under the GBM (geometric Brownian motion) condition and HARA utility function for the Brazilian and American adjusted monthly stock prices and indexes monthly points during January 2000 and March 2008, we reached the following: (1) results indicate that GSR for quadratic utility has high correlation level with SRc; (2) while the logarithmic utility showed lowest correlation level between GSR and SRc; (3) exponential utilities showed a high level of correlation between GSR and SRc. The results showed that GSR with exponential utility kept the biggest behavior difference for the GSR with quadratic utility. Based on the knowing problems of the quadratic utility, GSR with gama=1 seems to be a better index choice for risk assets classification.

ASSUNTO(S)

finanças investment potential fator de desconto estocástico função de utilidade sharpe ratio Índice de sharpe market price of risk finance investimentos teoria da utilidade risco utility theory pricing bandas do índice de sharpe Índice potencial de investimento preço do risco precificação risk Índice de sharpe generalizado utility function generalized sharpe ratio stochastic discount factor sharpe ratio bounds investment

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