| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 103 === Previous study found that uncertainty include risk and ambiguity. Researchers found that ambiguous measure can capture the variation of investor expectations regarding the underlying probability distribution of future stock returns. Ehsani, Krause and Lien (2013) proposed mean distance (MD) and Brenner and Izhakian (2012) provided four times the variance of the probability of loss during the month as omega. Baltussen, Bekkum and Grient (2013) proposed standard deviation of implied volatility during the month as VOV. These three measures are calculated based on normal distribution assumption. Many papers pointed out that return is not normal distributed, so our study extends normal distribution to fat-tailed t and lognormal distribution. Furthermore, we use the three ambiguous measures to predict the S&P 500 index returns and evaluate the prediction ability among them.
Modern portfolio theory focuses on the relationship between risk and return. This paper assumes that ambiguity can affect asset prices and test relationship between risk, ambiguity and return. We found that ambiguity has negative effect on return and risk mostly has negative effect on return. Ambiguity measure use t distribution or lognormal distribution on predicting return is better than normal distribution. Omega has the best prediction ability for S&P 500 index return. Additionally, the prediction ability for S&P 500 index return in this study is better than those for predicting individual stock returns in the studies of Brenner & Izhakian (2012) and Ehsani, Krause & Lien (2013).
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