Many early empirical investigations of the standard two-moment CAPM pay attention to the natural implications that arise from the theory. For instance, investors should be only compensated for bearing the systematic covariance risk. The quantity of compensation is determined by the product of beta and the risk premium. However, Kraus and Litzenberger (1976) find that a measure of the co-skewness risk (the third moment of return distributions) can be used as a supplement to the covariance risk to explain individual stock returns. Sears and Wei (1988) emphasize that the ignorance of the co-skewness risk may bias the estimates in the tests for the risk-return trade-off. Fang and Lai (1997) find that investors are compensated by higher expected returns for bearing the systematic co-kurtosis risk (the fourth moment of return distributions), besides the systematic covariance and/or co-skewness risks.

    Focusing on the Taiwan stock market, one of the fast growing markets in Asia, this paper investigates the relationship between risk and returns. First, to justify the necessity to consider the higher-order moments in returns, we study distributional properties of market returns, using monthly return data from January 1974 to December 1998. We find that the distributional asymmetry in market returns is significant. Furthermore, skewness and (excess) kurtosis in returns are persistent through time. These two observations support the worthiness of introducing the impacts of higher-order moments in returns in the Taiwan stock market.

    After confirming the asymmetry in stock returns, we test the unconditional CAPM, we observe that the models perform poorly in the Taiwan stock market, regardless of the introductions of co-skewness and co-kurtosis measures. Then, following Pettengill, Sundaram, and Mathur (1995), we extend the unconditional CAPM to the model conditional on market conditions to examine the risk-return relationship of individual stock returns. Separating the full data period into up- and down- market sub-periods, our purpose is to distinguish the difference between ex-ante expectations and ex-post realizations.

    As a result, we find much more reasonable results particularly over the up-market sub-periods. That is, investors expect a lower (higher) return when the return distribution demonstrates positive co-skewness (co-kurtosis) with the market returns over the up-market sub-periods. Moreover, we find that the relative importance of the co-skewness and the co-kurtosis risks, compared to that of the covariance risk, is not trivial in explaining risk-return relationship. Again, this argument holds only over the up-market sub-periods in the Taiwan stock market.

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    過去許多論文運用傳統二階CAPM，探討風險與報酬間之關聯性中，往往著重於由理論衍生出的現象。例如，投資人會期待較高報酬，如果報酬分佈與市場報酬分佈展現正向同變異的關聯性。此額外報酬取決於貝它值與風險貼水。然而 Kraus and Litzenberger (1976)與Sears and Wei (1988)提出報酬分佈的偏態亦有解釋能力。Fang and Lai (1997)發現投資人亦會考慮報酬分佈的峰態。

針對正在快速發展的臺灣股票市場，此篇論文主要探討風險與報酬間之關聯性，加入報酬分佈偏態與峰態的考量。第一：我們探討市場報酬的分佈特性，並以此特性分析四階CAPM在臺灣股票市場的必要性。我們發現市場報酬的分佈是顯著不對稱。報酬的偏態與峰態有持續性。此二者觀察支持採用四階CAPM在臺灣股票市場的必要性。

    第二：我們測試非條件CAPM，並發現此類模型在臺灣股票市場表現不盡人意，無論是否加入偏態與峰態的考量。然後，依循Pettengill, Sundaram, and Mathur (1995)，加入 市場情勢之條件重新檢視風險與報酬間之關聯性。我們發現在股票市場上漲時，四階CAPM可合理解釋投資人的喜好。