套利訂價理論隱含了預期報酬是經濟體中風險溢酬的線性組合。然而，最適因子數目與因子的內涵卻仍有爭議。而我們的研究在於檢驗能夠解釋時間序列股票報酬的因子。首先我們利用Connor and Korajczyk (1986, 1988) 所提出的主成分分析法從個股報酬中萃取因子，並使用Bai and Ng (2002) 所提出的六個模型選擇準則來決定最適因子數目。最後，我們將萃取出來的主成分與實證上常用的因子做比較，包括市場因子，Chen-Roll-Ross (1986) 的總體經濟因子，Fama and French (1993) 的SMB 與HML，Carhart (1997) 的動能因子和Lettau and Ludvigson (2001) 所提出的cay 因子。我們發現市場報酬的解釋能力明顯優於其他因子，且Fama and French (1993) 所提出的因子也有很好的解釋能力。 Arbitrage pricing theory (APT) implies that the expected return is approximately a linear function of the risk premiums in the economy. However, the optimal number of factors and essence of them are left as an open question. Our study examines the factors that explain time-series stock returns. We first apply asymptotic principle components proposed by Connor and Korajczyk (1986, 1988) to extract factors from stock returns and determine the optimal number of factors by six criteria suggested by Bai and Ng (2002). We then compare the CK factors with several commonly-used factors, such as market portfolio, Chen, Roll and Ross (1986 macroeconomic variables, Fama and French (1993) SMB and HML, Carhart’s (1997) momentum factor and cay factor suggested by Lettau and Ludvigson (2001). We find that market portfolio dominates other factors in explaining CK factors, and Fama-French factors also play important roles in our empirical results.
