Analysis for the January Effect with the Volatility Model

[[abstract]]本研究擷取道瓊工業指數、紐約證交綜合指數、日經指數與倫敦金融時報指數的月報酬和月變幅資料，並且利用GARCH模型與CARR(Conditional Auto-Regressive Range)模型，分析是否有一月效應的存在。結果顯示道瓊工業指數與紐約證交綜合指數的報酬數列有明顯的一月效應，且不只是存在於小公司投資組合中，日經指數與倫敦金融時報指數則否，而且加權指數的計算方式並不會影響一月效應的產生。再以GARCH的延伸模型GARCH-M與GARCH-M-X加入外生變數探討市場波動性對一月效應的影響，並以變異數方程式的條件變異數做為市場波動性的代理變數。結果發現四個加權指數的波動性皆具有一月的季節性循環，而且是在波動性變數觀察到一月效應。另外本文更添加使用條件自我迴歸變幅模型，補充說明變幅變數，的確可以代替報酬率衡量波動性，且本研究GARCH模型所得之結論，與CARR模型結論一致。[[abstract]]This study uses monthly return and range of Dow Jones Industrial Average Index New York Stock Exchanage Composite Index Nikkei225 and FTSE-100 Index GARCH and CARR models are used to whether the January effect exists and we found that January effect is obvious in the return of DJIA index and NYSE index but not in Nikkei225 and FTSE-100 The calculation of weighted-index generation does not affect the January effect We also use augmented GARCH model：GARCH-M and GARCH-M-X to analyze exogenous impact for market seasonality and the conditional variance is a proxy variable for market risk The result suggests that January effect is observed in the whole samples and due to volatility Thus we found that range can indeed replace return to measure volatility by CARR model The empirical result of CARR is consistent with the result of GARC