最佳投資組合研究-以台灣50指數為例

范沛綱(Pei-Kang Fan)

指導教授 ： 鄭光甫

國立中央大學/理學院/統計研究所/碩士(2005年)

摘要

台灣證交所為了活絡市場，健全金融體系並考量到避險者的需求，於是和英國富時公司合作編制全新的「臺灣50指數」，並由此發展出許多衍生性金融商品。在本文中，將探討「臺灣50指數」當中的權重配置是否有較高的報酬率。我們使用MV模型，並用兩種方法去估計平均數、變異數與共變異數求出新的權重。本文中使用之兩種估計方法為：（一） 傳統MV模型的做法－使用歷史市場報酬率之平均數、變異數與共變異數（二）時間序列方法－將歷史市場報酬率以AR/ARCH模型加以配適，預測出平均數及變異數。將兩種權重的投資組合報酬率與市場權重的投資組合報酬率做一比較，判斷市場上使用的權重是否有好的投資績效。實證後發現使用「台灣50指數」的權重，相對於使用上述兩種方法所求得之新的權重，有較佳的投資組合報酬率。此外也比較傳統MV模型的做法與時間序列方法的優劣性，結果發現，使用時間序列方法比起傳統MV模型的做法，前者的權重配置比起後者有更佳的投資組合報酬率。

關鍵字

效率前緣

並列摘要

In this paper , I will discuss that if the weight of each stock in
Taiwan 50 Index can lead to higher portfolio return . We use Meanvariance
model（MV model）and apply two methods below to the
estimation of mean , variance and covariance in the MV model .
1. Traditional way--Use the historical return data to obtain mean
variance and covariance as the estimators.
2. Time Series—Fit historical return data by AR/ARCH model to
forecast mean , variance and covariance as the estimators.
By the estimators from the two methods , the best allocation of weight of
the portfolio is determined. Compare the portfolio returns calculated by
both methods advanced here with that calculated by the given weights in
the Taiwan 50 Index to verify if the weights of Taiwan 50 Index have
better portfolio return. My research attested that the portfolio return using
the given weight in the Taiwan 50 Index is superior to that calculated by
the weight from the two methods. In addition , we also compare the two
methods themselves. And we reached the result that the weight from time
series method is more preferable due to its higher portfolio return than
traditional way’s.

並列關鍵字

ARCH model ； efficient frontier

參考文獻

Heteroskedasticity in Time Series Models,Journal of Time

[2]B. Mandelbrot (1963),The Variation of Certain Speculative

Means,Variances,and Covariances on Optimal Portfolio Choice

Journal of Portfolio Management,19,6-11.

and Mathematical System,227,74-87.