共同基金績效的連續週期環比與分析

Abstract

在金融界中有許多用於評量共同基金績效的指標，例如夏普指標、半變異數指標、貝他係數、傑生指標等等，近來陸續有許多以這些指標來衡量關於共同基金績效的文獻。這些指標都是以比率的方式來呈現報酬與風險之間的關係，然而這些指標呈現出的數字，都與計算該指標時所選取的計算期間長短與計算時間起點、終點有關，因此這些指標所表現出來的一種平均績效，欲藉此了解到在計算期間內績效的起伏狀況實不容易。 本研究的目標期能以一個可靠的方法來分析複雜且龐大的資料，對共同基金作績效評量，提供一般投資大眾選擇基金的標的。本研究同時考量到多個指標來以最小化風險指標與最大化報酬指標來求得基金績效，所選取的指標包括有：報酬率標準差、貝他係數、基金管理費率、報酬率與凌駕指標。 為了能看出基金績效在連續週期間的績效起伏，本論文將資料包絡分析法（Data Envelopment Analysis）與Malmquist生產力指標方法結合，求得各基金於各週期績效的升降數值；之後再利用竹節排序法（Bamboo Ranking），賦予不同週期的生產力指標不同的權重，藉此對基金作排序。

There are many numerical indices are used to measure mutual funds performance in financial market, such as Sharpe index, reward-to-half-variance index, reward-to-variability ratio and Jensen’s measure. In the last few years, many researches have further studies about these indices. These indices are ratios between the expected excess return of mutual funds and a risk indicator. But the magnitudes of the index values are dependent on the covered measuring period. For this reason, these indices just are an average performance during the covered measuring period. One could not figure out the trend of the performance directly. This research develops an analytical method to provide investors with a benchmark of mutual funds. Five indices are used to measure the performance: standard deviation of return,β-coefficient, management fee, half-year return and stochastic dominance index. The first three and the last two indices are to-be-minimized and to-be-maximized indices, respectively. In order to find out the trend of fund performance during successive periods, we calculated the Malmquist Productivity Index that is composed by four DEA performance values. Then we use Bamboo Ranking Method to rank mutual funds according to Malmquist indices with different weight.