美國大型指數股票型基金之效率評量

Abstract

本研究主要目的是探討美國大型指數型股票基金短中長期之效率評量。有別於過去ETFs之績效評估多採用如CAPM、Treynor、Jensen、t檢定等傳統指標，本文採用資料包絡分析法來彌補傳統指標不足之處。本研究分析2007年到 2017年4月，103支美國大型股票型基金效率評量，以年報酬率為產出變數，淨費用率、標準差為投入變數，利用投入導向的BCC-DEA模型進行效率評量，並求出其共同邊界效率、分群邊界效率和技術缺口比率。實證結果如下：(1)短年期來看，大型混和型、大型成長型、大型價值型共同邊界效率差異不大。(2) 中長期來看，大型混和型、大型成長型共同邊界效率表現較好。(3)無論是短中長期，大型混和型的技術落差皆為最小，跟共同邊界效率結果一致。(4)追蹤基礎指數如S&P 500 index、Dow Jones U.S. Large-Cap Total Stock Market index、Nasdaq-100 index的指數型股票基金，在短中長期的效率表現較佳。

The purpose of this study is to conduct an efficiency assessment of exchange-traded funds (ETFs) in U.S.A. Unlike traditional methods such as CAPM, Treynor, Jensen, and t-test, this paper adopts the input-oriented BCC (Banker-Charnes-Cooper) data envelopment analysis (DEA) model to measure the efficiency of 103 U.S. equities from the time period of 2007 to April 2017. Annual returns serve as the output variable while net expense ratio and standard deviation serve as the input variables. We then calculate the metafrontier efficiency, group frontier efficiency, and technology gap ratio. The empirical results indicate the following: 1. The metafrontier efficiency does not present significant difference for large blend, large growth, and large value funds in a short-term period. 2. Large blend and large growth show higher metafrontier efficiency in the mid and long term periods. 3. Regardless of whether it was short, middle, or long term periods, large blend show the least technology gap corresponding with metafrontier efficiency. 4. ETFs track the underlying index, S&P 500 index, Dow Jones U.S. Large-Cap Total Stock Market index, and Nasdaq-100 index show good efficiency in short, mid, and long term periods.