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Kathy苏苏 · 2021年07月12日

tracking error

NO.PZ2019012201000050

问题如下:

Winthrop and Tong agree that only the existing equity investments need to be liquidated. Tong suggests that, as an alternative to direct equity investments, the new equity portfolio be composed of the exchange-traded funds (ETFs) shown in Exhibit 1.

Based on Exhibit 1 and assuming a full-replication indexing approach, the tracking error is expected to be highest for:

选项:

A.

XIU

B.

SPY

C.

EFA

解释:

An index that contains a large number of constituents will tend to create higher tracking error than one with fewer constituents. Based on the number of constituents in the three indexes (S&P/TSX 60 has 60, S&P 500 has 506, and MSCI EAFE has 933), EFA (the MSCI EAFE ETF) is expected to have the highest tracking error. Higher expense ratios (XIU: 0.18%; SPY: 0.10%; and EFA: 0.33%) also contribute to lower excess returns and higher tracking error, which implies that EFA has the highest expected tracking error.

老师,请帮我看下我的这两个理解是否正确:

1.benchmark中的股票数量越多,就越不好跟踪,tracking error就越大;

2.给定benchmark中的股票数量,我们所构建的要跟踪benchmark的那个portfolio中的股票数量约接近benchmark中的股票数量,跟踪的就越好,tracking error就越小。

谢谢!

2 个答案

伯恩_品职助教 · 2021年07月12日

嗨,爱思考的PZer你好:


老师,第二个理解中我指的是种类数量,如果是种类数量,我第二个理解对吗? 给定benchmark中的股票的种类的数量,我们所构建的要跟踪benchmark的那个portfolio中的股票种类数量约接近benchmark中的股票种类数量,跟踪的就越好,tracking error就越小。——理解的是对的。

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伯恩_品职助教 · 2021年07月12日

嗨,从没放弃的小努力你好:


1.benchmark中的股票数量越多,就越不好跟踪,tracking error就越大; ——这个一般来说是的。这是一般原理。原因很多,比如其中一条,股票数量越多,要完全跟踪,就得都买,什么要求就必须好?对,要求大洋必须多,没那么多大洋,都不够买股票的,跟踪肯定不好。这是其中一个原因,帮助你去理解。

2.给定benchmark中的股票数量,我们所构建的要跟踪benchmark的那个portfolio中的股票数量约接近benchmark中的股票数量,跟踪的就越好,tracking error就越小。——我理解你说的数量应该是种类数量,而不是每个的具体数量,因为只要比例一样也是可以的,比如benchmark有十个股票,每个股票100股。跟踪的组合这些股票都买,但是只买10股,也是可以完全跟踪的。(买的多了反而还要考虑花费,导致拖累收益,进而可能tracking error增大)


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