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滴滴姐姐~ · 2022年12月24日

U shape 与 tracking error

  1. CFA III
  2. Equity

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.

An index that contains a large number of constituents will tend to create higher tracking error than one with fewer constituents.


不是说。。Ushape吗？那解析第一句咋整个这？变成单调减函数了？

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1 个答案

笛子_品职助教 · 2022年12月25日

嗨，从没放弃的小努力你好：


不是说。。Ushape吗？

是的。tracking error存在U shape。


那解析第一句咋整个这？

解析的这句话An index that contains a large number of constituents will tend to create higher tracking error than one with fewer constituents.

是有一个默认假设的，就是只针对这道题有效。

60只股票的benchmark是很好复制，500只股票的benchmark就难复制了，900只股票的benchmark就非常难复制了。

所以这句话并没有错，它针对这道题的具体场景是有效的。


变成单调减函数了？

是的。在这道题里，是单调函数。

实际上就是针对这道题的情形，取了U -shape上的某一段，这一段是单调的。


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