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Zunniyaki · 2021年03月31日

这道题目和U型图是什么关系？

  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.

老师，请问下U型图左右两端tracking error都很大，怎么知道C选项的933支股票数量一定比A选项60支股票数量的tracking error大呢？

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1 个答案

maggie_品职助教 · 2021年04月01日

嗨，努力学习的PZer你好：


首先解释下full-replication indexing approach，只有全买才是完全复制，那么指数包含的股票数量越大，全买的难度就越大（因为很多股票流动性很差），因此跟踪误差就会越大。

 其次U型图解释的是当我们要完全复制大型指数时可能会遇到的问题。大型股指由于包含大量股票，很多都是流动性不好或交易量很小的股票，那么当组合包含的股票数量上升超过一定数量时，跟踪误差不降反升（U型图），就是因为越买交易费用越大。

 而对于小型的股指，他本身包含的数量就少，而且通常都是大盘股，只要基金管理规模够大，那么我们进行完全复制就不会存在任何问题即追踪误差很小。注意这里的大型和小型指的是指数包含股票数量的多少。

根据这道题表格中给出三个指数所包含的成分股数量来看，933一定是大型股指，那么进行完全复制就会遇到u shape的问题。

 然后我也百度了一下，S&P 60是加拿大大盘股指数，MSCI EAFE是在美国纳斯达克交易的小盘股指数。

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努力的时光都是限量版，加油！

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