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Amour紫色冰棱 · 2022年08月28日

NO.PZ2019012201000050

  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.

为什么这题A不对呢？根据书上的U- SHAPE，即使股票数量越多，考虑了费用之后还是没有比股票数量低的时候费用高啊，考试碰到这种题是不是就看费用率？

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1 个答案

笛子_品职助教 · 2022年08月29日

嗨，爱思考的PZer你好：


direct equity investments这道题说的是直接复制。

直接复制的话，自然是index的股票数量少的，portfolio更容易复制。

60只股票的index，要比933只股票的index，更容易复制。

越容易复制，tracking error就越小。


full replication方法下，portfolio直接复制index，那么portfolio的股票数量是和index股票数量一样多的。

那么index股票数量遵循U 曲线。太多了，portfolio很难复制。太少了，portfolio也很难复制。

例如index只有1只股，portfolio就没法复制，因为这只股容量有限，portfolio买不进去。


所以u shape只是理论情形，现实中，index股票数量不会太少，一般都有30只以上。


在解题时，通常遵循现实情形，越少的（但大于30只），full replication越容易，对于使用full replication方法的portfolio，tracking error越小。

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