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AnnaZ · 2024年02月20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.


这个图形,在不考虑trading cost情况下,单独考虑成分股数量,不应该是那条向下倾斜的虚线吗?意思是成份股数量越大(讲课举例接近5000),tracting error逐渐减小吗?没理解这个点

3 个答案

笛子_品职助教 · 2024年02月22日

嗨,从没放弃的小努力你好:


那么tracking error大,到底是因为cost引起的,还是因为数量太多难以模拟引起的。

full replication下,是由于cost引起的。

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笛子_品职助教 · 2024年02月20日

嗨,努力学习的PZer你好:


我想问的是这个题里面最下面那个portfolio里成份股最多,答案说越多越难模拟,所以tracking error最大。为什么两个冲突的。


同学说,如果不考虑trading cost,即如果假设trading cost为0,则数量越多,tracking error越小,这是对的。


答案是考虑了trading cost的,数量越多,trading cost越大,因此增加了tracking error。


不同的假设前提,结论不同。在解题的时候,默认需要考虑trading cost,也就是U曲线。


实际上也不用想这么复杂,一般只要看到是中小盘的index,就不适合使用full replication

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

AnnaZ · 2024年02月22日

那么tracking error大,到底是因为cost引起的,还是因为数量太多难以模拟引起的。

笛子_品职助教 · 2024年02月20日

嗨,爱思考的PZer你好:


这个图形,在不考虑trading cost情况下,单独考虑成分股数量,不应该是那条向下倾斜的虚线吗?意思是成份股数量越大(讲课举例接近5000),tracting error逐渐减小吗?没理解这个点


同学理解正确。

在不考虑trading cost情况下,单独考虑成分股数量,确实就是那条向下倾斜的虚线。

意思是成份股数量越大(讲课举例接近5000),tracting error逐渐减小。

所以是:trakcing error gross of trading cost:意思是,不考虑trading cost后的tracking error。

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AnnaZ · 2024年02月20日

我想问的是这个题里面最下面那个portfolio里成份股最多,答案说越多越难模拟,所以tracking error最大。为什么两个冲突的。

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