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biguo · 2024年05月20日

关于constituents数量

  1. CFA III
  2. Equity

NO.PZ2019012201000050

问题如下：

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

Basedon Exhibit 1 and assuming a full-replication indexing approach, the trackingerror 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 tocreate higher tracking error than one with fewer constituents. Based on thenumber of constituents in the three indexes (S&P/TSX 60 has 60, S&P 500has 506, and MSCI EAFE has 933), EFA (the MSCI EAFE ETF) is expected to havethe 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, whichimplies that EFA has the highest expected tracking error.

这里的数量是benchmark index里的个数吧？个数越多，越难模拟，TE越高。那这个和U shape是不是没关系？U shape应该是portfolio里的个数吧，越多的话考虑trading costTE越大？另外，有的题目在三种方法里选，选full replication条件是asset size sufficient还有liquid，是说要有钱且好交易对吧，那对于成分数量是不是适中比较好呢？

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1 个答案

笛子_品职助教 · 2024年05月20日

嗨，爱思考的PZer你好：


这里的数量是benchmark index里的个数吧？

Hello，亲爱的同学~

这里的数量，不是benchmark的数量。

是跟踪benchmark的portfolio的数量。

例如：标准普尔500指数，作为index，它永远只会有500只股票，不可能有506只股票。

只有跟踪它的portfolio，才会有506只股票。


个数越多，越难模拟，TE越高。那这个和U shape是不是没关系？

是的，这和U shape没关系。


U shape应该是portfolio里的个数吧，越多的话考虑trading costTE越大？

是的。

同学注意：U shape只对应full replication方法。

如果一个index不适合使用full replication方法，而强制使用这个方法。

才会有U - shape问题。

所以U - shape较少在解题的时候使用。

因为，如果一个index不适合用full replication，那么就会使用抽样或最优化。

而抽样与最优化不存在u shape问题。


另外，有的题目在三种方法里选，选full replication条件是asset size sufficient还有liquid，是说要有钱且好交易对吧，那对于成分数量是不是适中比较好呢？

大盘股index用full replication。

中盘股，小盘股的index用抽样或最优化。


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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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