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七七 · 2024年07月24日

full replication 和 stratified sampling的界限

NO.PZ2023010903000028

问题如下:

Välimaa next considers the transition of the Fund’s portfolio holdings, which have a total market value of EUR 150 million. She is constructing the portfolio using individual equities and considers the following methods: full replication, stratified sampling, and optimization. The benchmark for the portfolio is the FTSE Eurotop 100 Index, which is based on market capitalization and consists of 100 of the largest publicly traded European companies. The investment committee prefers not to use sophisticated algorithms that are difficult to understand.

Determine, from the three methods that Välimaa is considering, the most appropriate method for constructing the equity portfolio. Justify your response.

选项:

解释:

Answer

Full replication is suitable.

The value of the Fund’s equity portfolio is EUR 150 million and is large enough to follow a full replication approach of the FTSE Eurotop 100 Index. The constituents of this index are the top 100 large capitalization European equities, which are likely liquid and available for trading. The full replication approach requires owning each of the securities in the benchmark portfolio. Tracking error is likely to remain low since the number of constituents in this index is not large.

Stratified sampling is less appropriate since it does not track the index as closely as full replication, which would result in higher tracking error relative to full replication. The board prefers not to use sophisticated algorithms that are difficult to understand, making the optimization approach less appropriate.

No.PZ2023010903000028 (问答题)

请问老师,这题没有强调要最小化tracking error。因为看题目中说fund规模150 million,属于小规模投资者,从这个角度判断, stratified sampling比full replication更合适。这个思路为什么不对?

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已采纳答案

笛子_品职助教 · 2024年07月25日

嗨,努力学习的PZer你好:


在equity科目里,fund规模150MIllion,并不一定属于小规模投资者。

equity科目,并没有关于小规模投资者的量化定义。

equity科目,并未规定多少金额以下,是小规模。多少金额以上,是大规模。没有这个金额的标准。

因此这里,需同学结合日常,用常理来推断。


这个公司fund有1.5亿,只需要买100个流动性好的大盘股。每个股票平均可以买150万元。

资金完全是够买的。可以用full replication。


如果改一下,这个公司的fund只有150万,而不是150百万。

那么每个股票只能买1.5万元,而不是150万元。

1.5万元就不够买了,对于一些高价股,都买不了1手。

这个时候采用抽样法。

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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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