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滴滴姐姐~ · 2020年02月27日

问一道题：NO.PZ2019012201000050 [ CFA III ]

  1. CFA III
  2. Equity

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.

看了之前的提问和回答。。。们。。 依旧一脸懵逼。。。 1.大概是懂了“n越大 tracking error越小” 但是吧。。2. 怎么理解那个U型曲线。。。是不是那个是加引号的tracking error曲线。。只是想随意聊一下trade-off呀。。 3.不然怎么判断60和933在曲线上的相对位置。。

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2 个答案

圣灵霜子 · 2020年03月03日

对于不同的index或者说benchmark，包含的股票数量越多，越难完全复制，交易成本越大，tracking error越大，这也是这道题考的。 对于同一个benchmark（比如xxx3000，benchmark里有3000只股票），如果你只买100只股票，离benchmark差太多了，tracking error就会很大，但是你买3000只，交易成本太高了，tracking error也会很大，买个2000只反而tracking error最小，这是u型图的意思。 这道题和型图没关系。

maggie_品职助教 · 2020年02月28日

嗨，爱思考的PZer你好：


1、U型图是针对要复制的指数包含大量成分股的时候，不适用小型（小型指的是成分股很少）的指数比如这道题SP/TSX60. 对于小型指数来说，组合包含的股票数量越大即越接近指数中的股票数量，跟踪误差越小。

2、对于大型指数，像EFA933。一开始n越大 tracking error越小只解释的U型图左半部分，随着N上升越买越多，交易费用也在上升，我们被动的复制股票的目的在于获得和大盘一样的收益率（此时追踪误差最小），但是我们买的越多（都是先买流动性好的股票，然后流动性以此递减），买到后来交易费用就会上升的很快，这样就会削减我们能获得的收益（追踪误差上升）。所以并不是全买追踪误差就最小，其实是有一个trade off的，正如75页讲义所所画是个U型。

3、如果题目没给组合里的N，只给你了指数的N（像这道题），越大型的指数由于有交易成本会使得跟踪误差先抑后扬（U型），你做完全复制跟踪误差越大。


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