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滴滴姐姐~ · 2020年02月27日

问一道题:NO.PZ2019012201000050 [ CFA III ]

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。。

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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