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jeffrey19861001 · 2020年02月12日

问一道题: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.

怎么去区分讲义里76页讲的?我看到有别的学员也提了类似的问题,但是解答并没有说清楚,讲义里也没有说什么我们构建组合数量和index里数量的区别?而且讲义的这张图,我没记错的话,去年李老师还画错了(画错的时候,还是一样这么讲的),后来又改的,这就把我搞的很混乱,再配上这个题目,更混乱了。

2 个答案

maggie_品职助教 · 2020年02月21日

讲义这页截图上三个小点点的不是独立的,而是要一起看的:第一个小点点,随着组合中包含的股票数量上升,跟踪误差下降,没有错,但是这句话还没说完,你们看下第二小点点第一个词“but”,随着指数中流动性好的股票买完后,继续增加指数中包含的交易量较小的小盘股会使得交易成本上升。所以这页讲义第一个小点和第二个小点是合起来的一段话。他们就是在解释下面U型图的形状。当组合包含的股票数量上升时,跟踪误差一开始是下降的, 随着N上升,交易费用也在上升,而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)。所以在这里我们要解释的是并不是全买追踪误差就最小,其实是有一个trade off的正如讲义所所画是个U型。

maggie_品职助教 · 2020年02月14日

1、这道题和U SHAPE图讲的是一致的哦。两者都说的是指数中包含成分股数量越大,如果有组合要跟踪它特别是full replication(全买)的情况下,跟踪误差越大。你看这道题给你的三个指数,EFA成分股最多,且交易费率最高,说明组合把EFA指数全买下来,跟踪误差最大。

2、U shape 图那页的讲义确实没有明确说指数的情况,可是这页讲义讲的是“Full Replication”,没有指数,我们Replicate谁呢?所以这个图的意思是当组合中包含的股票越多,它隐含的是意思也就是当我们要复制的指数中成分股越多,由于交易费用导致的跟踪误差,即便我们资金够把所有成分股都买下来,也能获得和大盘的一样的业绩。

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