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Yoyo1234567 · 2020年01月14日

问一道题:NO.PZ2019012201000070

问题如下:

For the large-cap US equity portion of Sapphire’s investment portfolio, Cullen believes that there are some existing passive indexed-based funds that track the S&P 500 Index that the foundation should consider. Cullen presents Exhibit 2 to Sapphire’s board.Exhibit 2 S&P 500 Index Funds

Based on Exhibit 2, the portfolio manager most likely to have the largest tracking error is:

选项:

A.

Manager A

B.

Manager C

C.

Manager B

解释:

Tracking error indicates how closely the portfolio behaves like its benchmark and measures a manager’s ability to replicate the benchmark return. Manager C is most likely to have the largest tracking error for three reasons:

l The portfolio contains a smaller number of the index holdings than the other two portfolios, resulting in a lower level of replication.

l Dividends are reinvested the day following receipt rather than the same day, which would cause cash drag relative to Manager B.

l The portfolio is reconstituted less frequently than the other two portfolios.

Although Manager C has a slightly lower management fee, which would result in a lower tracking error, the benefit is unlikely to offset the combined higher tracking error related to the other portfolio characteristics.

A and C are incorrect.

导致tracking errror原因包括有1.fees charged 2.number of securities

1.如果一个半年rebalance 一个每季度 相比之下每季度cost 会高啊 为什么说每季度rebalance tracking error 低呢?如果说rebalance会让portfolio与index更像 意思就是rebalance越频繁tracking error越低 那为什么讲义又说cost高了 tracking error高呢

2.关于number of securities, 到底是包含股票数目多tracking error低呢 还是包含股票数目多tracking error 低? 我理解是如果一个portfolio fully replicate,包含数目与index一样。 如果index里很多illiquid股票的话,容易产生tracking error。tracking error和portfolio 包含的股票数目没有关系吧?

考试的时候如何能选出正确答案?感觉讲义和题目矛盾。

2 个答案

jli · 2020年02月10日

Manager C的成分股最少(TE高)

Manager C的股息在投资有Cash drag(TE高)

Manager C的管理费最低(TE低)

Manager C的Rebalance同频率(TE同)

Manager C的Reconstruction频率低(TE高)

silviaws · 2020年01月14日

导致tracking error的原因有四个,分别是:

1)The fees charged. 指数基金的管理费越高,就会拉低超额收益,而追踪误差的定义式就是超额收益的标准差,因此导致tracking error 高。在该题目中即为management fee,很明显,manager B的追踪误差最高;

2)The numbers of securities held by the portfolio versus the benchmark index.注意是比较指数基准和基金组合的持股数的差,两者的差越大,tracking error自然就越高。而不是你所说的只看指数基准。比如,某基金的业绩基准为中证500,但是有一些股票当前停牌或者因为其他原因买不到,那么可能组合就只有480,追踪误差自然就更大。某基金的业绩基准为沪深300,只有个别股票买不到,那组合就是298,追踪误差没那么大。题目中很显然,A的差为2,B的差为4,C的差为25,所以manager C的追踪误差最高;

3)intra-day trading.日间交易.指数都是以指数所包含的所有个股当日收盘价生成当天的指数点位,如果指数基金日内交易价格与收盘价不一致就会导致追踪误差。本题不涉及;

4) cash-drag.由于指数基准是没有现金的,但是因为个股分红、基金申购以及其他收益等原因会造成指数基金持有现金增加,从而产生追踪误差。所以降低组合持有现金可以缩小误差。在本同题中的dividend reinvested就是降低持有现金比例,很明显,B是红利当天再投资,cash drag最小,AC相对比较大;


最后一个是对组合构建中的reblance和reconstitution。这一点上是个trade-off。总体而言,调整的频率越高组合的个股及权重越接近指数,但是同时也拉高了trading cost,所以大多数宽基指数基金以季度调整为主。注意这里的trading cost跟fees charged不一样,trading cost是佣金,fees charged是管理费。

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