Normy · 2024年02月07日

如题

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问题如下：

Had the trade in the technology sector not occurred, the selection and interaction measure would have been closest to:

选项：

A.0.35%. B.0.42%. C.1.23%.

解释：

Solution

A is correct. The formula to determine selection and interaction is as follows:Selection + Interaction = W_i(R_i – B_i) + (w_i – W_i)(R_i – B_i), where

W_i = Benchmark weight

R_i = Portfolio return

B_i = Benchmark return

w_i = Portfolio weight

Selection + Interaction = (0.20)(0.1250 – 0.1109) + (0.25 – 0.20)(0.1250 – 0.1109)

= 0.0035, or 0.35%.

B is incorrect. This result would be generated by incorrectly using the portfolio weight as W_i in the selection measure calculation:

Selection + Interaction = W_i(R_i – B_i) + (w_i – W_i)(R_i – B_i).

Selection + Interaction = (0.225)(0.1250 – 0.1109) + (0.25 – 0.20)(0.1250 – 0.1109)

= 0.0042, or 0.42%.

C is incorrect. This result would be generated by incorrectly using the original portfolio return as R_iand the revised portfolio return as B_i:

Selection + Interaction = W_i(R_i – B_i) + (w_i – W_i)(R_i – B_i).

Selection + Interaction = (0.20)(0.1740 – 0.1250) + (0.25 – 0.20)(0.1740 – 0.1250)

= 0.0123, or 1.23%.

Without this trade, the portfolio’s technology sector return would have only been 12.50% 这句话是说benchmark return？怎么看出来的

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2 个答案

笛子_品职助教 · 2024年02月11日

嗨，从没放弃的小努力你好：

如果我直接用 interaction公式为什么算不出答案呢？

Hello，亲爱的同学～

这道题要求计算Selection + Interaction

Selection + Interaction = (0.20)(0.1250 – 0.1109) + (0.25 – 0.20)(0.1250 – 0.1109)

= 0.0035, or 0.35%.

同学直接用Interaction公式是算不出答案的，因为少算了Selection

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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笛子_品职助教 · 2024年02月07日

嗨，从没放弃的小努力你好：

Without this trade, the portfolio’s technology sector return would have only been 12.50% 这句话是说benchmark return？怎么看出来的

Hello，亲爱的同学~

我们先看这道题如何解题，再回答同学的问题。

本题让求的是selection and interaction effect，直接代入公式：

Wi(Ri – Bi) + (wi – Wi)(Ri – Bi)

= (0.20)×(0.1250 – 0.1109) + (0.25 – 0.20)×(0.1250 – 0.1109)

= 0.0035，

所以选A

公式的出处，同学可以复习一下强化讲义中关于return Atribution的知识点。

回到同学的问题：

这句话是说benchmark return？怎么看出来的

这句话说的并不是benchmark return。

只能看出来是portfolio return。

同学看老师的公式。

Wi(Ri – Bi) + (wi – Wi)(Ri – Bi)

= (0.20)×(0.1250 – 0.1109) + (0.25 – 0.20)×(0.1250 – 0.1109)

= 0.0035，

12.5%这个数据，是Ri的数值。

而Ri在公式里的含义，是portfolio return。

而同学说的benchmark return，公式里表示为Bi，Bi是11.09%。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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