问一道题：NO.PZ2015121810000022

问题如下：

You are analyzing three investment managers for a new mandate. The table below provides the managers’ ex-ante active return expectations and portfolio weights. The last two columns include the risk and the ex-post, realized active returns for the four stocks. Use the following data for the following two questions:

Suppose all three managers claim to be efficient in portfolio construction. According to the full fundamental law of active management, which manager is the best at building to make full use of their ability to correctly anticipate returns?

选项：

Manager 1

Manager 2

Manager 3

解释：

B is correct.

The proper statistic to calculate is the transfer coefficient and it is defined as follows:

The TC is the cross-sectional correlation between the forecasted active security returns and the actual active weights, adjusted for risk.

The three managers have the following TCs:

Manager 2 has the highest TC.

考点: The Fundamental Law of Active Management

解析：三个基金经理都声称自己在构建组合时是有效的，而题目问哪个基金经理能够完全实现构建组合的想法，因此衡量指标是TC，也就是调整风险后的forecasted active returns与active weight之间的相关性。TC越大，构建组合时受到的限制越小，那么基金经理越能够实现自己的想法。

计算公式为$TC=COR(\frac{\mu_i}{\sigma_i},\triangle w_i\sigma_i)$。如英文答案中的表格所示，首先计算Risk-weighted forecasts return和Risk-adjusted weights，然后使用计算器求correlation：

以Manager 1为例：

首先清除历史记录【2nd】【7】【2nd】【CLR WORK】

依次输入两组数据：X01=0.1765【↓】Y01=-0.0213【↓】X02=0.4000【↓】Y02=0.0025【↓】X03=0.4167【↓】Y03=0.0090【↓】X04=0.2400【↓】Y04=0.0063

求出相关性系数：【2nd】【8】一直按向下的箭头，直到出现r，r=0.7256。（与英文答案略有差异，是保留小数点的误差。）