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是选择IC还是TC

NO.PZ2015121810000078

问题如下：

You are analyzing three investment managers for a new mandate. The following table 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.

Suppose all three managers claim to be good at forecasting returns. According to the expanded fundamental law of active management, which manager is the best at efficiently building portfolios by anticipating future returns?

选项：

A.Manager 1
B.Manager 2
C.Manager 3

解释：

C is correct.

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

${l}IC=\rho\left(\frac{R_{Ai}}{\sigma_i},\frac{\mu_i}{\sigma_i}\right)\\$

A manager is a good forecaster if his or her ex ante, active return expectations (forecasts) are highly correlated with the realized active returns. The information coefficient requires that these forecasts and realized returns be risk-weighted. When this is done for the three managers, the risk-weighted forecasts and realized returns are:

The ICs are found by calculating the correlations between each manager’s forecasts and the realized risk-weighted returns. The three managers have the following ICs:

Manager 3 has the highest IC.

考点: The Fundamental Law of Active Management

解析：三个基金经理都声称自己擅于预测收益率，而题目问哪个基金经理预测未来收益率能力最强，因此衡量指标是IC，也就是调整风险后的forecasted active returns与realized active returns之间的相关性。IC越大，预测能力越强。

计算公式为 $IC=COR(\frac{R_{Ai}}{\sigma_i},\frac{\mu_i}{\sigma_i})$ 。如英文答案中的表格所示，首先计算Risk-weighted forecasts return和Risk-weighted realized return，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=0.176【↓】Y01=0.353【↓】X02=0.400【↓】Y02=0.700【↓】X03=0.417【↓】Y03=0.333【↓】X04=0.240【↓】Y04=0.080

求出相关性系数：【2nd】【8】一直按向下的箭头，直到出现r，r=0.5317。（与英文答案略有差异，是保留小数点的误差。）

通过题目“forecasting returns”可以判断研究的是IC，information coefficient。

但是干扰字眼：building portfolios让我疑惑是否需要用的事TC。怎么理解？

同学你好，

对比原版书中的这两种说法：

①Suppose all three managers claim to be good at forecasting returns. According to the full fundamental law of active management, which manager is the best at efficiently building portfolios by anticipating future returns?

②Suppose 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 portfolios to make full use of their ability to correctly anticipate returns?

可以看出，两种说法都是building portfolios，所以这点无法区分。区分点在于：

①中强调的是good at forecasting returns的能力（黑字），所以这是在考察IC。

②中强调的是portfolio construction（黑字），这是基金经理构建组合的能力，也就是考察TC。

本题即是上述第①种问法。

是选择IC还是TC

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