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 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?
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:
{$table2}A manager is a good forecaster if his or her ex-ante active return expectations (forecasts) are highly correlated with the realized active returns. The information coefficient requires that these forecasts and realized returns be risk-weighted. When this is done for the three managers, the risk weighted forecasts and realized returns are:
{$table3}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:
{$table4}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 。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。）
请问计算E(R)和Rai 的时候，为什么不成以权重啊？
