又因为Z*的每一列都为Y*每列为线性组合，Y*每列的平均值为零，Z*每列的平均值也为零。所以，Z是由Z*矩阵第j列加上Wj的暂时平均得到的。

总结，Z的协方差是与历史数据W相同的，同时Z的第j列与历史数据Wj的平均值相同。而且Z每行的大量数据能够提供W更精确的发生概率。

在Z中的第i行第j列元素zij可用来计算实际的Pj值，既是第j个合同的赔付款额。由1到j的之和Pj之和得到实际的PN值[Eq. (3)]。对比Z各产品各行计算的结果和直方图中所显示的数据以及CPDF的到PN值（图3）。这里用到的方法，不像前面仅仅有一份合约时所描述的，并没有包含CPC预报的样本频率。因此，它并没有考虑历史数据的在一段相关的长时间尺度上不稳定的可能性(e.g.,Livezey and Smith 1999)。后面的研究需要一种方法考虑样本偏差频率对CPC预报值的影响，同时保证不同地理位置的正确相关性。

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