B选项，答案里面的36是怎么算的？

问题如下：

To address Concern 1 when designing Monte Carlo simulation, Yuen should:

选项：

model each factor or asset on a standalone basis.

calculate the 15 covariance matrix elements needed to calibrate the model.

specify a multivariate distribution rather than modeling each factor or asset on a standalone basis.

解释：

C is correct. Under Monte Carlo simulation, the returns of Portfolios A and B are driven by the returns of the nine underlying factor portfolios (based on nine common growth factors). In the case of asset or factor allocation strategies, the returns from six of the nine factors are correlated, and therefore it is necessary to specify a multivariate distribution rather than modeling each factor or asset on a standalone basis.

A is incorrect. The returns of six of the nine factors are correlated, which means specifying a multivariate distribution rather than modeling each factor or asset on a standalone basis.

B is incorrect because the analyst should calculate the elements of the covariance matrix for all factors, not only the correlated factors. Doing so entails calculating 36, not 15, elements of the covariance matrix. Monte Carlo simulation uses the factor allocation strategies for Portfolios A and B for the nine factor portfolios, the returns of which are correlated, which means specifying a multivariate distribution. To calibrate the model, a few key parameters need to be calculated: the mean, the standard deviation, and the covariance matrix. For 9 assets, we need to estimate 9 mean returns, 9 standard deviations, and $\frac{9\times(9-1)}{2}=36$elements of the covariance matrix.

Assuming just the 6 correlated assets, the calculation is $\frac{6\times(6-1)}{2}=15$