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ZF Everyday · 2023年02月05日

补充B

  1. CFA II
  2. Portfolio

NO.PZ2021101401000010

问题如下：

Yuen and Ruckey design a Benchmark Portfolio (A) and a Risk Parity Portfolio (B), and then run two simulation methods (the historical simulation and Monte Carlo simulation) to generate investment performance data based on the underlying nine factor portfolios.

Yuen and Ruckey discuss the differences between the two simulation methods. During the process, Yuen expresses a number of concerns:

• Concern 1: Returns from six of the nine factors are correlated.

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

选项：

A.

model each factor or asset on a standalone basis.

B.

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

C.

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 the elements of the covariance matrix is 9×(9−1)2=36\frac{9\times(9-1)}{2}=36

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

老师，能在解释一下，B答案，为什么是用9计算，而不是用6计算呢？

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3 个答案

星星_品职助教 · 2023年02月23日

@K

参照原回复的截图，计算参数数量时，K对应的是asset的数量。

星星_品职助教 · 2023年02月21日

@K

1）这句话说得是如果B选项正确，那么题干中正确的描述应该是什么样子的。

2）计算correlation时，基于的是asset的数量，而不是return的数量。所以需要看asset是多少个。

K · 2023年02月23日

所以factor应该理解为asset吗？例如这题portfolio里有9个factor，就是投组一共投了9个assets，而不是这个投组有9个特征，例如对大盘的敏感度、对利率的敏感度、对通胀的敏感度之类？

星星_品职助教 · 2023年02月06日

同学你好，

参照讲义公式。有9个factor portfolio，correlation的数量就是9*8/2=36。跟有几个return关联没有关系。

K · 2023年02月21日

所以“假设只有6个资产相关，要算的correlation=6×5/2=15”，是什么意思？不是说跟相关features的个数没关系吗？另外不是在讨论feature吗怎么突然跑出来asset？

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2024-04-27 22:25 1 · 回答

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