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Branson · 2024年04月09日

有没有更全面的解析

NO.PZ2023091901000057

问题如下:

Analyst Bob tests company B's expected returns based on a two-factor model. Initially, the company expected a return of 12 per cent. Bob identifies GDP and five-year interest rates as two factors in the factor model. Assume that the following data is used:

√ GDP growth forecast to 4%

√ Interest rate rate prediction = 2%

√ the GDP factor beta = 1.50

√ the rate factor beta = -2.00

Suppose GDP ends up growing by 6% and five-year interest rates end up at 3%. It is also assumed that during this period, the company unexpectedly experiences a reputational crisis, leading to a substantial loss. Thus, over this period, the firm-specific return was -4%. Using the 2 factor model with the revised data, what are the company's expected return?

选项:

A.

-1%

B.

1%

C.

1.5%

D.

9%

解释:


这个题目考核的内容是哪一章节,可以详细写一下如何计算出结果的吗?

1 个答案

李坏_品职助教 · 2024年04月09日

嗨,努力学习的PZer你好:


题目最后问的是,让我们用2 factor model (双因子模型)去计算公司股票的收益率。

这部分属于ARBITRAGE PRICING THEORY的考点(缩写是APT,即套利定价模型,本质上就是多因子模型)

根据FRM原版书的套利定价模型(APT)的基本公式:

APT模型认为股票的收益率=初始收益率 + 因子的超预期变动带来的风险溢价+残差。

本题是让我们用双因子模型,所以股票收益率 = 初始收益率+β1 * (因子1的变动) + β2 *(因子2的变动) + 残差.


E(Ri)是题目中告诉我们的12 per cent(12%). 本题用到的是两个因子:GDP和interest rate,GDP的β是1.5,interest rate的β是-2,

所以β1 = 1.5, β2 = -2.


因子1的变动 = GDP的增长率6% - GDP的预测增长率4% = 0.02, 因子2的变动=利率的真实值3% - 利率的预测值2% = 0.01.

而最后的残差是公司的特有风险带来的,题目说firm-specific return was -4%.,所以残差是-0.04


所以,股票收益率 = 0.12 + 1.5*0.02 - 2 * 0.01 - 0.04 = 9%

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努力的时光都是限量版,加油!

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