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dognmnm · 2023年02月06日

如何判断长短期, 以及无风险利率

NO.PZ2018091901000059

问题如下:

An Australian investor currently holds a A$240 million equity portfolio. He is considering rebalancing the portfolio based on an assessment of the risk and return prospects facing the Australian economy. Information relating to the Australian investment markets and the economy has been collected in the following table:

Using the information in the table and the Grinold–Kroner model, calculates the expected annual equity risk premium.

选项:

A.

6.25%

B.

3.95%

C.

3.45%

解释:

B is correct.

The Grinold–Kroner model states that the expected return on equity is the sum of the expected income return (2.4%), the expected nominal earnings growth return (7.3% = 2.3% from inflation + 5.0% from real earnings growth) and the expected repricing return (3.45%). The expected change in market valuation of –3.45% is calculated as the percentage change in the P/E level from the current 14.5× to the expected level of 14.0×: (14 – 14.5)/14.5 =–3.45%. Tus, the expected return is 2.4% + 7.3% – 3.45% = 6.25%.

Expected equity return – Current 10-year government bond yield =Expected equity risk premium

6.25% – 2.3% = 3.95%

解析:

从表格中直接可得Expected annual income return= 2.4%

The expected nominal earnings growth return=Expected annual real earnings growth + Expected inflation rate=5%+2.3%=7.3%

对于The expected repricing return,我们可以通过预期P/E值与当前P/E值得变化率求出,即: (14−14.5)/14.5 =−3.45%.

所以最终的收益率为2.4% + 7.3% 3.45% = 6.25%.

Expected annual equity risk premium=Expected equity return Current 10-Year government bond yield=6.25% – 2.3% = 3.95%

注意到上述公式中之所以使用10-Year government bond的当前收益率是因为题目中没有给出与之对应的未来收益率,所以我们只能用当前收益率作为替代。

1. 我如何判断这个题目不是一个长期的情况? 为何capital gain不是直接等于gdp增长?

2. 无风险利率我该选哪个? 这题目很怪, 最后减掉无风险利率那边有没有个统一标准?

3 个答案

源_品职助教 · 2023年02月07日

嗨,爱思考的PZer你好:


不好意思,第二个问题的确看漏了。

本题表格提供两个无风险利率,一个是过去十年的2.8,一个是当前的2.3

因为题目是让我们预期未来的equity risk premium,那么不能选过去的。

也只能选当前的,如果表格最后一列有对于未来无风险利率预期,那么最好选未来的。

但是表格最后一列,没有这类数据,所以就选当前的。

这里无风险利率没有统一标准,主要还是看题目怎么问的。

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努力的时光都是限量版,加油!

源_品职助教 · 2023年02月07日

嗨,爱思考的PZer你好:


比如像这题所述,Using the information in the table and the Grinold–Kroner model, expected annual equity

题目说了用GK模型,那么如果题干里没有明确提及长期,那么就是计算短期,因为模型数据一般不默认为0,要自己算。

最后题目是让我们计算,expected annual equity risk premium, annual本身也是一个短期的概念。


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虽然现在很辛苦,但努力过的感觉真的很好,加油!

源_品职助教 · 2023年02月06日

嗨,努力学习的PZer你好:




CME中没有明确对于长短期利率的划分界限

一般而言说的是BILL,就是短期的,说的是BOND就是长期。

短期通常小于半年,长期至少要1年以上。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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